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Doctoral Thesis
Thermodynamic modelling and calculation of phase equilibria inthe Bi-Sr-Ca-Cu-O system
Author(s): Risold, Daniel
Publication Date: 1996
Permanent Link: https://doi.org/10.3929/ethz-a-001616132
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ETH Library
Diss. ETH No. 11642
Thermodynamic Modellingand
Calculation of Phase Equilibriain the
Bi-Sr-Ca-Cu-O System
A dissertation submitted to the
SWISS FEDERAL INSTITUTE OF TECHNOLOGY
ZURICH
for the degree of
Doctor of Technical Science
presented byDANIEL RISOLD
Dipl. Phys. ETH
born 1.5.1966
citizen of Bas-Vully FR
accepted on the recommendation of
Prof. Dr. L. J. Gauckler, examiner
Dr. H. L. Lukas, co-examiner
Zurich 1996
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Ackowledgments
I am grateful to Prof. L. J. Gauckler for giving me the opportunity to enter the
fascinating field of material science and for offering me a perfect support duiing this
thesis. I particularly appreciated the large freedom in managing this project, the
possibility to present the results to the international community, the constant new
impulses, and the many enriching discussions.
I wish to thank Dr. H. L. Lukas who very kindly welcomed me at the Max-Planck-
Institut fur Metallforschung. PML, to teach me the basics of thermodynamic modelling.
The work in Stuttgart was a wonderful mixture of extreme scientific rigour and many
laughs. I also thank the colleagues met at PML for their fruitful discussions, in partic¬
ular Dr. S. G. Fries. Dr. H. J. Seifert. and Dr. P. Majewski.
I am especially indepted to Dr. B. Hallstedt for achieving the work presented here.
This thesis is greatly marked by his fingerprints and is the fruit of several years of
close scientific collaboration. During that time, I have also enjoyed and benefited from
Bengt's many skills in wine tasting, mountain hikes or contemporary arts.
I would like to thank Prof R. 0. Suzuki at Kyoto University for the very helpfuldiscussions of experimental aspects and the fruitful collaboration in phase eciuilibria
studies.
I am grateful to Prof. G. Bayer for useful suggestions and for improvements in the
quality of this manuscript.
I wish to express my thanks to the many colleagues and friends met at the Institut fur
Nichtmetallische Werkstoffe for their support, their help, and the good time we shared.
For a better understanding of the "practical" aspects in processing superconductors, I
am particularly grateful to Dr. R. Muller, Dr. T Schweizer, Dr. B. Heeb, D. Buhl and
T. Lang.
I would like to remember Dr K. Girgis* who contributed to the beginning of this project
and was always bursting of a very communicative enthousiasm and cheerfulness.
I thank my parents, my wife Prisca, my friends and my relatives for their continuous
encouragement throughout these past years.
Financial support from the Swiss National Science foundation (NFP30) and the Swiss
Federal Institute of Technology is gratefully acknowledged.
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Contents
Summary
Zusanimenfassung
Aim of the study
I Calculation of Phase Diagrams
1.1 Principles
1.2 Thermodynamic Modelling of Heterogenous Syst
12 1 General consideiations
12 2 Iomc solid solutions
12 3 Iomc liquids
1.3 Experimental Input
13 1 Phase diagiam vs crystal chemistry
13 2 Phase diagram vs thermodynamics
1.4 Computation of Phase Equilibria
14 1 Calculation of single eqiuhbimm
14 2 Mapping of phase diagiams
14 3 Graphical repiesentations
1.5 Thermodynamic Optimization
15 1 Data assessment
15 2 Deteimmation of parameteis
15 3 Reliability of extrapolations
1.6 Outlook
16 1 Towards fiist pimciples methods
16 2 Towaids kinetic simulations
6
II The Bi-Sr-Ca-Cu-O System 53
II. 1 Overview 54
11.1.1 The metallic part 55
11.1.2 The binary oxide systems 56
11.1.3 The ternary oxide systems 57
11.1.4 The Bi-free and Cu-free phases 57
11.1.5 The superconducting and other Phases 58
11.2 The Bi-O System 68
11.3 The Sr-O System 90
11.4 The Sr-Cu-O System 102
11.5 The Ca-Cu-O System 123
11.6 The Sr-Ca-Cu-O System 143
III Equilibrium States along Processing Routes 173
111.1 Phase Diagrams and Large Scale Applications 174
111.2 Bi-2212 Superconductors 176
111.2.1 Stability of the 2212 phase 176
111.2.2 Melting relations and meltprocessing 182
111.2.3 Stability of secondary solid phases in the partially melted state. . .
186
111.2.4 Composition dependence, crystal growth and precipitates 195
111.2.5 Solidification cases 200
111.3 Bi-2223 Superconductors 207
111.3.1 Domain of stability 207
111.3.2 Domain of formation 208
111.4 Outlook 213
7
Curriculum vitae 223
Publications 224
Appendix 226
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9
Summary
This study presents a consistent thermodynamic description of the five-component Bi-
Sr-Ca-Cu-0 (BSCCO) system suitable for phase diagram calculations. The systems"s
phases are modelled in terms of their Gibbs energy and the models parameters are
optimized based on both phase diagram and thermodynamic data. The method is
described in Part I. This thesis was part of a larger project aiming, on one hand, at the
thermodynamic evaluation of the BSCCO system and. on the other hand, at a better
understanding and an improvement of the meltprocessing of Bi-based superconductors.
Some of the results are shown in Part II and Part III respectively.
Details of the thermodynamic optimization work are presented in Part II for the sub¬
systems Bi-O, Sr-O, Sr-Cu-O, Ca-Cu-0 and Sr-Ca-Cu-O. In all these subsystems,
the experimental data were reviewed and assessed, and optimized sets of thermody¬
namic functions are given. The calculated phase relations reproduce well the main
features of these systems. In several cases, inconsistencies between phase diagram,
calorimetric. and electrochemical measurements could be identified and the most con¬
sistent data were selected. Phase diagram regions of larger uncertainties are pointed
out and suggestions for further experimental studies are made.
The Sr-Ca-Cu-0 system is characterized by solid solutions arising from the substi¬
tution of Ca for Sr. Complete solid solutions are found in the phases (Sr,Ca)0 and
(Sr,Ca)2Cu03. Partial solubility towards calcium is found in all the other strontium
cuprates SrCu02, Sri4Cu2404i, and SrCu202, whereas no significant solubility towards
strontium has been reported for the calcium cuprates Ca0 83CUO193 and CaCu203. The
thermodynamic properties of the solid solutions (Si,Ca)0, (Sr,Ca)2Cu03, (Si, Ca)Cu02,
and (Sr, Ca)!4Cu2404i are of particular importance since these phases are the major
secondary phases appearing when processing the superconducting Bi-2212 and Bi-2223
phases. The calculated phase relations are in good agreement with experimental ob¬
servations even though very little data exist on the thermodynamics of these solid
solutions.
The melting relations around the two superconducting phases Bi-2212 and Bi-2223 are
presented in Part III.
First, the stability ranges of the secondary phases forming upon melting of Bi-2212 are
discussed. These are mainly the Bi-free phases (Sr,Ca)0, (Sr,Ca)2Cu03, (Sr. Ca)Cu02,
and (Sr, Ca)14Cu24041, and the Cu-free phases BigSrnCa5Ox and Bi2(Sr,Ca)306.
(Sr, Ca)14di2404i and BigSrnCajOj. are the main decomposition products of Bi-2212 in
1 bar 02. The Bi-free phases transform in the order (Sr, Ca)i4Cu2404i, (Sr, Ca)Cu02,
(Sr, Ca)2Cu03, and (Sr,Ca)0 either by increasing the temperature or decreasing the
oxygen partial pressure. The Cu-free phase BigSruCasOj, is stable only at higher oxy¬
gen partial pressures whereas Bi2(Sr,Ca)30e is a dominant secondary phase at lower
oxygen partial pressures. Many processing studies are aimed at avoiding large grains
of these secondary phases. With the help of preliminary calculations, a composition
window for meltprocessing Bi-2212 in a two-phase field 2212+liquid is proposed.
The Bi-2212 phase is known to form directly from the liquid. Its formation during
solidification is controlled by the rate of oxygen uptake from the surrounding atmo¬
sphere and by redistribution of the cations through the dissolution of the secondary
10
phases. Calculations, simulating the cases when no oxygen uptake or no redissolution
of the secondary phases occur, showed that the 1-layer compound 11905 is then ex¬
pected to form instead of 2212. Tliese results are in good agreement with experimentalobservations.
The Bi-2223 phase is known to form in a very narrow range of temperature and the
presence of a liquid phase has been suggested to be necessary in the formation process.
The 2223 phase is furthermore surrounded by very flat multiphase fields which means
that the fraction of 2223 decreases drastically with only slight deviations from the ideal
stoichiometry. The present calculations show that one of the influence of the liquidphase is to open the flat multiphase fields on the Bi-rich and Cu-rich side. Equilibriawith the liquid thus increase the composition window where larger fraction of the 2223
phase can be obtained.
Zusammenfassung
Diese Arbeit stellt eine konsistente theniiodynamische Beschreibung des funf-kompo-
nentigen Systems Bi-Sr-Ca-Cu-0 (BSCCO) dar, die fur Phasendiagramniberechnun-
gen anwendbar ist. Die Phasen des Systems sind in Bezug auf ihre Gibbs Energiemodelliert und die Modellparameter wurdeii sowohl mit Hilfe von Phasendiagrammenals audi thermodyiiamischen Daten optimiert. Die Methode ist ini Teil I beschrieben.
Diese Dissertation ist Teil eines grosseren Projekt, dessen Ziel war auf einer Seite, die
therniodynamische Eigeiischaften des System BSCCO zu beschreiben, und auf der an-
dere Seite, das Schmelzverfahren zur Herstellung vom Bi-Supraleitern besser zu verste-
hen und zu verbessern. Einige dieser Resultate sind im Teil II bzw. Teil III dargelegt.
Im Teil II sind die thermodynamische Optimierungen der Untersysteme Bi-O, Sr-
O, Sr-Cu-O, Ca-Cu-0 und Sr-Ca-Cu-0 in Einzelheiten widergegeben. Piir jedesUntersystem wurden alle experimentellen Resultate zusammengefasst und analysiert,und daraus optimierte thermodynamische Funktionen gewonnen. Die berechneten
Phasenbeziehuiigen geben die charakteristischen Eigeiischaften von diesen Systemengut wieder. In mehreren Fallen wurden Inkonsistenzen zwischen Phasendiagramm,kalorimetrisclien, und elektrochemisclien Messungen geortet, und die konsistenten Daten
wurdeii herausgestrichen. Die mit grosserer Ungenauigkeit behafteten Phasendiagram-mgebiete wurden gezeigt und Vorschlage fur weitere Untersunchungen gemacht.
Charakteristisch fiir das System Sr-Ca-Cu-0 sind Festloslichkeiten, die aus der Substi¬
tution von Ca durch Sr entstehen. Die Phasen (Sr,Ca)0 und (Sr,Ca)2Cu03 zeigen eine
durchgehende Loslichkeit. Die Strontium Kuprate SrCu02, Sr^Ci^C^i, und SrCu202zeigen nur eine partielle Loslichkeit in Richtung Kalzium, wobei die Kalzium KuprateCa083CuOi93 und CaCu203 keine Loslichkeit in Richtung Strontium aufweisen. Die
thermodyiiamischen Eigeiischaften der Festloslichkeiten (Sr,Ca)0,(Sr,Ca)2Cu03, (Sr, Ca)Cu02, und (Sr, Ca)i4Cu24041 sind von besonderem Interesse,da diese Phasen als Hauptsekundarphasen des Schmelzverfahrens von Bi-2212 und
Bi-2223 Supraleitern auftreten. Die berechneten Phasenbeziehungen sind in guter Ue-
bereinstimmung mit experimentellen Beobachtungen obwohl wenig Daten zur Thermo-
dynamik diesen Festloslichkeiten vorhanden sind.
11
Die Sclimelzbezielmngen mn die zwei supraleitenden Phasen Bi-2212 und Bi-2223 sind
im Teil III gezeigt.
Zuerst sind die Stabilitatsgebiete der Sekundarphasen diskutiert, die beim Schmelzen
von Bi-2212 auftreten. Diese bestehen hauptsachlich aus den Bi-freien Phasen (Sr.Ca)O,
(Sr,Ca)2Cu03, (Sr, Ca)Cu02, und (Si,Ca)i4Cu2404i, und den Cu-freien Phasen
BigSrnCasOj. und Bi2(Sr,Ca)306. (Sr, Ca)14Cu2404i und Bi9Sr1iCa50I sind die Haupt-
zersetzungsprodukte von Bi-2212 in 1 bar 02. Die Bi-freien Phasen zersetzen sich in
der Reihenfolge (Sr, Ca)14Cu2404i, (Sr, Ca)Cu02, (Sr, Ca)2Cu03, und (Sr,Ca)0 sowohl
bei einer Erhohung der Temperatur als audi bei einer Erniedrigung des Sauerstoffpar-
tialdruckes. Die Cu-freie Phase BigSinCasOj ist nur bei hohem Sauerstoffpartialdruck
stabil, wobei Bi2(Sr,Ca)3Oe eine dominierende Sekundarphase bei tiefen Sauerstoffpar¬
tialdruck ist. Viele Studien iiber Schmelzverfahren zielen darauf, grSssere Korner von
diesen Phasen zu vermeiden. Mit Hilfe der vorlaufigeii thermodynamischen Beschrei-
bung konnte ein Fenster in der Zusammensetzuug gefunden werden, die ein Schmelzver¬
fahren im zwei-Phasen Gebiet 2212+Flussigkeit erlauben wiirde.
Die Phase Bi-2212 kann sich aus der Fliissigkeit bilden. Die Bildung von 2212 beim
Erstarren wird bestimmt, einerseits, durch die Wiederaufnahme von Saueistoff aus
der Atmosphare und, andererseits, durch die Nachlieferung der Kationen via einer
Auflosung der Sekundarphasen. Berechnungen, die die Behinderung der Sauerstof-
faufnahme und die Auflosung von Sekundarphasen simulieren, zeigten dass, in beiden
Falle, die Bildung der Einschichterphase H905 anstelle von 2212 vorgezogen wird.
Diese Resultate sind in guter Uebereinstimmung mit expeiimentellen Beobachtungen.
Die Phase Bi-2223 wird bekanntlich nur in einem schmalen Temperaturintervall gebildet,
und es wird vermutet, dass die Teilnahme einer fiiissigen Phase im Bildungsprozess
notwendig ist. Die Phase 2223 ist auch von sehr flachen Mehrphasenfeldern umgeben,sodass kleinste Abweichungen von der idealen Stoichiometrie zu markanter Erniedri¬
gung des 2223 Phasenanteiles fiihren. Die hiesigen Berechnungen zeigen, dass ein Ein-
fluss der Fliissigkeit darin liegt, die flachen Mehrphasenfelder auf der Bi-reichen und
Cu-reichen Seite zu offnen. Gleichgewichte mit der Fliissigkeit konnen so das Fenster
in der Zusammensetzung erweitern, wo ein grosserer Phasenanteil von 2223 resultiert.
12
Aim of the Study
The applications of promising new functional ceramics, such as high-temperature su¬
perconducting oxides, are often limited by the difficulties in processing these materials
with the desired properties. In the case of the oxide superconductors, considerable dif¬
ficulties exist even 10 years after their discovery since the superconducting properties
are extremely sensitive to small changes in the processing conditions. Understandingand controlling the complex reaction mechanisms which occur during the fabrication
of these multicomponent ceramics represents a tremendous challenge for the material
scientists.
Of big help for the material scientist on the long adventureous journey in processing new
materials is to get a good "road map", which means the phase diagram of the system
(see e.g. [91Hay, 93Ald, 95Alp]). This "diagram" is a representation of the equilibriumstates and shows which phases are stable under given conditions. This information is
usually gathered using many different types of experimental methods and is related to
typical questions of material development such as: are there any phase transformations
to be expected, which ones, what is the stability range of this phase or the solubilitylimit of any element in it, what is the dependency on temperature, concentrations,
partial pressures, etc. This quickly leads to a huge amount of experimental work. In
particular, the description of multicomponent systems requires the knowledge of many
lower order systems.
A phase diagram is a representation of the equilibrium state of a system and is thus an
expression of the differences in energy between the various phases. It follows from the
thermodynamic properties of the phases. This means that the entire information on the
phase diagram and the thermodynamics is contained in a small set of functions, which
can be expressed by the free energies of the phases. Appropriate model descriptionsof these functions may be used to calculate any equilibrium state or thermodynamic
property.
The use of thermodynamic modelling for the calculation of phase equilibria can con¬
tribute to a significant reduction of the experimental effort needed to understand the
phase relations and determine optimal compositions and processing parameters (seee.g. [95Dum]). Incompatibilities between various types of data may be detected and
extrapolations can be made with more reliability into not yet experimentally investi¬
gated areas as well as higher order systems. The resulting thermodynamic descriptionsare consistent and allow to store a huge amount of thermochemical information into
databases using only few functions. The thermodynamic description is then an im¬
portant tool for predicting and understanding processing routes as well as providinga basis for treating the kinetics of phase transformations. The benefits increase with
the amount of components and the complexity of the system. This is important for
high-value-added materials, where the great benefit lies in the time gained for the
development of new products.
The Bi-Sr-Ca-Cu-0 (BSCCO) system is particularly interesting as it contains three
superconducting phases BinSi'gCusOj, (U905), Bi2Sr2CaCu20;e (2212) and
Bi2Sr2Ca2Cu30j, (2223), of which the latter two are favourite candidates for power
applications. These applications require bulk material, tapes, wires, or thick films.
13
This interest for 2212 and 2223 comes from the fact that these phases have relatively
high critical temperatures (Tc = 95 and 110 K respectively), that they can be produced
without poisonous constituents, and retain reasonable properties also in bulk form. See
e.g. [95Hel] for a review on the material technology aspects. A large experimental effort
has already been made worldwide to study the crystal chemistry, phase diagrams, and
thermodynamic properties related to the BSCCO system. This effort is however by far
insufficient, especially more data on phase equilibria and thermodynamic properties
are needed in order to improve and achieve reproducibility in the processing of these
materials [94Pet].
The aim of this work was to use thermodynamic modelling as a tool to study the phase
equilibria of the Bi-Sr-Ca-Cu-0 system under ambient atmosphere. The analysis is
focused on the ranges of temperature and oxygen partial pressure useful for processing
large scale materials i.e. from room temperature to the melting temperature of the
highest melting compounds (around 3000 K) and foi oxygen partial pressures lying
between that of an argon atmosphere and a pure oxygen atmosphere (about 10~5 to
1 bar). The modelling approach was expected to be especially useful for the under¬
standing of the melting relations. The first part of this thesis gives an introduction to
the computation of phase equilibria, the second part summarizes the current results
on the modelling of a consistent thermodynamic description of the Bi-Sr-Ca-Cu-0
system, and the third part shows with preliminary calculations how to investigate the
thermodynamic implications on the processing of 2212 and 2223 superconductors.
References
[91Hay] F. H. Hayes, Ed., User Aspects of Phase Diagrams, The Institute of Metals
(1991).
[93Ald] F. Aldinger and H. J. Seifert, '"Phase Diagram Studies as a Key to the De¬
velopment of Materials", Z. MetaUUe., 84(1), 2-10 (1993) in German.
[94Pet] D. Peterson and S. W. Freiman, "Summary of NIST/DOE Workshop: Phase
Diagrams for High Tc Superconductors". Appl. Supercond., 5(5), 367-372
(1994).
[95Alp] A. M. Alper, Ed., Phase Diagrams in Advanced Ceramics, Academic Press
(1995).
[95Dum] L. F. S. Dumitrescu and B. Sundman, "Computer Simulation of /3'-Sialon
Synthesis", J. Eur. Ceram. Soc. 15, 89-94 (1995).
[95Hel] E. E. Hellstrom, "Processing Bi-Based High-Tc Superconducting Tapes,
Wires, and Thick Films for Conductoi Applications", in High-Temperature
Superconducting Materials Science and Engineering. D. Shi, Ed., Pergamon
(1995).
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Part I
Calculation of Phase Diagrams
16 CALPHAD
1.1 Principles
Phase diagiams are graphical representations of the stability domains of the phases in
a system and thus can be directly calculated from the thermodynamic properties of
these phases. This was already understood in the early times of thermodynamics, but
calculations applied to real systems were practically impossible due to the complexityof the relations between thermodynamics and phase equilibria. With time, phase di¬
agram studies and thermodynamic measurements were performed by different groups
and evolved into separate fields. This led to the analysis of phase diagrams using
mainly topological considerations, leaving the thermodynamic origin behind [64Pal].Large efforts on the interaction between thermochemistry and phase diagrams were
re-initiated in the fifties. This new impulse coincided with the first developments of
computers which opened new horizons. The major contributions to phase diagramcalculations from the pre-computer era are due to van Laar at the beginning of the
century and to Meijering in the fifties. Their work has been recently reviewed byKaufman [81Kau].
The first computer calculated phase diagrams appeared in the work of Kaufman and
Bernstein [70Kau]. The computation of phase equilibria spread out rapidly and estab¬
lished itself as a research activity with the creation of the CALPHAD (CALculation of
PHAse Diagrams) conference and journal [77Kau], dedicated to the coupling of phase
diagrams and thermodynamics. Since then the calculation strategies and the thermo¬
dynamic models have been improved, and many software packages and thermodynamicdatabases for phase diagram calculations have been developped. Overviews of current
leading softwares and thermodynamical databanks can be found in e.g. [90Bal, 93Ball].
An important aspect in the development of thermodynamic databases is the need for
broad cooperations. Laige multicomponent databases of industrial interest can only be
achieved in reasonable time if the efforts of various groups and the results of previouswork can easily be joined, i.e. if the modelling work of different authors is compatible.In order to have a basis on which to build on, it is necessary, for example, to use
the same energy reference states and to have compatible models. In this work, the
thermodynamic description of the elements is therefore taken from the standards of
the Scientific Group Thermodata Europe (SGTE) [91Din] which has played a leadingrole in the establishment of a broad international cooperation since 1987.
The general approach to the calculation of phase equilibria based on thermodynamicmodels has been described by many authors e.g. [83Hen]. Our short overview of the
subject is illustrated in Fig. 1.1.1.
In a first stage, an appropriate model has to be formulated foi the Gibbs energy of
every phase known to exist in the system. This implies that a minimum of experimentalinformation must be available from phase diagram studies, but no phase predictioncan be expected from this approach. Further information on the crystal structure
and chemistry is also considered in order to formulate solution models as realistic as
PRINCIPLES 17
EXPERIMENTAL INPUT
Crystal Chemistry
Phase Diagram
Thermodynamics
MODEL
DESCRIPTION
Set of G(T,xi) with
adjustable parameters
THERMODYNAMIC
OPTIMIZATION
Creation of a Thermodynamic Database
Set of G(T,xi) with
optimized parameters
Application of a Thermodynamic Database
Kinetic Data
Morphological Data
THERMODYNAMIC DATABASE
for
PHASE EQUILIBRIA CALCULATIONS
MODELLING OF PHASE TRANSFORMATIONS
MODELLING OF MATERIALS PROPERTIES
Figure I.l.l: Creation and apphcahons of thermodynamic databases for phase
gram calculations.
18 CALPHAD
possible. This first stage is characterized by the choice of thermodynamic models
and results in a set of Gibbs energy functions containing adjustable parameters. The
thermodynamic description of heterogeneous systems and in particular the models used
in this work are presented in Chap. 1.2. The type of experimental input used for the
choice of models and also for the adjustment of parameters in the next stage are brieflydiscussed in Chap. 1.3. The interdependence between the various kinds of data is
emphasized with some examples.
In a second stage, the model parameters have to be determined in order to be able
to perform the desired calculations of phase equilibria. The special strength of the
thermodynamic modelling is the coupling of both phase diagram and thermodynamic
data, which results in calculated phase relations that are thermodynamically consis¬
tent. This optimization process should be viewed as a complementary tool to the many
experimental methods used during phase equilibria studies, since it allows to detect
incompatibilities between various kinds of data and facilitates the assessment of ex¬
perimental results. The optimized description is then more reliable than the sum of
individual measurements. It is a concentrate of the whole information on thermody¬namics and phase relations which is consistent and can be stored in a compact way.
Furthermore, the optimization can help in the planning of new experiments by indi¬
cating which key data are missing or which uncertainties remain. Extrapolations can
be made in unknown regimes or higher order systems.
The calculation of phase equilibria from a set of Gibbs energy functions is part of the
optimization process as well as of any application of thermodynamic databases. The
distinction made in Fig. 1.1.1 between the creation of a thermodynamic database and
its application is not a chronological flow chart. Both efforts are often made in parallel.What evolves is the reliability of the thermodynamic description and of the predictivecalculations which improves as new data become available. The flow chart of Fig. 1.1.1
emphasizes the aim for which equilibrium calculations are made. Some insights in the
black box of the calculation are presented in Chap.1.4. Some crucial points of the
optimization procedure are discussed in Chap.1.5.
The CALPHAD approach has now become a standard technique in phase diagramstudies. Further developments are presented as outlook in Chap. 1.6. We can see two
major trends. On one hand, the inclusion of information from the microscopic level in
order to obtain thermodynamic descriptions as realistic as possible and thus to improvethe predictive potential of the calculations. On the other hand, the development of
software for treating kinetic problems which make use of thermodynamic database and
programs for equilibrium calculations.
This work was mainly concerned with the creation of a thermodynamic database for
the BSCCO system. The present optimization work is presented in Part II and some
first applications are given in Part III.
THERMODYNAMIC MODELLING 19
1.2 Thermodynamic Modelling of Heterogenous
Systems
1.2.1 General considerations
Thermodynamics express the energy of a system in terms of macroscopic quantities
such as temperature, pressure, volume, concentrations of elements, electromagnetic
field. The equilibrium state corresponds to a minimum in energy, for example at
constant temperature and constant volume to a minimum in Helmholtz energy and
at constant temperature and constant pressure to a minimum in Gibbs energy. In
practical applications the pressure and not the volume is usually the parameter which
can be controlled, so that it is justified to consider the Gibbs energy of the system
(instead of the Helmholtz energy) for phase diagram calculations. In this work, the
thermodynamic properties of the BSCCO system have been modelled as a function of
temperature and concentration only. Dependences of the Gibbs energy on pressure,
electric or magnetic fields have not been considered.
All calculations have been made at a total pressure of 1 bar. The influence of higher
oxygen partial pressure has sometimes been tested by calculations up to 100 bar O2
where the influence of the total pressure on the condensed phases can still be assumed
to be small. No attempt was made however to treat the high pressure range (up to
several GPa) of the Sr-Ca-Cu-0 system in which several possibly superconducting
compounds have been reported [94Hir, 94Ada, 95Sha]. The pressure dependence of
the Gibbs energy could be treated by using data on the thermal expansion coefficient
and the isothermal compressibility which are rarely available. Examples of such models
can be found in the work of Fernandez Guillermet et al. [85Ferl, 85Fer2, 86Fer, 87Fer].
Magnetic contributions should be considered in systems with phases exhibiting var¬
ious magnetic states. For example, a magnetic term due to the energy difference
between ferromagnetic and paramagnetic states needs to be added to the Gibbs en¬
ergy of a-Fe in order to reproduce the stability regions of the various Fe modifications.
This ferromagnetic contribution has been treated using the Inden-Hillert-Jarl formalism
[76Hil, 85Fer2]. In the BSCCO system, several phases can exhibit superconductivity
or antiferromagnetism. All these phase transitions occur however at low temperatures
where the present work is not intended to be applied. These magnetic contributions
are included in the values of the enthalpy and entropy at 298 K upon which the present
thermodynamic description is built.
Temperature dependence
The Gibbs energy of elements or stoichiometric phases is represented as a function of
temperature only. The present thermodynamic description is aimed for use at higher
temperature and its validity is not intended to extend below 298 K. From room tern-
20 CALPHAD
perature upwards, the specific heat can be well represented by the expression :
cp = -c-2dT-6eT2 - 2fT~2 (1.2.1)
where — c is the Dulong-Petit value, d and e are corrections due to anharmonic and
electronic contributions, and / is a parameter allowing to describe the decrease of the
specific heat at lower temperatures.
The temperature dependence of the Gibbs energy is obtained by integration of the
above expression for cp and is represented here according to the standard of SGTE
[87Ans, 91Din]. The Gibbs energy is referred to the entropy at 0 K and the enthalpyof the elements in their standard state at 298 K (SER reference state) :
°Gf( T) - #,SER(298.15 K) = a + &T+cTln(T) + dT2 + eT-1+/T3
+jT7 + kT~9 (1.2.2)
Different sets of the coefficients a to k may be used in different temperature ranges.
The coefficients j and k are for metastable ranges only, i.e. liquid below the melting
temperature or solid above the melting temperature respectively [87And].
Composition dependence
There is a tremendous amount of references on the modelling of composition depen¬dence in thermodynamic models. For reviews, see e.g. [52Gug, 72Ans, 91Pel]. The
models that we have used are presented in the next two sections, where ionic solid
solutions (1.2.2) and ionic liquids (1.2.3) are discussed separately. Here we would like
to point out only some of the most important concepts which these models are based
on.
The different behaviours of a solution are usually first discussed in terms of the energy
of mixing of the solution. The energy of mixing represents the difference between the
eneigy of a mechanical mixture of the elements and the energy of the real solution.
The molar Gibbs energy of a solution G,„ is given by the expression :
G,n = X>.^« = I>.^+AG"m (1-2.3)
where p,% is the chemical potential of the species : in the solution and n° the one of
the pure phase of i. In most textbooks, the energy of mixing is illustrated by usingthe model of a binary regular solution [29Hil]. In that model, the entropy of mixingis obtained by assuming random mixing and the enthalpy of mixing is taken as a
symmetric function of the composition. The energy of mixing can then be written as :
AG'"" = RT[xA\n{xA) + xBln{xB)} + LxAxB (1.2.4)
where x, is the mole fraction of i and L a parameter characterizing the enthalpy of
mixing. Thiee extreme cases can be distinguished when mixing two different species.If L is zero, the solution is said to be ideal and is characterized by random mixing. If L
is positive, the energy of the mixture will be increased compared to the ideal solution.
THERMODYNAMIC MODELLING 21
This creates a tendency for phase separation which results in a miscibility gap at low
enough temperature. Finally if L is negative, a tendency for ordering exists which can
lead to the formation of an ordered structure.
The thermodynamic behaviour of solution phases depends on various microscopic prop¬
erties of the mixed species such as atomic size, shape, electronegativity, etc. or in
other words on the resulting electronic configuration of the system. The aim of ther¬
modynamic models is to include as much as possible from the microscopic reality in a
phenomenological description. From this point of view, one of the most useful concepts
is that of bond energies between atoms. This concept has been used in many kinds
of approximations and represents a convenient bridge between statistical mechanical
techniques and thermodynamic functions. In the simple case of a binary A-B system
with only nearest neighbour interactions, the bond energies between A-A, B-B, and
A-B pairs are usually taken to be independent from the atoms surrounding each pair
and are given by the numbers EAA, EBB, and EAB respectively. Under the assumption
of random mixing, this bond energy model leads to a regular solution expression for
the energy of mixing, where the parameter L is given by :
L = NA^[EAB-^(EAA + EBB)\ (1.2.5)
Here is NA Avogadro's number and Z the number of nearest neighbours.
The thermodynamic properties of many solutions cannot be accounted for by such
a simple description and often the energy of mixing is described by more complex
functions. In such cases, most models keep however the assumption of random mixing
and the concept of excess energy is introduced, which represents the difference in energy
between the real solution and an ideal solution :
Gm = Y,n^°,-TS'dea' + AGexee3' (1.2.6)
The excess energy can be described by any function. This correction term can be ex¬
pected to represent a good approximation for solutions of very similar species. When
the mixed species become less similar, it may no longer be able to describe well enough
the thermodynamic properties of the solution. The reason is that the use of a grow¬
ing excess energy term added to an ideal entiopy contribution represents an internal
contradiction. This approach does not include the influence of short-range order.
When the species are sufficiently different and lead to the appearance of long-range
order, the concept of sublathce is introduced. The structure of ordered phases is split
into sublattices. The sublattice models consider unsimilar species to be located on
different sublattices and similar species to mix within the same sublattice. Ionic systems
are thus described using at least two sublattices, one for cations and one for anions.
Within each sublattice random mixing may be assumed and the deviation from ideality
is treated similarily as mentioned before using excess energy terms.
Let us come back to the internal contradiction mentioned above. All models based on
the approximation of random mixing corrected by an excess energy term cannot prop¬
erly describe the influence of short-range order (sro) as they do not solve the problem
of the real configurational entropy. One of the major consequences of not modelling
22 CALPHAD
the configurational entropy is that the approach cannot be "phase predictive". The
description of sro can be taken into account with bond energy models by consideringinteractions between atoms which extend beyond the nearest neighbours approxima¬tion. These statistical mechanical problems are then treated with methods such as the
cluster variation method (CVM) or the Monte Carlo method (MC) (see 1.6.1).
1.2.2 Ionic solid solutions
All solid solutions are described in this work using the formalism of the Compound
Energy Model (CEM) [86And], whose formulation of the Gibbs energy is characterized
by a large flexibility and allow to treat any multicomponent, multisublattice phases.
The description of a solution phase in terms of sublattices defines a volume in com¬
position space in which the phase is contained. The Compound Energy Model is
based on the Gibbs energy of the corner points of this volume, which are regardedas "compounds". For ionic solutions, some corner points may correspond to charged
compounds which are then used purely in a formal way. Only neutral compounds can
have a physical meaning. Furthermore, the neutral corner points may represent stable
and metastable compounds as well as unstable Active ones.
The Gibbs energy for one mole of formula unit of a phase with n sublattices and ii
species on sublattice k is given by an expression of the type :
Gm = E-£»„••».."G., U-TSM + AG"«" (1.2.7)
where the y,k are the site fractions of species %i on sublattice k. Thus £ ytl = 1 for
all k. Applications of this model to oxide systems can be found in many articles. For
more information, the reader is referred to [88Hil, 92Bar].
In the Sr-Ca-Cu-0 system, solid solutions arise between the Sr and the Ca sides as
these elements are very similar. An example of a phase exhibiting solid solution on one
sublattice is the compound (Sr,Ca)2Cu03. The corresponding sublattice descriptionis (Sr+2,Ca+2)2(Cu+2)i(0~2)3 and the Gibbs energy of the compound is given after
Eq.I.2.7 by :
Gm = 2/Sr0Gsr2Cu03 + «/Ca°G'caiCu03 +-Rr(!/Si -hl(ySr) + 2/Ca-ln(^Ca))
+AGexces" (1.2.8)
where ?/si and !/ca are the site fractions of Sr+2 and Ca+2 on the sublattice. °Gsr2cu03and 0Grca2Cu03 are the Gibbs energies of the ternary oxides which are coming from
the subsystems Sr-Cu-0 and Ca-Cu-O. °Gsr2cu03 and °Gca2Cu03 are omy functions of
temperature.
In the BSCCO system, the solution behaviour of many phases is further complicated
by the fact that Bi, Sr, and Ca can often occupy the same crystallographic sites. For
example, the high-temperature stable form of bismuth oxide, <5-Bi203, can dissolve
some Sr and Ca. 5-Bi2C>3 has a defect fluorite structure with 25% vacancies randomlydistributed on the oxygen sublattice [78Har]. The phase can be represented by the for¬
mula (Bi+3,Sr+2,Ca+2)2(0-2,Va)4 and is thus defined inside the concentration volume
THERMODYNAMIC MODELLING 23
Sr:Va
Ca:0 Bi:08-Bi203
Bi:Va
Figure 1.2.1: Extension of the phase (Bi.Sr,Ca)2(0,Va)i in composition space. The
charges of the ions have been dropped since there is no risk of ambiguity. The shaded
area represents the surface of neutral compositions.
shown in Fig. 1.2.1. In the following, the charges of the ions have been diopped since
there is no risk of ambiguity. Double points are used to separate species on different
sublattices. The molar Gibbs energy of the 5-phase is given according to Eq. 1.2.7 :
GL = B.2/0°GBl O + </Sr2/0°GSr O + 2/Ca2/0°<?Ca o
-J/B,«/Va°GB,Va+ 3/Sr2/\a°GsrVa+ 2/CaJ/Va°GcaVa
+ST [ 2 (j/Bl In ym + ySt In ySl + j/Ca In J/Ca) + 4 (y0 In y0 + «/VaIn 2/Va) ]
(+EC1) (1.2.9)
The model parameters to be determined are the six °G of the corners. These corners
represent charged "compounds", but the only accessible part of the composition square
is for neutral combinations of these corners, i.e. on the neutral surface. From a practical
point of view, the basic compounds, for which one should optimise parameters, are
the end points of this neutral surface. These three end points of the neutral surface
represent <5-Bi203, Sr2C>2 and Ca2C>2 and their Gibbs energies can be formulated in
terms of the model parameters (the °G of the corners) using Eq.I.2.9. The resulting
new functions are :
, lo/-it>I + I «R
^SrO + 2 ^SrVa _
lo^xJ I lo^-to
4i?T(|lni + ilni)
o,o<£-Bi2 03
^81202
2°GlS + 4
(1.2.10)
(1.2.11)
l+ 4i?T(iln| '08202
~»CaO1
aS= 2°G^0 + Adc, + B^T (1.2.12)
The function 0G|~^023°3 is the Gibbs energy of pure <5-Bi203 and is taken from the binary
Bi-0 system. The functions "Gf^Q., and °Gq^0 represent the Gibbs energy of 2 moles
24 CALPHAD
of SrO in the fluorite structure and can be referred to the stable halite structure of
SrO. The energy difference is here expressed as a linear function in temperature with
the coefficients AsSl, B|r, Asc„ and B£a.
Three more equations are needed to determine all six unknown "G functions. Two
further independent equations can be obtained from reciprocal relations between the
six corners, i.e. :
OSlS|
o/~tS O/ld o/-y£ A {~t& (T ct -i Q\^810+ ^Si Va
~~
"BiVa- ^Si 0— ^ "i 1 (1.4.16)
°Gl o + °GCa va" °Gl Va
- °GCa o= A Gsr2 (1.2.14)
This gives us five independent equations, which is the maximum that can be obtained
from the neutral surface. The extra degree of freedom which always appears in the
modelling of ionic phases corresponds to the difference in the dimension of the neutral
surface and the dimension of the volume where the phase is defined. As nothing is
known on the energy of the charged compounds, an arbitrary reference state has to be
chosen. In this case, we chose the value :
°Gb, Va=C ~ !°G0r + RT^ U1 4 - 3 hl 3) (L2-15)
The parameters to be optimized are now A$t, B|r, AsC!t, Bq^, AGJ?i, and AGj2. As
an alternative to the reciprocal relations AGfj and AC*2 it is possible to introduce
an excess Gibbs energy EGm. This EGm can consist of several terms, each of which
is a product of an interaction parameter with the corresponding site fractions of the
interacting species. The number of independent interaction terms is therefore limited
and depends on the sublattice model. Here an excess Gibbs energy term described by
independent parameters could be :
EGm = 2te.2/Sr2/o^Bi,SiO + 2teiJ/s»2/Va-tB.SrV» (1.2.16)
+ 2/B!2/Ca2/o£Bi,Ca O + 2/B^Cai/VaiBi.Ca Va (1.2.17)
+ 2/S, 2/Ca2/0iSr,Ca O + 2/Sr2/CayVa£sr,Ca Va (1.2.18)
Each interaction parameter can be expanded in a function of the site fractions and lead
to many new unknown coefficients.
Reciprocal relations and interaction parameters are not independent from each other.
They can have a similar influence on the Gibbs energy or even be identical in same
cases. For example here, if the interaction parameters are choosen constant and do not
depend on which species is on the other sublattice, one obtains :
SteiS'SiSfoiBi.Si 0 + |/Bi2/Sr2/VaiBi,Si Va = 2/Bi2/Si^l
2/B.2/Ca2/0iB.,Ca,0 + 2/Bi2/Ca«/VaiB.,CaVa = l/BiS/S^ (1.2.19)
The interaction parameters Lx and L2 are comparable to the reciprocal relations AGj?uand AGj2. In general, we decided to optimise reciprocal relations without using any
interaction parameters. In case precise data on the thermodynamic properties of the
phase are available it might be favourable to use interaction parameters since with
those we can introduce a composition dependence, thus allowing more flexibility. It
is important to note, as indicated above, that the various possible reciprocal relations
and interaction parameters are not independent [92Bar].
THERMODYNAMIC MODELLING 25
The CEM offers a flexible way to describe the thermodynamic properties of solid so¬
lutions. One of the limitation of this approach is that it is usually difficult to give
a physical interpretation to the reciprocal relations or to the interaction parameters.
This can limit the comparison of values obtained from this model with results based on
atomic modelling methods. Alternative models based on defect chemistry have been
used for phases with limited solution ranges or close to ideality. For example, the
thermodynamic properties of the superconducting phase (La,Sr)2Cu04_z have been
modelled in that way [90Ide, 920pi, 940pi]. A better compatibility with ab initio
models could be obtained from a model formulation based on bond energies instead of
compound energies. Efforts towards a flexible model based on bond energies applica¬
ble to any multicomponent. multisublattice phase are still in progress [920at. 930at].It is however difficult to see how these efforts will lead to a better treatment of the
configuratioual entropy without using the methods mentioned in section 1.6.1.
1.2.3 Ionic liquids
The ionic solid phases are characterized by the ordering of cations and anions on
different sublattices. The long-range order vanishes at the melting point, but the
short-range order between cations and anions may be preserved well above it. In other
words, at certain compositions where the tendency for ordering is large, each cation
remains practically surrounded by anions (and vice-versa) also in the liquid state.
For example, let us consider the Cu-0 system (see [94Hal]) which contains the two
stable oxides Cu20 and CuO. Above the melting point of Cu20, a strong tendency
for ordering is maintained. This influences drastically the thermodynamic properties
of the Cu-0 liquid as can be seen in Fig. 1.2.2. The variation of the oxygen content
in the liquid as a function of temperature and oxygen partial pressuie is considerably
different on one side of the C112O composition than on the other. Furthermore, be¬
tween Cu and CU2O, the liquid shows complete miscibility at high temperature and
exhibits a miscibility gap at lower temperature. The physical reality in the liquid has
to change continuously from a metallic liquid in which some oxygen is dissolved to an
oxide liquid where a strong tendency for ordering exists near Cu20. Thus, the ther¬
modynamic properties of the liquid cannot be reproduced without taking into account
the characteristics of both the metal and the oxide part.
The thermodynamic descriptions of such liquids are either based on the analogy with
the solid compounds or with a gas containing various molecules. In the first case,
the tendency for ordering is approximated by long-range order and a two-sublattice
model is used [85Hil]. Charged vacancies are introduced on the oxygen sublattice as
a formal way to ensure a continuous description from the metal to the oxide liquid.
In the second case, the existence of molecules is assumed and the term "associate"
model is used [82Soml, 82Som2]. The liquid then consists of a mixture of elements
and associates. The result of both approaches is to produce a set of functions for the
liquid pure elements, the fictive liquid oxide compounds, and the interaction parameters
between them.
Even if both models are based on rather different analogies, they can usually be made
mathematically equivalent with the appropriate choice of associates or sublattice de-
26 CALPHAD
1750
1700
g 1650-
_i i i_ 10s. air
0.15 0.20 0.25 0.30 0.35 0.40 0.45
Mole fraction O
Figure 1.2.2: Enlarged part of the Gu-0 phase diagram with isobars of equilibrium
oxygen partial pressure showing the change in the thermodynamic properties of the
liquid above CU2O.
scription. For example, in the Bi-0 system (see Chap. II.2.1), the same expression for
the Gibbs energy of 1 mol of liquid is obtained by considering the associate Bi2/30 or
the sublattice formula (Bi+3)p(Va-q,0-2,0), :
+ RTq[yv*-<i m(2/va-0 + Vo-> Mvo-I
a ^excess
2/0-111(2/0)]
(1.2.20)
Here G^ (equivalent to G^+3 Va_tl) represents the Gibbs energy of 1 mol of pure bis-
-rliqmuth liquid, Gb?2o3 (standing for G^+3 0_2) represents the Gibbs energy of 5 mol of
-fhqatoms of ideal non-dissociated Bi203 liquid, and G0 (standing for GB^+3 0) representsthe Gibbs energy of 1 mol of pure Active oxygen liquid. The excess energy term contains
interaction parameters between Bi, Bi203, and O.
One practical problem in modelling oxide liquid lies in the determination of the pa¬
rameters on the oxygen side. The extension of the liquid phase towards pure oxygen
is in reality always limited and the liquid properties close to pure oxygen are not onlyunknown, but simply Active. In the Bi-0 system, the few experimental data 011 the
liquid concentration indicate that the liquid never extends beyond the Bi203 compo¬
sition at atmospheric pressure. It is most probable that this is also the case for the
slightly higher oxygen partial pressures where our thermodynamic description is ex¬
pected to give reliable extrapolations without pressure terms. In this case, the neutral
oxygen terms could be removed from the model and the sublattice formula reduced
to (Bi+3)p(Va-q,0-2),. The liquid is then only defined between Bi and Bi203. If the
EXPERIMENTAL INPUT 27
liquid was to extend beyond Bi203, the question is if it would be more realistic to let
it extend up to neutral oxygen or if a new associate B12/5O (respectively Bi+ 011 the
cation sublattice) should be introduced. The question seems unimportant for the Bi-0
system, but is of concern for example in the Cu-0 system, where the liquid composition
at 1 bar 02 lies between Cu20 and CuO. In that case, two different descriptions have
been proposed : a sublattice model with (Cu+1,Cu+2)p(Va~<l,0~2)g [94Hal] (equiva¬
lent to an associate model with Cu, C112O. and CuO [95Ran]) and an associate model
with Cu, Cu20, and O [83Sch. 92Bou] (corresponding to (Cu+1)p(Va-q,0-2,0),) .
The differences between the two approaches appear practically only at oxygen partial
pressure above 1 bar.
In this work, we have used the two-sublattice model with the formula :
(Bi+3,Sr+2,Ca+2,Cu+1,Cu+2)„(Va-SO-2)9
The Gibbs energy of the liquid is given by
i= cat
+ Y, PRTV> MV.) + £ iRTy, bid,,)> = cat .= Va,0-2
+ EGhq (1.2.21)
where cat stands for the cations Bi+3, Sr+2, Ca+2, Cu+1, and Cu+2. The functions
°C?I'va represent the Gibbs energy of the pure metals, while the °<?]'0-2 represent the
Gibbs energy of the ideal non-dissociated liquid binary oxides. The excess termE Giq
is the sum of all contributions due to interaction parameters of the subsystems.
The larger contributions come from the extrapolation from the binary systems. Ternary
contributions between the different ideal liquid binary oxide have been found necessary
in all systems. Further contributions from higher order systems are small if any. Some
negative parameters were introduced in the higher order systems in order to let the
liquid phase appear more stable and to reproduce precisely the value of various invariant
temperatures which were accuratly known from experimental studies. This was at least
necessary at a preliminary stage of modelling. In the first quaternary system which
was recently considered as finally "optimized" (Sr-Ca-Cu-O, Chap. II.6), the liquid
phase could be well described using only binary and ternary contributions.
1.3 Experimental Input
Experimental methods of phase diagram or thermodynamic studies are presented in
many books and articles. We do not want to list the various measurement types, but
rather to point out some of the relations between these data which are often better
revealed with the help of thermodynamic modelling. For presentations of experimental
methods in phase diagram studies see e.g. [84Ips. 94Mor], for reviews oftheimodynamic
measurement techniques see e.g. [81Kub, 83Kom, 90Pra]. This chapter is divided
into two parts which correspond to the first stage of the model formulation using
phase diagram and crystallographic information and the second stage of the parameters
28 CALPHAD
determination using phase diagram and thermodynamic data.
1.3.1 Phase diagram vs. crystal chemistry
Phase diagram studies of unknown systems usually start by annealing some samples of
various compositions undei various conditions. The phase assemblage is usually anal¬
ysed using x-ray diffraction (XRD), electron probe microanalysis (EPMA), or scanningelectron microscopy (SEM) combined with an x-ray analysis of the phase compositions(EDX or WDX). If an unknown XRD spectrum or phase composition is found, crys-
tallographers are eager to identify the possible new phase. Therefore, experimentalevidences for a new phase exist and the crystal structure is often well known before
the phase is included in thermodynamic modelling.
Crystal structure investigations play an important role in the determination of the
composition of the new compound. In the case of solid solutions, the combination of
information on the crystal chemistry and the phase relations is crucial to formulate the
most appropriate sublattice model. In particular, the problem is to define a composition
range in which the phase may exist. This aspect is illustrated in the following with an
example taken from the Bi-Sr-0 system [96Hal].
Several phase diagram studies of the Bi203-SrO section have been published and two
recent ones [90Rot, 91Con] are shown in Pig. 1.3.1. Various contradictions can be
seen between the two diagrams, but for the purpose of this example, we only look at
the range of solid solution found for the rhombohedral ji phase which is indicated as
Rhomb.ss by Roth et al. [90Rot] and ss/3 by Conflant et al. [91Con].
These phase diagram studies alone do not allow to conclude on the endpoints of the
solution and disagree on the possible extension of the /3 phase towards SrO at highertemperature. Fortunately, the structure of this phase, both the low and the hightemperature form, has been investigated in detail by Mercurio et al. [94Mer] usingsingle crystal neutron diffraction (see Fig. 1.3.2). The /3-phase has a layered structure
consisting of fluorite-like sheets stacked in a regular' repetitive fashion. There is one
cation site in the sheet with mixed Sr/Bi occupancy (M(l)) and two cation sites at
the sheet interface occupied by Bi only (M(2)). There are two fully occupied oxygensites in the sheet (0(1)) and there are two different main oxygen positions at the sheet
interface, each with two sites (0(2)). They are both partly occupied. One of these
positions shows some splitting into sub-positions, three for each site, at all temperaturesand the other shows splitting in the high temperature form only. For our purposes it
is enough to describe the /3-phase with the formula :
(Bi+^^Sr^MO-^fO-2^The /?-phase is, thus, defined for compositions between 0 < usr < 1/3. The ugt frac¬
tion is here an abbreviation for the cation ratio ssr/(a^, + xsr). This implies that the
solubility data in one of the studies [91Con] are in contradiction with the crystallo-graphic results and that therefore the other values will be used for the determination
of parameters.
Thus the use of crystal structure data in combination with phase diagrams allowed first
to formulate a realistic sublattice model for the /?-phase, and second to resolve some
EXPERIMENTAL INPUT 29
1 1 1 1 /9
1 '
9 1210±10°
•
•
/ • -
925±S° „ c ,„, ss/ •
•
I ° ^&&/ <>85±50
« fl ©
•
1 96S±5°
-
| *t
//*^tf^M.S* -•» 1.
• • _
• 3 / 925*5°
/830°_ / * •" ~82iJ / • •
J 720°g
Rhomb ss*
• ••
• •< 1
* * /*i 65±5°V|
i
• •
u *
1 1
r> i
1 .
0
1/2(Bi203)40 50
Mo! %
100
SrO
TCC»
900
800
700
Figure 1.3.1: Experimental Bi203 SrO sections A) [90Rot] , B) [SlCon]
30 CALPHAD
contradictions between different phase diagram studies. The Bi-Sr-0 system has been
recently optimized by Hallstedt et al. [96Hal] and a calculated Bi203-SrO section in
air is shown in Fig. 1.3.2.
1.3.2 Phase diagram vs. thermodynamics
The optimization procedure is based on the coupling of phase diagram and thermody¬namic data. This is essential because the use of one type of data exclusively bringsserious limitations in the accuracy of the calculated values and in the confidence of
extrapolations.
If only phase diagram data are used, the energy functions cannot be determined with
reliability since the same phase relations can be obtained by any shifts in the energy of
all phases. In consequence, the extrapolation potential of the thermodynamic descrip¬tion is seriously reduced. If only thermodynamic data are used, the chances are small
that the correct phase relations will be obtained. The reason is that thermodynamicvalues can be determined to an uncertainty below 1 kJ only in the best cases, whereas
energy differences of a few hundred Joules can be enough to drastically change the
phase relations in multicomponent systems. An example of this sensitivity of phaserelations on small variations in energy is shown in Chap.II.6 for the stability field of
the infinite-layer compound in the Sr-Ca-Cu-0 system.
The relations between different mesurements can be seen in Chap.II.2 for the Bi-0
system. The heat capacity of Bi203 lias been measured at low temperature by adi-
abatic calorimetry and is given at high temperature by the slope of enthalpy incre¬
ments measured using drop calorimetry (Chap.II.2,Fig.3). These enthalpy increments
show jumps at the transition temperature of a-Bi203 to S-Bi203 and at the meltingpoint. The temperatures and enthalpy changes related to these phase transformations
have been also determined from thermal analysis techniques (DTA,DSC) as well as
from the change in slope vs. temperature of electromotive force (emf) measurements
(Chap.II.2,Table 4 and 5). The emf measurements themselves have been made in the
two-phase fields Bi(l)+a-Bi203, Bi(l)+<S-Bi203, and Bi(l)+Bi203(l) and in the liquidphase (Chap.II.2,Fig.4). The Gibbs energy of formation of Bi203 has been derived
from the data in the two-phase fields and the solubility limits of the liquid from the
change in slope at the transition from the two-phase fields to the liquid single phasefield. These data on the solubility limits of the liquid can finally be compared with
results from the chemical analysis of quenched samples (Chap.II.2,Fig.2).
A last example, which is frequent in these oxide systems, are phase transformations
involving the absorption or release of oxygen. The temperature vs. oxygen partialpressure dependence of these transformations has sometimes been determined by either
thermogravimetry or emf measurements (see Chap. II.4 and II.5). The comparison of
results from these different experimental techniques has proven to be helpful in trackingsystematic errors and is discussed further in the section on data assessment.
EXPERIMENTAL INPUT 31
S8Eod)-0(2)-
0(2)-0(1)-0(1)=0(2)-
-CM(2)
:j>(D:cm(2)
-KM(2),-D
:>0)
— MM'
o©:0(1);0(1)-0(2)-
,M(2)
>(1)
JM(2)
:> lone pair E oBi »Bi;La
0 0.2 0.4 0.6 0.8 1.0
Bi°1.5 xs/(XSr + XB,> SrOB
Figure 1.3.2: The existence range of the 0 phase. A) Structural investigations
[94Mer] support the sublattice model ^Bi+3;2^Bi+3,Sr+2;1 (0-2)2(0-2,Vs,)4. B) Op¬
timized Bi203-SrO section in air compared with experimental data on the solubility
limits of the /3 phase.
32 CALPHAD
1.4 Computation of Phase Equilibria
One great benefit of thermodynamic modelling is the ability to concentrate and store
all informations on the phase diagram and the thermodynamic properties in a small
set of functions. One critical problem is thus to ensure a reliable reproduction of this
information by the calculations, which is a none trivial matter. The computer output
may not always give the correct equilibrium state without certain precautions taken
by the user. Thus a minimum of ciitical attitude towards the calculated results is
always healthy and it may not be so simple for the occasional user of a thermodynamicdatabase to detect these errors. Much effort is currently being put into the develop¬ment of user-friendly reliable software e.g. [93Ball, 93Jan]. Some familiarity with the
principles on which these "black boxes" operate and of course also with the phases of
the system under consideration is still very useful. This chapter will try to give a short
overview of the strategies used in the calculation of phase diagrams and to illustrate
some of the encountered problems with examples from the BSCCO system. These lines
are intended for the occasional users of the thermodynamic database developped here.
The basic principles of phase equilibria calculations have been discussed by several
authors. The following summary is based on the articles of Hillert [79Hil, 80Hil, 81HilJand Lukas [82Luk]. The strategies and problems related to the calculation of phase
diagrams cover many aspects. A convenient approach to the subject is to consider first
the principles involved in the calculation of a single equilibrium, and then to discuss
the "mapping" of whole diagrams and their graphical representations.
1.4.1 Calculation of single equilibrium
Strategies
The aim of program developpers is to create a software able to handle any kind of
equilibria and any type of models. The need for a general approach to ensure flexi¬
bility in thermodynamic calculations has been nicely expressed by Hillert [80Hil] in a
comparison with the game of chess : "In order to teach a computer to play chess one
must instruct the computer about the rules and teach the computer some strategy. If
the strategy is primitive, it may also be necessary to teach the computer a number
of tricks to be used in special situations, in particular during the opening part of the
game. However the better the strategy, the less tricks are required. In the game of
thermodynamics, the question is whether such a good strategy could be found that no
tricks are required. In order to find such a strategy it is necessary to go back to the
fundamentals of thermodynamics and to find a way to instruct the computer about
them, such that the same instruction can be used by the computer in various kind of
situation."
Many strategies have been developped for calculating phase equilibria from thermo¬
dynamic functions. The choice of the stiategy for equilibrium calculations depend
COMPUTATION OF PHASE EQUILIBRIA 33
mainly on the way of formulating the equilibrium conditions. Two equivalent formu¬
lations are usually used for the equilibrium state of a system under constant pressure
and temperature :
1) The Gibbs energy of the system has a minimum at equilibiium
2) For each element in the system, the value of its chemical potential is identical in all
phases of the system.
/<: = /<? = - (1.4.1)a 0
P,= n,
=-
These two equivalent formulations lead to completely different numerical treatments.
In the first case, one has to search for the minimum of the function and hill-climbing
techniques are applied. In the second case, one has to solve simultaneously a set of
non-linear equations.
The first approach has been used for the calculation of chemical equilibria in single-
phase systems like gases or aqueous solutions since the appearance of computers (see
[70van] for a review). It seems however less suited for calculations in multiconiponent
multiphase systems. Some drawbacks are that it may be difficult to have a large
flexibility in the choice of equilibrium conditions (such as constant chemical potential,
fixed phases, etc.) without using many tricks and making many modifications to the
program [80Hil]. Calculations may furthermore be slow and thus mapping of entire
phase diagrams may become too time consuming.
The second approach of solving a set of equations has, to our best knowledge, been pre¬
ferred in all the programs developped for handling equilibria involving many condensed
phases. The set of non-linear equations can be solved for the composition variables after
elimination of the chemical potentials or the other way around. The problems arising
with these methods have been discussed by e.g. [79Hil, 82Luk]. With the elimination
of the chemical potentials, the system of equations may take various forms depending
on the situation (conditions, models) so that no geneial strategy can be used. With
the elimination of the composition variables, the set of equations can be reduced to
the same number as the independent variables so that one has data of only one phase
in each equation. This is a convenient strategy which is used for example in the Lukas
programs for binary to quaternary systems (BINFKT, TERFKT, QUAFKT) [82Luk].In any case, using either method of elimination of variables, some serious difficuties
arise for complex solutions having internal degrees of freedom such as the site fractions
in sublattice models.
Now it is helpful to realize that the formulation of the equilibrium state given in 2) is
derived from 1). This allows to improve the strategy by deriving the most appropriate
set of equations from the general formulation of the equilibrium state of 1), which can
then be numerically solved as in 2).
The Gibbs energy of a system with elements i and phases a can be written as G =
Y.a Ga where the condition for a closed system is expressed by Y.a n" = ni- Using
34 CALPHAD
Lagrange formalism, the minimum of G corresponds to the minimum of the function :
a t a
The /i, are Lagrange multipliers which in the following are found to be equal to the
chemical potentials of the elements i. The equilibrium is defined by :
^ = ^-,=0 (L4.3)
and from this follows the set of equations expressed in 1.4.1.
This general formalism can be used to consider various conditions imposed on the equi¬librium. This was successfully applied by Hillert [79Hil], who showed that when mole
fractions are introduced instead of number of moles, there are two types of conditions
(X)<» naxf — n, and Y,a x? = 1) which result in two kinds of equations :
8L
8na
8L „8G:
8x?
(?:-E/<,i; = o (i.4.4)
p,t n° + Xa = 0 (1.4.5)
When complex sublattice models are considered, the same formalism can be used to
include conditions on the site fractions, on the electrical neutrality, etc. This leads
to sets of equations which are more complex but the strategy is powerful and flexible
[84Jan2].
The most important consequence of Eqg.I.4.4 and 1.4.5 is that the equilibrium cal¬
culation can be divided into two steps. The chemical potentials are evaluated after
Eq.I.4.4 using initial estimations of the composition variables. Improved values of the
composition variables can be calculated for each phase separately using Eq 1.4.5. These
iterative steps are repeated until convergence is obtained. The calculation of the com¬
position variables for each phase separately in the second step allow to reduce the
computation time. But more important, the dependence of the Gibbs energy models
on the composition variables does not influence the calculation in the first step. This
brings a large flexibility since new models can be easily implemented and do not re¬
quire changes of the calculation procedure. Another important gain in flexibility comesfrom the ability of choosing a wide variety of conditions which include any intensive or
extensive properties, imposing stable phases, etc.
The most versatile software are based on that two-step iterative strategy of the equi¬librium calculation. It was first introduced by Eriksson [71Eri, 75Eri] in the SOL-
GASMIX program. The general formulation summarized above was given by Hillert
[79Hil. 80Hil, 81Hil] and forms the basis of the Gibbs energy minimizer POLY [84Jan2]used in the THERMO-CALC package. Other programs based on this approach include
the Lukas program for multicomponent systems (PMLFKT) and the program SAGE
[90Eri] (newer version of SOLGASMIX) used by the databanks THERDAS [90Spe]and F*A*C*T [93Bal2j. The THERMO-CALC program was used throughout this
work with the exception of some binary systems where calculations with the Lukas
program were made.
COMPUTATION OF PHASE EQUILIBRIA 35
Reliability
The user's main question is, did the program find the equilibrium state ? In our
work, we have experienced two typical types of problems. First, it may happen that
no equilibrium state can be calculated, and second, that a metastable equilibrium is
found.
The first case frequently arises if many solution phases have start values of the site
fractions which are too remote from their equilibrium values. Anothei possibility occurs
if the equilibrium is not well defined by the conditions given. In many cases this
allows the user to learn more about thermodynamics, in particular about which set of
conditions really uniquely defines the equilibrium state. A typical problem occurs when
the chosen composition lies exactly in a phase which is defined in a volume of lower
dimensions than the number of elements. This means that along a certain composition
line that existence range of the phase consists in a point. Numerically speaking, the
equilibrium can be defined only as an equilibrium with other phases on either side
of the composition scale. For example, our model description of the superconducting
Bi2+a!Sr2_j_j/Cai+j/Cu208-(-{ phase (see section II.1.5) assumes that the copper content
of the phase does not change and that the phase only exists in the plane of 28.57%
CuO. All calculations made exactly in that plane are not well defined and the program
might jump from one equilibrium found with phases lying on one side of the plane to
another one with phases lying on the other side. For calculations in that plane, the
composition should be selected slightly off the plane.
The second situation can happen if at least one of the stable phases is a solution with
tendency for immiscibility or has many internal degrees of freedom and the start com¬
positions are either far from equilibrium 01 on the wrong side of the miscibility gap.
A typical example of the BSCCO system is the liquid phase which exhibits a misci¬
bility gap between the metal and the oxide part at the temperatures of interest for
the processing of superconducting phases. Thus, if calculations are made in the oxide
part of the system and the starting composition of the liquid lies on the metallic side,
metastable equilibrium above the liquidus line may be obtained. If the starting compo¬
sition lies in the oxide part, the stable melting relations will be obtained. This problem
can be avoided by always checking that the calculated composition of solution phases
is "meaningful", which requires some familiarity with the system under consideration.
1.4.2 Mapping of phase diagrams
Strategies
The lines separating the phase fields in a phase diagram are phase boundaries, i.e.
there is always a phase appearing or disappearing when a line is crossed. This means
that each line is related to an equilibrium where the phase whose stability limit is
reached participates in the equilibrium but with a content of 0 mole. This equilibrium
formulation of the phase boundaries allows to construct a very efficient method for
mapping phase diagrams [84Jan2]. The whole diagram can be traced by following
an equilibrium between prescribed phases and checking at each step if another phase
should become stable.
36 CALPHAD
This method represents a combination of two strategies which have been used in early
programs (see [82Luk]). The first strategy (e.g. [70Kau]) is to compute the equilibriabetween sets of prescribed phases (regardless if they are stable or metastable) and
to select the most stable ones afterwards. The second strategy (e.g. [75Eri]) is to
calculate the stable phases under selected conditions and to scan the whole diagramalong these conditions. The first one is more flexible but the second one is easier to
be fully automated. The method mentioned above brings an optimal combination of
these advantages. All mappings made in this work in ternary and higher order systemswere made with the program THERMO-CALC which uses this elaborate strategy.
Reliability
We experienced two typical problems during mapping of diagrams. On one hand,some calculated lines are metastable because at some point the equilibrium with a
stable phase was missed and a metastable equilibrium was found. On the other hand,it happens that only one part of the phase diagram is mapped by the starting pointbecause the diagram consists of topologically independent parts or because some equi¬librium could not be calculated. Thus several starting points are needed. In any case,
individual calculations at various starting conditions should be made to test that the
results of single equilibrium calculations fit into the mapped diagram.
1.4.3 Graphical representations
Graphical representations are often the best way to understand the phase equilibriaand to use this understanding in material processing. The phase diagram of a mul-
ticomponent system is however a multidimensional entity which can only be viewed
through a series of cuts and projections, so that it is not always simple to find the most
appropriate representation. Calculated diagrams in the higher order systems such as in
the complete BSCCO system can rapidly become confusing when the number of phasefields is large. Thus, the mapping of diagrams is often followed by many single equilib¬ria calculations to complete the desired information. It is in particular very helpful for
isothermal or isoplethal sections to have some further knowledge on the mole fraction
of the phases found in the equilibria.
One problem of graphical representations as a function of composition arises when
the selected composition section goes along a phase which is only defined in a surface
included in the cut. As mentioned previously, the composition axis should be selected
to be slighlty different from the one of the phase in order for the equilibria to be defined.
One consequence is that the calculated plot will not show the single-phase field but
one or several multiple phase fields in which the phase being close to single-phase will
represent most of the phase fraction.
This is illustrated in Fig.I.4.1 for a section through the single phase field of 2212. The
desired cut should follow the composition change 2+x in Bi2+3.(Sro6Ca0 4)3-1 Cu208+^,but the calculation has to be made at a slightly different copper content than 2. The
calculated diagram shown in Fig.I.4.1.A was made for a copper content of 1.999.
In order to obtain a graphical representation of the phase relations as they would be
in the plane of copper content 2, all the phase boundaries shoud be removed, which
THERMODYNAMIC OPTIMIZATION 37
represent multiphase equilibria ending in the single phase field of 2212 as the value
of the copper content approaches 2. These multiphase fields equivalent to the single
phase field of 2212 can be identified by plotting the phase content which should consist
almost exclusively of 2212. The resulting modified diagram is shown in Pig.I.4.1.B.
1.5 Thermodynamic Optimization
The aim of thermodynamic modelling is to obtain the best possible description of the
system based on the phase diagram and thermodynamic data. But what is ''best'' ?
The best description should give an optimal fit to all types of data in all parts of the
system and have the highest extrapolation reliability. The question is then how the
data are fitted, which data are considered or how these are weighted. Further questions
are how realistic the model description is, which parameters are considered, and which
ones are relevant. All these factors influence the reliability of the extrapolation which,
at the end, is the point of major concern for the user. As there is no established
measure of reliability in the field of thermodynamic optimization and as a certain part
of subjectivity is involved in the assessment of data and the choice of models, we will
briefly comment on these problems below.
The key tool for the assessment is a program enabeling to fit the model parameters
to any kind of phase diagram or thermodynamic data and to minimize the error.
The programs developped by Lukas (BINGSS, TERGSS) [77Lukj were the first to
incorporate an optimization routine and have become a standard tool in assessment
work. Another optimizing routine called PARROT is provided by the THERMO-
CALC system [84Janl]. All the assessments and calculations made in this work were
performed using these optimizers which were the only ones available at the beginning
of the project.
1.5.1 Data assessment
More often than desired, various sets of the same data type show discrepancies between
them which force us to assume that some systematic errors have to be identified. The
first step in locating possible sources of systematic errors lie in the critical analysis of
the experimental procedure. A second possibility is given by thermodynamic modelling
which allows the comparison of different types of data and may thus help in finding
out which controversial set of data is the most compatible with the other types of
measurement.
The analysis of experimental procedures is a very difficult task and requires a profound
knowledge of many experimental techniques. Furthermore, experimental procedures
are often presented without details so that only the experienced scientist who is able to
read between the lines may spot a source of error. When no answer can be found from
the description of experimental procedure or the discussion, the assessment has to rely
on the comparison with other types of data. Some examples of systematic errors which
have been encountered in the BSCCO system are mentioned below with reference to
38 CALPHAD
2.00 2.05 2.10 2.15 2.20
2+x in Bi2+x(Sr06Ca04)3.xCu2O8
900-
L +02X1+01x1
2.00 2.05 2.10 2.15 2.20
A2+x in Bi2«(Sr0 6Ca0 4)3-xCu2°8
Figure 1.4.1: Phase relations around the 2212 phase with varying Bi content: A)calculated for a copper content of 1.999, B) as expected for a copper content of 2.
THERMODYNAMIC OPTIMIZATION 39
the chapter where more details on the corresponding system are given.
A frequent source of systematic errors are emf measurements. Fig. 1.5.1 shows the
discrepancies which can arise in the temperature dependence as well as in the abso¬
lute value of the derived Gibbs energy. In the case of Ca2Cu03, both emf studies
agree on a Gibbs eneigy of formation of about -1.8 kj at 1200 K. The temperature
range of measurements is however limited and a reliable temperature dependence could
only be obtained using calorimetric data on the enthalpy of formation at 298 K (see
Chap.II.4). In the case of Sr14Cu2404i, the absolute value of the Gibbs energy could
only be fixed with the help of further data such as those concerning the reaction
Sr14Cu2404i -H-Si'diO^-l-CuO-l-O^. Controversial emf values have also been reported
for this reaction, but at least one set of data is in very good agreement with thermo-
gravimetric results and thus probably much closer to reality (see Chap.II.5).
In the Bi-0 system (see Chap.II.2), some discrepancies are found between measure¬
ments of the oxygen activity in the metallic liquid. These values influence the oxygen
solubility limit and thus the miscibility gap, so that the discrepancies can also be
resolved with the help of data from the oxide part of the system.
1.5.2 Determination of parameters
The determination of parameters in both the Lukas and the THERMO-CALC op¬
timizers are based on a least square minimization of errors. This criterion for the
best fit requires that the different equilibria must be independent of each other and
that they obey a Gaussian normal distribution. Further details are given in references
[77Luk. 84Janl].
The requirement of a Gaussian normal distribution of the data implies that outliers
should not be considered and contradictory experimental results must be assessed prior
to the optimization. In both programs, the experimental data can be weighted in two
steps. A first weight factor considers the relative experimental uncertainty of each data
point. The uncertainties given in the original papers usually cannot be taken, as their
meaning may be very different and often is not clear enough (e.g. mean error, error
of 99.9% reliability, etc.). Important for the least squares method is, that for values
of the same quantity appioximately the same uncertainty is assumed. This represents
a statistical analysis of the data. An additional weight factor can be introduced to
change the lelative weight of some types of data relative to others in order to obtain
a satisfying agreement between selected measurements in the whole system. This is
typically used to give a comparable weight to different kinds of experimental studies
which, for example, strongly differ in the number of reported measured points, such
as for calorimetric vs. emf data. It is also very useful to test the influence of various
contradictory results of a certain type of measurements on the other properties of the
system. This second weight factor may be viewed as a way to deal with systematic
errors.
One of the numerical problems in the determination of parameters lies in their start
values. If the start values of the parameters are too far from an optimal description, it
can happen that the program will not be able to calculate some equilibria and thus will
40 CALPHAD
-2
o
£ -3
o-4
O.K.
CD°
<
-6
-7-
E3
-8-
o[93MatJ
0[94Suz]
H298 [kJ/mol] Ref
+1 57 [94SuzJ, emf
-4 86 [93Mat], emf
-7 8 [93lde], calonmetry
-7 3 This work
500 1000
Temperature [K]
1500
-150
-200-
,-250
-500
-550
[90Sko]O [90AIC]© [92Jac]
500 1000
Temperature [K]
1500
Figure 1.5.1:
Sri4CU24U4i-
Gibbi energies of formation and emf data A) Ca2Cu03. B)
THERMODYNAMIC OPTIMIZATION 41
not be able to perform an optimization. This means that in a first stage of optimization
of a complex system, the parameter values may have to be tested by trial and error.
The quality of an optimization program is therefore partly dependent on its ability to
cope with poor start values.
1.5.3 Reliability of extrapolations
The quality of the model description is not simply given by the best possible fit of the
available data, but is slowly revealed by the reliability of the extrapolation. This means
that an optimal balance between the model simplicity and the accuracy of the fit has
to be found. The criteria that could be used to quantify this aspect are the sum of
error squares as measure for the best fit, the variance as measure for the scatter of the
data from the fit, the relative standard deviation of parameters as measure for their
influence on the fit, and the correlation matrix between the parameters as measure
for their independence. There are however up to now no internationally established
appreciations of optimizations based on such values. The relevance of different ther¬
modynamic parameters depending on the data available have been discussed by several
authors e.g. [910ka, 92Smi, 93Sch]. The basic guideline used here is to consider the
simplest possible model and to introduce a further parameter only if the sum of error
squares is significantly reduced and if the parameter is well defined by the available
data so that its relative standard deviation remains small.
The extrapolations can be tested in several ways. It is important to verify that phases
stable at low resp. high temperature do not reappear at much higher resp. lower
temperature. In the same way, it must be checked that solution phases do not appear
unintentionally to be stable in other parts of the system. To prevent this, inegalitieson energies of formation can be introduced as Active data during the optimization.These inegalities may force the stability or instability of a phase in selected parts of
the system.
The reliability of extrapolated values can be tested by making new measurements or by
using only part of the available data to determine the parameters and then comparingthe remaining data with the extrapolation. For example, the phase relations in the Bi-
Sr-Ca-0 system have been experimentally studied [95Miil] parallel to the modellingwork. The thermodynamic description of some solid solutions (91150, 23x0) was first
modelled using only the data from two isothermal sections at 1093 and 1173 K. One of
these sections is shown in Fig. 1.5.2 together with the corresponding calculation [95Hal],The extrapolation reliability was then tested by comparing two calculated isoplethal
sections (along the 9U50 and the 23x0 phases) with some data on the solubility limits
of these phases. The results are shown in Fig. 1.5.3. The agreement is good which is
an encouraging sign for the adequacy of the models used throughout this work.
42 CALPHAD
SrO
900°C,Air
BiO1010
CaO
B
BiO 0
900°C
in air
0.2 0.4"""
0.6 0.8
xCa^XBi+xSr+xCa)
1.0CaO
Figure 1.5.2: Isothermal section of the Bi-Sr-Ca-0 system at 1173 K : A) experi¬
mental study [95M&1], B) calculated section [95Hal].
THERMODYNAMIC OPTIMIZATION 43
0.4 0.6
xCa'(xCa + xSr)
B
Figure 1.5.3: Isoplethal sections in the Bi-Sr-Ca-0 system in air: A) along the phase
23x0, B) along the phase 9U50.
44 CALPHAD
1.6 Outlook
1.6.1 Towards first principles methods
One of the limitations of the CALPHAD approach is its dependence on experimentalvalues. The method does not help in predicting new phases and has to rely on estimated
values when experimental information on the energy of some phases is not available.
In some cases, the information needed may not be obtained at all experimentally. A
constant problem, for example, is the determination of thermodynamic parameters for
endpoints of solid solutions which are not stable (i.e. which are metastable or possiblyunstable), but which are used in models such as the Compound Energy model. It is
thus desirable to obtain values for the lattice stability of metastable compounds from
atomistic calculations. As a next step, first principles methods could be used to treat
phases showing ordering phenomena and then combined with the CALPHAD approachto describe the whole system [90Sun]. The far motivation might be, as suggested in
a book title [87Haf], to compute phase diagrams directly from the Hamiltonian of the
system.
First principles methods are concerned with the problem of tracing the structural
and functional properties of materials back to the behaviour of many atomic nuclei
and electrons subject to the electromagnetic interaction. There are mainly two stepsfrom the Schrodinger equation for systems of many nuclei and electrons to the phasediagram. First, electronic band structures and the ground state energy at 0 K are cal¬
culated using various approximations of the full problem. A recent review of the state
of the art in these ab initio calculations has been given by Whinner [93Wim]. The
total energy at finite temperature is then computed using either effective interaction
potentials obtained from the ab initio calculations or empirical potentials. Two sta¬
tistical mechanical methods are commonly used for the prediction of phase equilibriae.g. [88Kik, 91Ind, 92Bin] : the Cluster Variation Method (CVM) and the Monte Carlo
method (MC).
In CVM, the equilibrium state is obtained from the minimization of the Helmoltz free
energy :
F = -kEThi(Q)
which is calculated from the energy of all possible configurations. The partition func¬
tion Q is a sum over the energy Ea of each atomic configuration a :
The energy of each configuration is extended into a summation over the energy of
selected clusters of lattice points. The energy of each cluster is itself calculated from
the effective interactions between atoms mentioned above.
OUTLOOK 45
In the MC method, the equilibrium state is obtained as the most stable configuration
from a sufficiently large number of i andomly simulated configurations.
The CVM approach has the advantage of leading to an analytical function for the free
energy, whereas the MC simulation yields a complete fine-scale information about the
atomic configurations and the correlations at large distances. Both methods are often
used simultaneously in phase diagram calculations. The reliability of the predicted
phase relations depends in both cases strongly on the choice of the effective interaction
potentials. This is well illustrated by a recent comparison of various potentials used
for the calculation of solubility limits in the CaO-MgO system [95Tep].
The calculation of phase diagram in complex oxide systems using these methods is still
scarse. To our knowledge, the phase YBa2Cu3Oz is the only superconducting cuprate
studied by CVM and MC so far [88Ber. 93Tet]. Ground state energy calculations are
more frequent. In this work, we could use predictions of the enthalpy of formation of
the orthorhombic and tetragonal phases (Sr,Ca)Cu02 [94A11] (see Chap.II.6).
1.6.2 Towards kinetic simulations
Thermodynamic modelling results in a consistent set of functions which allows to calcu¬
late any phase equilibrium in the system of interest. Furthermore, it brings information
as towards which stable state the system is aiming at. At each equilibrium, the drivingforces for various possible processes can be obtained. This information represents the
starting point for any kinetic treatment and combined with diffusion data it may allow
to simulate phase transformations and reaction processes. The research activities de¬
voted to the simulation of these complex processes are mainly aimed at metallurgical
applications. A couple of examples are given below.
One of the leading groups in the simulation of phase transformations is at the Division
of computational thermodynamics at KTH Stockholm, which is currently developpingthe program DICTRA for the simulation of diffusion controlled phase transforma¬
tions. Results have already been published for steel systems and for simple geometries
[94Eng]. The program DICTRA uses THERMO-CALC and the assessed databases in
the subroutine treating the thermodynamics of the system. Another example of the
use of THERMO-CALC as a subroutine is given in the work of Kurz and coworkers
(Physical Metallurgy, EPFL) on the simulation of solidification and microstructure
evolution [95Gil].
We are not aware of comparable studies in ceramic systems. In the present work,
the solidification behaviour during meltprocessing of Bi2Sr2CaCu2Oa was treated by
making equilibrium calculations under various conditions. For example, the solidifica¬
tion of thick films was approximated by assuming thermodynamic equilibrium with the
surrounding atmosphere and thus setting a constant oxygen partial pressure, whereas
in the solidification of bulk materials, the calculations were made at constant oxygen
content to account for the inhibition of the oxygen diffusion (see Chap.III.2).
46 CALPHAD
References Part I
[29Hil] J. H. Hildebrand, "Solubility. XII. Regular Solutions", J. Am. Chera. Soc,51, 66-80 (1929).
[52Gug] E. A. Guggenheim, Mixtures, Clarendon Press, Oxford (1952).
[64Pal] L. S. Palatnik and A. I. Landau, Eds., Phase Equilibria in MulticomponentSystems, Holt, Rinehart a2id Winston, Inc. (1964).
[70Kau] L. Kaufman and H. Bernstein, "Computer Calculation of Phase Diagrams",in Refractory Materials, A Series of Monographs, Vol.4, 3- L. Margrave, Ed.,Academic Press (1970).
[70van] F. van Zeggeren and S. H. Storey, Eds., The Computation of Chemical Equi¬
libria, Cambridge University Press (1970).
[71Eri] G.Eriksson, "Thermodynamic Studies of High Temperature Equilibria", Acta
Chem. Scand., 25(7), 2651-2658 (1971).
[72Ans] I. Ansara, "Prediction of Thermodynamic Properties of Mixing and
Phase Diagrams in Multicomponent Systems", in Metallurgical Chemistry,O. Kubaschewski, Ed., NPL, London, pp. 403-430 (1972).
[75Eri] G. Eriksson, "Thermodynamic Studies of High Temperature Equilibria",Chem. Scnpta, 8, 100-103 (1975).
[76Hil] M. Hillert and L.-I. Staffansson, "A Thermodynamic Analysis of the Phase
Equilibria in the Fe-Mn-S System", Metall. Trans. B, 7, 203-211 (1976).
[77Kau] L. Kaufman, "Foreword", Calphad, 1(1), 1-6 (1977).
[77Luk] H. L. Lukas, E. T. Henig, and B. Zimmermann, "Optimization of phase dia¬
grams by a least squares method using simultaneously different types of data",
Calphad, 1, 225-236 (1977).
[78Har] H. A. Harwig, "On the Structure of Bismuthsesquioxide: The a,/3,7,and<5-Phase", Z. an org. dig. Chem., 444, 151-166 (1978).
[79Hil] M. Hillert, "Methods of Calculating Phase Diagrams", in Calculation of Phase
Diagrams and Thermochemistry of Alloys, Y. A. Chang and J. F. Smith, Eds.,The Metallurgical Society, Proc. Conf. AIME Fall Meeting Sept. 17-18, 1979,Milwaukee, pp. 1-13 (1979).
[80Hil] M. Hillert, "Fundamental Aspects of the Use of Thermodynamic Data", in
The Industrial Use of Thermochemical Data, T. I. Barry, Ed., The Chemical
Society, Proc. Conf. Sept. 11-13, 1979, University of Surrey, pp. 1-14 (1980).
REFERENCES 47
[81Hil] M. Hillert, "Some Viewpoints on the Use of a Computer for Calculating Phase
Diagrams", Physica, 103B, 31-40 (1981).
[81Kau] L. Kaufman, "J.L. Meijering's Contribution to the Calculation of Phase Dia¬
grams- A Personal Perspective", Physica B, 103B, 1-7 (1981).
[81Kub] O. Kubaschewski, "Experimental Thermochemistry of Alloys", Physica B,
103B, 101-112 (1981).
[82Luk] H. L. Lukas, J. Weiss, and E.-T. Henig, "Strategies for the Calculation of
Phase Diagrams", Calphad, 0(3). 229-251 (1982).
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Leer - Vide - Empty
Part II
The Bi-Sr-Ca-Cu-O System
54 THE BSCCO SYSTEM
II. 1 Overview
This first chapter presents an overview of the work on thermodynamic modellingand optimization in the Bi-Sr-Ca-Cu-0 (BSCCO) system. The metallic part of the
BSCCO system is not included in this description. Some explanations for this choice
are given below. The subsystems of the oxide part and the phases appearing in those
are summarized in Table II. 1.1. The standard abbreviation for the phases of this sys¬tem lists the cation ratio in the order Bi, Sr, Ca, and Cu. The phase Sr14Cu24041 is
thus abbreviated as 014024- lu the Sr-Ca-Cu-0 system, this compound shows solid
solubility towards Ca so that it is then denoted by 014x24. More details on the de¬
nomination of phases, in particular on the various formulas reported in the literature
for the same compounds, are given in the respective references listed in Table II. 1.1.
The thermodynamic description of a multicomponent system is obtained from the suc¬
cessive extension of lower order systems to higher ones by the addition of new elements.
The model description is thus conveniently divided into building blocks correspondingto the various subsystems. Bach subsystem may show a very different amount of phases,of reported data, and finally of level of reliability. The extrapolation to a higher order
system is therefore a crucial test for the compatibility between the thermodynamicfunctions of the subsystems. When differences are found between extrapolated val¬
ues and experimental results in higher order systems, it is sometimes justified to use
new parameters (e.g. for a new phase), but it can happen as well that corrections in
the subsystems are needed This leads to a backward and forward analysis of binary,ternary, etc. systems. Extrapolations to higher order systems not only are interestingfor compatibility tests but also for predictive calculations useful in the developmentof processing routes. One is thus often interested in obtaining a preview of possiblephase relations even if the thermodynamic models are very preliminary. Following the
motto: any prediction is better than no prediction.
This modelling work has been influenced by the backward and forward analysis from
binaries to the complete BSCCO system. The results can be seen as progressing in
two waves. The first wave has reached the complete system and allowed a preliminarydescription, testing of extrapolations, and establishing first links to the processingconditions. The second wave is still under progress and consists in publishing the results
on the subsystems which have been satisfactorily tested in the higher order system.This should lead to a reliable and consistent thermodynamic description applicable for
phase diagram calculations. The references to optimized thermodynamic descriptionscurrently available for the BSCCO system are given in Table II.l.l. Some of these
articles are included in the next chapters.
OVERVIEW 55
Table II.1.1: The subsystems and phases of the oxide part of the Bi-Sr-Ca-Cu-0
system
System Phases (which are not already part of the subsystems) Ref.
Bi-0
Sr-0
Ca-0
Cu-0
Bi-Sr-0
Bi-Ca-0
Bi-Cu-0
Sr-Cu-0
Ca-Cu-0
Sr-Ca-0
Bi-Sr-Ca-0
Bi-Sr-Cu-0
Bi-Ca-Cu-0
Sr-Ca-Cu-0
BSCCO
a-Bi203, <5-Bi203 [95Ris2]
SrO, Sr02 [96Risl]CaO [93Sel]
Cu20, CuO [94Hal]
S, 0, 7, Bi2Sr04. Bi2Sr205, Bi2Sr306. Bi4Sr6015, [96Hal3]Bi2Sr60n
5, (3, 7, Bi14Ca5026, Bi2Ca04, BieCa4Ol3, Bi2Ca205 [96Hal2]
Bi2Cu04 [96Hal4]
Sr2Cu03, SrCu02, Sr14Cu24041, SrCu202 [96Ris2]
Ca2Cu03, Cai_,.Cu02_i, CaCu203 [95Risl]— [96Ris3]
2110, 9U50
U905, 2201, 2302, 4805
SrlCai_ICu02
2212, 2223
[96Ris3]
II.1.1 The metallic part
The phase relations in the metallic part of the system are of interest for processing
routes based on metal precursors. The main reason for using metal precursors lies
in the ductility of the alloy, which allows to draw easily fine filaments and to obtain
multifilament wires and tapes. In the BSCCO system, the metal precursor technique
has been mainly applied to produce wires and tapes of the 2223 compound e.g. [90Gao,
930tt, 950tt]. The superconducting phase can be formed fairly rapidly by a subsequent
oxidation annealing of the multifilament composite material as the diffusivity of oxygen
in the silver core and in the BSCCO phases is high. The thermodynamic modelling
of the metallic part of the system would aim at the preparation of an homogeneous
precursor powder of the finely dispersed alloying elements.
After a short survey of the experimental data on the metallic part of the BSCCO
system, it became evident that very little information was available and that a study
of all metallic subsystems for aiming at such applications was beyond the scope of
the present project. Furthermore, one major problem occuring in processing wires
and tapes of 2223 is the narrow stability field of this phase both in temperature and
oxygen partial pressure. This aspect can be addressed by modelling the oxide pait of
the system only and we have given it a higher priority than the search for improved
synthesis of metal precursors.
A study of the metallic part of the Y-Ba-Cu-0 (YBCO) system and the application of
thermodynamic modelling in search of synthesis routes for metal precursors has been
56 THE BSCCO SYSTEM
presented by Konetzki et al. [94Kon]. Of particular interest was the question whether
a fine dispersion of the metallic elements at the composition of the superconducting
compound 123 could be obtained from the liquid phase. The study showed that a
miscibilty gap in the liquid phase exists in the Ba-Y system and extends considerably
into the ternary. The miscibility gap remains beyond 1800 K at the 123 composi¬
tion making it impossible to obtain the desired fine dispersion from the liquid by any
solidification route. The consequence was to use other synthesis techniques such as
mechanical alloying of the metallic elements which is precisely what has been applied
by Otto et al. [930tt] in the case of the BSCCO system.
In the Bi-Sr-Ca-Cu system, thermodynamic descriptions are available only for the
Bi-Cu [89Tep], Sr-Ca [86Alc], Sr-Cu and Ca-Cu [96Ris4] systems. The Bi-Sr and
Bi-Ca systems have barely been studied, but some compounds are known [58Han].None of the binary systems exhibits a miscibility gap in the liquid phase, so that it
cannot be excluded that the synthesis of metallic precursors from the liquid phase
might be more successful in the BSCCO than in the YBCO system.
II. 1.2 The binary oxide systems
The Bi-0 and Cu-0 systems are particularly important due to their influence on the
thermodynamic properties of the liquid and the gas phases. Bi203 has the lowest
melting point of the binary oxides in the BSCCO system. The liquid phase is thus
always Bi-rich and its stability with respect to solid phases is influenced by the relative
stability of the oxide liquid respective to solid B12O3. The thermodynamic properties of
oxygen in the metal liquid are mainly given by these two binaries as the stability of the
oxides SrO and CaO is large and consequently the oxygen solubility in the Sr-Ca metal
liquid is extremely low. The oxygen content in the oxide liquid is mainly determined by
the copper valency, and thus by parameters coming from the Cu-0 system. In ternary
systems, the extrapolated oxygen content can only be slightly influenced, for example,
by differences in the size of parameters between CuO(l)-MO(l) and Cu20(l)-MO(l)where M stands for Bi2/3, Sr, or Ca. Since the oxygen content in the liquid plays an
important role in the meltprocessing of the 2212 compound, particular attention was
paid to the Cu-0 binary. A review of this system and a optimized thermodynamic
description was given by Hallstedt et al. [94Hal]. The Bi-0 system is furthermore
important if the influence of the gas phase is considered. The vapour pressures of
bismuth species in the gas phase are already large at the temperatures of interest
in meltprocessing. In practice, Bi2Al409 powder is therefore included in the furnace
to saturate the atmosphere with bismuth and to minimize the bismuth loss due to
evaporation [92Shi]. The thermodynamic optimization of the Bi-O system [95Ris2]is presented in the Chap.II.2.
The Sr-0 and Ca-0 systems are very similar and characterized by the large stabilityof the oxides SrO and CaO. The thermodynamic properties of the oxide liquid in
these systems are practically unknown, but as both oxides have a very high melting
point (above 2500 K), these uncertainties should not be too important for the phase
equilibria in the temperature range of interest in this work. The values of the adopted
melting points influence however the liquidus curve and may thus be responsible for
OVERVIEW 57
some small dicrepaucies in the strontium and calcium contents of the liquid phase.
The thermodynamic description of the Ca-0 system is taken from Selleby [93Sel], the
Sr-0 system [96Risl] is presented in Chap.II.3.
II. 1.3 The ternary oxide systems
The ternary systems contain most of the oxide phases, as can be seen from Table II.l.l,
and is the most time consuming part of the assessment work. The number of phases
diminishes rapidly in higher order systems which increases the efficiency of extrapo¬
lations. The compatibility between the energy functions of all these ternary oxides is
critical for the calculation of phase equilibna in the higher order systems.
The bismuth containing ternaries have been studied by Hallstedt et al. [96Hal4, 96Hal3.
96Hal2] and are not presented here in detail. Some examples from the Bi-Sr-0 system
were shown in Part I. The Bi-Cu-0 system [96Hal4] contains one ternary oxide and
is characterized by a miscibility gap in the liquid phase which extend all the way from
the Bi-0 to the Cu-0 system. The Bi-Sr-0 [96Hal3] and Bi-Ca-0 [96Hal2] systems
show many similarities. Many compounds are found in these two systems, some ofthem
show considerable solid solutions. The structure of these phases are often complex, the
phase diagram data are in some cases contradictory, and the thermodynamic measure¬
ments are scarse. Nevertheless a reasonable preliminary description could be obtained
which, as shown in further examples, lead to extrapolations in good agreements with
observations in the higher order systems.
The Sr-Cu-0 [96Ris2] and Ca-Cu-0 [95Risl] systems are presented in Chap.II.4 and
II.5. The quaternary Sr-Ca-Cu-0 is mainly based on these two subsystems. The last
ternary Sr-Ca-0 contains, as only solid phase, the solution (Sr,Ca)0. The modelling
of this phase was included in the optimization of the Sr-Ca-Cu-0 system (Chap. II.6).
II.1.4 The Bi—free and Cu—free phases
Two important quaternary systems are Bi-Sr-Ca-0 [95Hal] and Sr-Ca-Cu-0 [96Ris3]since they contain most of the secondary phases which appear during the processing
of the superconducting compounds. To a fairly good appioximation the solubility of
Bi resp. Cu in the Sr-Ca-Cu-0 resp. Bi-Sr-Ca-0 phases can be neglected. As a
consequence, these compounds are often named as Bi-free or Cu-free phases. The Sr-
Ca-Cu-0 system is presented in Chap.II.6 and is not discussed any further here. Some
isoplethal and isothermal sections of the Bi-Sr-Ca-0 system were shown in Chap.I.5.3.
Two phases, 23x0 and 91150, are often found in equilibrium with the 2212 compound.
91150 is stable at low temperature or high oxygen partial pressure and is found when
2212 is melted in air or in pure oxygen. 23x0 is stable at higher temperature or lower
oxygen partial pressure and is found together with Cu20 and the eutectic liquid at
composition close to 2212.
There are no new phases appearing in the Bi-Ca-Cu-0 system so that the thermody¬
namic description can be entirely obtained by extrapolation from the ternaries. The
phase equilibria and in particular the extension of the licjuid phase in this system have
58 THE BSCCO SYSTEM
been extensively studied by Tsang et al. [95Tsa] in isothermal sections at 1 bar 02 over
the temperature range of 1023 to 1273 K. These recent results offer a good test for the
reliability of the extrapolated values. Two calculated isothermal sections at 1073 and
1123 K are compared with the experimental results in Fig. II.1.1 and II.1.2 respectively.It should be paid attention that the composition of the experimental results are plottedrespective to Bi203, whereas the calculated values are plotted respective to BiOj.. This
causes a stietch along the Bi axis. The experimental study shows that with increas¬
ing temperature the liquid phase progresses towards the Ca-Cu-0 system and that in
consequence the equilibria with Bi6Ca4Oi3+CuO and Bi2Ca205+CuO are replaced byL+CaO and L+Ca3Cu03. The liquid phase extends further to the Ca-Cu-0 side in
the calculations than experimentally observed, but the general agreement is good.
II. 1.5 The superconducting and other Phases
The superconducting phases are found in the Bi-Sr-Cu-0 (H905) [87Mic] and Bi-Sr-
Ca-Cu-0 (2212, 2223) [88Mae] systems. These phases belong to the same structural
family, they are commonly described by the formula Bi2Sr2Ca„_1CitnOa. (n=l,2,3)and therefore named 1-, 2-, or 3-layer compounds. Phases with n>3 could not be
stabilized so far. The end member of this series corresponds to the formula CaCu02and is referred to as infinite-layer compound. It can be stabilized at ambient pressure
in the Sr-Ca-Cu-0 system (see Chap.II.6), but does not show superconductivity.
The Bi-Sr-Cu-0 system contains altogether four stable quaternary phases [89Ike,90Rot2, 91Jac, 92Slo]. Two structurally related phases are found near the compositionBi2Sr2CuOa! [89Sag, 89Cha, 90Rotl]. One of them is the 1-layer superconductingphase which forms a solid solution Bi and Cu richer than the ideal 2201 stoichiometry.The other phase, often called "collapsed" 2201, does not show a significant range of
nonstoichiometry and is very close to the 2201 composition e.g. [89Sag, 89Cha, 89Ike,90Rot2]. The 1-layer compound, also called Raveau phase, is therefore abbreviated here
by H905 and the collapsed structure by 2201. The other two stable phases, 2302 and
4805, belong to a family of tubular structures which have been described by the formula
(Bi2Sr2CuOI)„(Sr8Cu60!,) [89Fue, 92Cal]. Only the phases with n=4 (4805) and n=7
(2302) have been observed in phase diagram studies [89Ike, 90Rot2. 91Jac, 92Slo].Minor differences are found between these reported phase relations. In the Bi-Sr-Ca-
Cu-0 system, the only reported phases are the 2- and 3-layer compounds.
The present thermodynamic description of the Bi-Sr-Cu-0 and Bi~Sr-Ca-Cu-0 sys¬tems is rather preliminary. The three phases 2201, 2302, and 4805 can be described in
good approximation as stoichiometric compounds. The superconducting phases have
been described as solid solutions using the following sublattice model [96Hall] :
(Bi+3,Bi+5)2(Sr+2,Ca+2,Bi+3)2(Ca+2)„_1(Cu+2,Cu+3)„(0-2)4+2n(0-2,Va)IThis description, of course, does not account for the whole complexity of these struc¬
tures. The model should be able to describe the major known features of these solid
solutions, namely a pronounced solubility of Bi or Ca for Sr, and an oxygen nonstoi¬
chiometry.
This can be due, besides the substitution of Bi+3 for Sr+2, to either the oxidation of
OVERVIEW 59
800°C
B^Ca2Os
D Liquid held
O Liquid
(•) Bulk composition
Solid solution
CaO CuO
BiO„
in 1 bar O,
1073 K
Bi.CuO.
CaOOCuO„
Figure II.1 1: A) Eipinmnital [95Tsa] and Dj puditfid isothtinial sittions of tin
Bi Ca Cu 0 at 101 i A in 1 bin O,
60 THE BSCCO SYSTEM
850°C
Liquid field
O Liquid
® Bulk composition
Solid solution
CaO CuO
BlO„
CaOOCuO„
Figure II 1 2 A) Eipunmntal [95Tt>a] and B) pudiittd uotlieimal sections of tin
BiCiCuO at mi A in 1 bai O
OVERVIEW 61
Bi+3 to Bi+5, or Cu+2 to Cu+3. This sublattice description, which uses the Compound
Energy model, produces a large number of unknown Gibbs energy parameters. The
number of independent parameters can however be reduced to five. These parameters
are : 1) the Gibbs energy of the ideal stoichiometric composition, and four other terms
representing the energy change due to 2) the oxidation of Bi+3 to Bi+5, 3) the oxidation
of Cu"1"2 to Cu+3, 4) the substitution of Bi+3 for Sr+2, and finally the substitution of
Ca+2 for Sr+2. The stability of the compound respective to the other phases depends
mainly on the first parameter. The second and third parameters can be determined
from data on the oxygen nonstoichiometry, the fourth and the fifth ones from data on
the cation nonstoichiometry.
This solution model was applied to 11905 and 2212. As there is very little information
on the 2223 phase, it has been treated as a stoichiometric compound at this prelimi¬
nary stage of modelling. With the present model, the solid solution range caused by
the Bi, Sr, and Ca nonstoichiometry is limited to the Bi-rich and Ca-rich side. The
nonstoichiometry in copper has been neglected. This is a good approximation for 2212
as the nonstoichiometry in copper is known to be very small [92Miil]. On the other
hand, this simplification may be too inaccurate for H905 which shows a range of non¬
stoichiometry of a few mole percent in copper [90Rotl, 91Jac]. The maximum oxygen
content x could not be derived from crystallographic considerations. It was arbitrarily
choosen for each superconducting phase independently, based on measurements of the
oxygen content as function of temperature and oxygen partial pressure.
The treatment of the 2212 phase is shown here as an example since the calculations
presented in Part III deal mainly with this compound. The first step was to fix a
maximum oxygen content x for the phase. The oxygen content in 2212 has been
measured as a function of temperature and oxygen partial pressure by several authors
[90Ide2, 91Shi, 93Sch, 95Ide]. The experimental technique employed was always the
same. The relative oxygen content was measured by thermogravimetry, the absolute
concentration was determined by iodometric titration. The second point is critical and
can be responsible for shifts found between the various investigations. The assessment
of the results is complicated by the fact that the different studies have not been made at
the same cation ratio. Shimoyama et al. [91Shi] and Schweizer et al. [93Sch] measured
at the composition 2212. Idemoto et al. measured at Cu-rich [90Ide2] and Bi-rich
[95Ide] compositions. The first study of Idemoto et al. [90Ide2] shows the highest values
of oxygen content in 2212 slightly below 8.35. The other investigations obtained highest
oxygen contents around 8.25. For a preliminary description, we could not assess all
the data and considered these differences as unimportant. More important was to use
enough consistent points which determined the model parameters without ambiguity.
The results of Idemoto et al [90Ide2] were then used and the maximum oxygen content
in 2212 was taken as 1/3. The sublattice model is then :
(Bi+3,Bi+5)2(Sr+2,Ca+2,Bi+3)2(Ca+2)1(Cu+2,Cu+3)2(0-2)s(0-2,Va)1/3
The experimental data on the oxygen content in 2212 as function of temperature and
oxygen partial pressure are compared to calculated values in Fig. II.1.3. As mentioned
above, the results have not been assessed. As the maximum oxygen content in 2212 does
not exceed about 8.25 in most studies, it is very probable that the current description
overestimates the oxygen content by about. 0.05.
62 THE BSCCO SYSTEM
-3 -2 -1 0
Log(P02, atm)
Figure II.1.3: Calculated oxygen content in the Bi2Sr2CaCu208+^ phase comparedwith experimental values.
The cation-nonstoichiometry in 2212 has been studied by several authors [91Gol,91Hon, 92Maj, 92MU1, 92Sin, 92Hol, 93Hol, 93Ghi, 93Kni, 95Mac]. A summary of
most results is shown in Fig. III.4.A. after [93Km']. It is important to note that these
various investigations have been made at different temperatures and oxygen partial
pressures. For a preliminary description, we optimized model parameters so that the
calculated single-phase region of 2212 lies approximative^ in the center where the dif¬
ferent experimental studies intersect. The range of solid solution where 2212 may exist
according to the present model is shown in Fig. II.1.4.B together with the calculated
single-phase region at 1123 K in pure oxygen.
The stability of 2212 respective to other phases is discussed in section III.2.1.
OVERVIEW 63
A
Fig 5 Comparison of single-phase compositions found tn our
work (•) with single-phase regions determined in refs {I T.21 ]
Ref [17] (---) 850'C, air, XRD, EMA, Ref [18] ( )
860°C,air,XRD,EMA,Ref [19] (- - -) varying T, air, XRD,
EMA, Ref [20] ( ) 830°C.air,XRD,EMA, Ref [21] ( )
865 "C, oxygen,TEM
in air
850 °C
B
Figure II.1.4: A) Experimental results on the smgle-phase field of 2212 (summarized
by [93KniJ) B) The maximum smgle-phase field allowed by the model is indicated by
the dashed hne, the solid line shows the calculated smgle-phase field at 1123 K m 1 bar
02
64 THE BSCCO SYSTEM
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OVERVIEW 65
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K. Togano, H. Maeda, K. Nomura, and M. Seido, "Improvement of Repro¬
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66 THE BSCCO SYSTEM
[93Ghi] P. Ghigiia, G. Chiodelli, U. Ansehm-Tamburini, G. Spinolo, and G. Flor,"Homogeneity Range, Hole Concentration, and Electrical Properties of the
Bi^Srs-tCajCuaOs+y (1 < x < 2) Superconductors", Z. Naturforsch., A,48(12), 1214-1218 (1993).
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Malozemoff, "Multifilamentary Bi-2223 Composite Tapes made by a Metallic
Precursor Route", IEEE Trans. Appl. Supercond., 3, 915-922 (1993).
[93SchJ Th. Schweizer, R. Muller, P. Bohac, and L. J. Gauckler, "Oxygen Nonstoi-
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Editrice Iberica, pp. 611-616 (1993).
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the Copper-Oxygen System", J Phase Equilibria, 15(5), 483-499 (1994).
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Cu System: Thermodynamic Modelling, Experiments and Application", Z.
Metallkde., 85(11), 748-755 (1994).
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of the Bi-Sr-O, Bi-Ca-O, and Bi-Sr-Ca-0 Oxide Systems", Presented at
CALPHAD XXIV, Kyoto, Japan (1995).
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Oxides of the Bi-2212 Phase", Physica C, 21,9, 123-132 (1995).
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Quaternary Phase Relations Near Bi2Sr2CaCu208+;l! in Reduced OxygenPressures", Physica C, 251, 71^88 (1995).
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Bismuth-Oxygen System", J. Phase Equilibria, 16(3), 1-12 (1995).
OVERVIEW 67
[95Tsa] C. F. Tsang, J. K. Meen, and D. Elthon. "Phase Equilibria of the Bismuth
Oxide - Calcium Oxide - Copper Oxide System in Oxygen at 1 atni", J.
Am. Ceram. Soc. (1995). submitted.
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[96Hal2] B. Hallstedt, D. Risold. and L. J. Gauckler, "Thermodynamic Assessment of
the Bi-Ca-0 Oxide System", J. Am. Ceram. Soc. (1996). submitted.
[96Hal3] B. Hallstedt, D. Risold, and L. J. Gauckler, "Thermodynamic Assessment of
the Bi-Sr-0 Oxide System", J. Am. Ceram. Soc. (1996). submitted.
[96Hal4] B. Hallstedt, D. Risold, and L. J. Gauckler, "Thermodynamic Evaluation of
the Bi-Cu-0 System", J. Am. Ceram. Soc, 7fl(2), 353-358 (1996).
[96Risl] D. Risold, B. Hallstedt, and L. J. Gauckler, "The Sr-0 System", Calphad
(1996). accepted.
[96Ris2] D. Risold. B. Hallstedt, and L. J. Gauckler. "Thermodynamic Assessment of
the Sr-Cu-0 System", J. Am. Ceram. Soc. (1996). accepted.
[96Ris3] D. Risold, B. Hallstedt, and L. J. Gauckler, "Thermodynamic Modelling and
Calculation of Phase Equilibria in Sr-Ca-Cu-0 System at Ambient Pres¬
sure", J. Am. Ceram. Soc. (1996). accepted.
[96Ris4] D. Risold, B. Hallstedt, L. J. Gauckler, H. L. Lukas, and S. G. Fries, "Ther¬
modynamic Optimization of the Ca-Cu and Sr-Cu Systems", Calphad, 20
(1996). to be published.
68 THE BSCCO SYSTEM
II.2 The Bi-O System
This chapter was published in J. Phase Equilibria 16 [3] (1995) 1-12.
The Bismuth-Oxygen System
Daniel Risold, Bengt Hallstedt, Ludwig J. Gauckler
Nomnetallic materials, Swiss Federal Institute of Technology,Sonneggstr. 5, CH-8092 Zurich, Switzerland
Hans Leo Lukas and Suzana G. Pries*
Max-Planck-Institut fur Metallforschung,Heisenbergstr.5, D-70569 Stuttgart, Germany
*Present address: Lehrstuhl fur theoretische Hiittenkunde
RWTH Aachen, Kopemikusstr. 16, D-52074 Aachen, Germany
ABSTRACT The phase diagram and thermodynamics data of the Bi-0
system are reviewed and assessed. An optimized consistent
thermodynamic description of the system at 1 bar total pres¬
sure is presented. The stable solid phases (solid Bi, a-Bi203,and <5-Bi203) are all treated as stoichiometric. The liquidphase is described by an ionic two-sublattice model and the
gas phase is treated as an ideal solution. Calculated phasediagrams and values for the thermodynamic properties of the
bismuth oxides and the liquid are shown and compared with
experimental data.
1 Introduction
The aim of the present study is to provide a consistent thermodynamic description of
the Bi-0 system at 1 bar total pressure, which is needed for the modelling of phaseequilibria in multicomponent Bi-containing oxide systems, such as high-temperaturesuperconductors or ionic conductors.
The thermodynamic descriptions of solid and liquid pure bismuth and liquid pure
oxygen are taken from Dinsdale [91Dinj, while those of the gaseous species Bi, Bi2,Bi3, B14, O, and 02 are from the selected data of the Scientific Group Thermodata
Europe [94SGT]. The experimental data on the pure elements are thus not treatd
here, and only experimental data on oxides of bismuth are reviewed in the followingsection. Structural studies and investigations on metastable compounds are brieflysummarized. The phase diagram and thermodynamic data on the liquid and the two
stable oxides, o>Bi203 and <5-Bi203, are assessed and used to optimize a consistent set
of Gibbs energy parameters for these phases.
BI-O 69
For compatibility with other subsystems, the liquid phase is described by a two-
sublattice model, which then easily can be extended to multicoinponent systems. A
thermodynamic description of the gas phase is also included, since the bismuth partial
pressure increases relatively fast with temperature and bismuth evaporation often can
be an important practical problem, but it has not been treated in the optimization. The
gas phase is described as an ideal solution of selected species, whose thermodynamic
data have been adopted from Sidorov et al. [80Sid].
2 Experimental data
2.1 Equilibrium diagram
The Bi-0 phase diagram at 1 bar total pressure as calculated from the present op¬
timized description is shown in Fig.II.2.1 and II.2.2 together with the experimental
data on the solubility limits of the liquid phase. The liquid exhibits a miscibility gap
between Bi and Bi203. Four phases are found at the composition Bi203, which are
commonly written as a-, /?-, 7-, and <5-Bi203. Only two of them, a-Bi203 and 5-Bi2C>3,
are stable at 1 bar total pressure.
The solubility limits in the Bi2C>3-i'ich liquid have been studied by Isecke et al.
[77Ise, 79Ise]. The bismuth solubility limit was measured between 1173 and 1623 K by
taking samples from the oxide liquid in equilibrium with the Bi-rich liquid and deter¬
mining the oxygen content of the samples from the weight change after reduction. The
oxygen solubility limit in the Bi203-rich liquid was measured between 1173 and 1473
K at several oxygen partial pressures by thermogravimetry. The thermogravimetric
results indicate that the oxygen content in the liquid never exceeds 60 mole percent.
At the highest temperature (1473 K) und lowest oxygen partial pressure (2700 Pa)
measured, the oxygen loss in B12O3 liquid remains below 1 percent.
The oxygen solubility limit in the bismuth-rich liquid has been investigated by several
authors using chemical analysis [53Gri, 77Ise, 79Ise] and electrochemical techniques
[77Ise, 79Ise, 79Hah, 80Fit. 81Hes]. These results are shown in Fig.II.2.1 and II.2.2.
Griffith et al. [53Gri] measured the oxygen content in samples equilibrated between
673 and 1023 K from CO-C02 gas equilibrium analysis. Isecke et al. [77Ise, 79Ise] de¬
rived the oxygen solubility limit between 950 and 1473 K from series of electromotive
force measurements (emf) performed at constant oxygen content. At 1273 K, they an¬
alyzed samples taken from the melt as described above and found the value xo = 0.024,
which is in good agreement with the results obtained from emf measurements. Halm
and Stevenson [79Hah] determined it between 1073 and 1223 K using coulometric
titration. The oxygen solubility limit has finally been derived from measurements of
the oxygen diffusivity in the bismuth-rich liquid by Fitzner [80Fit] and Heshmatpour
and Stevenson [81Hes] using potentiostatic titration techniques. The contradiction
appearing between these studies is discussed in the optimization procedure.
The polymorphism ofBi203 has been widely studied. References to early works and re¬
view of the subject can be found in the publications of Levin and Roth [64Levl, 64Lev2]and Harwig and Gerards [79Har]. Bi203 has two stable modifications, the low tem¬
perature phase (a-Bi203) has a monoclinic structure and the high temperature one (S-
Bi2Os) has a fee structure. The transition temperature between a-Bi203 and 5-Bi203
has been measured by differential thermal analysis (DTA) [62Gat, 65Lev, 69Rao,
79Har] and differential scanning calorimetry (DSC) [76Kor. 79Har]. It has also been
70 THE BSCCO SYSTEM
derived from enthalpy increment data [67Cub] and from the change in slope of emfmea¬surements vs. temperature [71Rao, 76Meh, 77Ise, 80Fit, 84Sch, 91Kam, 92Kam]. The
mouotectic temperature has been similarily obtained from several emf measurements
[73Rao, 76Meh, 77Ise, 84Ito] while the melting point of S-B12O3 has been measured
by DTA [62Gat, 65Lev, 79Har] These results are shown in Table II.2.1. The values
obtained from thermal analysis and calorimetric studies show a good agreement within
a few K. The values derived from emf measurements are somewhat lower and show a
larger scatter, which most probably reflects the uncertainty in the evaluation of the
small changes in the slope of the emf. Thermal analysis studies are thus expected to givethe more reliable values. In this optimization we have used for the transition tempera¬ture the results of [65Lev, 67Cub, 69Rao, 76Kor, 79Har]. It is noteworthy that thesevalues are close to those found in recent emf investigations [80Fit, 91Kam, 92Kam].a-Bi203, d"-Bi203 and solid Bi are regarded as stoichiometric compounds as there are
no experimental data reporting deviations from the ideal composition and, as other
experimental evidence implicitely shows, the possible deviations are very small.
2.2 Metastable Phases
Two metastable modifications of Bi203 have been observed, /3-Bi203 with a tetragonalsymmetry and 7-Bi203 with a bcc lattice. They appear upon cooling from the high-temperature phase (5-Bi203: /?-Bi203 at around 920K and 7-Bi203 at around 910K.
Which intermediate phase is formed depends on the amount of impurities in the sample[64Gat, 64Levl, 64Lev2, 79Har]. /3-Bi203 transforms to the stable monoclinic phasesomewhere between 920 and 700 K on further cooling, whereas 7-Bi203 can be pre¬served to room temperature.
/?-Bi203 has also been obtained at low temperatures from thermal decomposition ofbismutite (Bi203-C02) [64Levl], from reactions between bismuth salts and alkalinesolutions [72Aur], and from oxidation of pre-reduced Bi2Mo06 [87Buk]. Oxygen-deficient /3-Bi203 [71Zav, 75Med] and other metastable phases in the Bi-Bi203 partof the system [64Zav, 65Zav, 68Zav] have been obseived in thin films, prepared byevaporation of bismuth oxide.
Higher bismuth oxides have been prepared under various conditions by hydrolysis of
bismuthates obtained by oxidation of bismuth(III)-compounds. References to earlier
publications can be found in the most recent reviews [80Gat, 89Begl, 89Beg2]. Gattowand Klippel [80Gat] observed five different phases in the composition range BiOi 65 to
Bi0248, which they described as Bi02, a-, f3-, 7- and 5-Bi205 solid solutions. However,due to the low quality of the x-ray patterns, they could not determine the structure of
these compounds. Begemann et al. [89Begl, 89Beg2] studied the phases obtained bythermal decomposition of amorphous Bi205 under high oxygen pressure. They iden¬
tified two phases with cubic structures of compositions BiO180 and BiOi92, and one
compound with a triclinic structure of composition B14O7. Recently, Kinomura and
Kumada [95Kin] obtained a compound Bi204 with monoclinic structure by hydrother-mal treatment of NaBi03nH20 at 413 K. Very little is known on the thermodynamicsof the phases beyond 60 mole percent oxygen. They are not considered in this work
even if some may be stable at 1 bar 02 and low temperature.
BI-O 71
2000
Figure II.2.1: The Bi-0 phase diagram at 1 afm total pressure. The optimized
diagram is represented by solid lines.
-0.6
-0.8
-1.0
"k, -1.2
§ -1.4
-1.6
-1.8
-2.0
L,+a-Bi203
-6 -5 -4 -3
Log[x0]
Figure II.2.2: Oxygen solubility in bismuth-rich hqwd.
72 THE BSCCO SYSTEM
Table II.2.1: Invariant Equilibria.
Reaction References Method T[K] logio(Po2) xq in L
L2 -H- <5-Bi203 [64Gat] DTA 1097
(melting point of Bi203) [65Lev] DTA 1098
[67Cub] drop cal. 1101
[79Har] DTA 1097
This work 1098 0 0.6
L2 «-» L!+(5-Bi203 [73Rao] emf 1093 -8.6
(monotectic) [76Meh] emf 1095 -8.3
[79Ise] emf 1090 -8.6
[84Ito] emf 1077 -8.6
This work 1061 -9.0 0.592 0.005
<5-Bi203 -H- a-Bi203 [62Gat] DTA 990
(+Li) [65Lev] DTA 1003
(solid state transition) [67Cub] drop cal. 1003
[69Rao] DTA 1000
[76Kor] DSC 1003
[79Har] DSC 1003
[79Har] DTA 1002
[71Rao] emf 978 -10.8
[76MehJ emf 991 -10.1
[79Ise] emf 980 -10.5
[80Fit] emf 997 -10.2
[84Sch] emf 974 -10.6
[91Kam] emf 997 -10.1
[92Kam] emf 997 -10.1
This work 1002 -10.0 0.003
Li -H- Bi+a-Bi203 This work 544 -27.1 4 • 10"7
(eutectic)critical point [79Ise] 1668
This work 1677 -2.9 0.293
2.3 Crystal structures
Crystal structure data are summarized in Table II.2.2. The structural relations between
the four polymorphs of Bi203 have been discussed by Harwig and Weenk [78Har2].Structural investigations have accorded a particular attention to the oxygen sites, a-
Bi203 has monoclinic symmetry [37Sil]. The positions of the oxygen atoms have been
investigated by Mahnros [70Mal] and Harwig [78Harl]. <5-Bi203 has a fluorite struc¬
ture with disordered vacancies on the oxygen sublattice [62Gat, 78Harl]. /3-Bi203has a distorted defect fluorite structure with ordered vacancies in the oxygen sublat¬
tice [72Aur, 88Blo]. 7-Bi203 is isomorphous with or closely related to the Bi12Ge02ostructure [45Aur, 78Harl, 87Kod].
BI-O 73
2.4 Thermodynamics
Bi203: The heat capacity of a-Bi203 has been measured between 60 and 289 K by-
Anderson [30And] and between 11 and 50 K and at 298 K by Gorbunov et al. [81Gor].The reported values of the heat capacity and entropy at 298 K are listed in Table II.2.3.
The values of Gorbunov et al. [81Gor] given in Table II.2.3 are the smoothed values
that they obtained by combining their results with those of Anderson [30And]. En¬
thalpy increment measurements at higher temperatures have been performed by Hauser
and Steger [13Hau] and Cubiciotti and Eding [67Cub] using drop calorimetry. They
are shown in Fig.II.2.3.The enthalpy of transition between a-Bi203 and <5-Bi203 and the enthalpy of melting
have been obtained from DTA [65Lev, 69Rao, 79Har], DSC [76Kor, 79Har], enthalpy
increment measurements [67Cub], and calculated from the derivative with respect
to temperature from emf studies [71Rao, 73Rao, 76Meh, 77Ise, 80Fit]. The results
are listed in Table II.2.4 for the enthalpy of transition and Table II.2.5 for the en¬
thalpy of melting. The values for the enthalpy of transition from DSC measurements
[76Kor, 79Har] are in excellent agreement with each other and compare well to the
enthalpy increment results [67Cub]. They represent the most reliable values.
The enthalpy offormation ofa-Bi203 at 298K has been determined by solution calorime-
tiy [1892Dit,09Mix] and more recently by combustion calorimetry [61Mah]. It has also
been derived from emf measurements [71Rao, 73Cha, 78Cah, 84Ito, 84Sch] and mass
spectrometry data [80Sid]. These results are listed in Table II.2.6. The values from
measurements at higher temperatures are relatively scattered but they are compati¬
ble with the low temperature data. The mean value obtained from calorimetric data
(—573.2 kj/mol) is in good agreement with the mean value obtained from emf mea¬
surements (-570.2 kJ/mol).Many authors have used reversible galvanic cells to study the oxygen chemical po¬
tential of the Bi-rich liquid in equilibrium with Bi203, which allows the determina¬
tion of the Gibbs energy of formation of Bi203. Table II.2.7 presents an overview
of these results. The obtained functions for the Gibbs energy of formation of a-
Bi203 [71Rao, 73Cha, 76Meh, 77Ise, 80Pit, 84Sch, 91Kam, 92Kam], ,5-Bi203 [73Rao,
73Cha, 76Meh, 77Ise, 78Cali, 80Fit, 84Ito, 84Sch, 91Kam, 92Kam], and liquid Bi203
[72Cod, 73Rao, 76Meh, 77Ise, 79Hah, 84Ito] are listed together with the corresponding
temperature interval and cell arrangement. The measured oxygen chemical potentials
are shown in Fig.II.2.4. Fig.II.2.4 also includes activity data in the Bi-rich liquid, which
are discussed below.
Liquid: The oxygen activity in the Bi-rich liquid has been measured as function of tem¬
perature and oxygen content by several authors using coulometric titration techniques
[79Hah, 810ts] and emf measurements combined with titration through addition of
Bi203 pellets [77Ise, 79Ise, 83Ani]. Isecke et al. [77Ise, 79Ise] performed emf measure¬
ments as function of temperature up to 1473 K at fixed oxygen contents ranging from
zo=0.0013 to 0.063 (see Fig.II.2.4), and as function of oxygen content from 3-o=0.024
to the saturation limit between 1523 and 1673 K. Anik [83Ani] measured at 1473
K between zo=0.01 and 0.05. In the coulometric titration experiments. Halm and
Stevenson [79Hah] measured potentiometrically up to the saturation limit at 1073,
1123, 1173, and 1223 K. while Otsuka et al. [810ts] measured the oxygen activity
at 973, 1073, and 1173 K using a potentiostatic method. These results are compared
in Fig.II.2.5. For simplicity, only the data measured at a certain temperature by at
74 THE BSCCO SYSTEM
least two groups have been included in the figure. The values obtained by Isecke et al.,Otsuka et al, and Anik agree fairly well. The activity values measured by Hahn and
Stevenson are considerably larger and the obtained solubility limit, as seen in Fig.II.2.2,is much lower than in the other studies.
Fitzner [80Fit] and Heshmatpour and Stevenson [81Hes] measured the diffusivity of
oxygen in the Bi-rich liquid by coulometric titration using a potentiostatic method and
a cylindrical geometry. The activity coefficient for the dissolution of oxygen in liquidbismuth as well as the solubility limit of oxygen were derived from these measurements.
The data of Fitzner agree with those of Isecke et al. and Otsuka et al The values ob¬
tained by Heshmatpour and Stevenson lie between the results of Hahn and Stevenson
and those of the other studies.
Gas: The thermodynamic data on the Bi-0 vapour system have recently been re¬
viewed by Marschman and Lynch [84Mai]. There are numerous studies on the bis¬
muth oxide vapor species, but unfortunately little agreement between the reporteddata. Marschman and Lynch considered the work of Sidorov et al. [80Sid] to be the
most complete and authoritative study to date. In this work we also base the thermo¬
dynamic description of the gas phase on the results of Sidorov et al.
Sidorov et al. [80Sid] studied the composition of the gas phase in equilibrium with
Bi203 in the temperature range from 1003 to 1193 K by Knudsen effusion mass spec¬
trometry. They found the saturated vapor to contain 02, Bi, Bi2, BiO, Bi203, Bi202,Bi406, Bi20 and Bi304 molecules. They reported the various thermodynamic proper¬ties of these gas species in tables but did not give functions for the Gibbs energies. In
this work we fitted functions for the Gibbs energy of every bismuth oxide species to
the values of Sidorov's tables, referring them to the pure elements in their stable states
at 298.15 K.
Table II.2.2: Crystal structure data.
Phase Pearson
symbol
Space
group
prototype References
Bi hR2 R3m As [69Sch]BiO hR2 R3m BiO [65Zav]Bi607 tI38 I4/mmm Bi607 [68Zav]BigOu til 4 I4/mnun Bi80„ [64Zav]a-Bi203 mP20 P2i/c Bi203 [70Mal, 78Harl]/3-Bi203 tP20 P42i/c Bi203 [72Aur, 88Blo]7-Bi203 cI66 123 Bi203 [78Harl, 87Kod](5-Bi203 cF36 Fm3m Bi203 [78Harl]BiOx 80 cF12 Fm3m CaF2 [89Beg2]Bid 92 cF12 Fm3m CaF2 [89Beg2]Bi204 mC24 C2/c /?-Sb204 [95Kin]Bi407 aP* Bi3Sb07 [89Beg2, 95Kin]
BI-O 75
Table II.2.3: Heat capacity and entropy o/a-Bi203 at 298 K (per mole of B\2Oz)-~"ReT Cp [J/mol-K] S29S [J/mol-K]
[30And] 112 151
[81Gor] 113.4 150
This work 112.1 148.5
Table II.2.4: Enthalpy of transition from a-Bi203 to <5-Bi203 (per mole of JH203).
Ref. Exp. Method T[K] AH [kJ/mol]
[65Lev] DTA 1003 41.4
[67Cub] drop cal. 1003 30.6
[69Rao] DTA 1000 36.8
[76Kor] DSC 1003 29.7
[79Har] DSC 1003 29.5
[71Rao] emf 978 56.9
[76Meh] emf 991 43.3
[79Ise] emf 980 39.7
[80Fit] emf 997 44.0
This work 1002 30.0
Table II.2.5: Enth alpy of melting ofS-BUO3 (per mole ofRef. Exp. Method T[K] AH [kJ/mol]
[65Lev] DTA 1098 16.3
[67Cub] drop cal. 1101 16.7
[79Har] DTA 1098 10.9
[73Rao] emf 1093 26.8
[76Meh] emf 1095 58.8
This work 1098 15.9
76 THE BSCCO SYSTEM
COenCM
20- 1 l
18- [13Hau]
O [67Cub]-
16-•"
14-
12- 08
10-
8-
6-
4-
2-
E4
0- I I
300 600 900
Temperature [K]
1200
Figure II.2.3: o/Bi203
|2 1000
-90
H0 [kJ/mol]
Figure II.2.4: Optimized oxygen potential diagram, he solid lines show the calculated
oxygen chemical potential in the two-phases fields. The calculated oxygen chemical
potentials m the liquid as function of temperature at several fixed oxygen concentrations
are represented by dashed lines and compared to experimental data [77Ise, 79Ise].
BI-O 77
T[K]= 973 1073 1173 1473
[83Ani] h-
[810ts] o O
[79Hah] »
[77lse] a o <!> X
Log[x0]
Figure II.2.5: Oxygen activity in the bismuth-rich liquid. Solid lines show the opti¬
mized oxygen activity along several isotherms. The calculated oxygen saturation limit
is indicated by a dashed line.
3 Thermodynamic Modelling and Optimization
3.1 Description of the Phases
3.1.1 Pure Elements
The pure elements in their stable states at 298.15 K were chosen as the reference state
of the system. For the thermodynamic functions of the pure elements the SGTE phase
stability equations published by Dinsdale [91Din] were used. The equations are given
ill the form :
3 Gf( T) #,SER(298.15 K) = a + b T + c T ln( T) + <
+j-T7 + k- T-9
T2 + e T-1 + //Tl3
(1)
as a function of temperature, where the Gibbs energy of element i in the phase <j> is
described relative to the stable element reference (SER) at 298.15 K. Different sets of
the coefficients a to k may be used in different temperature ranges. The coefficients
] and k are for nietastable ranges only, liquid below the melting temperature or solid
above the melting temperature respectively [87AndJ.
78 THE BSCCO SYSTEM
Table II.2.6: Enthalpy of formaUon o/a-Bi203 at 298 K (per mole of Bi203j.Ref. Exp. Method AH [kJ/molJ
[1892DU] sol. cal. -576.6
[09Mix] sol. cal. -569.0
[61Mah] comb. cal. -573.9
[80Sid] mass spectr. -587.5
[71Rao] emf 3r,Jlaw -567.4
[73Cha] emf 3"'law -550.6
[78Cali] emf 3r,1law -581.6
[84Ito] emf 2n<ilAw -590.2
[84Ito] emf 3"'law -563.4
[84Sch] emf 3r<Jlaw -567.8
This work -570.3
Table II.2.7: Gibbs energy of the reaction 2Bi+i.502=Bi203.
Ref. Cell Bi203 T[K] AG [J/mol]
[71Rao] Pt/Bi,Bi203/CSZ/Cu,Cii20 a 773-978 -629608 + 334.5T
[72Cod] Fe/Bi,Bi203/CSZ/Pb,PbO 1 1000-1300 -373422+156.9T
[73Rao] NiCr/Bi,Bi203/CSZ/Cu,Cu20 5 978-1093 -572613+ 277.3T
1 1093-1150 -545681 + 252.8T
[73Cha] W/Bi,Bi203/CSZ/air a, 5 795-1095 -560196+ 265.4T
[76Meh] Bi,Bi203/CSZ/Fe,FeO a 885-991 -600990+ 315.2T
5 991-1095 -557685 +271.5T
1 1095-1223 -498900+ 217.8T
[78Cah] W/Bi/Bi203/02 § 949-1076 -563585 + 267.8T
[79Hah] W/Bi,Bi203/YSZ/air 1 1073-1223 -415471 + 129.7T
[79Ise] Pt/Cr203/Bi,Bi203/CSZ/air a 823-980 -583592 + 293.9T
5 980-1090 -543905 + 253.4T
1 1090-1623 -518007+ 229.7T
[80Fit] W/Bi,Bi203/CSZ/Ni,NiO a 951-997 -605283+ 314.42T
5 997-1100 -561271 + 270.3T
[84Ito] Ir/Bi,Bi203/CSZ/air S 975-1075 -540020 + 253.72T
1 1100-1374 -520840 + 235.91T
[84Sch] W/Bi,Bi203/CSZ/Cu,Cu20 a 740-976 -581994+ 292.8T
5 1017-1081 -532247+ 241.8T
[91Kam] Ii-/Bi,Bi203/CSZ/Ni,NiO a 888-997 -582520 + 293.94T
5 997-1065 -549700+ 261.06T
[92Kam] Ir/Bi,Bi203/YSZ/Ni.NiO a 838-997 -582500 + 293.4T
5 997-1070 -549700+ 261.IT
BI-O 79
3.1.2 Binary phases
The Gibbs energies of the phases as functions of the concentration and temperature
are represented by the following models :
Solid phases.
Bi, a- and J-Bi203 are described as stoichiometric phases :
gt _ #ser = a + b T + c T -ln(T) + d T2 + e T-1 + f T3 (2)
Liquid phase.
The thermodynamic properties of the liquid can be equally well described by an asso¬
ciation or a two-sublattice model. The two-sublattice ionic liquid model [85Hil] with
the formula (Bi+3)p(Va~q,0~2,0)Q is applied here for compatibility with other systems
(e.g. Cu-0 [94Hal]) and applications in multicomponent systems. It is mathematicaly
equivalent to the association model having the associate with non-integer stoicliiometry
numbers Bi067O. Differences may arise in higher order systems.
The Gibbs energy for one mole of formula units is given as :
GH _ #ser = ,,va_q .Q-(G^- ff|,ER)+ 2,0— (G&, 0-,
- 2 • tfJ,ER - 3 • H*)
+ 2/oo-(?-(G0q-^ER)+ R T Q [^a-q • ln(j/Va-<.) + 2/„0_2
• ln(«/j,0_2) 4- y„Q0 ln(j/„o0)]+ i/Va-'l
' V0-' P-k&Vs Va-1,0"2+ ^B^3 \-a"<i,0-2
' (2/Va-l - I/O"2)-]
+ 2/Va-.• I/O" ["igi+S Va_„i0
+ XIb?+3 Va-1,0' (2/Va- ~ 2/0»)-]
+ 2/o-2 • 2/0° • [°£b?+3 o-2.o+ 1lb?+3 o-2,o
• (2/o-2 - Vo«)-] (3)
Gas phase.
The gas phase is described as an ideal gas considering the species Bi, Bi2, Bi3, Bi4,
O, 02, BiO, Bi20, Bi202, Bi203, Bi304 and Bi406. The Gibbs energy for one mole of
formula units is given as :
Ggas_ffsER = Y^vrWr - #.SER + R-T-Hv,)) + R-T-\n(p) (4)3=1
The thermodynamic functions choosen for Bi. Bi2, Bi3, Bi4. O, and 02 [94SGT] are
consistent with the Gibbs energies of the oxide species obtained from Sidorov et al.
[80Sid]. The partial pressures in the saturated vapour over Bi203 measured bei Sidorov
et al. at 1104 K are compared with the calculated values in Table II.2.8.
The variables in the above equations have the following definitions:
80 THE BSCCO SYSTEM
fftSER enthalpy of element % at 298.15 K in its stable state
HSER is an abbreviation for £ n,H^ER
if,SER is an abbreviation for £ v,HfER for gas specie j = Bi„jO„2
G* Gibbs energy of 1 mol of phase <p
P, Q Number of sites on the sublattices, Q = 3, P depends on the
composition, P = 3 •
j/va-q + 2 •
j/o-2
j/va-ii 2/o-2) ilo" Site fraction of the species (i.e. fraction of the species on the
sublattice)
Ggq Gibbs energy of 1 mole of atoms of pure liquid Bi
G^+3 0_2Gibbs energy of 5 moles of atoms of ideal non-dissociated
liquid Bi203
Go'1 Gibbs energy of 1 mole of atoms of pure O in the fictive liquidstate
"£^+31 i/-th interaction parameter between species z and j
G;gas — H^ER Standard Gibbs energy of 1 mol of species j of the gas phasem number of species considered in the gas phase
j/, mole fraction of species j in the gas phase
The parameters G^+31 - HSER, Gfs - HSER and "I^+31; are functions of the tem¬
perature after eq. (1), for the "L£+31 usually only the coefficients a and b are used
(linear functions of temperature).
3.2 Selection of the adjustable parameters
a- and <5-Bi203.
The enthalpy of formation, the standard entropy, the specific heat values, the H(T)-
H(298K) data, the Gibbs energy of formation and the enthalpy of the a-Bi203 to
<5-Bi203 transition allow for a-Bi203 the determination of the coefficients a to e and
for (5-Bi203 the determination of the coefficients a to c of eq. (1).
Liquid phase.
The parameters (Ggq - Hi?R)i representing liquid pure bismuth, and (G0q - H%ER),representing the fictive liquid pure oxygen are given by Dinsdale [91Din]. The coeffi¬
cients a to c of the parameter (GB"'+3 0_2— 2 • #J,ER — 3 • HqER) can be adjusted to the
experimental data of the liquid near the composition Bi203.
Prom the ^-parameters only "L^+3 Va_q Q^2can be determined. The data on the misci-
bility gap and the oxygen activity in the liquid allow the determination of a concentra¬
tion as well as a temperatuie dependence for "L^+3 v Q_2.Two coefficients (a and 6)
for the first parameter °L^+3 Va_q 0_2and one coefficient (a) for the second parameter
1£g'+3 Va-q 0-2can be well defined from the experimental data.
The parameters ,,£^+3.Va-q 0and "L£+3 0_2 0
do not significantly contribute to Ghq, as
the species 0° never is present in significant concentrations. The parameter "L^1^ 0_2 0
BI-O 81
is fixed to the large positive value 100000 J/mol in order to keep the calculated value
of the oxygen rich phase boundary of the liquid near Bi2C>3, as theie is no experimental
evidence of significant solubility of excess O in liquid Bi2C>3. The parameter L^+3 ^a_q 0
is set to zero. The themiogravimetric data [77Ise, 79Ise] show that up to 1 bar of
oxygen the homogeneity range of the liquid is constrained between Bi and Bi203.
Gas phase.
The data of the gas phase were taken from [94SGT] and [80Sid] and not adjusted
during the optimization, as there are no experimental data giving sufficient information
for an improvement.
3.2 Optimization procedure
The calculations were carried out using the programs developed by Lukas [77Luk.
92Luk]. The optimization routine is based on a least squares minimization. This in
principle requires a Gaussian normal distribution of the data, and thus outliers should
not be considered and contradictory experimental results must be assessed prior to the
optimization. The experimental data are weighted in two steps. A first weight factor
considers the relative experimental uncertainty of each datum and is estimated. The
uncertainties given in the oiiginal papers usually cannot be taken, as their meaning
may be very different and often is not clear enough (e.g. mean error, error of 99.9%
reliability, etc.). Important for the least squares method is just, that for values of
the same quantity approximately the same uncertainty is assumed. This represents
a statistical analysis of the data. An additional weight factor can be introduced to
change the relative weight of some types of data relative to others in order to obtain
a satisfying agreement with the various measurements in the whole system. This is
typically used to give a comparable weight to different kinds of experimental studies
which, for example, strongly differ in the number of reported measured points, such
as for calorimetric vs. emf data. It is also very useful for the assessor to test the
influence of various contradictory results of a certain types of measurements on the
other properties of the system. This second weight factor may be viewed as a way to
deal with systematic errors.
In a first step, the solid and liquid phases were treated separately, since the thermody¬
namic properties of a-Bi2C>3 and <5-Bi203 are much more precisely known than those
of the liquid. The parameters of a-Bi203 and <5-Bi203 were optimized and fixed. The
contradictory data on the liquid phase then were analysed and the choice of the ad¬
justable parameters for the liquid tested. In a final step all parameters weie optimized
simultaneously.
No major contradictions were found among the various data on the solid phases. Since
the transition and the melting enthalpies of Bi203 are relatively small, i.e. the changes
in slope of the Gibbs energy vs. temperature are small, it is difficult to derive reliable
values on these transformations from the emf data. Only DTA and DSC values were
used as fitting data for the transition and melting temperatures, while only calorimetric
results were used for enthalpy values.
Contradictory results are found for the activity of oxygen in the Bi-rich liquid and the
related solubility limit (see Fig. II.2.2 and II.2.5). A relatively good agreement exists
between most measurements [77Ise, 79Ise. 80Fit. 810ts, 83Ani]. The other results
82 THE BSCCO SYSTEM
[79Hah, 81Hes] lead to smaller values for the oxygen solubility limit and larger values
for the activity of oxygen. A better fit of these latter data leads to an increase of the
miscibility gap and brings further contradictions with phase diagram data [77Ise, 79Ise]by increasing the value of the critical point and shifting the bismuth solubility limit
towards lower bismuth contents. The results of [77Ise, 79Ise, 80Fit, 810ts, 83Ani], on
the other side, can be well fitted together with the phase diagram data at higher oxygencontent. The data of [79Hah, 81Hes] were thus discarded and the thermodynamicproperties of the Bi-rich liquid were optimized from the data of [77Ise, 79Ise, 80Fit,810ts, 83Ani].
Table II.2.8: Partial pressures of gas species in the saturated vapor over BJ2O3 at
1104 K. (The calculated values were obtained for xq=0.512 and a total pressure of 0.19
Pa, which correspond to the conditions calculated from the partial pressures of Sidorov
et al.jMolecule Partial pressures [Pa]
[80Sid] This work
Bi 0.118 0.117
02 6.15 • 10"2 6.25 10"2
BiO 4.93 • 10"3 5.05 lO"3
Bi406 2.47 • 10"3 2.71 10-3
Bi2 1.71 • 10"3 1.17 10"3
Bi203 8.20 • 10~4 8.56 10~4
B13O4 4.20 • 10~4 4.46 10-4
Bi202 1.45 • 10~4 1.51 10-4
Bi20 7.68 • 10"5 8.70 lO'5
4 Results and Discussion
The set of parameters for the Gibbs energy functions obtained in this optimization is
shown in Table II.2.9. Most phase diagram, electrochemical, and calorimetric mea¬
surements are quantitatively well reproduced by the calculated values, as can be seen
in Pig. II.2.1 to II.2.5 and in Tables II.2.1 and II.2.3 to II.2.6. The calculated phasediagram at 1 bar total pressure is shown in Pig. II.2.1 and compared with experimentaldata. The calculated phase boundaries and experimental data at low oxygen content
are shown in Fig. II.2.2. The calculated oxygen potential diagram is compared to
results from emf studies in Fig. II.2.4.
The invariant equilibria are listed in Table II.2.1. The transition and melting temper¬atures of Bi203 are well known to an uncertainty of a few K. The temperatures of the
critical point and the monotectic reaction are less certain. Both are strongly depen¬dent on the shape of the miscibility gap, which is very sensitive to small changes in the
thermodynamic description of the liquid. With the given sets of data and the chosen
model, the choice of experimental data for the oxygen activity in the Bi-rich liquid de¬
termines the values obtained for these temperatures. In this optimization the activityof oxygen in the liquid has been fitted to the data of [77Ise, 79Ise, 810ts, 83Ani]. This
increases the critical point and lowers the monotectic temperature by about 10-20 K
BI-O 83
compared to the values obtained from [77Ise, 79Ise] only. When the activity values are
fitted to the data of [79Hah], the miscibility gap extends until equilibrium with the
gas phase is reached. The monotectic temperature is also influenced, to a lesser extent,
by the liquidus slope near the melting point of <5-Bi203, which is mainly determined by
the enthalpy of melting. Further terms in ^+3.Va-q 0-2do not contribute significantly
to a better fit of these phase diagram and thermodynamic data. The three interac¬
tion coefficients optimized in this work for the liquid phase are necessary for a good
qualitative thermodynamic description of the Bi-0 system They are also sufficient for
obtaining quantitatively satisfying calculated values.
The specific heat of a-Bi203 is in good agreement with the experimental data [30And,
81Gor, 67Cub] from 200 K to the transition temperature. The optimized values of the
specific heat and entropy at 298 K are compared with the experimental data [30And,
81Gor] in Table II.2.3. The calculated enthalpy increments at higher temperatures
are compared with the measured values in Fig. II.2.3. The enthalpies of transition
and of melting are compared in Table II.2.4 and II.2.5 respectively. The reported and
optimized values for the enthalpy of formation aie given in Table II.2.6. The emf
measurements on the Gibbs energy of the reaction 2Bi + 1.502 = Bi203 are shown in
Fig. II.2.4. The good agreement obtained with all these data indicates that the Gibbs
energies of a-Bi203 and (5-Bi203 are well established to an uncertainty of a few kJ/mol.
The calculated equilibria with the gas phase depend on the data of [80Sid]. There is
not yet an experimental check. An experimental verification of the azeotropic boiling
point at 1950 K is desirable.
5 Conclusion
The thermodynamic properties of o-Bi203, <J-Bi203, and the liquid phase have been
assessed and an optimized set of Gibbs energy parameters is proposed. A good agree¬
ment is found between most phase diagram, electrochemical, and calorimetric data
on one side, and between these experimental results and the calculated values on the
other side. The presented functions offer a consistent thermodynamic description of
the Bi-0 system at 1 bar total pressure.
Acknowledgments
Financial support of the Swiss National Science Foundation is gratefully acknowledged.
84 THE BSCCO SYSTEM
Table II.2.9: Thermodynamic Description of the Bi-0 System.All parameters aie given in SI units, referred to 1 mol of formula units as
a + b-T + c-T-ln(T) + d T2 + e • T"1 + / • T3
The unary parameters G$°lnb ~ #J,ER> gb? - #b,EH- and <?£" - H$m, are taken from
[91Din].The parameters G^~HifR, G§T2-2H^, Gg-3fl|,BR, G^-iHi, G^-H^,and Gg" - 2i^ER of the gas phase are from [94SGT].
Phase / Parameter b c (f-103 e
OJ-B12O3:
ga-Bi203 2#|ER -609970 656.5 -118.5 -9.1 524285
<J-Bi203:
-601060 854.6 -149.7
liquid:
r>l"l O J/SER o rrSE
JyBi+3 Va-l,0-->
^Bi+3 Va-i,0-i
0 rll(l^Bi+s 0-2,0
574501 762.5
202379 -75.8
-17866
100000
-140
gas:
based on [80Sid]:
/^SM 9 f/SER rrSER
^BijOfCj.) Zi3Bi~
aO
/ogas 0 rrSER rrSER
"BiaO(D,„i) ZIiBi~
nO
GSlo, - 2Hl ~ 2^oER
Gir2so3-2ffBSER-3^ERGCoJ-3fl|1ER-4^ERGi:06-4ff|;ER-6ffaER
110358 -0.0463 -36.34 -0.327 175580
93365 71.59 -57.21 -0.302 301750
70643 121.4 -61.37 -0.303 323270
-58943 211.1 -82.49 -0.239 320250
265698 385.2 -107.1 -0.331 664700
472767 625.1 -155.8 -0.767 883670
901174 1079 -234.0 0.154 1413970
BI-O 85
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86 THE BSCCO SYSTEM
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BI-O 87
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systems, Dissertation, TU Berlin (1977) in German.
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diagrams by a least squares method using simultaneously different types of
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[78Harl] H. A. Harwig, "On the structure of bismuth sesquioxide: the a, j3, 7. and
(5-phase", Z. anorg. dig. Chem., 444, 154-166 (1978).
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mony+oxygen and bismuth+oxygen using solid-state electrochemical tech¬
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tem", Z. Phys. Chem. Neue Folge, 115, 17-24 (1979) in German.
[80Fit] K. Fitzner, "Diffusivity, Activity and Solubility of Oxygen in Liquid Bis¬
muth", Thermochim. Acta, 35, 277-286 (1980)
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Chem., 410, 25-34 (1980) in German.
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Solubility and Diffusivity of Oxygen in the Respective Liquid Metals Indium.
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trochem., 130, 47-55 (1981).
88 THE BSCCO SYSTEM
[810ts] S. Otsuka, T. Sano, and Z. Kozuka, "Activities of Oxygen in Liquid Bi, Sn,
and Ge from Electrochemical Measurements", Metall. Trans., 12B(3), 427-
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EMF method using solid electrolytes", J. Japan Inst. Metals, 1^8, 293-301
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Bi2Mo06", J. Catal, 108, 247-249 (1987).
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BI-O 89
[92Kam] K. Kameda, K.Yamaguchi, and T.Kon, '"Activity of liquid Tl-Bi alloys mea¬
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129-134 (1995).
90 THE BSCCO SYSTEM
II.3 The Sr-O System
Submitted for publication in Calphad, Nov. 1995
THE STRONTIUM-OXYGEN SYSTEM
Daniel Risold, Bengt Hallstedt, and Ludwig J. Gauckler
Nomnetallic Materials, Swiss Federal Institute of Technology,
Sonneggstr. 5, CH-8092 Zurich, Switzerland
ABSTRACT Experimental information on the Sr-0 system is limited to
the properties of pure Sr, SrO, Sr02, and O. The data on the
thermodynamic properties of SrO, Sr02, and the liquid are
reviewed and a consistent set of Gibbs energy functions for
the Sr-0 system is presented.
1 Introduction
The aim of this article is to review the experimental studies on the thermodynamic
properties of the oxides of strontium, and to provide a consistent thermodynamic de¬
scription of the Sr-0 system, which is needed for the modelling of phase equilibria in
multicomponent strontium-containing oxide systems.
The Sr-0 system includes two oxides SrO and Sr02- The thermodynamic properties of
SrO presented in most compilations are based on a combination of early measurements
and estimated values. There is no complete review including the most recent investi¬
gations [85Irg, 90Cor, 930no, 94Cor]. The experimental data on the thermodynamic
properties of Sr02 are scarse and subject to a large uncertainty, while those on the
liquid are limited to few points close to the melting point of SrO. These pieces of infor¬
mation have been brought together and a phase diagram calculated from the resultingthermodynamic description is shown. The Gibbs energy function of SrO adopted here
is also compared with alternative descriptions by JANAF [85Cha] and SGTE [94SGT].
2 Experimental data
2.1 SrO
The melting temperature of SrO has been measured by a few authors, but a relatively
large discrepancy exist between these results, as can be seen in Table II.3.1. JANAF has
adopted the highest value [65Foe] and attributed the low value obtained by Schumacher
[26Sch] to contamination by the Tungsten container. The two newest values [69Nog,85Irgj lie in between. Such large differences have been found for many refractory oxides.
It may be helpful to compare in this case the melting points of other oxides reported
SR-O 91
by the same authors. Of particular interest is the closely related CaO. Arguments have
recently been presented by Wu et al. [93WuJ for a lower melting point of CaO than the
higher value of Foex adopted by JANAF. A lower value for SrO is found by Irgashov
et al. [85Irg], who performed measurements under various conditions using Tungsten
and Molybdenum containers and did not observe significant vaiiations in the value of
the melting point, which would arise by contamination. Interestingly, however, they
reported a higher melting point than Foex for CaO. Noguchi [69Nog] measured the
melting point of various oxides using a solar furnace like Foex. His value for SrO lies
between the results of Foex and Irgashov et al. and his results also agree with a lower
melting point for CaO. In this work we have adopted a melting point of 2870 K, which
is close to Noguchi's result and represents also the average temperature obtained if
Schumacher's value is not considered. Wu et al. [93Wuj mentioned that a lower value
for the melting point of CaO shows a better agreement with solidus and liquidus data
in the CaO-MnO system. We have made similar observation for SrO and CaO in the
Bi-Sr-Ca-Cu-0 system.
The heat capacity of SrO has been studied using adiabatic calorimetry by [35And,69Gme, 94Cor]. These measurements extend between 56 and 299 K [35And], 4 and
300 K [69Gme], and 5 and 350 K [94Cor]. The results are shown in Fig. II.3.1. A
good agreement is found between the results of Anderson [35And] and Cordfunke et
al. [94Cor]. The values given by Gmelin [69Gme] are slightly larger, they show more
scatter and contains some typographical errors which have been corrected by JANAF.
The values for the entropy at 298 K obtained from these studies are shown in Table
II.3.2. The value given in that table for Gmelin is the one obtained by JANAF from
corrected and smoothed data.
Enthalpy increments have been measured using drop calorimetry by [51Lan, 85Irg,
94Cor]. The data were obtained between 363 and 1266 K [51Lan], 1180 and 2950 K
[85Irg], and 470 and 877 K [94Cor]. The measured values are presented in Fig. II.3.2.
The differences between these data is bettei seen in Fig. II.3.3. The results of Irgashov
et al. [85Irg] and Cordfunke et al. [94Cor] are compatible with each other. The values
reported by Lander [51Lan] are up to 3 kj larger, but are probably subject to a bias
from a calibration based on Pt [85Cha].
The enthalpy of formation of SrO has been investigated using combustion calorimetry
[63Mah] and solution calorimetry [23Gun, 66Ada, 66Fli, 69Par, 72Mon, 78Bri, 90Cor].In solution calorimetric studies, the enthalpy of formation of SrO is derived from the
difference in enthalpy between several reactions (dissolution in HC1 of Sr, SrO, ...).Most authors did not measure all the reactions but used to some extent previous
results so that it is more meaningful to assess the results of each reaction instead of
taking the final reported values. As the enthalpy values of all involved reactions have
been discussed recently by Cordfunke et al. [90Cor] we do not present details here.
We adopt his assessed value (Afl)(SrO) = —592.15 kJ/mol) and refer to his article
for a complete list of the measured values. Most results from solution calorimetry are
within a few kJ/mol. The results obtained from combustion calorimetry and activity
data have much larger uncertainties. The value giveii by Cordfunke et al is in good
agreement with the value A#}(SrO) = —592.04 kJ/mol previously assessed by JANAF.
These values are summarized in Table II.3.3.
92 THE BSCCO SYSTEM
The Gibbs energy of formation of SrO has been recently obtained in the temperature
range 1373 to 1773 K by Ono et al. [930no] from a chemical equilibration technique.The activity of Sr in Ag was first determined by equilibrating Ag and SrC2 in a graphitecrucible. The Gibbs energy of formation of SrO was then derived by equilibrating SrO
and Ag in a graphite crucible. These results are plotted in Fig. II.3.4. The enthalpyof formation of SrO derived by Ono et al. from their data is given in Table II.3.3. The
agreement is good in view of the numerous possible sources of error in this method.
Table II.3.1: Melting temperature of Table II.3.2: Entropy of SrO at
SrO 298 K
Reference T,„ [K]
2703[26Sch]Reference g298 [J/mol-Kj
[85Irg] 2805 [35And] 54.4
[69Nog] 2872 [69Gmej* 55.52
[65Foe] 2938 [94Cor] 53.63
[85Cha] 2938 [85Cha] 55.52
[94SGT] 2805 [94SGT] 55.56
This work 2870 This work 53.58
corrected by JANAF
Table II.3.3: Enthalpy of formation of SrO at Table II.3.4: Enthalpy of298 K formation of Sr02 at 298 K
Exp. Method Aif/(SrO)[kJ/mol] Reference Ai^fSrOa)
[90CorJ* solution cal. -592.15[kJ/mol]
[63Mah] combustion cal. -604.3 [08deF] -635
[930no] activity data [52Ved] -631
2nd law -643 [94SGT] -633
yd law -595 This work -636
[85Cha] -592.04
[94SGT] -591.01
This work -592.15
* all solution calorimetric results
are discussed in [90Cor]
2.2 Sr02
The synthesis of peroxide Sr02 has been investigated by several authors in the first
half of this century. A review of these early studies was given by Vannerberg [62Van].Sr02 is found to be stable in oxidizing atmospheres at low temperature, but few precisedata seem to be available even though we were unable to access all the early references.
SR-O 93
Information on the stability of Sr02 has be gained from works on the synthesis of Sr02
through oxidation of SrO. Sr02 was synthesized through the direct oxidation of SrO
as early as 1818 by Thenard [1818The] who obtained a yield of 16% SrC>2 by oxidising
at 673 K in 100 atm 02. The stability limit of Sr02 at high oxygen pressure was
determined by Holtermami [40HolJ for several temperatuies from the change in yield
of SrC>2 as function of the oxygen piessure.
The stability limit of Sr02 was studied at pressure below the atmospheric pressure by
Blumental [34Blu] and Holtermami [40Hol]. The leactiou kinetic of either oxidation
of SrO or reduction of Sr02 is very slow under these conditions and equilibrium is
difficult to reach. The reversibility of the reaction was only observed by Holtermann
[40Hol], who could measure at given temperatures and pressures the change in pressure
of SrO-Sr02 samples due to either reduction or oxidation of the mixture.
The slope of the decomposition pressure vs. temperature measured by Blumental
shows a large discrepancy with calorimetric data on the enthalpy of formation of Sr02.
The results of Holtermann obtained at high oxygen pressure and below atmospheric
pressure are consistent with each other and are in good agreement with calorimetric
data on the enthalpy of fomiation of Sr02. These latter values have thus been used
for the optimization. An overview of the data on the stability limit of Sr02 is given in
Fig. II.3.5. In many thermodynamic tables, the decomposition temperature of Sr02
is given at 488 K in 1 atm 02 with reference to Brewer [53Bre] who himself refers
to Bichowsky and Rossini [36Bis]. We could not access this last reference, but it
seems most probable that this experimental result correspond to the one of Blumental
[34Blu].
The enthalpy of formation of Sr02 was measured by de Forcrand [08deF] and Vedeneev
et al. [52Ved]. These values are in good agreement with each other and are shown in
Table II.3.4.
2.3 Liquid
The data of Irgashov et al. [85Irg] are the only calorimetric measurements on liquid
SrO. The enthalpy of melting of SrO and the heat capacity of liquid SrO have been
determined from the few measured points.
2.4 Gas
The thermodynamic data on the gas phase aie not treated in this article. The experi¬
mental data on the thermodynamic properties of the gaseous strontium oxide molecules
have been reviewed by Lamoreaux et al. [87Lam]. Thermodynamics of the dissociation
and sublimation of SrO has recently been studied by Samoilova and Kazenas [94Sam].
3 Thermodynamic description
The pure elements in their stable states at 298.15 K are chosen as the reference state
of the system (SER). The solid phases are considered stoichiometric. There are no ex¬
perimental indication of a significant solution range for metal Sr and SrO. SrO might
dissolve extra oxygen and Sr02 probably has a tendency to allow oxygen deficiency as
both compounds could be viewed as a single phase with the formula (Sr+2)(0~2.02~2).Recently, Range et al. [94Ran] calculated a composition of S1O195 from the crystal
94 THE BSCCO SYSTEM
structure refinement of SrC>2 single crystals obtained at 1673 K in 20 kbar O2. The un¬
certainty in the Gibbs energy of Sr02 is however to large to go beyond a stoichiometric
approximation. The description of fee and bec Sr is taken from Dinsdale [91Din]. The
Gibbs energy of SrO is obtained from the data of [85Irg, 90Cor. 930no, 94Cor], while
the Gibbs energy of Sr02 is based on the measurements of the stability limit [40Hol]and of the enthalpy of formation [08deF, 52Ved].
The ionic liquid model [85Hil] has been chosen by the authors for the treatment of
the liquid phase in systems containing strontium cuprates. This model is thus also
applied here with the formula (Sr+2)2(Va_cl,0_2)2. In this description it is assumed
that 0° or Oj2 species are not present in the liquid under ambient pressure so that the
liquid phase does not extend beyond the SrO composition. If the liquid can dissolve
a significant amount of extra oxygen, a dependence of the melting point of SrO oil
oxygen partial pressure should be observed. The only experimental information on the
liquid concerns pure liquid Sr and liquid SrO. In the absence of any other data, the
solution behaviour of the Si-SrO liquid is obtained from a comparison with the similar
Ba-0 [95Zimj and Ca-0 [93Sel] binaries. In both systems lelatively small interaction
terms have been derived based on liquidus data (Ba-O) and melting point depressionof Ca (Ca-O). The interaction term of the Ba-BaO liquid varies from -23000 to -30000
between 1000 and 2000 K, while the one of the Ca-CaO liquid is about +17000. The
Sr-SrO liquid is expected to lie somewhere in between and is thus described here as
an ideal solution between liquid Sr and liquid SrO. The Gibbs energy of the liquid (forone mole of formula unit) is given by :
GJi" = 2j/va ,°Gsr + 22/o^°G1s'rqo + 2JRT[2/Va-q • ln(yva-<.) + Vo-* Myo-*)]
where y, is the site fraction of the specie % on the respective sublattice. °GS'' represents
the Gibbs energy of 1 mole of atoms of pure liquid Sr and is taken from Dinsdale
[91Din]. °Gs'rO represents the Gibbs energy of 1 mole of atoms of ideal non-dissociated
liquid SrO, and is the only parameter for the liquid optimized in this work. A constant
value of 73.1 J/mol-K for the specific heat of liquid SrO is obtained from the data
of Irgashov et al. [85Irg], compared to 66.9 J/mol-K as estimated by JANAP from
other oxides. The remaining two coefficients have been obtained from the enthalpymeasurements of Irgashov et al. and the adopted melting temperature.
The gas phase is described as an ideal gas containing an equilibrium mixture of the
species Sr, Sr2, Sr20, SrO, O, and 02. The thermodynamic description of the species
Sr, Sr2, Sr20, and SrO is taken from Lamoreaux et al. [87Lam], while the descriptionof the oxygen species is taken from SGTE [94SGT].
4 Results and Discussion
The thermodynamic description proposed in this work for the Sr-0 system is summa¬
rized in Table II.3.5. The phase diagram calculated from this description is shown in
Fig. II.3.6. Assessed values for the thermodynamic properties of SrO are comparedto experimental data in Table II.3.1 to II.3.4 and Fig. II.3.1 to II.3.5 as discussed in
section 2.
SR-O 95
Table II.3.5: Thermodynamic description of the Sr-0 system
All parameters are given in SI units. The parameters for pure solid and liquid Sr
are from Dinsdale [91Din] while those for O and 02 are from [94SGT]. Parameters
for the gas species Sr, Sr2, Sr20, and SrO are from Lamoreaux [87Lani]. These
parameters are not reproduced in this table.
SrO:
GSrO _ Hser = _ 607870 + 268.9- T - 47.56- T-ln( T) - 0.00307- T2 + 190000- T'1
Liquid:
Gsrq0 - Hsm = - 566346 + 449.0- T - 73.1- T-ln(T)
Sr02:
GSr02 = qStO + Q 5 Q02 _ 43740 + 7Q . T
The enthalpy increment data of [85Irg] show a pronounced curvature in the tempera¬
ture dependence which is most clearly seen in Fig. II.3.3. The data of Irgashov et al.
and Cordfunke et al. can be simultaneously well fitted by including in the temperature
dependence of the specific heat terms such as T2, T3 [94Cor], T2 • e~T [85Irg], or
by considering various temperature intervals [94SGT]. These terms lead to a marked
increase in cp above 2500 K and should be compensated in order to avoid the liquid
becoming less stable than solid SrO when extrapolating to higher temperatures, using
e.g. a term in T~9 as in the SGTE method [87And]. An alternative possibility to
supress the risk of having solid SrO stable again at higher temperatures is to refer the
Gibbs energy of liquid SrO to solid SrO [94SGT]. The pronounced curvature of the
enthalpy measured above 2500 K may also well be an experimental artifact. In view of
these considerations, we preferred to use a single function for SrO valid from 200 K to
the melting point, which does not need a compensation term for higher temperatures,
and which gives enthalpy, entropy, and Gibbs energy values to a satisfying degree of
accuracy.
The enthalpy and entropy values at 298 K are fitted to the experimental data of
Cordfunke et al. [90Cor, 94Cor]. The differences between the various Gibbs energy
functions seen in Fig. II.3.4 are mainly due to the differences in entropy values which
are also reflected in Table II.3.2.
The stability limit of Sr02 is shown in Fig. II.3.5. The reported values for the enthalpy
of formation are compatible with the adopted values of the decomposition pressure.
Acknowledgments
Financial support from the Swiss National Science Foundation (NFP30) is gratefully
acknowledged.
96 THE BSCCO SYSTEM
50<!> [35And]Q [69GmeO [94Cor]
150 200 250 300 350
T[K]
400 450
Figure II.3.1: Heat capacity of SrO
250
200-
o
E
CO
CM
X 100
50
_i_
a [51Lan]o [84lrg]A [94Cor]
[85Cha]- - [94SGT]— This work
500 1000 1500 2000 2500 3000
T[K]
Figure II.3.2: Enthalpy of SrO
SR-0 97
fc.X
62
60
58 H
56
54
52
50
48
46
44
[51Lan]O [84lrg]A [94Cor]
[85Cha]- - [94SGT]- [94Cor]- This work
0 500 1000 1500 2000 2500 3000
T[K]
Figure II.3.3: Mean heat capacity ("ZZStP) for SrO
J l L_
1000 1200 1400 1600 1800 2000
T[K]
Figure II.3.4: Gtbbs energy of formation of SrO(s) referred to Sr(fcc) and 02(g)
98 THE BSCCO SYSTEM
-2 0
Log(P02 [bar])
Figure II.3.5: Stability limit of Sr02
4000
3500
3000-
f 2500
2» 2000CDQ.
§ 1500
1000
500 H
0
liquid
.-Sr1*0
-SrTC
•— liquid
SrO SrO,
0 0.2 0.4 0.6 0.8 1.0
Sf Mole fraction O O
Figure II.3.6: Sr-0 phase diagram at 1 bar total pressure
SR-O 99
References Chapter II.3
[1818The] L. J. Thenard, Ann. Chim. Phys.. 8, 313 (1818). cited from 62Van.
[08deF] M. deForcrand, "Study of the Oxides of Lithium, Strontium, and Barium",
Ann. Chim. Phys., 15, 433-490 (1908) in French.
[23Gun] A. Guntz and F. Benoit, Ann. Chim. Pans, 20, 5 (1923).
[26Sch] E. E. Schumacher. "Melting Points of Barium, Strontium and Calcium Ox¬
ides", J. Am. Chem. Soc, 48, 396-405 (1926).
[34Blu] M. Blumental, J. Chim. Phys., 31, 489 (1934). cited from 40Hol,62Van.
[35And] C. T. Anderson, "The Heat Capacities at Low Temperatures of the Oxides
of Strontium and Barium", J.Am. Chem. Soc, 57.429-431(1935).
[36Bis] Bischowsky and Rossini, The Thermochemistry of the Chemical Substances,
Reinhold Publishing Corporation, New York (1936). cited from 53Bre.
[40Hol] C. B. Holtermann, "Experimental Study of Direct Oxidation under High
Pressure. Oxides of Strontium, Barium, Lead, Manganese, and Cobalt", Ann.
chim., 14, 121-206 (1940) in French.
[51Lan] J. J. Lander, "Experimental Heat Contents of SrO, BaO. CaO. BaC03, and
SrC03 at High Temperatures. Dissociation Piessures of BaC03 and SrCOs",
J. Am. Chem. Soc., 73, 5794-5797 (1951).
[52Ved] A. V. Vedenew, L. J. Kazarnovskaya, and I. A. Kazarnovskii, Zh. Fiz. Khim.,
26, 1808 (1952). cited from 62Van.
[53Bre] L. Brewer, "Thennodynamic properties of the oxides", Chem. Rev., 52, 1
(1953).
[62Van] N.-G. Vamierberg, "Peroxides, Superoxides, and Ozonides of the Metals of
Groups la, Ha, and lib", Prog. Inoig. Chem., 4, 125-197 (1962).
[63Mah] A. D. Mali, "Heats and Free Energies of Formation of Barium Oxide and
Strontium Oxide", U.S. Bur. Mines Rep. Inv. 6171 (1963).
[65Foe] M. Foex, "Solidification Points of several Refractory Oxides", Solar Energy,
9{l), 61-67 (1965).
[66Ada] L. H. Adami and K. C. Conway, "Heats and Free Energies of Foimation of
Anhydrous Carbonates of Barium, Strontium, and Lead", U.S. Bur. Mines
Rep. Inv. 6822 (1966).
100 THE BSCCO SYSTEM
[66Fli] G. V. Flidlider, P. V. Kovtunenko, and A. A. Bundel, "Heats of Formation
of Strontium and Barium Oxides'', Russ. J. Phys. Chem., </0(9), 1168-1169
(1966).
[69Gme] E. Gnielin, "Thermal Properties of Alcaline-Earth-Oxides", Z. Naturforsch.,24A. 1794-1800 (1969).
[69Nog] T. Noguchi, "High Temperature Phase Studies with a Solar Furnace", Adv.
High Temp.-High Press., 2, 235-262 (1969).
[69Par] V. B. Parker, U.S. Nat. Bur. Stand. Report 10074, P- 164 (1969).
[72Mon] A. S. Monaenkova and A. F. Vorob'ev, Khim.Tehwl, 15, 191 (1972) in
Russian.
[78Bri] I. J. Brink and C. E. Holley, "The Enthalpy of Formation of Strontium Monox¬
ide", J. Chem. Thermodynamics, 10, 259-266 (1978).
[85Cha] M. W. Chase, Jr., C. A. Davies, J. R. Downey, Jr., D. J. Frurip, R. A.
McDonald, and A. N. Syverud, "JANAF Thermochemical Tables, 3rd ed.",J. Phys. Chem. Ref. Data, ^(Suppl. 1) (1985).
[85Hil] M. Hillert, B. Jansson, B. Sundman, and J. Agren, "A Two-Sublattice Model
for Molten Solutions with Different Tendency for Ionization", Metall. Trans.
A, 16A{2), 261-266 (1985).
[85Irg] K. Irgashov, V. D. Tarasov, and V. Y. Chekhovskoi, "Thermodynamic Prop¬
erties of Strontium Oxide in the Solid and Liquid Phases", High Temperature,
23(1), 81-86 (1985).
[87And] J.-O. Andersson, A. Fernandez-Guillermet, P. Gustafson, M. Hillert, Bo Jans¬
son, Bo Jonsson, Bo Sundman, and J. Agren, "A new method of describinglattice stabilities", Calphad, 11, 93-98 (1987).
[87Lam] R. H. Lamoreaux, D. H. Hildeubrand, and L. Brewer, "High-TemperatureVaporization Behaviour of Oxides II. Oxides of Be, Mg, Ca, Sr, Ba, B, Al,
Ga, In, Tl, Si, Ge, Sn, Pb, Zn, Cd, and Hg", J. Phys. Chem. Ref. Data, 16
(3), 419-442 (1987).
[90Cor] E. H. P. Cordfunke, R. J. M. Konings, and W. Ouweltjes, "The Standard
Enthalpies of Formation of MO(s), MCl2(s), and M2+(aq,oo) (M=Ba,Sr)",J. Chem. Thermodynamics, 22, 991-996 (1990).
[91Din] A. T. Dinsdale, "SGTE data for pure elements", Calphad, 15, 317-425
(1991).
[930no] H. Ono, M. Nakahata, F. Tsukihashi, and N. Sano, "Determination of Stan¬
dard Gibbs Energies of Formation of MgO, SrO, and BaO", Metall. Trans.
B, 24B, 487-492 (1993).
[93Sel] M. Selleby, "A Reassessment of the Ca-Fe-0 System", Trita-mac 508, RoyalInstitute of Technology, Stockholm, Sweden. (Jan. 1993).
SR-O 101
[93Wu] P. Wu, G. Eriksson, and A. D. Pelton, "Critical Evaluation and Optimization
of the Thermodynamic properties and Phase Diagrams of the CaO-FeO. CaO-
MgO, CaO-MnO, FeO-MgO, FeO-MnO, and MgO-MnO Systems", J. Am.
Ceram. Soc., 76(8), 2065-2075 (1993).
[94Cor] E. H. P. Cordfunke, R. R. van der Laan, and J. C. van Miltenburg, "Ther-
mophysical and Thermocliemical Properties of BaO and SrO from 5 to 1000
K", J. Phys. Chem. Solids, 55(1), 77-84 (1994).
[94Ran] K. J. Range, F. Rau, U. Schiessl, and U. Klement, "Verfeinerung der Kristall-
struktur von Sr02", Z. anorg. dig. Chem., 620, 879-881 (1994) in German.
[94Sam] I. O. Samoilova and E. K. Kazenas, "Thermodynamics of Dissociation and
Sublimation of Stiontium Oxide"', Russian Metallurgy, 3, 30-33 (1994).
[94SGT] The SGTE substance database, version 1994, SGTE (Scientific Group Ther-
modata Europe), Grenoble, France, 1994.
[95Zim] E. Zimmermann, K. Hack, and D. Neuschiitz, "Thermocliemical Assessment
of the Binary System Ba-O", Calphad, 19(1), 119-127 (1995).
102 THE BSCCO SYSTEM
II.4 The Sr-Cu-O System
Submitted for publication in J. Am. Ceram. Soc, Dec. 1995
Thermodynamic Assessment of the Sr-Cu-O System
Daniel Risold, Bengt Hallstedt, and Ludwig J. Gauckler
Nonmetallic Materials, Swiss Federal Institute of Technology,Souneggstr. 5, CH-8092 Zurich, Switzerland
ABSTRACT The phase diagram and thermodynamic data on the Sr-
Cu-O system at 1 bar total pressure have been reviewed
and assessed. Gibbs energy functions for the ternary ox¬
ides Sr2Cu03) SrCu02, Sr14Cu24041, SrCu202, and the liquidphase have been optimized and a consistent thermodynamicdescription is presented. Calculated SrO-CuO„ phase dia¬
grams in air and 1.01 bar 02, oxygen potential diagram, and
various thermodynamic properties are shown and comparedwith experimental data.
1 Introduction
The purpose of the present study is to obtain a consistent thermodynamic descriptionof the Sr-Cu-O system at 1 bar total pressure, which can be used for calculations of
phase equilibria and thermodynamic properties in the multicoiiiponent superconduct¬ing cuprate systems.
The phase relations in the Sr-Cu-O system can be divided, as in the Ca-Cu-0 [95Ris2]system, into an oxide and a metal part along the line SrO-Cu20, and the metal partitself divided along the SrO-Cu line. The metallic phases are all in equilibrium with
SrO. The metal and oxide parts are separated at higher temperature by a miscibilitygap in the liquid phase. There are no experimental data on that part of the system but
a similar behaviour as in the Ca-Cu-0 system is expected, where the metal liquid iscontained in the Cu-0 binary and complete miscibility in the liquid is reached as the
binary Cu-0 miscibility gap vanishes. The oxide part of the system has been the sub¬
ject of many studies since the discovery of the superconducting cuprates. Pour ternarycompounds are stable in the Sr-Cu-O system at ambient pressures (Sr2Cu03, SrCu02,Sri4Cu2404i, and SrCu202) and they appear more than usually desired as major sec¬
ondary phases in the processing of Bi-Sr-Ca-Cu-0 superconductors. Contradictoryexperimental results on their thermodynamic properties have been reported and need
to be assessed. Of particular importance are also the melting relations for which few
data are available. Two other family of phases could be stabilized at high pressure
SR-CU-O 103
(Sr„_iCu„4.i02n, Sr„+iCu„02„-i-i+<5). Both series converge towards the infinite-layer
phase. These compounds are not included in this description even though some of
them may be stable at ambient pressure and low temperature. An overview of the high
pressure system has been given Hiroi and Takano [94Hir, 94Tak].
In the following, thermodynamic modelling is applied to assess the experimental data
on the oxide part of the system and to provide a consistent thermodynamic description
of the Sr-Cu-0 system which includes the liquid phase. All calculations were performed
with the help of the Thermo-Calc software package [85Sun]. This evaluation is based
on previous assessments of the Sr-0 [95Risl], Cu-0 [94Hal], and Sr-Cu [96Ris]
systems.
2 Experimental data
2.1 Phase diagram
Four ternary oxides have been found stable in the Sr-Cu-0 system at ambient pres¬
sures; Sr2Cu03, SrCu02. SrCu202, and Sr14Cu24O.ii. The first three compounds were
first reported by Teske and Miiller-Buschbaum [69Tes, 70Tes2, TOTesl] in a system¬
atic study of ternary oxides of alkali-earth metals, whereas the compound Sri4Cu2404i
appeared as a by-product in the search for superconducting compounds, first in the
La-Sr-Cu-0 system [87Hah, 87Tor] and then in the Bi-Sr-Ca-Cu-0 system [88Kat,
88Lee]. Phase diagram studies have been made using XRD analysis of quenched
samples [89Rot, 90Hwa, 90Lia, 91Bou, 94Nev, 92Jac, 92Suz] and thermal analysis
[90Lia, 91Bou, 94Nev, 92Kos].
The reported phase relations along the SrO-CuO, section in air [89Rot, 90Hwa,
90Lia, 91Bou, 94Nev] and 1.01 bar 02 [91Bou, 94Nev] are similar. At 1.01 bar 02,
Sr2Cu03, SrCu02, and Sr14Cu2404i melt peritectically and a eutectic reaction between
Sr14Cu2404i and CuO is found. The 4-phase invariant equilibrium between SrCu02,
Sri4Cu2404i, CuO and the liquid must be close to the air partial pressure. In air,
Hwang et al. [90Hwa] could not distinguish between the eutectic reaction and melting
of Sri4Cu2404i, Boudene [91Bou] found Sri4Cu2404i to decompose below the eutec¬
tic reaction, while the other authors [90Lia, 94Nev] report the peritectic melting of
Sr14Cu2404i. The eutectic composition in air is found around 74 [90Lia], 80 [94Nev],and 85 mol % CuO [90Hwa, 91Bou]. The liquidus was determined at a few compo¬
sitions by Hwang et al. [90Hwa] from the wetting behaviour of the melted sample.
These points are subject to a large uncertainty. These SrO-CuOj, sections are shown
in Pig. II.4.1 and II.4.2 and the measured peritectic and eutectic temperatures are
listed in Table II.4.1. At these higher oxygen partial pressures the compound SrCu202
is not stable.
The phase relations have also been investigated as function of the oxygen partial pres¬
sure in isothermal sections at 1173 K by Jacob et al. [92Jac] and Suzuki et al. [92Suz].Both studies are in good agreement and the phase relations determined experimentally
are the same as the calculated ones shown in Fig II.4.3.
The phases stabilized at high pressure were mainly studied at pressures of a few GPa.
There are however indications that some compounds may be stable at ambient pressure
and low temperature, in particular those stabilized by high oxygen partial pressure. For
104 THE BSCCO SYSTEM
exemple, the first member of the Sr„+iCu„02„-n-i-i serie, Sr2Cu03+J!(tertagoiial sym¬
metry), has first been obtained through oxidation, at 673 K at 160 bar 02, of the ambi¬
ent pressure phase Sr2Cu03 (orthorhoinbic symmetry) [90Lob]. Recently, Sr2Cu03+a.was synthetized at 643 K in 1.01 bar 02 from a copper hydroxometallate precursor
[94Mit]. Its stability at 1.01 bar 02 was studied using TG and high-temperature XRDand Sr2Cu03+I was found to decompose iireversibly to ortliorhombic Sr2Cu03 at 723
K [94Mit].
Table II.4.1: Melting relations in air and 1.01 bar 02.
Reaction T[K] Method Reference
(air) (1.01 bar 02)
1. L + SrO + 02 1498 XRD [90Hwa]o Sr2Cu03 1492 DTA [90Lia]
1513 1535 DTA [91Bou]1518 DTA [92Kos]1493 1530 DTA [94Nev]1494 1532 This work
2. L + Sr2Cu03 + 02 1358 XRD [90Hwa]<H- SrCu02 1350 DTA [90Lia]
1370 1390 DTA [91Bouj1357 DTA [92Kos]1351 1379 DTA [94Nev]1346 1381 This work
3. L + SrCu02 + 02 1228 XRD [90Hwa]H- Sr14Cu24041 1243
1303
DTA
DTA
[90Lia][91Bou]
1255 1303 DTA [94Nev]1248 1298 This work
4. L + 02 1228 XRD [90Hwa]<-> Sr14Cu2404i 4- CtiO 1233 DTA [90Lia]
1246 1284 DTA [94Nev]1244 1284 This work
SR-CU-O 105
i7nn i i i i
|o [90Hwa]
x [goLia]
1600- I \O [91Bou]
[94Nev]
* 1500-
Liquid
3
« 1400- \I .
CDO.
CO
[ / o
I= 1300-
o
yCO
jq ..
o
>y"V
1200-
3
o
o
CO
I I I i
0 0.2 0.4 0.6 0.8 1.0
Sr0 <„ /fx.. + X ^ CuC>
Figure II.4.1: Optimized SrO-CuO^ phase diagram m air. The symbols indicate the
measured temperatures and liquid compositions of various equilibria
1700
1600
* 1500-
(1)
-)
CO 1400-(1)o.
E
H 1300-1
1200
1100
Figure II.4.2: Optimized SrO-CuOx phase diagram in 1.01 bar 02. The symbols
indicate the measured temperatures and liquid compositions of various equilibria.
106 THE BSCCO SYSTEM
Figure II.4.3: Phase relations m the Sr-Cu-0 system at 1173 K. The cross in the
S-phase field SrCu02-CuO-Cu20 indicates the concentration of the first oxide liquidwhich appears at 1192 K.
2.2 Crystal structure and phase composition
The crystal structure of Sr2Cu03 has been determined from single crystal X-ray diffrac¬
tion [69Tes] and powder neutron diffraction [89Wel, 91Lin]. The symmetry is or-
thorhombic with space group Immm. Sr2Cu03 is probably well approximated as a
stoichiometric compound. There are no phase diagram study reporting significantcation nonstoichiometry and the measured variations in oxygen content do not exceed
the experimental uncertainty. Alcock and Li [90Alc] observed by thermogravimetryvery little excess of oxygen at 1193 K in the oxygen partial pressure range from 10 to
105 Pa, but do not quantify it. On the other hand, a small oxygen deficit of about one
percent was reported from equilibrium pressure measurements at 1173 K [92Kriij.
The crystal structure of SrCu02 has been determined from single crystal X-ray diffrac¬
tion [70Tes2, 94Mat] and powder neutron diffraction [89Wel]. The symmetry is
orthorhombic with space group Cmcm. Matsushita et al. [94Mat] calculated the cop¬
per valence and oxygen occupancies of their sample using the bond valence method.
They obtained some amount of oxygen vacancies for samples which were cooled in
air. Experimentally, the oxygen content of SiCu02 has been determined using ther¬
mogravimetry [90Alc, 92Jac] and from the slope of emf measurements as function of
oxygen partial pressure [92Jac, 92Vor]. At 1173 K, the oxygen content is found to vary
slightly with oxygen partial pressure from 2.04 [90Alc], 2.05 [92Jac] at 1 bar 02 to
1.98 [90Alc], 2.00 [92Jac] at about 100 Pa 02 where SrCu02 decomposes to Sr2Cu03and SrCu202.
SR-CU-O 107
The compound written here as Sri4Cu24041 has also been reported as SrioCu17029,
Sr3Cu508+,s, or Sri+a,Cu203+i. The crystal structure of SrMCu2404i has been studied
by X-ray diffraction [88Kat, 88Lee, 88McC, 88Sie, 90Kat, 93Ara, 93Jen, 94Uke] and
high-resolution electron microscopy and electron diffraction [90Zho. 91Will, 91Wu2,
92Mil]. Two interpenetrating incommensurate sublattices have been identified in al¬
most all these studies. One sublattice consists of a Sr2Cu203 block made of Cu203
planes separated by Sr chains. The other sublattice consists of Cu02 chains located
between the Sr chains. The two formulas Sr14Cu2404i [88McC. 88Sie. 93Ara, 91Wul.
91Wu2, 92Mil] and Sri0Cui7O29 [88Kat, 90Kat, 93Jen] arise from different supercell
description. The Sr10Cui7O29 supercell is derived from the length of the orthorhombic
cell which is obtained if, at first sight, the reflections are attributed to one sublat¬
tice and not to two individual incommensurate sublattices [93Jen]. The Sr14Cu2404i
supercell was obtained as the closest correspondence of the lattice constants of both
sublattices [88McC], and seems also to fit well with the period of a modulation ob¬
served by Milat et al. [92Mil]. The cation ratio of (Sr.Ca,La,Y,...)i4Cu2404i has been
measured in many phase diagram studies of various systems involving superconducting
cuprates and no indication of a significant deviation from the value 14/24 has been
reported. The oxygen content given by the formula Sr14Cu2404i is in agreement with
tliermograviinetric results [90Alc, 90Li, 92Jac] and emf measurements as function of
the oxygen partial pressure [92Jac, 92Vor]. No significant variation of the oxygen
content as function of the oxygen partial pressure [90Alc, 92Jac, 92Vor] or the tem¬
perature [90Li] has been observed. We have used the formula Si'i4Cu2404i in this
work. The formula Sr10Cui7O29 would fit the analytical results equally well.
The crystal structure of SrCu202 has been determined from single crystal X-ray diffrac¬
tion [70Tesl] and a tetragonal symmetry with space group IA\/ amd was observed. The
oxygen content of SrCu202 is approximatively constant as no significant variation of
the emf value as function of the oxygen partial piessure could be observed [90Kov].
2.3 Thermodynamics
The thermodynamic properties of the ternary compounds have been studied by several
authors using calorimetric and electrochemical methods.
The heat capacity of Sr2Cu03, SrCu02, and Sri4Cu2404i was measured between 15
and 350 K by Shaviv et al. [90Sha] using an adiabatic calorimeter. The experimental
values are slightly larger than the one calculated from the mle of Neumann-Kopp, but
the differences do not exceed 1 J/(K mol-at.). The heat capacity of Sr2Cu03 at 350 K
was also measured by Kriiger et al. [92Krii] using DSC. This value is less than 2 J/(K
mol-at.) lower than the one of Shaviv et al. The heat capacity and the entropy values
at 298 K derived by Shaviv et al. [90Sha] are given in Table II.4.2.
Enthalpies of formation were measured by solution calorimetry at 298 K [93Ide] and
973 K [91Bou]. Idemoto et al. [93Ide] measured the heats of dissolution of SrC03,
CuO, Sr2Cu03, SrCu02, and Sri4Cu24041 in a HC104 solution, while Boudene [91Bou]measured those of CuO, Sr2Cu03, and SrCu02 in a melt of lead borate. These results
are shown in Table II.4.3 and compaied with the values derived from emf measurements.
The differences are fairly large and are discussed in Section 4.
The Gibbs energies of solid state reactions have been investigated in numerous mea-
108 THE BSCCO SYSTEM
surements using Zr02, SrF2, and CaF2 solid electrolyte galvanic cells [92Jac, 92Suz,91Bou, 90Alc, 90Kov, 90Sko2, 90Skol]. These results are sunmiarized in Table II.4.4.
The discrepancies between the various studies remain fairly small at lower oxygen par¬
tial pressuies, but are in some cases considerable at higher oxygen partial pressures.
The studies of Jacob and Mathews [92Jac] and Skolis et al. [90Kov, 90Sko2, 90Skol]both show a good internal consistency, while those of Suzuki et al. [92Suz] and Boudene
[91Bou] do not iuchide enough cells to check the internal consistency. In the study of
Alcock and Li [90Alc], the Gibbs energy of Sr2Cu03 obtained from Zr02 and CaP2cells is subject to an inconsistency which was pointed out by Jacob and Mathews.
Comparisons to calorimetiic and phase diagram results are made in Section 4.
Table II.4.2: Heat capacity and entropy of the ternary oxides at 298 if.f
Phase Cp g298 Ref.
[J/(K-mol)] [J/(K-mol)]
Sr2Cu03 134.9 148.5 [90Sha]132.5 150.1 This work
SrCu02 86.75 96.91 [90Sha]87.43 94.32 This work
"1*14 (-U24W4i 1731 1906 [90Sha]1691 1837 This work
SrCu202 108 148 This work
f per mole of formula unit
3 Thermodynamic description
This evaluation is based an the thermodynamic description of the binary subsystems[95Risl, 94Hal, 96Ris]. The binary oxides C112O and CuO, respectively SrO, do not
show significant solubility for strontium, respectively copper, and are treated as stoi¬
chiometric compounds.
3.1 The ternary oxides
The four ternary oxides are described here as stoichiometric compounds. This treat¬
ment of Sr2Cu03, SrCu202, and Sr^Cu^O^i is well supported by the experimentalresults presented above. In the case of SrCu02, this description does not account for
the reported small variations in oxygen content. The present approximation, however,does not influence qualitatively the phase relations, but certainly slightly increases the
quantitative uncertainty in the calculated values.
The molar Gibbs energies of Sr2CuC>3, SrCu02, and Sri4Cu2404i are referied to the
binary oxides SrO and CuO, while that of SrCu202 is refered to SrO and Cu20. The
temperature dependence of these energies of formation is described here by linear func¬
tions. A closer fit to the heat capacity and entropy values at 298 K could be obtained
by introducing an excess heat capacity term. This would cause curvatures of the Gibbs
energies which would increase the discrepancy between calorimetric and emf results.
We preferred to use linear temperature dependences since the deviation from the rule
SR-CU-O 109
Phase AH [kJ/mol] Method Ref.
Sr2Cu03 -70.5 sol. cal. (298K) [93Ide]-87.4 sol. cal. (973K) [91Bou]-67.1 emf [90Alc]-31.8 emf [90Skolj-44.1 emf [91Bou]-32.2 emf [92Jac]-27.8 assessed (298K) This work
SrCu02 -23.4 sol. cal. (298K) [93Ide]-51.4 sol. cal. (973K) [91Bou]-31.1 emf [90Alc]-19.1 emf [90Skol]-65.0 emf [91Bou]-21.7 emf [92Jac]-22.7 assessed (298K) This work
Sri4Cll2404i -773 sol. cal. (298K) [93Ide]-659.4 emf [90Alc]-434.4 emf [90Skol]-582 emf [92Jac]-625.5 assessed (298K) This woik
SrCu202 -14.7 emf [90Alc]-12.0 emf [90Kov]-2.3 emf [91Bou]-16.1 emf [92Jac]-16.2 emf [92Jac]-15.5 assessed (298K) This work
t per mole of formula unit
110 THE BSCCO SYSTEM
of Neumann-Kopp is small and since the uncertainties in enthalpy and entropy contri¬
butions aie large.
3.2 The liquid phase.
The liquid phase is described by the two-sublattice ionic liquid model [85Hil]. This
model has pioved to be successful in describing the thermodynamic properties of oxide
systems showing different degree of ionization such as Fe-0 [91 Sun] or Cu-0 [94Hal],and we have applied it in all subsystems of the Bi-Sr-Ca-Cu-0 system.
Here the formula (Sr+2, Cu+1, Cu+2)p(Va""q, 0~2), is applied and the molar Gibbs en¬
ergy of the liquid is then given by the expression :
<?!,'," = <Z2/s>+2W^V Va+ ySl+2 y0-2°Gl£+2.0_2
+ ?J/Cu+> 0Va°<?c*+l Va+ VCU+1 VO'^G^+i Q^2
+ qycu+*yva°G>cl+i Va+ vc^vo-^g1^ o-*
+ pKr[</s,+2 •ln(3/Sl+2) + fc+i'Mfcti) + yCu+2 ln(j/Cll+2)]
+ ?RT[2/va • ln(j/Va) + S/o-2 • ln(y0-2)}
+ *<#-<, + 'G^_0 + *<&_cu + "GtI (H.4.1)
The functions °G;'Va represent the Gibbs energies of the pure liquid metals while the
°G'o-2 represent the Gibbs energies of ideal non-dissociated liquid oxide compounds.The BG^_B represent the main contributions to the excess Gibbs energy based on
extrapolations from the binary subsystems. These functions are all taken from the
respective binary optimizations [95Risl, 94Hal, 96Risj. The numbers p and q vary
with composition in order to maintain electroneutrality and are given by the relations
p = 2y0-2 + gj/va and q = 2j/Sl+2 + j/c„+i + 2j/Cu+2. The ys are the site fractions, i.e.
the fraction of the species s in a particular sublattice.
The last termEG^T is a ternary contribution to the excess Gibbs energy of the liquid
which contains the parameters optimized in this work :
EGt„ = 2/s,+22/cu+22/o-^sr+2,Cu+2o^+ 2/s.+22/cu+12/o-^41r+i,Cu+1.o-2 (n-4-2)
The parameters £s'|+2 Cu+i 0_2<uid L&+2 Ca+2 Q_2 represent interactions between SrO
and Cu20, and SrO and CuO respectively.
4 Data Assessment and Parameters Optimization
The optimization of the thermodynamic parameters as well as all calculations made
from the set of optimized Gibbs energies were performed with the Thermo-Calc data¬
bank system [85Suu]. All parameters can be optimized simultaneously consideringthermodynamic and phase diagram data, and the numerical weight of each data pointcan be adapted in order to obtain an optimal description in all parts of the system.The use of thermodynamic modelling is of considerable help when large discrepancies
reflecting systematic errors are found between the various experimental data. Several
combinations of data can be tested for compatibility until a satisfying agreement for
the whole system is achieved. The data which were found compatible with each other
system.
Cu-0
the
by
give
nare
reactions
these
as
listed
are
data
no
|
Fig.II.4.4.
in
shown
and
electrolyte
Zr02
the
with
measured
reaction
Effective
f
40.08T
-68975+
1049-1188
Zr02
[92S
uz]
46.99T
+-68998
900-1280
Zr02
[92Jac]
98.2T
+-147300
992-1196
Zi02
[92S
uz]
+91.6T
-146396
900-1280
Zr02
[92Jac]
100.63T
+-176831
900-1285
Zr02
[92J
ac]
93.8T
-167250+
1020-1220
Zr02
[90Alc]
Cu20
0.5
+SrCu02
«•
02
0.25
+SrCu202
SrCuOj
«
02
0.5
+SrCu202
+Sr2Cu03
02
0.5
Sr2Cu03
2o
SrCu202
+SrO
3
9.
fSrCu202
+*
02
1.31T
--16060
975-1235
SrF2
[92Jac]
4.2T
--12000
1076-1266
SrF2
[90K
ov]
0.98T
-
-16210
900-1275
Zr02
[92Jac]
8.62T
--4478
1010-1370
Zr02
[91B
ou]
2.28T
--14740
950-1225
Zr02
[90Alc]
SrCu202
<-¥
tCu20
+(SrCu202)
<->
02
0.5
+Cu
2+
(SrC
u202
)6.
Cu
+SrO
5a.
C+
SrO
[J/m
ol]
AG
[K]
TEl
ectr
olyt
eRef.
Reaction
Cell
measurements.
emf
bystudied
reactions
state
solid
ofenergy
Gibbs
II.4.4:
Table
system.
Cu-0
the
by
givenare
reactions
these
as
listed
are
data
no
|Fig.II.4.4.
in
shown
and
electrolyteZr02
the
with
measured
reaction
Effective
f
204.5T
+-584420
140.75T
-457919+
-641060+246.0T
148.41T
-
+6500
124.1T
-
-193
51.9T
-
-163800
-192150+129.53T
221.93T
-310618+
108.39T
-163608+
975-1210
1058-1257
1020-1180
975-1235
1065-1247
1030-1180
1017-1216
900-1225
1085-1247
SrF2
SrF2
CaF2
SrF2
SrF2
CaF2
Zr02
Zr02
SrF2
-113559+157.7T
1046-1215
SrF2
[90Skol]
0.68T
+-8120
4.863T
-12929+
16.74T
+-36030
975-1260
1032-1184
1035-1180
SrF2
SrF2
CaF2
[92Jac][90Skol][90Alc]
[92Jac][90SkolJ[90Alc]
[92Suz][92Jac][90Skol]
[92Jac][90Skol][90Alc]
Sri4Cu24041
O
02
1.5
+CuO
24
+SrO
14
15.
02
1.5
+SrCu02
24
+>
SrO
10
+Sr14Cu2404i
14.
Sr14Cu2404i
•fi
02
1.5
+lOCuO
+SrCu02
14
13.
02
0.5
+SrCu02
34
<->
Sr2Cu03
10
+Sr14Cu2404i
12.
Sr2Cu03
«SrCu02
+SrO
11.
%CuO
2+
(SrCu02)
<->
02
0.5
Cu20+
+(SrCu02)
10.
[J/mol]AG
[K]T
ElectrolyteRef.
Reaction
Cell
Cont'd
II.4.4:
Table
SR-CU-O 113
and which were used as a basis for the present thermodynamic description are discussed
below.
As Table II.4.3 shows, the enthalpies of formation obtained by solution calorimetry are
much more negative than the values derived from emfmeasurements. The calorimetric
results can usually be considered more reliable than values derived from emf data,
however in this case some doubts may exist. We first consider the case of Sr2Cu03 as
emf data at lower oxygen partial pressure show a relatively good agreement (see Fig.
II.4.4). Measured values for the Gibbs energy of formation of SrCi^Oj are summarized
in Table II.4.4 and shown in Fig. II.4.7. If the scattered data of Boudene are left
out a mean value of -14600(±2000) - 2.2(±1.5) • T is obtained. The Gibbs energy
of formation of Sr2Cu03 can be obtained from this value together with the data on
reaction 7 of Table II.4.4. This leads to about -28600(±5000) + 0.9(±3) • T. A much
more negative value for the enthalpy of formation of Sr2Cu03 like the one obtained in
the calorimetric studies would lead to po2 vs. T dependences in complete disagreement
with the emf studies, the entropy values or the phase diagram data. In the study
of Idemoto et al. [93Ide] the compound Sr2Cu03 is surprisingly reported with the
composition SrjgCui i03oi- Such a large deviation from the ideal stoichiometry has
not been reported in any phase diagram or crystallographic study and seems to be
unjustified. If one assumes that this sample composition consists of a mixture of
Sr2Cu03 and CuO it leads to an enthalpy of formation around —30kJ/mol which is
in good agreement with emf data. A value close to —30 kJ/mol for Sr2Cu03 together
with the other results of Idemoto et al. for SrosCai 5C11O3 and Ca2Cu03 would also
lead to an almost ideal enthalpy of mixing for the (Sr,Ca)2CuC>3 solid solution. This
thermodynamic behaviour is more compatible with other data on the Sr-Ca-Cu-0
quaternary system (see [95Ris3]). The enthalpy of formation of SrCu02 obtained by
Idemoto et al. agrees well with emfresults, while that of Sri4Cu2404i is about 20 % too
negative to be compatible with emf and phase diagram data. The excess oxygen of the
latter compound might possibly affect the measured value. In the study of Boudene
[91Bou] the heat of dissolution of SrO was not measured but directly taken from a
previous study [75K6t]. This large value greatly influences the enthalpies derived for
the ternary compounds and can be the source of a large uncertainty. The results of
Boudene could be in agreement with emf studies for both Sr2Cu03 and SrCu02 if an
error of 25% in the heat of dissolution of SrO is assumed, which is not unrealistic. In
view of these considerations we only used in the optimization the calorimetric data on
SrCu02 from Idemoto et al.
At higher oxygen partial pressure larger discrepancies are found in the emf studies.
The Gibbs energy of SrCu02 (if treated as a stoichiometric compound) is however well
constrained through entropy [90Sha] and enthalpy [93Ide] values at 298 K, the two
reactions 8 and 9 from Table II.4.4, and phase diagram data. The uncertainty in the
Gibbs energy of Si'i4Cii2404i is larger, but a compatible data set of emf and phase dia¬
gram results can be found. The emf measurements of reaction 15 from Table II.4.4 are
shown in Fig. II.4.5. The more negative results [90Alc, 92Jac] are in closer agreement
with the measured value of the enthalpy of formation [93Ide]. The data on reaction 13
is shown in Fig. II.4.6. The emf measurements of Jacob and Mathews [92Jac] are in
good agreement with the points obtained by thermogravimetry [90Li, 91Bou]. These
data are in better agreement with the entropy value [90Sha] and are consistent with
114 THE BSCCO SYSTEM
the more negative data in Fig. II.4.5. The Gibbs energy of Sr14Cu240,n was thus based
on these results.
The Gibbs energy of the liquid phase was fitted to the peritectic and eutectic temper¬atures summarized in Table II.4.1. Under the conditions of these experimental results
(in air and 1.01 bar 02) the liquid phase is expected to lie between CuO and C112O as
in the Ca-Cu-0 system. Thus two parameters were considered (Eq.2) which representinteractions between SrO and the two copper oxides. They were taken as temperature
independent as all experimental values are found in a limited temperature interval.
Table II.4.5: Optimized thermodynamic parameters for the Sr-Cu-0 system.
SrCu202
gS.CuO; = O^SrO + oqCu.O _ jggQg _ j gy
Sr2Cu03
Gsi2cu03 = 2°gSt0 + °GC"° - 27820 + 0.08 T
SrCu02
gSrCuO, = ogSrO + ogCuO _ 2274Q + % 37,
Sri4Cu2404i
GSr14Cu24041 = 14»GSrO + 24°GCu0 + L5»G02 _ g25500 + 354 T
Liquid
^.cu-o-^-129660
All parameter values are given in SI units (J, niol, K; R = 8.31451 J/niol K). For
a complete set of parameters the reader is referred to Refs. [95Risl, 94Hal, 96Ris]concerning the binary subsystems.
5 Results and Discussion
The lesulting set of optimized parameters is listed in Table II.4.5. The most globalrepresentation of the thermodynamics of the system is given by Fig. II.4.4, which is
an oxygen potential diagram showing all the calculated 3-phase equilibria. Nodes are
4-phase or invariant equilibria. The diagram is a projection (along the Sr or Cu po¬
tential) so that not all apparent line crossings actually represent 4-phase equilibria.The calculated invariant equilibria are listed in Table II.4.6 and indicated by the cor¬
responding letters in Fig. II.4.4. Fig. II.4.4 offers a good overview of the dependencebetween phase diagram, emf, and calorimetric data, and is to be kept in mind in the
following discussion of the various type of data. The data on reaction 13 of Table II.4.4
are compared to the calculated line in Fig. II.4.6, which is an enlargment of Fig. II.4.4.
The heat capacity, entropy, and enthalpy of formation of the ternary compounds at
II.4.4
Fig.
in
shown
not
are
line
dashed
the
below
listed
equi
libr
iaInvariant
liquid.
oxide
the
L2
and
liqu
idmetal
the
isLi
6•10"7
0.24
0.76
u-69
776
SrCu
+Sr
+SrO
<*
Li
4•lO"9
0.43
0.57
Li
-61
859
SrCu
+SrO
oSrCu5
+Lx
lO"13
0.79
0.21
Li
-44
1118
SrCu5
+SrO
+>
Cu
+Li
0.003
0.997
10~15
•6
Lj
-6.82
1354
SrCu202
+Cu
oSrO
+Lx
J.
0.402
0.397
0.201
L2
0.004
0.996
10~15
•8
Li
-6.66
1368
SrCu202
<+
SrO
+L2
+Lx
I.
0.391
0.446
0.163
L2
0.007
0.993
10~15
•2
Li
-6.22
1350
Cu
+L2
oSrCu202
+Li
H.
0.376
0.506
0.118
L2
-6.13
1284
Cu20
+SrCu202
«->
Cu
+L3
G.
0.370
0.532
0.098
L2
0.017
0.983
10~16
•3
Lj
-5.57
1340
Cu
+Cu20
«•
L2
+Lj
F.
0.414
0.388
0.198
L2
-3.34
1336
SrCu202
+Sr2Cu03
oSrO
+L2
E.
0.419
0.422
0.159
L2
-2.03
1274
SrCu202
+SrCu02
oSr2Cu03
+L2
D.
0.411
0.474
0.115
L2
-2.01
1194
Cu20
+SrCu02
+>•
SrCu202
+L2
C.
0.415
0.477
0.108
L2
-1.62
1192
SrCu02
«•
Cu20
+CuO
+L2
B.
0.423
0.464
0.113
L2
-1.01
1224
CuO
+SrCu02
<H>
Sr14Cu2404i
+L2
A.
x0
XCu
ZSr
[bar]
K
liquid
the
of
Composition
log(
Po2)
TReaction
116 THE BSCCO SYSTEM
298 K are listed in Tables II.4.2 and II.4.3. The heat capacities are well approximated
by the rule of Neumann-Kopp. The enthalpy values have been discussed in Section
4. The calculated enthalpy of formation of SrCu02 is in agreement with the data of
Idemoto et al. [93Ide]. The optimization however shows that the phase relations can
be well reproduced in the whole system if the enthalpy of formation of Sr2Cu03 and
Sr14Cu24C>4i are less negative than the reported calorimetric values.
The Gibbs energy of formation of SrCu202 is shown in Fig. II.4.7, the one of Sr^C^C^iis plotted in Fig. II.4.5. These optimized function are closer to the more negative re¬
sults so that the calculated properties of Sr2Cu03 and Si'i4Cu2404i come closer to the
calorimetric data on the enthalpy of formation and the entropy at 298 K.
The calculated phase relations between the ternary compounds at 1173 K are shown
in Fig. II.4.3. They are in agreement with experimental studies [92Suz, 92Jac]. The
composition of the eutectic oxide liquid is indicated by a cross. This eutectic reaction
correspond to the reaction B of Table II.4.6.
The calculated SrO-CuO^ sections in air and 1.01 bar 02 are shown in Fig. II.4.1
and II.4.2. The calculated and experimental melting temperatures are compared in
Table II.4.1. The calculated values are in good agreement with the experimental data.
It is to note that the thermodynamic properties of the liquid have been adjusted using
only two parameters. Further improvement of the model description to new data may
be obtained with parameters influencing the temperature dependence of the Gibbs
energy of the liquid.
Finally all equilibria involving SrCu02 can be slightly shifted due to small variation in
the oxygen content of this compound.
6 Conclusion
The experimental data on the phase relations and the thermodynamics of the Sr-Cu-
O system have been reviewed and assessed, and a consistent set of thermodynamicfunctions has been presented. Large discrepancies are found in the reported thermo¬
dynamic data and the results which are probably more reliable have been pointed out.
The optimized values of the thermodynamic properties should have a good reliabilityas they are compatible with phase diagram data in the whole system.
Of further experimental interest would be the measurement of enthalpy increments
and a redetermination of the enthalpy of formation for the ternary compounds. The
thermodynamic properties of the liquid should also be investigated, especially at lower
oxygen partial pressure.
7 Acknowledgments
The authors would like to thank Piof. R. O. Suzuki for valuable discussions on the
experimental data.
SR-CU-O 117
-10 -8 -6 -4 -2
Log[P0 (bar)]
Figure II.4.4: Sr-Cu-0 oxygen potential diagram. The calculated oxygen partial
pressures in S-phase fields are compared to emf and phase diagram data. The 4-phase
invariant equilibria are indicated with letters according to Table 2.
-150
-200
-500
-550
[90Sko]* [90AIO]o I
500 1000
Temperature [K]
1500
Figure II.4.5: Gibbs
and 02.
of formahon of Sri4Cii2404i from the component oxides
118 THE BSCCO SYSTEM
o
7.0
7.5
8.0
8.5
9.0
9.5
DTA-TG
a [90Li]
0[91Bou]
EMF
A [90Sko]
I I
Sr14Cu2404, = L + SrCu02 + 02^
Sr,40u24O4] + OuO = L + 02 —
SrCuO, + CuO = L + O- -
-3 -2 -1
Log[P02 (bar)]
Figure II.4.6: Stability limits of Sr^Ch^O^.
-10
-11
-12
--13
cM5
S-16-CD
<r-i7
-18
-19
-20
[90Kov]O [90AIC]A [91Bou]O [92Jac)
500
A
A
15001000
Temperature [K]
Figure II.4.7: Gibbs energy of formation o/SrCu202 from the component oxides.
SR-CU-O 119
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SR-CU-O 121
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[92Mil] O. Milat, G. van Tendeloo, S. Amelinckx, M. Mehbod, and R. Deltour, "The
Incommensurate Structure of (Sr, Ca^Ci^O-u: A Study by Electron Diffrac¬
tion and High-Resolution Micioscopy", Acta Crystallogr., A48, 618-625
(1992).
[92Suz] R. O. Suzuki, P. Bohac, and L. J. Gauckler, "Thermodynamics and "Phase
Equilibria in the Sr-Cu-0 System", J. Am. Ceram. Soc, 75(10), 2833-2842
(1992).
[92Vor] G. F. Voronin, "Thermodynamics of High-Temperature Superconducting Ma¬
terials", Pure Appl. Chem., 64(1), 27-36 (1992).
[93Ara] A. V. Arakcheeva and V. F. Shamrai, "Averaged Crystal Structure of In¬
commensurate (Ca7Sr7)(Cu23 62Bio38)041", Crystallogr. Rep., 38(1), 18-25
(1993).
[93Ide] Y. Idemoto, K. Shizuka. Y. Yasuda. and K. Fueki, "Standard Enthalpies of
Formation of Member Oxides in the Bi-Sr-Ca-Cu-0 System", Physica C,
211, 36-44 (1993).
[93Jen] A. F. Jensen, F. K. Larsen, lb. Johannsen, I. Cisarova, K. Maly, and
P. Coppens, "The Four-Dimensional, Incommensurately Modulated, Com¬
posite Crystal Structure of (Bi,Sr,Ca)10Cui7O29 at 292 and 20 K Refined
Including Satellite Reflections", Acta Chem. Scandmavica, 4% 1179-1189
(1993).
[94Hal] B. Hallstedt, D. Risold, and L. J. Gauckler, "Thermodynamic Assessment of
the Copper-Oxygen System", J. Phase Equilibria. 15{5). 483-499 (1994).
[94Hir] Z. Hiroi and M. Takano, "High-Pressure Synthesis as a Promising Method to
search for New Materials", Physica C, 235-240, 29-32 (1994).
122 THE BSCCO SYSTEM
[94Mat] Y. Matsushita, Y. Oyama, M. Hasegawa, and H. Takei, "Growth and Struc¬
tural Refinement of Orthorhombic SrCu02 Crystals", J. Sohd State Chem.,
114, 289-293 (1994).
[94Mit] J. F. Mitchell, D. G. Hinks, and J. L. Wagner, "Low-Pressure Synthesis of
Tetragonal Sr2Cu03+a. from a Single-Source Hydroxometallate Precursor",
Physica C, 227, 279-284 (1994).
[94Nev] M. Nevfiva and H. Kraus, "Studyof Phase Equilibria in the Partially Open
Sr-Cu-(O) System". Physica C, 235-240, 325-326 (1994).
[94Tak] M. Takano, "SrCu02 and Related High-Pressure Phases", J. Supercond., 7
(1), 49-54 (1994).
[94Uke] K. Ukei, T. Shishido, and T. Fukuda, "Structure of the Composite Crystal
[Sr2Cu203][Cu02]«(s = 1.436)", Acta Crystallogr., B50(l), 42-45 (1994).
[95Risl] D. Risold, B. Hallstedt, and L. J. Gauckler, "The Sr-0 System", Calphad
(1995). submitted.
[95Ris2] D. Risold, B. Hallstedt, and L. J. Gauckler, "Thermodynamic Assessment of
the Ca-Cu-0 System", J. Am. Ceram. Soc, 75(10), 2655-61 (1995).
[95Ris3] D. Risold, B. Hallstedt, and L. J. Gauckler, "Thermodynamic Modelling and
Calculation of Phase Equilibria in Sr-Ca-Cu-0 System at Ambient Pres¬
sure", J. Am Ceram. Soc. (1995). submitted.
[96Ris] D. Risold, B. Hallstedt, L. J. Gauckler, H. L. Lukas, and S. G. Fries, "Ther¬
modynamic Optimization of the Ca-Cu and Sr-Cu Systems", Calphad, 20
(1996). to be published.
CA-CU-O 123
II.5 The Ca-Cu-O System
Published in J. Am. Ceram. Soc. 78 [10] (1995) 2655-61.
Thermodynamic Assessment of the Ca—Cu-O System
Daniel Risold, Bengt Hallstedt, and Ludwig J. Gauckler
Nonmetallic Materials, Swiss Federal Institute of Technology,
Sonneggstr. 5, CH-8092 Zurich, Switzerland
ABSTRACT The experimental data on the Ca-Cu-0 system at 1 bar to¬
tal pressure have been reviewed and an optimized thermody¬
namic description based on previous assessments of the bi¬
nary systems is presented. Three ternary oxides are found
which do not show significant solid solution and have been
treated as stoichiometric compounds. The liquid exhibits a
miscibility gap as in the Cu-O binary. Only the copper oxide
liquid extends into the ternary field and has been modelled
with ternary parameters. A continuous thermodynamic de¬
scription of the liquid phase from the metal to the oxide part
has been obtained using the two-sublattice ionic liquid model.
The set of optimized parameters leads to a consistent and ac¬
curate thermodynamic description of the Ca-Cu-0 system at
1 bar total pressure. Calculated CaO-CuOj, phase diagrams
in air and 1.01 bar O2, oxygen potential diagram, isothermal
section at 1573 K. and various thermodynamic properties are
shown and compared with experimental data. In particular
the relative amounts of Cu+1 and Cu+2 in the oxide liquid
have been calculated in air and 1.01 bar 02.
1 Introduction
The purpose of the present study is to obtain a consistent thermodynamic description
of the Ca-Cu-0 system at 1 bar total pressure, which can allow the evaluation of
phase equilibria and thermodynamic properties in the multicomponent superconduct¬
ing cuprate systems.
The phase relations in the Ca-Cu-0 system are to a large extent characterized by the
high stability of CaO. The system can be divided into an oxide and a metal part along
the line CaO-Cu20 where the the oxygen partial pressure changes by about a factor
of 104. The metal part of the system is itself clearly separated by the CaO-Cu line
where the oxygen partial pressure changes by a factor larger than 1025. The metallic
124 THE BSCCO SYSTEM
phases are all in equilibrium with CaO. The liquid phase exhibits a miscibility gap
which results mainly from a reciprocal miscibility gap between Ca, Cu, Cu20, and
CaO on one hand and from the miscibility gap in the Cu-0 binary on the other hand.
The metallic liquid does not show a significant solubility in the ternary, it is contained
along the Ca-Cu binary and the Cu-0 binary, whereas the copper oxide liquid shows
an extended solubility towards CaO. Three ternary oxides are found between CaO und
CuO. but in contrast to the Ba-Cu-0 and Sr-Cu-0 systems, no ternary compoundwith copper in monovalent state is found in the Ca-Cu-0 system.
The experimental information on the metal part of the ternary system is limited to
few data points concerning the copper-rich liquid. These properties are so stronglydetermined by the properties of the binary systems that no attempt was made to
influence this description with ternary parameters. In the following the experimentaldata relevant to the ternary system are reviewed and assessed. Gibbs energy functions
for the three ternary oxides and interaction parameters in the oxide liquid have been
optimized. All calculations were performed with the help of the Thermo-Calc software
package [85Sun]. This evaluation is based on previous assessments of the Ca-0 [93Sel],Cu-0 [94Hal], and Ca-Cu [96Ris] systems.
2 Experimental data
The phase relations in the CaO-CuO-Cu20 part of the system have been studied bythermal analysis [65Sch, 66Gad. 90Lia] and X-ray diffraction (XRD) [90Lia, 89Rot,
90Sko, 91Rot, 93Mat, 94Suz, 94Tsa] mainly in air and 1.01 bar 02. Three ternaryoxides have been reported to be stable at ambient pressure : Ca2Cu03, CaossCuOi 93,
and CaCu203. Electron probe microanalysis (EPMA) [93Mat, 94Tsa], XRD [89Rot,91Rot], hydrogen reduction methods [93Mat, 91Hal], atomic absorption spectroscopy
[93Ped], iodometric titration and equilibrium pressure measurements [92Krii] have
been used to study the compositions of the ternary phases. No report of noticeable
solubilities of Ca in CuO and Cu20 or of Cu in CaO could be found, so that these
oxides were treated as stoichiometric phases. Their thermodynamic description is en¬
tirely given by the binary assessments [93Sel, 94Halj. The composition of the ternary
compounds and of the liquid are discussed below.
The thermodynamic properties of the ternary oxides have been partially investigated
by solution calorimetry [93Ide], diffeiential scanning calorimetry (DSC) [92Krti], and
electromotive force (einf) measurements using various solid electrolyte galvanic cells
[93Mat, 94Suz]. The thermodynamic properties of the oxide liquid have been studied
by equilibrium pressure [93Ped] and emf measurements [860is].
2.1 Ca2Cu03
Ca2Cu03 was first observed in thermogravimetric measurements of decompositioncurves by Schmahl and Minzl [65Sch], who found it to be in equilibrium with CaO and
Cu20 at 1273 K in 7370 Pa 02. The stability of Ca2Cu03 has been studied by XRD and
thermal analysis in air [66Gad, 90Lia, 91Rot] and 1.01 bar 02 [66Gad, 91Rot, 94Tsa],and by emf measurements between 900 and 1250 K [93Mat, 94Suz]. All authors found
that Ca2Cu03 is stable at high temperature and melts incongruently. At lower tem¬
peratures it decomposes into CaO and Caos3CuOi93 [91Rot, 93Mat]. Roth et al.
[91Rot] mentioned that Ca2Cu03 does not form at 973 K in 1.01 bar 02 but that
CA-CU-O 125
CaO and Caos3CuOi93 are in equilibrium. Mathews et al. [93Mat] have studied this
decomposition reaction using a CaF2 galvanic cell.
The crystal structure of Ca^CuOs was determined from XRD data by Teske and
Muller-Buschbaum [70Tes], it has an orthorhombic symmetry and is isostructural with
S12C11O3. The oxygen content of Ca2Cu03 has been investigated by a H2-reduction
method [91Hal] and by iodometric titration and equilibrium pressure measurements
[92Krii]. Halasz et al. [91Hal] measured the consumption of hydrogen for a total re¬
duction of copper to the metallic state during heating between 573 and 873 K and
obtained an oxygen content of 3.09 ± 0.1. Kriiger et al. [92Krii] report an oxygen
content of 2 965 at 1073 K from equilibrium pressure measurements and a value for
the oxygen nonstoichiometry not significantly higher than experimental errors from
iodometric titration at 673 K.
The specific heat of Ca2Cu03 has been measured at 350 K using DSC by Kriiger et al.
[92Krii], who found the value cp = 136.1 J/(mol K). The enthalpy of formation has been
measured by Idemoto et al. [93Ide] using solution calorimetry and reaches —7800 ±800
J/mol at 298 K. The Gibbs energy of formation between 900 and 1250 K can be derived
from emf measurements [93Mat, 94Suz]. The equilibrium oxygen partial pressure in
the region CaO-Ca2Cu03-Cu20 measured by Suzuki et al. [94Suz] and Mathews
et al. [93Mat] agree fairly well at the higher temperatures of measurement, but the
difference increases with decreasing temperature. This discrepancy in the temperature
dependence of the emf values leads to large differences in the values for the enthalpy
and entropy of formation which they derived from linear fitting of their data. The
results of Mathews et al. are found to be closer to the calorimetric data than those of
Suzuki et al.
2.2 Ca0 833CllOig3
This compound, more generally written as Cai_xCu02-{, was first leported by Roth
et al. [89Rot, 91Rot] who found it to be stable at low temperature and to decompose
into Ca2Cu03 and CuO with release of oxygen at higher temperature. The crystal
structure of Cai_xCu02_j has been studied extensively by means of X-ray diffraction
[90Sie, 91Bab], neutron diffraction [91Bab], and electron diffraction and microscopy
[92Mill, 92Mil2]. The crystal structure is closely related to that of NaCu02 but with
partial occupancy of the Ca sites. Differences in the Ca ordering have been found to
cause various modulated superstructures, and commensurate as well as incommensu¬
rate diffraction patterns have been observed. In the earlier crystallographic studies,
ideal stoichiometrics have been proposed ranging from x = 0.143 (i.e. Ca:Cu=6:7)
[91Bab] to x = 0.2 (i.e. Ca:Cu=4:5) [90Sie]. In the latest studies, Milat et al.
[92Mill, 92Mil2] identified two stacking variants of the Ca substructure and their twin
related structures whose various arrangements lead to the modulation of the Cu-0
substructure. They suggest an ideal commensurate structure with x = 0.167 (i.e.
Ca:Cu=5:6) and an incommensurability due to deviations from this composition.
The Ca:Cu ratio in samples of Ca!_xCu02-« has been investigated by XRD [89Rot]
andEPMA [93Mat]. Roth et al. [89Rot] measured Ca contents of x=0.172 for powder
samples annealed at 973 K in 1.01 bar 02 and of x=0.2 for flux grown crystals. Mathews
et al. [93Mat] also found a value of x=0.172 for powder samples annealed at 1073 K
in 1.01 bar 02. The oxygen content has been studied by Mathews et al. [93Mat]
126 THE BSCCO SYSTEM
from the weight change under Ha-reduction and by emf measurements as function of
oxygen partial pressure. Both methods lead to an oxygen content at 1073 K equal to
1.93 ± 0.01. The emf measurements indicate that the oxygen content does not change
significantly with oxygen partial pressure.
The thermodynamic properties of Ca1_xCu02_{ have been studied in several emf cells
[93Mat]. These experimental data allow the direct determination of the Gibbs energy of
formation of Ca!_xCu02-,s and furthermore relates it to that of Ca2CuC>3 through the
reactions Caj-jCuOa.,) <-» Ca2Cu03 + CuO + 02 and Ca2Cii03 + 02 o Ca1_3£Cu02_i
+ CaO. The reaction temperatures for Ca1_xCu02_; <-> Ca2Cu03 + CuO + 02 in air
and 1.01 bar 02 measured by emf [93Mat] are in good agreement with the results from
XRD studies [91Rot].
2.3 CaCu203
CaCu203 was first obtained and characterized by Teske and Miiller-Buschbaum [69Tes]from resolidification of partially molten samples heated between 1073 and 1373K, in
air and 02. The crystal stiucture has an orthorhombic symmetry [69Tes]. The same
phase relations involving CaCii203 have been reported from XRD studies in air [89Rot,91Rot] and in 1.01 bar 02 [94Tsa]. CaCu203 is stable in a narrow temperature range.
It forms at high temperatures from Ca2Cu03 and CuO, and decomposes just above
the eutectic temperature into Ca2Cu03 and liquid. The eutectic reaction between
CaCu203 and CuO was found at 1285 K in air [91Rot] and 1318 K in 1.01 bar 02
[94Tsa]. The compound CaCu203 was not observed in experimental studies based on
thermal analysis, but a eutectic reaction between Ca2Cu03 and CuO was reported.This eutectic temperature was found at 1286 K [66Gad] and 1273 K [90Lia] in air
and 1325 K [66Gad] in 1.01 bar 02.
The composition of CaCu203 has been investigated using EPMA by Tsang et al.
[94Tsa] who found a slightly higher Cu content than the ideal stoichiometry and which
can be expressed by the formula Ca0 9C112103. The oxygen content is not expected to
deviate significantly from the ideal stoichiometry. As Suzuki et al. [94Suz] pointed out,
the formation temperature does not seem to depend on the oxygen partial pressure, so
that CaCu203 has a negligible oxygen nonstoichiometry at this temperature.
The thermodynamic properties of CaCu203 are less well known. The enthalpy of
formation has been measured by Idemoto et al. [93Ide] who found a value equal to
-4100 ± 1800 J/mol at 298 K.
'
2.4 The liquid phase
The melting relations and the composition of the oxide liquid have been studied at lower
oxygen partial pressures across the miscibility gap [860is, 68Kux] and at constant
oxygen partial pressure in air [89Rot, 91Rot, 93Ped] and 1.01 bar [94TsaJ.
At high temperature by decreasing the oxygen partial pressure, the composition of the
oxide liquid approaches the CaO-Cu20 line. The lowest temperature at which this line
is reached represents the eutectic point of the CaO-Cu20 quasibinary and correspondsto the 4-phase invariant equilibrium CaO+Cu20 •«-> Li+L2. (In the following L^ and
L2 stand for the metal and the oxide liquid respectively.) The melting temperature of
CaO-Cu20 mixtures was first investigated by Waitenberg et al. [37War] who observed
the eutectic reaction at 1413 K at a Ca content in the liquid of about xca=0.20.
CA-CU-O 127
Kuxmann and Kurre [68Kux] measured the composition of the two liquids in the 3-
phase equilibrium Lx-L2-CaO as function of the temperature between 1350 and 1750
K. They observed the reaction CaO+Cu20 o Lj+L^ at 1419 K where the Ca content
in L2 reached xCa=0.08. Oishi et al. [860is] measured the composition of the two
liquids across the miscibility gap at 1573 K as function of the CaO content. Their
value for the CaO content at which the saturation occurs is in excellent agreement
with the data of Kuxmann and Kurre.
The melting relations in air and in 1.01 bar 02 have been described in previous sections.
The Ca:Cu ratio in the eutectic liquid in air has been estimated from XRD [91Rot] to
be about 20:80 ±5%. The composition of the oxide liquid along the air isobar at 1573
K has been investigated by atomic absorption spectroscopy by Peddada and Gaskell
[93Ped] who observed the CaO saturation at xCa=0.24. The composition of the liquid
in 1.01 bar 02 at various temperatures and Ca:Cu ratios has been measured by Tsang
et al. [94Tsa] using EPMA.
The thermodynamic properties of the oxide liquid have been studied at 1573 K as func¬
tion of the CaO content. Oishi et al. [860is] measured the equilibrium oxygen partial
pressure across the miscibility gap, while Peddada and Gaskell [93Ped] determined
the activity of copper along the air isobar. Their results at xca=0 can be compared
to the values calculated from the assessed Cu-0 system [94Hal]. The data of Oishi
et al. show a good agreement with the assessed binary values ( [860is]: xc„=0.703,
log(P0J=-3.48, [94Hal]: xCu=0.722, log(P0,)=-3.46) whereas a larger discrepancy
is found with the results of Peddada and Gaskell ( [93Ped]: xc,,=0.654, aCu=0.197,
[94Hal]: xCu=0.634, aCu=0.168).
3 Thermodynamic description
3.1 The ternary oxides
The three ternary oxides are treated here as stoichiometric compounds, as they do not
exhibit significant solid solutions and as very little is known on possible small deviations
from stoichiometry. The compositions of Ca2Cu03 and CaCu203 are given by the ideal
stoichiometry according to the structural data. The composition of Cai_xCu02_* was
choosen based on the Ca:Cu ration proposed in the crystallographic study of Milat
et al. [92Mil2] and the oxygen content measured by Mathews et al. [93MatJ and
is expressed by the formula Caos3CuOi93. The molar Gibbs energies of the ternary
oxides are refered to the binary oxides CaO and CuO and given by :
G0a2cu03 = 20GCa0 + °GCu0 + ^c^cuo, + Bca.cuo, T (H.5.1)
+ Cc»2cao3Tln{T)G<3ao83Cu0193 = 0.833°GCaO + °GCu0 + 0.0485°G°2 (II.5.2)
+^Ca0 83CuOi ,3+ -Scao 83C11O, 93
T
GOaCu203 = "G^^'G^+^CaCu^+BcaCu^T (H.5.3)
where "G* is the Gibbs free energy of phase 4> and A$ to Cj, are parameters to be
optimized.
3.2 The liquid phase.
The thermodynamic modelling of the liquid phase is mainly influenced by the Cu-0
128 THE BSCCO SYSTEM
system, where the liquid shows complete miscibility at high temperature and separates
into a metallic and an oxide part at lower temperature. These thermodynamic prop¬
erties can be modelled equally well using a sublattice model or an association model
[94Hal]. Both approaches can be made mathematically equivalent in the binary system,
differences might arise when extrapolating to higher order systems. The two-sublattice
ionic liquid model [85Hil, 91 Sun] which has been applied to the Cu-0 system [94Hal] is
extended here to the ternary system with the formula (Ca+2, Cu+1, Cu+2)p(Va_<1,0-2),.The charged vacancies are introduced as a foimal way to enable a continuous descriptionfrom the metallic to the oxide liquid and are not to be understood as a structural repre¬
sentation. The numbers p and q vary with composition in order to maintain electroneu-
trality and are given by the relations p = 2(/0-> + 92/Va and q = 2j/Ca+2 + (/cu+1 + 22/cu+2>where ys is the site fraction of s, i.e. the fraction of the species s in a particularsublattice.
The molar Gibbs energy of the liquid is given by :
<?»" = «2/Ca+2#Va0G'cqa+2 Va+ 2/Ca+2y0-2aG^+i 0^
+ <?2/C,l+1 2/Va°G!Cu+1 Va+ ^Cu+^O-^G'c'+l c-2
+ 92/Cu+2i/Va0Ggqu+2 Va+ 2/Cu+2«/o-2°Ggqu+2 0_2
+ pRT[|/Ca+2 •in(2/Ca+i) + s/cu+^Msfcu+O + ycu+'-Hyc^)}
+ 9RT[yVa-ln(j/va) + yo-*-lHVo->)]
+E Gcl-o + E Gcl-o + * Gcl-c +
E< (H.5.4)
where the functions "Gjy1 and EG^lB are directly taken from the respective binary
optimizations [93Sel, 94Hal, 96Ris]. The "G/va represent the Gibbs energies of the
pure liquid metallic elements while the "G/o-j represent the Gibbs energies of the pure
liquid oxide compounds. The EG^_B represent the main contributions to the excess
Gibbs energy based on extrapolations from the binary subsystems.E G^ is the ternary
contribution to the excess Gibbs energy of the liquid which contains the parameters
optimized in this work :
SGxer = yCa+22/Cu+22/0-iic'i+2)Cu+20_i + !fc»+2!'Cu+12/0-2£c'a+i,Cu+I.0-->+ 2/Ca+22/Cu+12/0-^Vai1ca+2Cu+l 0-2>Va (II.5.5)
The parameters L^+2 0u+i 0 2and L'^+2 Cu+2 0_2 represent interactions between CaO
and CU2O, and CaO and CuO respectively The parameter L^+2 Cu+i 0„2 Vais a recip¬
rocal interaction between the four corners Ca, Cu, CaO, and CU2O.
4 Optimization of parameters
The optimization of the thermodynamic parameters as well as all calculations made
from the set of optimized Gibbs energies were performed with the Thermo-Calc data¬
bank system [85Sun]. All parameters can be optimized simultaneously consideringthermodynamic and phase diagram data, and the numerical weight of each data pointcan be adapted to the relative experimental uncertainties. In the following the choice
of parameters is explained based on the available data.
CA-CU-O 129
The parameters A& and S^, of the ternary oxides have be determined from the corre¬
sponding measurements of the enthalpies of formation [93Ide], the Gibbs energies of
formation [93Mat], and the various invariant equilibria in air [66Gad. 90Lia, 91Rot]
and 1.01 bar 02 [66Gad, 91Rot, 94Suz, 94Tsa]. For Ca2Cu03 the measured value of
the specific heat at 350 K differs by 7.7 J/molK from the Neumanu-Kopp value, i.e.
the linear combination of the values of the pure oxides. This difference is significant
and justifies the introduction of the parameter CcO2Cu03-
The oxide liquid is mainly found in the triangle CaO-Cu20-CuO. so that its thermody¬
namic properties are expected to be satisfactorily described using the two parameters
£<^+2 Cu+1 0_2and L^+2 Cu+2 0_2
•Their contribution to the excess Gibbs energy is
proportional to the concentration of Cu+1 respectively Cu+2 in the liquid. Thus only
I^+2 Cu+i 0_2will affect the thermodynamic properties of the oxide liquid in equilib¬
rium with the metallic part of the system, while both parameters will influence the
calculated melting relations in the CaO-CuOj. phase diagram at higher oxygen par¬
tial pressure such as in air and in 1.01 bar 02. A linear temperature dependence for
^Ca+2 Cu+1 o-2can been considered since the data of Kuxmann and Kurre [68Kux]
cover a relatively large temperature interval. In air and 1.01 bar 02 only data on the
eutectic and peritectic temperatures [66Gacl, 90Lia, 91Rot, 94Tsa] have been consid¬
ered. The composition data of Peddada and Gaskell [93Ped] have not been used in
the optimization since they aie not compatible with the adopted Cu-0 description,
while the compositions measured by BPMA [94Tsa] are too scattered to be used in
a quantitative evaluation. The eutectic and peritectic temperatures are all found in a
limited temperature range only and therefore L£+i Cu+2 0_2was taken as temperature
independent. Calculations using only these two ternary parameters lead to oxygen
concentrations in the oxide liquid in equilibrium with the metal liquid which are larger
than experimentally reported by Oishi et al. [860is]. A good agreement with their
experimental results could be obtained by introducing the parameter L^2 Cu+i 0_2 v
which influences the reciprocal miscibility gap.
5 Results and Discussion
The resulting set of optimized parameters is given in Table II.5.1.
The various experimental data on the ternary oxides are compared with the calculated
values in Table II.5.2 and Fig. II.5.1 and II.5.2. The calculated enthalpy and entropy
of formation at 298 K are listed in Table II.5.2. The values for AiJ298 of Ca2Cu03
and of CaCu203 were weighted in the optimization in such a way that the optimized
values lie in the uncertainty range of the calorimetric measurements and lead to the
best possible fit of the emf measurements and the phase diagram data.
Fig. II.5.1 shows the oxygen potential diagram, where the lines represent three-phase
equilibria and the crossings four-phase (or invariant) equilibria. The diagram is a pro¬
jection (along the Ca or Cu potential) so that not all apparent line crossings actually
represent four-phase equilibria. The calculated invariant equilibria are listed in Ta¬
ble II.5.3 and indicated by the corresponding letters in Fig. II.5.1. Even though the
calculations were all made at 1 bar total pressure in this work, an extrapolation up to
an oxygen partial pressure of 100 bar is included in the diagram, where the influence of
the pressure on the condensed phases can still be assumed to be small. The calculated
130 THE BSCCO SYSTEM
Po2(T) curves are compared to the phase diagram data obtained at constant Po2 and
to the emf measurements performed using Zr02-electrolyte. The measured Gibbs en¬
ergy of reactions studied by emf measurements using CaF2 electrolyte are compared to
the calculated lines in Fig. II.5.2.
The calculated CaO-CuOj sections in air and 1.01 bar 02 are compared to the exper¬
imental data in Fig. II.5.3 and Fig. II.5.4 and the corresponding invariant equilibriaare listed in Table II.5.4 and Table II.5.5 lespectively.
This optimized thermodynamic description of the ternary compounds shows that a
good agreement can be found with the calorimetric values, the emf measurements and
most phase diagram data, and that no major incompatibilities arise between these
results. Some minor divergences are however observed between the thermodynamicresults and the phase diagram data :
1) During the optimization it was found difficult to have simultaneously the reported
phase relations around CaCu203 [91Rot, 94Tsa] and AH2g% values close to the calori¬
metric data [93Ide]. These results can be compatible only if the Gibbs energy of the
reaction Ca2Cu03 + CuO = CaCu203 is very small. This in consequence leads to
almost identical Po2(T) curves for the 3-phase fields involving CaCu203 + Ca2Cu03and CaCu203 + CuO as can be seen in Fig. II.5.1, and in particular the eutectic
reaction and the decomposition of CaCu203 cannot be distinguished.
2) The temperature difference between the reported decomposition temperatures of
Ca2Cu03 and CaCu203 [66Gad, 91Rot, 94Tsa] increases by about 20 K between air
and 1.01 bar 02, whereas it stays almost constant for the calculated values. Especiallyfor Ca2Cu03 a noticeable difference is observed in the dependence of the decomposition
temperature on oxygen partial pressure (see L2-Ca2Cu03-CaO line in Fig. II.5.1).This situation cannot be significantly improved by adding further parameters for the
liquid phase since these equilibria are found in a narrow temperature and composition
range. A closer fit to the phase diagram data may only be obtained through a change in
the temperature dependence of the Gibbs energy of Ca2Cu03 or CaCu203. We found
however that no such changes were possible without losing the correct phase relations
or getting values for the thermodynamic properties of the ternary oxides far from the
reported calorimetric and emf data.
The thermodynamic description of the liquid is based on relatively few experimentalobservations. At lower oxygen partial pressure the experimental studies are in goodagreement among each other and with the calculated values. The Ca content of the
oxide liquid in equilibria with CaO and the metal liquid is shown in Fig. II.5.5. Fig.II.5.6 shows the isothermal section CaO-Cu-CuO at 1573 K. The calculated composi¬tion of the oxide liquid across the miscibihty gap is compared to the data of Oishi et
al. [860is] in Fig. II.5.6, and the oxygen partial pressure in the oxide liquid across the
miscibihty gap at 1573 K is plotted in Fig. II.5.7. At higher oxygen partial pressure the
thermodynamic properties of the liquid are determined by the parameter L^+1 „+2 0_2
which was fitted to the eutectic and peritectic temperatures only. The calculated equi¬librium compositions of the liquid lie in the uncertainty range of the data of Roth et al.
[91Rot] for air and are in agreement with Tsang et al. [94Tsa] for 1.01 bar 02. This
assessment deviates from the results of Peddada and Gaskell [93Ped]. The calculated
relative amounts of Cu+1 and Cu+2 in the oxide liquid in air and in 1.01 bar 02 are
CA-CU-O 131
presented in Fig. II.5.8 and II.5.9.
6 Conclusion
A consistent thermodynamic description of the Ca-Cu-0 system has been presented,
which shows a good agreement with most calorimetric, emf, and phase diagram data.
The optimized set of tliermodynamic parameters has been obtained from relatively
few experimental studies, but which cover very complementarily a wide range of tem¬
peratures and oxygen partial pressures. Reliable calculations and extrapolations of
thermodynamic properties and phase equilibria may thus be expected. Examples have
been given ofsome properties which can then be calculated such as the relative amounts
of Cu+1 and Cu+2 in the oxide liquid at various oxygen partial pressure. Further ex¬
perimental studies, especially on the oxygen content of the liquid as function of oxygen
partial pressure, would contribute to the improvement of this description.
132 THE BSCCO SYSTEM
Table II.5.1: Optimized thermodynamic parameters for the Ca-Cu-0 system.
Liquid
(Ca+2, Cu+1, Cu+'yCT2, Va-q)gp = 2y0-2 + 52/va, q = 3?/Ca+i + yCu+i + 2yCu+2
L^J^o., = -109630
ic^.cu+'.o-.v. = -39600°
Ca2Cu03
Gca2cu03 = 2"GCM + 0GCuO - 7565 + 11.255T - 0.89Tln(T)
Cao 833CUO1 93
GCao ssCud 93= o.833°GCa0 + °GCu0 + 0.0485°G°2 - 12558 + 10.61 T
CaCu203
GCaCu2o3 _ oGCaO + 2°cCu0 - 3193.3 + 1.983 T
All parameter values are given in SI units (J, mol, K; R = 8.31451 J/mol K). For
a complete set of parameters the reader is referred to Refs. [93Sel, 94Hal, 96Ris]concerning the binary subsystems.
Table II.5.2: Thermodynamic properties of the ternary oxides.
Phase A#298 A"!>298 cp (350 K) References Exp. Method
[J/mol] [J/molK] [J/molK]
Ca2Cu03 — — +136.1 [92Kru] DSC
-7800 — — [93Ide] Sol. Calorim.
-4860 -2.65 — [93Mat] emf
+1570 +2.80 — [94Suz] emf
-7300 -5.29 +136.1 This work
Cao83CuO! 93 -10555 -8.85 [93Mat] emf
-12558 -10.61 This work
CaCu203 -4100 — [93Ide] Sol. Calorim.
-3193 -1.98 This work
1.02
1255
0.455
0.419
0.126
L2
1.34
1398
1.77
1398
0.464
0.401
0.135
L2
1.89
1423
0.469
0.387
0.144
L2
2.25
1447
-1.04
1255
0.416
0.498
0.086
L2
-0.90
1273
0.416
0.498
0.086
L2
-0.90
1273
0.414
0.497
0.089
L2
-1.04
1281
0.017
0.983
10~15
U-5.56
1340
0.357
0.571
0.072
L2
0.036
0.964
lO"13
U-4.72
1417
list
ed.
not
are
02
bar
10-10
below
equi
libr
iaInvariant
line
.dashed
the
below
listed
are
02
bar
100
to
up
equi
libr
iainvariant
Extrapolated
liquid.
oxide
the
L2
and
liqu
idmetal
the
isL1
Ca083CuO193
(+
CuO
+0a2CuO3
<H-
CaCu203
k.
L2)
(+
CaCu203
<->
CuO
+Ca2Cu03
j.
Cao83CuOi93)
(+
CaCu203
«•
CuO
+Ca2Cu03
i.
Ca2Cu03
+CuO
-H-
83C11O193
Ca0
+L2
h.
Ca2Cu03
oCa083CuO193
+CaO
+L2
g.
Cu20)
(+
CuO
+Ca2Cu03
<->
CaCu203
f.
CuO
+Cu20
+CaCu203
-h-
L2
e.
CaCu203
+Cu20
«->
Ca2Cu03
+L2
d.
Ca2Cu03
+Cu20
«->
CaO
+L2
c.
Cu
+Cu20
+CaO
<->
Li
b.
Cu20
+CaO
<->
L2
+Li
a.
xo
xCa
zCa
(bar
)K
composition
Liquid
log(
P02)
TReaction
parameters.
ofset
present
the
from
calculated
system
Ca-Cu-0
the
in
equilibria
Invariant
II.5.3:
Table
workThis920Ca083CuO193+CaO«Ca2Cu03
workThis1104
[91Rot]1108CaossCuO!93<-»CuO+Ca2Cu03
workThis
[94Tsa][94Suz]
1254
CuO+Ca2Cu03-h*CaCu203
workThis1.43
[94Tsa]—
0.83
1318CuO+CaCu203oL
1255
1250
1254
0.821326
0.83
1318
0.821326
0.83
1319
0.811341
0.821358
0.76
1353
workThis1.41
[94Tsa]—
0.83
1319CaCu203<-»Ca2Cu03+L
workThis1.43
[94Tsa]—
[66Gad]—
0.76
1353Ca2Cu03«CaO+L
Cu+1/Cu+2^ca)+W(acu
ReferencecompositionLiquid[K]TReaction
02.bar1.01inequilibriainvariantcalculatedandExperimentalII.5.5:Table
workThis82583C11O1.93Ca0+CaO«Ca2Cu03
workThis1021
[91Rot]1028CaossCuOigs«•CuO+Ca2Cu03
workThis
[91Rot]1258
CuO+Ca2Cu03oCaCu203
workThis1.90
[91Rot]—
0.80
1285CuO+CaCu203<->L
1255
1258
0.851286
0.80
1285
0.851286
—1291
0.841302
—1307
0.771303
—1299
workThis1.90
[91Rot]——1291CaCu203oCa2Cu03+L
workThis1.93
[91Rot]—
[66Gad]2.06
[90Lia]——1299Ca2Cu03-H-CaO+L
Cu+7Cu+2zca)+W(-«Cu
ReferencecompositionLiquid[K]TReaction
air.inequilibriainvariantcalculatedandExperimentalII.5.4:Table
SYSTEMBSCCOTHE134
CA-CU-O 135
Log[P02 (bar)]
Figure II.5.1: Ca-Cu-0 oxygen potential diagram. The calculated oxygen partial
pressures in 3-phase fields are compaied to emf and phase diagram data. The 4-phase
invariant equilibria are indicated with letters according to Table 3.
o
E
<
600 1400800 1000 1200
Temperature [K]
Figure II.5.2: Gibbs energy of various reactions compared to emf data.
136 THE BSCCO SYSTEM
1600-OI6]
'
M1500-
O[10]
[15] \ -
1400-
\ Liquid
O
K 1300- ffl „(St-\ X
3
o
o3
to*1(J
:
1 *©-»-=o
1_
IS 1200-
<D
E 1100-
H
fCaCu203
o
1000-
900-
d"
o8
o
CO
o
1 1 1 1
0
CaO
0.2 0.4 0.6
xCu ' (xCu + xCa)
0.8 1.0
CuO„
Figure II.5.3: Optimized CaO-CuO,, phase diagram in air. The s;
measured temperatures and liquid compositions of various equilibria.
1600
1500
1400
K 1300<»
I 1200
<D
E 1100CD
H
1000
900
800
ore]
O[10]
[12]
A [13]
0
CaO
Liquid
0.2 0.4 0.6 0.8
W^Cu + Xca)
1.0
CuO
Figure II.5.4: Optimized CaO-CuOx phase diagram in 1.01 bar Oi- The symbolsindicate the measured temperatures and liquid compositions of various equilibria.
CA-CU-O 137
1300
0.250.05 0.10 0.15 0.20
xCa/(xCa+xCu)
Figure II.5.5: Isoplethal section along the Cu20-CaO line
Cu20
o[18]
a [15]
1573K
/
-1 0.2
*CuO
0.6 Nx 0.8in airX
in 1 01 bar O.
TrCuO
1.0
Figure II.5.6: Calculated isothermal section at 1573 K The composition of the oxide
liquid in equilibrium with the metallic liquid is compared with the data of [18]. The
calculated composition along the air isobar is indicated by a dashed line and compared
to the data of [15].
138 THE BSCCO SYSTEM
0.05 0.10 0.15
xCa''xCa+xCu'
0.20
Figure II.5.7: Oxygen partial pressure m the oxide liquid across the miscibihty gap
at 1573 K.
CA-CU-O 139
1200 1300 1400 1500
T[K]
1600 1700
Figure II.5.8: Calculated relative amounts of Cu+1 and Cu+2 in the oxide hqind in
air for the system Ca-Cu-0
1.0
0.9
0.8
0.7-
\0.QO
^0.5o
o
0.4
0.3
0.2
0.1
0
[13] WtXca+Xcu*<D 0 90
n 0 83
A 0 70 (CaO sat)9 0 66
"
a 0 50"
O 0 20"
1200 1300 1400 1500
T[K]
1600 1700
Figure II.5.9: Calculated relative amounts of Cu+1 and Cu+2 in the oxide
1.01 bar 02 for the system Ca-Cu-O.
140 THE BSCCO SYSTEM
References Chapter II.4
[37War] H. v. Wartenberg, H. J. Reusch, and E. Saian. "Melting Diagrams of Refrac¬
tory Oxides. VII. Systems with CaO and BeO", Z. anorg. allg. Chem., 230,257-276 (1937) in German.
[65Sch] N. G. Schmahl and E. Minzl, "Thermodynamic Data of Double-Oxide For¬
mation from Equilibria Measurements", Z. Phys. Chem. NF, 4% 358-382
(1965) in German.
[66Gad] A. M. M. Gadalla and J. White, "Equilibrium Relationships in the SystemCuO-Cu20-CaO", Trans. Br. Ceram. Soc, 65(4), 181-190 (1966).
[68Kux] U. Kuxmann and K. Kurre, "The Miscibility Gap in the System Copper-Oxygen and the Influence on it by the Oxides CaO, Si02, A1203, MgO-Al203,andZr02", Erzmetall, XXI(5), 199-209 (1968) in German.
[69Tes] Chr.. L. Teske and Hk.. Miiller-Buschbaum, "On CaCu203", Z. anorg. allg.Chem., 370, 134-143 (1969) in German.
[70Tes] Chr.. L. Teske and Hk.. Miiller-Buschbaum, "On Ca2Cu03 and SrCu02", Z.
anorg. allg. Chem., 379, 234-241 (1970) in German.
[85Hil] M. Hillert, Bo Jansson, Bo Sundman, and J. Agren, "A Two-Sublattice Model
for Molten Solutions with Different Tendency for Ionization", Metall. Trans.
A, 16A(2), 261-266 (1985).
[85Sun] Bo Sundman, Bo Jansson, and J.-O. Andersson, "The Thermo-Calc Databank
System", Calphad, 9(2), 153-190 (1985).
[860is] T. Oishi, Y. Kondo, and K. Ono, "A Thermodynamic Study of Cu20-CaOMelts in Equilibrium with Liquid Copper", Trans. Japan Inst. Met, 27(12),976-980 (1986).
[89Rot] R. S. Roth, C. J. Rawn, J. J. Ritter, and B. P. Burton, "Phase Equilibria of
the System SrO-CaO-CuO", J. Am. Ceram. Soc., 72(8), 1545-1549 (1989).
[90Lia] J. K. Liang, Z. Chen, F. Wu, and S. H. Xie, "Phase Diagram of SrO-CaO-
CuO Ternary System", Solid State Commun., 75(3), 247-252 (1990).
[90Sie] T. Siegrist, R. S. Roth, C. J. Rawn, and J. J. Ritter, "Ca^^CuOs, a NaCu02-
Type Related Structure", Chem. Mater., 2(2), 192-194 (1990).
[90Sko] Yu. Ya. Skolis, S. G. Popov, L. A. Khranitsova, and F. M. Putilina, "Phase
Relations in the Subsolidus Region of Systems Formed by Strontium, Calcium,and Copper Oxides", Moscow Unw. Chem. Bull, 45(2), 38-40 (1990).
CA-CU-O 141
[91Bab] T. G. N. Babu and C. Greaves, "The Synthesis and Structure of the New
Phase CaossCuOz", Mater. Res. Bull, 2(7(6), 499-506 (1991).
[91Hal] I. Halasz, H.-W. Jen, A. Brenner, M. Shelef, S. Kao, and K. Y. S. Ng, "Deter¬
mination of the Oxygen Content in Superconducting and Related Cuprates
Using Temperature-Programmed Reduction", J. Solid State Chem., 92,
327-338 (1991).
[91Rot] R. S. Roth, N. M. Hwang, C. J. Rawn, B. P. Burton, and J. J. Ritter, "Phase
Equilibria in the Systems CaO-CuO and CaO-Bi203", J. Am. Ceram. Soc,
74(d), 2148-2151 (1991).
[91Sun] Bo Sundman, "Modification of the Two-Sublattice Model for Liquids", Cal-
phad. 15(2), 109-119 (1991).
[92Krii] Ch. Kriiger. W. Reichelt, A. Almes, U. Konig, H. Oppermann, and H. Scheler.
"Synthesis and Properties of Compounds in the System Si'2Cu03-Ca2Cu03",
J. Solid State Chem., 96, 67-71 (1992).
[92Mill] O. Milat, G. van Tendeloo, S. Amelinckx, T. G. N. Babu, and C. Greaves,
"The Modulated Structure of Ca0 85Cu02 as Studied by Means of Electron
Diffraction and Microscopy", J. Solid State Chem., 91, 405-418 (1992).
[92MU2] 0. Milat, G. van Tendeloo, S. Amelinckx, T. G. N. Babu, and C. Greaves.
"Structural Variants of CaossCuC^ (Ca5+i!Cue012)'\ J. Solid State Chem.,
101, 92-114 (1992).
[93Ide] Y. Idemoto, K. Shizuka. Y. Yasuda, and K. Fueki, "Standard Enthalpies of
Foimation of Member Oxides in the Bi-Sr-Ca-Cu-0 System", Physica C,
211, 36-44 (1993).
[93Mat] T. Mathews, J. P. Hajra, and K. T. Jacob, "Phase Relations and Thermo¬
dynamic Properties of Condensed Phases in the System Ca-Cu-O", Chem.
Mater., 5(11), 1669-1675 (1993).
[93Ped] S. R. Peddada and D. R. Gaskell, "The Activity of CuO0 5 along the Air Iso¬
bars in the Systems Cu-0-Si02 and Cu-O-CaO at 1300°C", Metall. Trans.
B, 24B, 59-62 (1993).
[93Sel] M. Selleby, "A Reassessment of the Ca-Fe-0 System", Ti-ita-mac 508, Royal
Institute of Technology, Stockholm, Sweden. (Jan. 1993).
[94Hal] B. Hallstedt, D. Risold, and L. J. Gauckler, "Thermodynamic Assessment of
the Copper-Oxygen System", J. Phase Equilibria, 15(5), 483-499 (1994).
[94Suz] R. O. Suzuki, P. Bohac, and L. J. Gauckler, "Thermodynamics and Phase
Equilibria in the Ca-Cu-0 System", J. Am. Ceram. Soc., 77(1), 41-48
(1994).
[94Tsa] C. F. Tsang, D. Elthou, and J. K. Meen, "Phase Equilibria of the Calcium
Oxide-Copper Oxide System in Oxygen at 1 atm". Submitted for Publication
in J. Am. Ceram. Soc. (June 1994).
142 THE BSCCO SYSTEM
[96Ris] D. Risold, B. Hallstedt, L. J. Gauckler, H. L. Lukas, and S. G. Fries, '-Ther¬
modynamic Optimization of the Ca-Cu and Sr-Cu Systems", Calphad, SO
(1996). to be published.
SR-CA-CU-O143
II.6 The Sr-Ca-Cu-O System
Submitted for publication in J. Am. Ceram. Soc, Dec. 1995
Thermodynamic Modelling and Calculation
of Phase Equilibria in the Sr-Ca-Cu-O
System at Ambient Pressure
Daniel Risold, Bengt Hallstedt, and Ludwig J. Gauckler
Nonmetallic Materials, Swiss Federal Institute of Technology,
Sonneggstr. 5, CH-8092 Zurich, Switzerland
ABSTRACT The phase diagram and thermodynamic data on the Sr-Ca-
Cu-0 system at 1 bar total pressure are reviewed and as¬
sessed. Gibbs energy functions for the (Sr.Ca)-solid solutions
and the liquid are optimized and a consistent thermodynamic
description is presented. Calculated phase relations are shown
in various isothermal and isoplethal sections and compared
with experimental data. Special attention is paid to the sta¬
bility of the infinite-layer compound as function of tempera¬
ture and oxygen partial pressure.
1 Introduction
The aim of our work is to provide a consistent thermodynamic description of multi-
component cuprate systems which can be used for the calculation of phase equilibria.
For this purpose, phase diagram and thermodynamic data are simultaneously assessed
using the CALPHAD approach [77Kau] and a consistent set of Gibbs energy functions
is obtained. This article presents a model description of the Sr-Ca-Cu-O system which
contains several phases appearing as major secondary phases during melt-processing of
Bi-Sr-Ca-Cu-Oxide superconductors. Some first applications of these equilibrium cal¬
culations to the study of the melt processing of Bi2Sr2CaCu2Ocl are reported elsewhere
[95Hal, 96Buh].
The present description is based on previous assessments of the ternary subsystems
Sr-Cu-0 and Ca-Cu-0 [95Ris2, 96Ris]. The Sr-Ca-Cu-O system is characterized
by solid solutions arising from the substitution of Ca foi Sr. Complete solid solutions
are found in the phases (Sr,Ca)0 and (Sr,Ca)2Cu03. Partial solubility towards cal¬
cium is found in all the other strontium cuprates SrCu02, Sri4Cii2404i, and SrCu202,
whereas no significant solubility towards strontium has been reported for the calcium
cuprates Cao83CiiOi93 and CaCu203. The phase commonly called infinite-layer (IL)
144 THE BSCCO SYSTEM
compound is stable in the Sr-Ca-Cu-0 system at ambient pressure around the com¬
position Cai_!Si'sCuC^ with 10 to 15 % Sr substituted for Ca. It is the only new
phase appearing in the quaternary system. In this work these phases are abbreviated
according to Table II.6.1, mamly for convenience in labeling the various phase fields.
In the following the phase diagram and thermodynamic data on the oxides in the Sr-
Ca-Cu-0 system are reviewed and assessed, and optimized Gibbs energy functions for
the solid compounds and the liquid are presented.
2 Experimental data
2.1 Phase relations
The phase relations between oxides of strontium, calcium, and copper have been in¬
vestigated in several isothermal studies [89Rot, 89Val, 90Lia, 90Maj, 90Het, 92Slo,92Pop, 94Suz, 95Geo, 95Jac]. Most of them have been performed in air, at 1123 K
[90Maj], 1173 K [89Val, 92Pop], 1193 K [94Suz], and 1223 K [89Rot, 92Slo]. In some
studies, the temperature of the isothermal section is not precisely defined. The phaserelations given by Liang et al. [90Lia] were obtained somewhere between 1123 and
1223 K, while those reported by Hettich et al. [90Het] were found between 1173 and
1223 K. Isothermal studies at other oxygen partial pressure have been made by Suzuki
et al. [94Suz] (lower oxygen partial pressure, 1153 K), Jacob et al. [95Jac] (1.01 bar
C-2, 1123 K), and George et al. [95Geo] (1.01 and 10 bar 02, 1223 K).
The IL compound was first obtained in the Sr-Ca-Cu-0 system by Roth et al. [89Rot,88Sie] at 1223 K in air, and shortly after by Yamane et al. [89Yam] at 1273 K in 1.01 bar
O2. With further studies, some contradictory results on the phase relations around the
IL compound and its stability as function of temperature and oxygen partial pressurehave been reported. These differences are summarized below. The DTA/TG data on
the formation and decomposition temperature of the IL compound are listed in Table
II.6.2.
In air, the IL compound has been found in all studies made between 1223 and 1233 K
[89Rot, 89Vak, 91Eli, 92Slo, 95Zho, 95Kik]. The isothermal section reported by Roth
et al. [89Rot] has been confirmed by Slobodin et al. [92Slo]. At these temperatures,the IL compound is in equilibrium with lxl at the Sr-rich side and with 2x1 and CuO
at the Ca-rich side. The decomposition temperature has been studied by DTA/TG[89Vak, 92Kos, 95Zho] and variation of the calcination temperature [95Kik]. It was
observed at 1253 [95Kik], 1258 [89Vak, 92Kos], and between 1247 and 1266 K [95Zho].These values of the decomposition temperature are in fairly close agreement. Kosmyninet al. [92Kos] report that the IL compound decomposes to CuO+2xl+lxl. The other
authors [95Zho, 95Kik] observed melting which is characterized by a larger oxygenrelease in TG and a larger heat effect in DTA than for solid state reactions. It seems
more probable that equilibrium with the liquid phase occurs since single crystal have
been grown from slow cooling of the melt [88Sie]. Liquid and mainly 2x1 have been
observed above 1273 K by Hettich et al. [90Het],
The formation temperature has been reported from DTA/TG studies at 1203 [92Kos]and 1231 K [95Zho]. The temperature reported by Zhou et al. [95Zho] is certainly too
high due to unreacted samples since in their study the IL phase formed immediatelyafter the decomposition of SrCOs. The value of Kosymin et al. [92Kos] is consistent
SR-CA-CU-O145
with most isothermal studies [89Rot. 90Maj, 92Pop. 92Slo, 94Suz]. Two authors
[89Val, 95Kik], however, observed the IL phase at the lower temperature of 1173 K.
The results of Vallino et al. [89Val] could not be confirmed by Popov et al. [92Pop]
who used the same starting materials (SrC03. CaC03, and CuO) and a longer total
annealing time but did not observe the IL compound at 1173 K. The results of Vallino
et al. [89Val] also differ from the other isothermal studies [90Lia, 90Het. 92Pop. 94Suz]
in that the equilibrium lxl-14x24-CuO was observed instead of 1x1-14x24-2x1. The
cooling rate does not seem to be a determinant factor in these differences as Popov
et al. [92Pop] did not observe changes in the phase relations by using various cooling
rates. Kikkawa et al. [95Kik] obtained the IL compound at 1173 K by a titration route
using the metal acetates. The IL compound which they observed was in equilibrium
with the Cao.83CuOx.93 phase. This is in contradiction with their own observation of
the decomposition of Cao 83CUO193 into Ca2Cu03+CuO at 1073 K in air. Interestingly,
they could not form the IL compound at 1273 K in 1.01 bar 02 using this synthesis
method.
In 1.01 bar 02, the IL phase was observed at 1223 [95Geo], 1273 [89Yam. 93Kij].
and 1293 K [93Liu]. The phase relations reported by George et al. [95Geo] include
some uncertain lines and a question mark. At the Sr-rich side, it was reported to be
in equilibrium with both lxl and 14x24 [95Geo]. Yamane et al. [89Yam] found IL
in equilibrium with 2x1 and 14x24, while unexpected equilibria with 012 or even 2x1
of two different compositions were also reported [93Liu. 93Kij]. At the Ca-rich side,
equilibrium with 2xl+CuO is found at 1223 K [95Geo] and with 2x1+012 at 1273 K
[89Yam, 93Kij],
The stability limits of the IL compound have also been studied between 0.01 and 1.01
bar O2 by Liu et al. [93Liu] from samples annealed under various conditions and by
DTA/TG. They reported from the DTA/TG analysis the formation temperature of
the IL phase at 1204 K in 0.03 bar 02 and at 1293 K in 1.01 bar 02. The value in
0.03 bar 02 is very close to the one determined in air by Kosmynin et al. [92Kos]. It
is however important to note for DTA/TG studies that the reactions observed might
not involve the IL compound. Close to these temperatures are the transformation of
CuO to Cu20 in 0.03 bar 02 and the reaction of 2x1+14x24 to lxl+CuO in air. The
temperature given by Liu et al. [93Liu] for 1.01 bar 02 corresponds most probably
to the first melting reaction. The stability of the IL compound was studied in 150 to
180 bar 02 by Strobel et al. [94Str]. At these higher oxygen partial pressure, the IL
compound decomposed to Ca0.83CuOi.93+lx0 at all annealing temperatures between
923 and 1248 K. They observed that the reaction was reversible and note that the
driving force must be the oxygen partial pressure and not the total pressure since the
density decreases at decomposition of the IL compound.
The same phase relations have been found in air [90Maj, 92Pop, 94Suz], 1.01 bar 02
[95Jac], and 10 bar 02 [95Geo] at the lower temperatures where the IL compound
is not stable. There, the two three-phase equilibria 14x24-CuO-2xl and 14x24-1x1-
2x1 are found. At lower oxygen partial pressure (10% to 1% 02), 14x24 disappears
aild CllO~lxl-2xl are found in equilibrium [93Liu, 94Suz]. By further decrease in
oxygen partial pressure, the equilibrium sequence lxl-2xl-Cu20, 2xl-Cu20-lx2, and
Cu20-lx2-CaO was observed [94Suz].
146 THE BSCCO SYSTEM
The melting relations have been studied in isoplethal sections at various CuO contents
by Shter et al. [91Sht] (33 mol % CuO) and Kosmynin et al. [92Kos, 95Kos] (50, 63,70, 75. 80, and 90 mol % CuO) using XRD and DTA. Kosmynin et al. [92Kos, 95Kos]reported at some compositions more DTA points than they could attiibute to the
different melting relations and several phase fields were not investigated by XRD.
Their data indicate however well in which temperature regions melting events can be
expected.
2.2 Solubility limits
The data on the solubility limits are summarized here together with the crystallographicresults on the variation of lattice parameters as these studies are often closely related.
The crystallographic data on the ternary compounds have been reviewed in the previousassessments [95Ris2, 96Ris]. A review of the XRD data on the (Sr,Ca)-solid solutions
was given by Reardon and Hubbard [92Rea].
The (Sr.Ca)O phase exhibits a miscibility gap at lower temperatures. The solubilitylimits have been investigated in air between 873 and 1273 K by Roth [91Rot]. Largersolubilities have been measured by Jacob et al. [95Jac] at 1123 K in 1.01 bar 02.Complete miscibility has been observed in samples annealed at 1773 K [680bs], 1573
K [42Hub], 1323 K [89Val], and 1223 K [91Rot]. The miscibility gap obtained byRoth shows an unusual shape with a flat top, which is thermodynamicaly unprobable.Roth mentioned that his measured solubilities may have been influenced by the partialpressure of C02. The upper temperature limit of his miscibility gap at 1223 K representthe lowest reported temperature for complete miscibility and is in agreement with the
results of Jacob et al. [95Jac]. These results are shown in Fig. II.6.1.
The (Sr, Ca)2Cu03 phase shows a complete miscibility. The variation of the lattice
parameters along the solid solution has been studied using XRD [89Val, 92Krii, 92Xu].These results are in good agreement with Vegard's law. Jacob et al. [95Jac] usingtheir data on the tielines between (Sr,Ca)0 and (Sr, Ca)2Cu03 found that the mixingbehaviour of (Sr, Ca)2Cu03 is close to an ideal solution.
(Sr, Ca)Cu02 and (Sr, Ca)i4Cu24041 show partial solubilities towards Ca. None of the
phases is stable in the Ca-Cu-0 system. The variation of the lattice parameters of
the (Sr, Ca)Cu02 solid solution have been measured by Gambardella et al. [92Gam]and Heinau et al. [94Hei]. The measured solubility limit at various temperatures and
several oxygen partial pressures are listed in Table II.6.3 for lxl and Table II.6.4 for
14x24. For lxl, the results are relatively scattered with most data lying between 60
to 70 % Ca. For 14x24, all values lie between 50 to 60 % Ca with several studies
reporting about 50 % Ca. There is a slight trend that the Ca solubility increases with
temperature in both phases, and that it decreases in lxl and increases in 14x24 as
function as the oxygen partial pressure.
The solubility limit of Ca in (Sr, Ca)Cu202 was determined in this work from the
change in lattice parameters as function of the Ca content. SrC03, CaC03, and CuO
powders were used as starting materials. Samples of composition (Sr1_ICaI)Cu202(x=0, 0.05, 0.1, 0.15, 0.2, 0.25, 0.30, and 0.50) were annealed at 1173 K in 8.25 Pa
02 for a total time of 550 ks with several regrindings. The samples were contained in
A1203 crucibles and cooled in the colder end of the quarz tube furnace under Ar flow.
SR-CA-CU-O 147
The lattice parameters were determined by XRD using Cu-KQ radiation and silicon
mixed to the powder sample as internal standard. The results are shown in Fig II.6.2.
A solubility limit of xcn/(xsr+xca)=0.18 was obtained from the lattice parameters data
and the value was confirmed by EDX. This result is in reasonable agreement with the
value 0.22 given by Suzuki et al. [94Suz] at 1153 K. We have adopted a value of 0.2
for the assessment.
The studies on the (Sr,Ca)-solubility range of the IL compound are summarized in
Table II.6.5 together with the data on the phase relations at both end points. The
single phase range observed at various temperature and oxygen partial pressure never
exceeds about 5 %. The solution range is slightly shifted to the Ca-side with increasing
oxygen partial pressure. No detectable change in the oxygen content of IL could be
measured by thermogravimetry in air and pure oxygen [89Vak].
2.3 Thermodynamics
Experimental data on the thermodynamics of the (Sr.Ca)-solutions are limited to the
calorimetric studies of Flidlider et al. [66Fli] for 1x0 and Idemoto et al. [93Idej for
2x1, lxl, 14x24, and the IL compound. In both studies, the enthalpy of formation of
the solid solutions were determined from the heats of dissolution of the pure oxides
and the solid solution in HCIO4. The data on the enthalpy of mixing of 1x0 are shown
in Fig. II.6.3. The values measured for the other compounds are plotted in Fig. II.6.4.
A good agreement between these values, emf results and phase diagram data could
be found for the calcium cuprates [96Ris]. The values obtained for Sr2Cu03 and
Sr14Cu24041 seem however too negative and have been discussed previously [95Ris2].
In the case of the (Sr, Ca)2Cu03 solution, the value optimized for the Sr end point
together with the data of Idemoto et al. [93Ide] at high Ca content lead to an almost
ideal enthalpy of mixing. This is in good agreement with the tieline data of Jacob et
al. [95Jac].
Important information on the solution behaviour can be obtained from the tielines
between these phases. Detailed experimental values have been leported by Popov et
al. [92Pop], George et al. [95Geo], and Jacob et al. [95Jac]. The tielines shown in
other diagrams without indication in separate tables of the samples composition have
not been considered, as these tielines are mostly schematicaly drawn or assumed here
to be so.
3 Thermodynamic description
The basis of this thermodynamic description is explained in more detail in previous
articles on the different subsystems [95Ris2, 96Ris, 94Hal, 95Risl, 96Ris]. The cop¬
per oxides CuO and Cu20 and the calcium cuprates Cao83Cu0193 and CaCu203 are
treated as stoichiometric phases and the Gibbs energy is given in the subsystems. The
models used for the (Sr,Ca) solid solutions and the liquid are presented below.
3.1 The (Sr,Ca) solid solutions
The phases 1x0, 2x1, lxl, 14x24, and 1x2 are described as (Sr,Ca) solid solutions
using the sublattice model commonly referred to as the Compound Energy Model
[86And, 88Hil]. Each (Sr.Ca) solid solution <j> is described by a formula where Sr+2 and
Ca+2 are distributed on the same sublattice while copper and oxygen occupy their own
148 THE BSCCO SYSTEM
sublattices. The Gibbs energy per mol of formula unit G* is given by an expression of
the form :
Gt = »&+»Glc»,o.+»c.«(&cCuf0. (II.6.1)
+RT[ySl+2-ln(ySl+2) + «/Ca+2• (»/Ca+2)]
+2/Sr+22/Ca+2iSr+iCa+2
where y, represent the site fractions of Sr+2 or Ca+2 on their sublattice. The functions
G*liCu 0_ and Gca.c.i o are 'he Gibbs energies of the respective ternary compoundsand are either given by the previous assessments or used as adjustable parameters if
the compound is not stable in the ternary system. Random mixing is assumed on the
(Sr+2,Ca+2) sublattice and possible deviation of the (Sr,Ca) solid solutions from an
ideal behaviour can be accounted for by the L^+2 Ca+2interaction parameters.
Valuable information on the metastable end points of the solid solutions can be gainedfrom calculations based on atomic parameters. This is especially important for phasessuch as the IL compound for which both endpoints are metastable in the ternaries
and furthermore for which no data on the mixing behaviour are available in the stable
range. Recently, the difference in heat of formation at 0 K of the endpoints of the
IL and lxl solid solutions have been predicted by Allan et al. [94A11] using atomistic
lattice simulation. Hckcu02 's predicted to be about 16 kJ/mol more negative than
^SrCuCv anc^ these values about 39 and 68 kJ/mol less negative than HqIqu02 and
fl&cuo2) respectively. This gives #caCu02 about 13 kJ/mol less negative than Hg^a0y3.2 The IL compound
The IL phase is described here as a stoichiometric compound since its solution rangeis relatively narrow and the few phase diagram data contain some contradictions. The
composition is choosen as Sr0i4Ca086CuO2. A thermodynamic description as solid
solution has been tried, but no simple model could bring satisfying results. The diffi¬
culties in modelling are briefly explained below.
No evidence of ordering of Sr on the calcium sites could be found in crystallographicstudies [88Sie, 89Yam, 89Vak]. The first approach was thus to consider the same
model as for the other (Sr,Ca) solid solutions, i.e. assuming random mixing of Sr
and Ca on one sublattice. The difficulties in modelling a Gibbs energy function for
the whole solution range is mainly due to two strong conditions. First the IL phaseshould not be stable in the Ca-Cu-0 system, which means that its Gibbs energyof formation referred to the binary oxides cannot be less negative than about —600
to —200 J/mol between 1000 and 1300 K. Second, it can only be stable near the
composition Cai-iSr^CuOa (0.1 < x < 0.15) if its Gibbs energy decreases to about
—6000 to —7000 J/mol at these temperatures. If the sharp decrease in Gibbs energy at
the Ca-rich side is described with a simple regular interaction term, very large values for
G|jCu02 and L^+2 Ca+2 are needed, which cannot be realistic. If the predicted difference
between G$;Cn02 and G^Cu02 is taken [94A11], then the Gibbs energy of mixing must
have a very asymmetric composition dependence in order to reproduce the observed
solubility limits. The measured data are however confined in a too limited temperatureand composition interval to determine a reliable shape for such a function.
An asymmetric function with sharp minimum at Ca-rich composition also means that
SR-CA-CU-O 149
strong interaction parameters are needed and it is a clear indication that there is a
tendency for ordering on the (Sr,Ca) sublattice. From neutron diffraction data and
lattice energy calculations [91Bil], deviations from perfect planarity were found in the
copper-oxygen layers which would give rise to short-range order. Addition of Sr to
CaCuC>2 stabilizes the IL phase. The minimum in lattice eneigy is expected near the
composition Sr0 uCao s6Cu02 [94A11J. Ordering models for the (Si\Ca) sublattice have
recently been discussed by Arakcheeva et al. [95Ara] based on a new XRD study. It
is beyond the scope of this work to model order-disorder phenomenan in the IL phase.
However to test the influence of ordered Sr and Ca atoms on the phase relations, we
have used the following simple model. Long-range order is assumed and two sublattices
for Sr+2 and Ca"1"2 are considered in order to model a "V" shape for the enthalpy of
mixing with a minimum at the composition Sr0 uCao 86C11O2. The parameters are
the functions Gg0 14Gao86c»o2> <?ctcu02, and Gsrccv R turns out that Phase relations
and solubility limits in closer agreement with the experimental data can be obtained
together with heats of formation at both endpoints which are compatible with the
predicted values [94All]. A tendency for ordering of the Sr and Ca atoms can thus
be expected from thermodynamic considerations as well and should be considered in
a thermodynamic modelling of the IL solution. At this stage, however, in view of the
large uncertainties in the stability field of IL as function of temperature and oxygen
partial pressure, we prefer to use a stoichiometric description.
3.3 The liquid phase
The liquid phase is described by the two-sublattice ionic liquid model [85Hil] which
has proved to be appropriate for the ternary subsystems [95Ris2, 96Ris]. The liquid
phase in the quaternary system is obtained as an extension from the ternaries and
can be represented by the formula (Sr+2, Ca"1"2, Cu+1, Cu+2)p(Va"q, 0~2)q. The molar
Gibbs energy of the liquid G)^1 is here entirely given by extrapolations from the ternary
systems.
c"q = Y,yMyv*°Gl;\ + y0i°G1;^
+ Yl pRTy, ln(j/,) + £ qRTy, • lu(j/,)•=<M( i=Va,0-2
+ EGhq (II.6.2)
Here cat stands for the cations Sr+2, Ca42, Cu+1, and Cu+2. The functions °Gj'Va
represent the Gibbs energy of the pure metals, while the 0Gj'o_2 represent the Gibbs
energy of the ideal non-dissociated liquid binary oxides. The excess termE G
'qis the
sum of all contributions due to interaction parameters of the subsystems:
E ril"i_
E ^'"1, E ^'"l 1
E r*l'q1E nh1 . E ,oll<l
U — ^Sr-0 + "Ca-O + ^Cu-O + "Sr-Cu + ^Ca-Cu
+ ^Sr-cu-o + GCa_Cu_0 + GSr_0a_0 (II.6.3)
The major contribution is due to BG£1_0. The terms BGgq_0, EG^a_0, BGs'q_Cu,
and E Gcq_Cu influence the metal liquid and are of little concern here. The terms
BGslq_Cu_0, BG,J.q_Cu_0, and EGgq_Ca_0 include interaction parameters between the
150 THE BSCCO SYSTEM
ideal liquid binary oxides. The first two terms represent necessary adjustment to the
Gibbs energy of the liquid to reproduce the melting relations in these two ternaries. The
mixing behaviour of SrO-CaO liquid is unknown, so that the last term,E G^._Cll_0, is
used in this work as fitting parameter in order to obtain a closer agreement between
the experimental and the calculated melting relations along the sections of constant
CuO content.
4 Determination of Parameters
The phases 1x0 and 2x1 are both stable in the Sr-Cu-0 and Ca-Cu-0 systems. The
Gibbs energy of both end points of the solid solutions are thus given by the ternaryassessments. The thermodynamic properties of the 1x0 phase have been predicted
by van der Kemp et al. [94Kemj from the enthalpy data of Plidlider et al. [66FH]and empirical comparisons with other binary mixtures of alkaline earth oxides. The
miscibility gap calculated from their estimated Gibbs energy of mixing is in agreementwith the data of Jacob et al. [95Jac]. We have used in this work the same function for
the excess term £^+2 Ca+2as considered by van der Kemp et al, but the parameters
have been slightly readjusted to fit the data of Jacob et al. [95Jac], The solution
behaviour of 2x1 is in good approximation ideal and no excess parameters were used.
For lxl, 14x24, and 1x2, the end points of the solid solution at the Ca-side are not stable
in the Ca-Cu-0 system. The Gibbs energies of CaCu02, Cai4Cu24041, and CaCu202are used as adjustable parameters. Furthermore data on tielines and enthalpy of mixing
suggest that the solution behaviour of lxl and 14x24 deviates from an ideal mixture and
that interaction parameters need to be considered. Temperature independent values
for these Gibbs energies and the interaction parameters can easily be optimized from
the phase diagram data. A separation of the Gibbs energy in enthalpy and entropycontribution is delicate without enthalpy data. Reliable values are available for lxl
only. The value of the enthalpy of formation CaCu02 is expected to be about —10
kj/mol considering the value assessed for SrCu02 [95Ris2] and the difference between
the Sr and Ca side predicted by atomistic lattice simulation [94A11]. This value is
consistent with the calorimetric data in the middle of the solution [93Ide], For 1x2,we considered a constant value for the Gibbs energy of CaCu202- For 14x24, it is
necessary to consider enthalpy and entropy contributions in Cai4Cii2404i in order to
reproduce the observed phase relations around the IL compound. The parameters of
Cai4Cu24041 can be constrained by data on the equilibria with lxl, 2x1, and CuO. The
uncertainty in the obtained enthalpy and entropy values is larger than for the other
phases.
The Gibbs energy of the IL compound is obtained from the data on the formation and
decomposition temperatures and the enthalpy of formation. The formation temper¬ature is uncertain, small changes in the energy of the IL phase create large shifts in
the stability limits. The values adopted in this assessment are discussed in the next
section.
For the liquid phase, a regular interaction parameter L^+2 Ca+2 Cu+i Cu+2 0_2is used to
slightly lower the calculated melting temperatures. This parameter is well defined bythe melting relations with 1x0, 2x1, or lxl, so that it does not influence the determi¬
nation of enthalpy and entropy terms for 14x24 and the IL compound.
SR-CA-CU-O 151
5 Results and Discussion
The resulting set of optimized parameters is listed in Table II.6.6. A complete com¬
parison of all experimental data with calculated values would require too many figures
and tables, so that only an overview of the characteristic features of the Sr-Ca-Cu-0
system is given below.
The stability limits of the phases as function of temperature and oxygen partial pressure
is shown in Fig. II.6.5. The 5-phase invariant equilibria and the 4-phase reactions are
indicated by labels according to Table II.6.7 and II.6.8. Several 4-phase reactions
end up in points which correspond to the 4-phase invariant equilibria of the ternary
systems. Contradictory results have been reported on the phase relations around the IL
compound. This is probably due to the fact that the 5-phase equilibrium between 2x1,
lxl, 14x24, CuO, and the IL compound is close to the conditions of many experimental
studies. The energy differences between the various phase fields and thus the driving
force for the reactions are small and equilibrium may be slow to reach.
At oxygen partial pressures below that of the 5-phase equilibrium 2x1-1x1-14x24-
CuO-IL, the IL compound forms from the phases 2x1, lxl, and CuO. The tempera¬
ture of this reaction is independent of Pq2 and is not affected by the stoichiometric
approximation for the IL phase. At higher P02 the IL phase forms from 2x1, 14x24,
and CuO. The dependence of the formation temperature on oxygen partial pressure
given from the stoichiometric approximation may be somewhat steeper than in reality,
but cannot deviate too much since the IL phase is known to decompose at high oxygen
partial pressure. A shift of the lower stability limit towards lower temperatures arise
by even small changes in the Gibbs energy of the IL phase. An example is shown in
Fig. II.6.6 where an enlarged part of Fig. II.6.5 (GgallCmtuCa02 = -4820 - 1.6T) is
compared to a calculation made with G$J! c Cxl0l= —4920 — 1.6 T. This shows
that no precise values for the stability limits can be expected from thermodynamic
data only, and that some reliable phase diagram points are needed.
The available data indicate two possibilities. Fiist, the IL compound would form
slowly and be stable at least down to 1173 K in air and 1223 K in 1 bai 02. The
studies in contradiction with this result would then not have succeeded in forming the
IL phase [92Pop, 92Kos. 94Suz]. Second, the IL phase forms easily and would have
remained iiietastable in some studies [89Val, 95Geo, 95Kik]. Several arguments made
us adopt the second possibility in this assessment. The equilibria between Cao gaCuOi 93
and the IL phase reported by Kikkawa et al. [95Kik] is most piobably above the
decomposition temperature of Ca0 83C11O193 and thus metastable. Vallino et al. [89Val]
found CuO+lxl more stable than 14x24+2x1 at 1173 K which is in contradiction with
the other studies [90Lia, 90Het, 92Pop, 94Suz]. Hettich et al. [90Het] observed at
compositions near Sr0 i4Ca0 86Cu02 that the kinetics of formation of lxl is faster than
that of 2x1. It is then plausible that the IL phase caii form and remain iiietastable at
1173 K in air.
The optimized stability limits of the IL phase follow from the above discussion of the
data in air. In 1.01 bar O2, the calculated formation temperature is higher than ex¬
pected from the data of George et al. [95Geo]. The latter results are compatible with
those of Vallino et al. [89Val] and Kikkawa et al. [95Kik] so that a lower stability
limit of the IL phase cannot be completely ruled out. The phase relations reported
152 THE BSCCO SYSTEM
by George et al. [95Geo] in 1.01 bar 02 include however some inconsistencies on the
equilibria between 2x1, lxl, and 14x24, which may indicate that they did not reach
equilibrium in all their samples. It is also important to remember that the stoichio¬
metric approximation presented here for the IL compound might not give a precisedependence of the formation temperature on the oxygen partial pressure. Almost all
authors have reported results at one temperature only. For a better understanding of
the lower stability limit for the IL phase, it would be desirable to have in the same
study some samples annealed at different temperatures.
Two kinds of phase relations are mainly expected around the IL compound. Character¬
istic examples for each kind are shown in Fig. II.6.7, the other possible phase relations
are limited to narrow ranges in temperature or oxygen partial pressure. At 1223 K in
air, the calculated isothermal section is in good agreement with the results of Roth et
al. [89Rot] and Slobodin et al. [92Slo]. The only discrepancy is that the calculated
maximal Ca solubility in lxl is about 10 mol.% lower than the experimental values.
At 1273 K in 1.01 bar 02, the IL compound is found in equilibrium with 2x1, 14x24,and CuO. The equilibrium IL-2xl-14x24 is consistent with the data of Yamane et al.
[89Yam] and has also been found in air between 1173 and 1223 K by Hettich et al.
[90Het]. At the Ca-rich side, the equilibria with CaCii2C>3 observed by Yamane et al.
[89Yam] and Kijima et al. [93Kij] is found in the calculation to be less stable than the
equilibria IL-2xl-CuO.
The phase relations at 1123 K, i.e. below the formation of the IL compound, are
shown in Fig. II.6.8 for several oxygen partial pressures. The same phase relations
are found in air (Fig. II.6.8A) and 1 bar O2. With increasing oxygen partial pressure,
the maximal Ca solubility decreases in lxl and increases in 14x24. The compoundCao.ssCuO! 93 appears at 1.5 bar 02. With decreasing oxygen partial pressure, the
reaction 2xl+14x24=lxl+CuO occurs (8510 Pa 02) and then 14x24 disappears (1580Pa 02). The phase relations at 3040 Pa 02 are shown in Fig. II.6.8B. At 477 Pa 02,CuO transforms to Cu20 and the phase 1x2 appears at 150 Pa 02. Fig. II.6.8C shows
the phase relations at 100 Pa 02. Two further reactions, lxl-t-Cu20=lx2-(-2xl (11 Pa
02) and 2xl+Cu2O=lx2+lx0 (9 Pa 02) lead to the phase relations found in a typicalAr atmosphere (1 Pa 02) and shown in Fig. II.6.8D.
The experimental data on the solubility limits of lxl and 14x24 in air as well as the
melting relations are compared with the calculation through some sections of constant
CuO content in Fig. II.6.9. The calculated solubility limits at a few temperatures and
Po2 are also listed in Table II.6.3 and II.6.4.
The calculated maximal Ca solubility in 14x24 is found to slightly decrease with increas¬
ing temperature and as expected to increase with increasing oxygen partial pressure.The majority of the calculated values are in agreement with the experimental data
shown in Table II.6.4. The calculated maximal Ca solubility in lxl lies in the rangeof the reported data. In air for example, the calculated values are always close to 60%Ca and are about 10% lower than in several studies (see Table II.6.3 and Fig. II.6.9).The values for lxl could not be influenced in the optimization without having verydifferent results for 14x24. With the models considered here, the Gibbs energy of 14x24
is dependent on the oxygen partial pressure whereas those of lxl, 2x1, CuO, and the
IL compound are independent of Pq2 •Small changes in the thermodynamics of the lxl
SR-CA-CU-O153
and 14x24 solutions greatly affect the solubility values. It is known from the Sr-Cu-0
ternary, that the lxl phase has a small range of oxygen nonstoichiometry, which has
not been considered in this modelling work. It is difficult to estimate quantitatively
the influence of a small variation in the stability of lxl as function as Po2, but this
could be the source of some discrepancies with experimental solubility values.
The calculated melting relations are in good agreement with the experimental data at
lower Cu content. At high Cu content, some melting events are observed at higher
temperatures than the calculated ones. The discrepancies are in fact limited to the liq¬
uidus line, whereas the calculated lines lepiesenting peritectic reactions compare well
with the DTA results. As can be seen in phase diagrams on the ternary systems, the
liquidus is rather steep near the eutectic point and small variations in the composition
cause large differences in the liquidus temperature. The differences in liquidus tem¬
peratures between the data of Kosmynin et al. [95Kos] and the present calculations
are mostly due to differences in the ternary systems and cannot be influenced in the
quaternary. The data of Kosmynin et at. [95Kos] indicate that the liquidus in the
Sr-Cu-0 system might be closer to the Cu-side than given by the assessment.
The phase relations at low temperatures or high oxygen partial pressures are not dis¬
cussed here. As can be seen from Fig. II.6.9A, the calculation predicts that the phase
relations for Ca-rich composition should change as 1x1+1x0 or 14x24+1x0 get more
stable than 2x1.
The thermodynamic properties of the solid solutions are shown through data on the
tielines and the enthalpy of formation. Tiehne data are compared to calculated values
in Pig. II.6.10 and the enthalpies of formation of the (Sr,Ca)-solid solutions are shown
and compared to the data of Flidlider et al. [66Fli] in Fig. II.6.3 and of Idemoto et al.
[93Ide] in Fig. II.6.4. The assumed ideal solution behaviour of (Sr, Ca)2Cu03 is con¬
sistent with the phase diagram data (Fig. II.6.10A) and part of the calorimetric values
(Fig. II.6.4). The calculated thermodynamic properties of the (Sr, Ca)Cu02 solution
are close to the measured enthalpy data of Idemoto et al. [93Ide] (to the exception of
the composition j/Ca = 0.2), the value predicted by Allan et al. [94A11], and the tieline
data (Fig. II.6.10B). The calculated enthalpy of formation of the (Sr, Ca)14Cu2404i
solution is less negative than the calorimetric values, but the solution behaviour is
similar and in agreement with tieline data (Fig. II.6.10C). The optimized value for
the enthalpy of formation of the IL compound is in the range of uncertainty of the
calorimetric value.
6 Conclusion
The experimental data on the phase relations and the thermodynamics of the Sr-Ca-
Cu-0 system have been reviewed and assessed, and an optimized set of thermodynamic
functions has been presented. The present calculations reproduce well the main features
of the Sr-Ca-Cu-0 system and the resulting consistent thermodynamic description can
serve as a powerful tool for the prediction of phase equilibria in higher order systems.
The results show that the present thermodynamic description is in a general good
agreement with most phase diagram and thermodynamic studies. The major uncer¬
tainties were found in the stability limits of the IL compound. It has been shown that
the phase relations around that phase are very sensitive to small changes in Gibbs
154 THE BSCCO SYSTEM
energy, and that further phase diagram studies are necessary to obtain a more precisethermodynamic description.
7 Acknowledgments
The authors would like to thank Prof. R. 0. Suzuki for valuable discussions on the
experimental data.
Table II.6.1: Oxide phases of the Sr-Ca-Cu-0 system.Phase Abbreviation
(Sr,Ca)0 1x0
(Sr,Ca)2Cu03 2x1
(Sr, Ca)Cu02 lxl
(Sr, Ca)i4Cu2404]t 14x24
(Sr, Ca)Cu202 1x2
Cai_sSra!Cu02 IL
Cao.83CuO1.g3 Oil
CaCu203 012
CuO CuO
Cu20 Cu20
Table II.6.2: Formation and decomposition temperature of the IL compound.Reaction P0;> [bar] T [K] Ref.
Formation of IL
Decomposition of IL
0.03 1204 [93Liu]1189 This work
0.21 1203 [92Kos]1231 [95Zhoj1194 This work
1.01 1295 [93Liu]1267 This work
0.03 1203 This work
0.21 1258 [89Vak, 92KosJ1247-66 [95Zho]1253 [95Kik]1260 This work
1.01 1295 This work
SR-CA-CU-O 155
Table H.6.3: Ga solubility limit in (Sri-xCaI)Cu02.
T[K] X Phases in equilibrium Ref.
1123 0.36 2x1+14x24 [90Maj]1123 0.6-0.7 2x1 [92Gam]1123 0.61 2x1+14x24 This work
1123-1223 0.65 2x1+14x24 [90Lia]1153 0.5-0.6 2x1 [92Gam]1173 0.62 2x1+14x24 [92Pop]1173 0.70 IL [89Val]1173 0.62 2x1+14x24 This woik
1173-1223 0.45 2x1+14x24 [90Het]1193 0.59 2x1+14x24 [94Suz]1223 0.75 IL [89Rot]1223 0.70 IL [92Slo]1223 0.61 2x1+14x24 This work
1229 0.69 IL [95Zho]298-1318 ? 0.57 IL [94Hei]
1123 0.68 2x1+14x24 [95Jac]1123 0.53 2x1+14x24 This work
1223 0.62 2x1+14x24 [95Geo]1223 0.55 2x1+14x24 This work
1223 0.36 2x1+14x24 [95Geo]1223 0.44 2x1+14x24 This work
156 THE BSCCO SYSTEM
Table II.6.4: Ca solubihty limit in (Sri-^Ca^ju Cvqi On
P02 [bar] T[K] X Phases in equilibrium Ref.
0.21 1123 0.50 2xl+CuO [90Maj]1123 0.56 2xl+CuO This work
1123-1223 0.50 2xl+CuO [90Lia]1173 0.57 2xl+CuO [92Pop]1173 0.50 lxl+CuO [89Val]1173 0.53 2xl+CuO This work
1173-1223 0.50 IL+CuO [90Het]1193 0.57 2xl+CuO [94Suz]1223 0.50 lxl+CuO [89Rot]1223 0.50 lxl+CuO [92Slo]1223 0.48 lxl+CuO This work
1.01 1123 0.52 2xl+CuO [95Jac]1123 0.60 2xl+CuO This work
1223 0.59 IL+CuO [95Geo]1223 0.55 2xl+CuO This work
10 1223 0.61 2xl+CuO [95Geo]1223 0.62 2xl+CuO This work
Table II.6.5: Solution range of the IL compound Ca\-xSrxCu02-
Pq2 [bar] T[K] X Phases in equilibrium Ref.
Sr-side Ca-side
0.03 1213 0.12-0.16 lxl 2xl+CuO [93Liu]0.21 1173 0.15 lxl 2xl+CuO [89Val]
1173 0.10-0.16 011 [95Kik]1173-1223 0.15 2x1+14x24 2xl+CuO [90Het]
1223 0.15 lxl 2xl+CuO [89Rot]1226 0.16 lxl 2xl+CuO [95Zho]1233 0.10-0.16 [95Kikj
1.01 1223 0.10-0.16 2x1,1x1,14x24 ? 2xl+CuO [95Geo]1273 0.09 2x1+14x24 2x1+012 [89Yam]1273 0.09-0.14 2x1+2x1+012 2x1+012 [93Kij]1293 0.08-0.12 2x1+2x1 [93Liu]
SR-CA-CU-O 157
Table II.6.6: Optimized thermodynamic parameters for the Sr-Ca-Cu-0 system.
(Sr,Ca)0
L\% Co+2= +23000 - 3 T + 1185( «,Ca+,
- ySt+2)
(Sr,Ca)2Cu03
LSr+i Ca+-!- U
(Sr, Ca)Cu02
Gclcuo, =-9400 +12 T
L\% Ca+2= -16000
(Sr, Ca)14Cu24041
G^Ou24o41 = -259000 + 330 T
Llt& ca+'= -400000
(Sr,Ca)Cu202
G&L.O, = +15550
^Sl+2 Ca+2- U
IL compound
< „C..c«o,=-4820-1.6 T
Liquid
All parameter values are given in SI units (J, mol, K; R = 8 31451 J/mol K) per
mole of formula unit. For a complete set of parameters the reader is referred to Refs.
[95Ris2, 96Ris] concerning the ternaries Sr-Cu-0 and Ca-Cu-O.
158 THE BSCCO SYSTEM
Table II.6.7: Invariant equilibria m the Sr-Ca-Cu-0 system calculated from the
present set of parameters.Equilibrium r[K] log(P02) [bar]
A. L + IL + CuO + 2x1 + 14x24
B. L + IL + 2x1 + lxl + 14x24
C. L + IL + CuO + lxl + 14x24
D. IL + CuO + 2x1 + lxl + 14x24
E. L + 012 + 2x1 + Cu20 + CuO
F. L + IL + CuO + Cu20 + 2x1
G. L + IL + CuO + Cu20 + lxl
H. L + IL + CivjO + 2x1 + lxl
I. IL + CuO + 2x1 + lxl + Cu20J. L + lxl + 2x1 + Cu20 + 1x2
K. L + 2x1 + Cu20 + 1x2 + 1x0
L. lxl + 2x1 + Cu20 + 1x2 + 1x0
2x1 + lxl + 14x24 + CuO + Oil
L + Cu + Cu20 + 1x0 + 1x2
1315 0.40
1277 -0.29
1274 -0.35
1189 -0.73
1273 -0.90
1225 -1.31
1223 -1.33
1223 -1.35
1189 -1.65
1205 -2.92
1209 -3.10
1071 -4.70
793 -3.17
1261 -6.37
Table II.6.8: Some 4-phase reactions of the Sr-Ca-Cu-0 system.Label Reaction Label Reaction
1 IL=2xl+14x24+CuO 17
2 2xl+14x24=lxl+IL 18
3 14x24+IL=lxl+CuO
4 14x24+2xl=lxl+CuO 19
5 2xl+lxl+CuO=IL 20
6 CuO=Cu20 (+2x1+1x1) 21
7 IL=Cu20+2xl+lxl 22
8 CuO=Cu20 (+IL+2xl) 23
CuO=Cu20 (+IL+lxl) 24
9 2xl+CuO+14x24=L 25
10 IL=L+CuO+2xl 26
11 IL+14x24=L+2xl 27
12 IL+14x24+CuO=L 28
13 2xl+14x24=L+lxl 29
14 IL+lxl=L+2xl 30
15 IL+lxl=L+CuO 31
16 CuO+lxl+14x24=L 32
2xl+CuO=L+012
CuO=Cu20 (+L+2xl)CuO=Cu20 (+L+lxl)Cu20+lxl=L+2xl
Cu20+lxl=L+lx2
Cu20+lx2=L+2xl
lxl+Cu20=2xl+lx2
lx2+lxl=L+2xl
L+lx0+Cu2O+2xl
lx2+2xl=L+lx0
lx2+Cu2O=L+lx0
2xl+Cu2O=lx2+lx0
2xl+Cu20=lxl+lxO
lxl+Cu20=lx2+lxO
1x1+1x0=1x2+2x1
2xl+CuO=14x24+011
1x1+2x1=1x0+14x24 (Po2<3 bar)1x1+1x0=2x1+14x24 (P02>3 bar)
SR-CA-CU-O159
i i i i
1400^© [29]
[15]
1300-
- [47]
(Sr.Ca)O -
v11200-
(3d0 o ©
o
-
Temperature[
1100-
1000-
900-
800-
700-
600-
500-
O
ll
©
\°-
I i i i
(Sr
) 0.20
0.4 0.6 0.8 1.0CaO
Figure II.6.1: Miscibihty gap of the (Sr,Ca)0 solution. The solid line is calculated
from this work and compared to the estimation of Kemp et al. [94Kem] and experimental
data [91Rot,95Jac].
5.50
CO
5.45
9.90
9.80
9.705.40
Figure II.6.2: Lattice parameters of 1x2. The Ca-solubility of 1x2 in equilibria with
1x0 and Cu20 reaches 18 % at 1173 K.
0.1 0.2 0.3 0.4 0.5 0.6
xCa ^ (xSr + xCa)
160 THE BSCCO SYSTEM
0SrO
0.4 0.6 0.8 1.0CaO
Figure II.6.3: Enthalpy of mixing of the (Sr,Ca)0 solid solution. The experimentaldata [66FH] are compared with several calculated curves ([94Kem]: dashed line, [95Jac]:dotted line, this work : solid line).
~Ca'1 (XCa + XSr)
Figure II.6.4: Enthalpy of mixing of the (Sr,Ca) solid solutions. In this plot, the
enthalpy values are given per mole of cations for comparison between the differentphases. The experimental points are joined by dashed lines, the calculated values are
indicated by solid lines.
SR-CA-CU-O 161
Log(P02 [bar])
Figure II.6.5: Oxygen potential diagram. The invariant equilibria are labelled accord¬
ing to Table II.6.7. The A-phase reactions are numbered after Table II.6.8. The end
point of several lines correspond to the invariant equilibria of the ternary systems. The
filled circles correspond to the conditions of the isothermal sections in Fig. II.6.8 and
the filled squares to those in Fig. II.6.7.
162 THE BSCCO SYSTEM
B
-2.5 -2.0 -1.5 -1.0 -0.5 0 0.5 1.0
Log(PQ [bar])
1400
1350-
-1.5 -1.0 -0.5
Log(P0 [bar])
1.0
Figure II.6.6: Stable field of the IL compound (shaded area): A. Stability limits of ILcalculated from the optimized description (GgfgiiCtKial.Cxl02 = —4820—1.6 T). B. Shift mthe stability limit obtained by a small energy change (G^014Cao 86cuo2
= —4920 — 1.6 T)
SR-CA-CU-O 163
Po2= °-21 bar
T=1223K
CuO
.rt* 14x24//
* 1x1 Y^Mi(i iO^M.—«.\\\
>c? 2x1./''/ !/;LLl\''-) K^V^y^1"'^
SrOO
-*7S—
0.6 0.8
XCa' (xSr+xCa+XCu)
CaO
B
pn =1.01 bar1 -°;
T=1273K
CuO
0.4 0.6 0.8 1.0
XCa l (xSr+xCa+XCu)
Figure II.6.7: Characteristic phase relations around the IL compound: A) at 1223 K
vn air, B) at 1273 K in 1.01 bar 02. The CuO contents of the uopleths of Fig. 9 are
indicated by the arrows 9A to 9D.
164 THE BSCCO SYSTEM
CuO
p0 = 0.21 bar
SrO 0
CaO
XCa' 'XSr+XCa+XCu'
CuO
B
p0 = 0.03 bar
\
r? 1x1
3* 2x1./ ', •', InLiJj '-' J V'"^
SrO 0 0.2 0.4 0.6
Xca^Sr+Xca+Xcu)
CaO
Figure II.6.8: Isothermal sections at 1123 K at several oxygen partial pressures: A)0.21, B) 0.03, C) 10~3, and D) 10~b bar.
SR-CA-CU-O 165
1.0^CU2°
pO2=10"3bar
CaO
SrO 0 0.2 0.4 0.6 0.8
xCa / (xSr+xCa+xCu)
1.0^Cu2°
po = 10'5bar
CaO
SrO 0
D xCa ^ (xSr+xCa+xCu)
Figure II.6.8: Cont 'd
166 THE BSCCO SYSTEM
1500-
g1 so¬
0)1_ lace ^£
Q.
E1200-
*Ca /(xSr + xCa)
Figure II.6.9: Isoplethal section in air at various CuO contents: A) S3, B) 50, C)63, and D) 80 mol.% CuO.
SR-CA-CU-O167
A [9]EJ[12] |X[7]
V[13]|+ [6]*[11]<S[27]
0.4 0.6 0.8
W^r^Ca)
1.0
1600
0[27]
xCa ^ (xSr + xCa)
Figure II.6.9: Cont'd
168 THE BSCCO SYSTEM
Figure II.6.10: Representation of tiehnes between A) 1x0 and 2x1, B) 2x1 and 1x1,and C) lxl and 14x24- The optimized lines are calculated under the various conditions
given by the experimental studies They are however almost identical.
SR-CA-CU-O169
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Part III
Equilibrium States along
Processing Routes
174 PROCESSING
III.l Phase Diagrams and Large Scale
Applications
In this final part, we would like to discuss some phase diagram regions of inter¬
est for processing superconducting components of the Bi2Sr2CaCu20„ (Bi-2212) and
Bi2Sr2Ca2Cu30I (Bi-2223) phases. The calculations presented here were obtained from
a preliminary thermodynamic description of the complete Bi-Sr-Ca-Cu-0 (BSCCO)system (see Chap.II.l). This description is not optimized, it is based only on a few
selected experimental data and does not contain the results of the most recent opti¬mizations [95Risl, 95Ris2, 95Ris3, 96Hal2, 96Hall]. The data set used in Part III is
summarized in the Appendix. The calculated diagrams are preliminary ones and givetrends without attempt being correct in details.
These preliminary results are however of interest for several reasons. On one hand,they are a first approximation of the phase equilibria in the five component BSCCO
system and represent an important test in as much the thermodynamic descriptionsof the lower order systems can be used for extrapolation. On the other hand, the
interest lies in the knowledge of the effective phase relations under given conditions as
much as in how these phase relations change with the temperature, the oxygen partialpressure, or the composition. If the present extrapolations cannot be expected to
have a high reliability in giving absolute values, they can however be useful to outline
general tendencies and relative changes in the phase relations. Their comparison with
experimental results from processing studies might open up new possibilities for better
compositions and processing conditions.
The number of experimental reports which contain informations on the phase relations
in the BSCCO systems is considerable. In the following, we have always referred to
the most relevant articles that we are aware of, but we have no claim to present an
extensive literature review as was the case in the optimization work of Part II.
Most large scale applications of the new superconducting cuprates are related to the
electric power engineering e.g. [95Dew, 95Duz]. The devices of interest include current
limiters, transformers, generators, power transmission cables or energy storage systems.The superconducting parts have to be processed as wires, tapes, thick films, or in bulk
form. In such applications, the material has to sustain large transport currents and
one of the required key properties for the superconducting part is to have a sufficientlyhigh critical current density. In polycristalline materials, the critical current densityis limited by the size of the iutergraiii currents. The two bismuth-based cuprates Bi-
2212 and Bi-2223 belong to the favourite candidates for large scale applications, as
they can have a good iutergraiii "connectivity" and sustain large transport currents,if the superconducting grains are sufficiently aligned. Thus, the choice of an adequatecompound depend on the properties of the superconducting phase as well as on the
ability to process it with the optimal microstructure e.g. [95Eib]. One prerequisit for
having significant iiitergrain currents at all is to have dense materials. This is a key
PHASE DIAGRAMS AND LARGE SCALE APPLICATIONS 175
requirement for any processing route.
In the case of the 2212 phase, the densification can be obtained via a meltprocessing
route [89Boc]. This technique has been applied to bulk e.g. [89Boc, 93Hee2, 94Gor],
thick films e g. [90Kas, 95Has, 95Hol2, 96Buh], wires or tapes e.g. [95Holl, 95Mot,
95Shi, 95Zha]. During meltprocessing. the material is heated above the decomposition
temperature of 2212 in ordei to produce a sufficient amount of liquid for densification.
The 2212 phase has then to be reformed out of the liquid and the secondary phases
during solidification or in subsequent annealing treatments. Large remaining grains of
secondary phases should be avoided as they can considerably reduce the current carry¬
ing fraction of the material and as they affect the alignement of the superconducting
grains. Some finely dispersed small grains of secondary phases may however have a
positive influence on the superconducting and mechanical properties of the material
e.g. [93Xul, 95Majl]. The phase diagram regions relevant to these aspects of melt¬
processing 2212 are presented in Chap.III.2. The discussion focuses on the stability
of 2212 in section III.2.1, on the melting line and the liquid composition in III.2.2, on
the stability of secondary phases in the partially melted state in III.2.3, on the regions
suitable for crystal growth of the 2212 phase or for the introduction of precipitates in
III.2.4, and on some solidification examples in III.2.5.
In the case of the 2223 phase, no direct processing route could yet be found, which
produces enough liquid for densification in a fiist step and where the 2223 phase can
form upon solidification in a second step. The densification of 2223 has therefore only
been obtained with the application of an additional mechanical pressure, i e. after hot
rolling for wires and tapes e.g. [91Ich, 95Per] or pressing for thick films e.g. [95Yos]and bulk parts e.g. [94Gor, 95Hon]. The stability of the 2223 phase is discussed in
section III.3.1, and thermodynamic considerations on the importance of the equilibria
between 2223 and the liquid for the formation of 2223 are presented in III.3.2
The phase relations in the BSCCO system are complex. Those encountered in pro¬
cessing conditions are even more complicated since several additional elements have to
be added to the system. Of particular interest is the influence of carbon, silver, and
lead. Carbon is often present in the system because SrC03 and CaC03 are commonly
used as starting materials. The influence of the C content on the phase relations is
unknown. Silver is currently the favourite substrate material used for BSCCO com¬
pounds. Since melting starts at the Ag/BSCCO interface, silver is also often mixed
to the starting BSCCO powder in order to obtain a homogeneous distribution of the
melting point. The influence of Ag on the phase relations is not fully understood, but
it seems that Ag can dissolve practically only in the liquid phase, and that the major
influence is to lower the temperature of the melting reactions [94Lan, 94Joo, 94Has].Lead addition was found to promote the formation of the 2223 phase [88Tak], and
most investigations are available on Pb-doped 2223. There are very few studies on the
undoped Bi-2223 compound.
176 PROCESSING
III.2 Bi-2212 Superconductors
III.2.1 Stability of the 2212 phase
The present model for the 2212 phase is explained in section II.1.5. The experimentalstudies on the cation- and oxygen-nonstoichiometry of 2212 are briefly summarized
there too. They were used to determine the parameters influencing the size of the
single-phase region. The stability of the 2212 phase with respect to the other phaseswas based on experimental data concerning the enthalpy of formation of 2212 [93Ide]and the melting temperature of 2212 in air and in 1 bar 02. The latter data are
presented below and, in the following, the phase relations around the 2212 phase are
discussed.
Stability limits
The stability of a phase as a function of the temperature and the oxygen partial pressure
is conveniently represented in terms of its stability limits. The stability limit separatesthe domain where the phase is stable from those where it is not stable. The single-phase field forms only one part of the domain where the phase is stable. The phaserelations are also dependent on the composition and it is clear that the stability limits
of a solution phase can change for each composition. If the phase does not show a
large range of solid solution, it can however be expected that the phase equilibria,at different compositions around the phase, will probably be similar if the phase is
not stable. Thus, as the solution range of 2212 is fairly small, we can expect that
its stability limits will not change too much with composition. This is illustrated in
Fig. III.2.1 where the stability limits of 2212 are shown for two different composition:1) Bi2 iSri 93Ca0 97C112OJ which lies on the Bi-rich, Sr-rich side of the single-phase field
(solid line), and 2) Bi2 iSri gCai 3(^20^ which lies on the Bi-rich, Ca-rich side (dashedline). The calculated stability limits are compared with experimental data in a wide
range of temperature and oxygen partial pressure in Fig. III.2.1.A and a close up of
the melting line is shown in Fig. III.2.1.B.
The melting temperature of 2212 as a function of oxygen partial pressure has been
studied by DTA/TG e.g. [90Idel, 93Hee2, 93Hol, 93Kan, 94Lan, 95Moz], HTXRD e.g.
[92Has, 93Pol, 95Mis], coulometric titration [92Rub, 94Mac, 95Moz], dilatometry andresistivity measurements [95Moz]. These results are summarized in Fig. III.2.1. Values
of the melting temperature of 2212 in air and in 1 bar 02 are listed in Table III.2.1. The
melting temperature varies with composition. The highest melting points are found at
Sr-rich compositions (see Fig III.2.16). The stability limit shown in Fig. III.2.1 should
approximatively be equal to the highest melting point. All DTA measurements listed
in Table III.2.1, except one [90Ide2], were obtained from samples of ideal composition2212. Idemoto et al. [90Ide2] measured samples of a Ca-rich composition, which can
explain their lower values. It is interesting to note that observations based on HTXRD
in air give values comparable to that of Idemoto et al. [90Ide2] even though samples of
ideal composition 2212 were used.
BI-2212 SUPERCONDUCTORS 177
B
-2 -1
Log(P0 [bar])
Figure III.2.1: Calculated stability limit of the 2212 phase compared with experimental
data. The solid line corresponds to the composition 'Bi2iS:r1c)iC<^g7Cxi2Ox. the dashed
line to Bi2 iSr16Cai.3Cu20j..
Values of the stability limit of 2212 at low temperature have been sviggested in a few
studies, but precise data are lacking. XRD analysis of samples annealed at different
temperatures below about 800^0 in air have shown the appearance of secondary phases
e.g. [93Wu2, 95Che, 95Moz]. Wu et al. [93Wu2] investigated the decomposition of 2212
single-crystals. At 400^, no decomposition products were detected, whereas at GSCC,
178 PROCESSING
Table III.2.1: Melting point of 2212 in air and 1 bar Q2-
Ref. Experimental Melting point of 2212f [°C]method hi air 1 bar 02
[90Idel] DTA/TG 870 898
[93Hee2] DTA/TG 890 908
[93Hol] DTA/TG 884 895
[93Kan] DTA/TG 894 906
[93Pol] HTXRD 870
[94Lan] DTA/TG 880 893
[94Has] DTA/TG 883
[94Mac] Coul. titr.f 891 904
[95Moz] DTA/TG 886 903
Dilatometry 888 898
[95Mis] HTXRD 870
[96Lan] DTA/TG 888 905
fDTA/TG data are onset values on heating.^Interpolated values.
11905 and a Cu-free phase were observed at the surface of the sample. However at lower
temperatures, the observation of a possible decomposition is limited by the extremelyslow cation diffusion, and at higher temperatures, the Bi evaporation becomes no longernegligeable and little can be said from the observations at the surface of a specimen.Chernyaev et al. [95Che] observed U905 and 01x1 as secondary phases in samplesannealed below 700*C. The composition of the 2212 phase in the multiphase field was
shifted to higher Ca content and lower Sr content. They conclude on a lower stabilitylimit around 700*0, even though there is no information on the lower stability limit
of Ca-rich 2212 compounds. Mozhaev et al. [95Moz] reported the lower stability limit
of 2212 at 790*0 and 795*0, in air and 1 bar 02 respectively, based on resistivitymeasurements. Samples of the ideal composition 2212 annealed at 840°C were found
to be single-phase by XRD whereas samples annealed at 770*0 were found to contain
only 90 to 95 % of the 2212 phase. The other phases were 11905 and 2110. This
information shows that the sample is no longer detected as single-phase, which is not
surprising as, according to most phase diagram studies, the ideal composition 2212
is probably not in the single-phase region. The observed phase transformation maybe related to the limit of the single-phase field, but certainly does not correspond to
the stability limit of 2212. The most reliable information on the lower stability limit
of 2212 are probably obtained from investigations of the crystallization behaviour in
glasses with the 2212 composition. The 2212 phase has been observed to form at
temperatures above 600*O [91Lee, 93Hol]. The crystallization products consist mainlyof 2212 and 11905. In conclusion, it seems probable that the extension of the 2212
single-phase region decreases not only by approaching the melting limit but also bydecreasing temperature. The lowest stability can be estimated to lie below 600*O in
air.
BI-2212 SUPERCONDUCTORS 179
The stability limit of 2212 at high oxygen partial pressure has been studied by a few
authors [91Tri, 95Chm]. The phases 11905 and 91150 were found as decomposition
products [95Chm] from XRD analysis of annealed samples. At low oxygen partial
pressure, the 2212 phase has been reported to decompose mainly into the phases 23x0
and Cu20 [94Mac, 95Mac]. These two phases have also been reported in solidification
studies under Ar atmosphere [93Hee2, 93Hol] to form an eutectic structure. The
calculated region of stability of 2212 extends to much too high oxygen partial pressures
iii comparison to experimental data. This is certainly due to an overestimation of the
excess oxygen content in 2212 which was based on the data of Idemoto et al. [90Ide2]
(see II.1.5). By reducing the calculated values of the oxygen content in 2212 to be in
closer agreement with other data [91Shi, 93Sch], the stability field of 2212 should be
shifted to lower oxygen partial pressure. The stability of the 2212 phase as a function of
the oxygen partial pressure is in fact very sensitive to the values of the excess oxygen
content in phases such as 2212, H905, 014x24. or 91150. (The term excess oxygen
content is here related to oxidation states of bismuth and copper which exceed the
value of +3 and +2 respectively.)
The calculated values of the melting temperature of 2212 in the range of oxygen partial
pressures between 10-2 and 1 bar O2 are in close agreement with experimental obser¬
vation. Certain aspects of the melt-processing in that region may thus be investigated
with some confidence even with this preliminary thermodynamic description.
Phase relations
The phase equilibria around the 2212 phase are complex and often change consider¬
ably in small intervals of temperature, oxygen partial pressure, or composition. Thus,
many experimental results may appear controversial due to only slight differences in
the effective conditions experienced by the samples. Comparisons between different
experimental studies or even with calculated equilibria are difficult to represent graph¬
ically due to the many dimensions of the system and the nature of the phase diagram
information. In the following, only a few equilibria are discussed as example.
Many phase equilibria studies in the BSCCO system have been made at constant tem¬
perature and constant oxygen partial pressure. This allows to represent the phase
relations in a compositional tetrahedron. Most investigations have been made in char¬
acteristic sections or lines of composition. Some are shown in Fig. III.2.2. Two com¬
mon sections are at constant Sr/Ca ratio (Fig. III.2.2.A) and at constant CuO content
(Fig. III.2.2.B). Phase equilibria studies along composition lines have often been made
along the line joining the superconducting phases (HTSC line), or to test the influence
of the Bi content (Bi-line) and the Sr/Ca ratio (Sr-Ca line).
An overview of the experimental studies on the phase equilibria around the 2212 phase
is given in Table III.2.1. The regions of the phase diagram which were investigated are
specified according to the notation in Fig. III.2.2. Table III.2.1 clearly shows that very
few studies have been made at other oxygen partial pressures than air.
The representation of the phase relations in the plane of 28.57% CuO content is par¬
ticularly interesting since the non-stoichiometry in copper is known to be very small.
In the present model desciiption, the 2212 phase is only defined in that plane (see
Chap.1.4). The calculated phase relations around the 2212 phase at 850*0 in air are
180 PROCESSING
Sr2,3Ca1/30 SrO
1 o4 1 0-Y
0 9/ V Plane of constant 0 9-/ V/ \ CuO content S Calna
-s 08-/ Y 0 8-/ Vf 07
B line
-s 07-/ Y
A6/ f 06
#*0 6/ V HTCSIne
V*£ or*'U905
^03/
05» <>-*» V0
/a2i2 X:
A* /
•\~ 0 4V
^03/.2212
"C ^2223
•^0 2-/ 0 2-/01-/ 01-/
0-J<- 75—/\ A A X0 02 04 06 08 10 0 02 04 06 08 1 0
B,0x *cu 'lxB,+xSr+)lC.+xCu) °U0 BlO„ *Ca ' (xB!+xSr+xCa) CaO
A B
Figure III.2.2: Representative cuts through the compositional tetrahedron of the
BSCCO system A) plane of fixed Sr/Ca ratio, B) plane of fixed CuO content Representative lines ate indicated by dashed lines the HTCS line, the Bi line, and the Si Ca
line Explanations are given in the text
shown in Fig III 2 3 The coiiespondmg 4-phase eqmhbiia aie listed 111 a sepaiateTable
SrO
Calculated 4-phase equilibriaaround 2212 at 850=0 in air
05A 2212 +
050i a 11905 + 014x24 + CuO
0 45-Kl)\\ Y b 11905 + 014x24 + 01x1? Ax*" 0 40 -SCa-i
\\' V c 11905 + 01x1 + 91150
^^/d\ d 02x1 + 01x1 + 91150* 0 35/ h
0** /,---'^4 T\ e 02x1 + CaO + 91150
^ 0 30^--'^ 2212^*^^ Vf L + 02x1 + CaO
025/ \^^ 9 \ \ g L + 02x1 + CuO
020-/ \ h L + 11905 + CuO/ L + CuO \
15 -Jf a' \
01 02 03 04 05
B|0, X / (XBl+XSr+XCa) CaO
Figure III.2.3: Calculated phase relations around 2212 in the plane of 28 57%CwOiontent at 85IPC in air
Most phases calculated to be m equihbiium with 2212 m Fig III 2 3 have also been
obseived 111 the expenmental studies made 111 an and 1 bai 02 For example, the
4-phase equihbiium between 2212, H905, 014x24, and CuO (a) has been lepoited in
many studies e g [90Lee, 92Mul, 94Majl, 95Mac] In general the studies agree on
BI-2212 SUPERCONDUCTORS 181
Table III.2.2: Experimental studies] on the phase equilibria around the 2212 phase.
Ref. T P02 Tetr.J Planes Lines Other
[<] [bar] Sr/Ca CuO HTSC Bi Sr-Ca
[89Tom] 0.21 X
[90Suz] 850 0.21 X
[90Hon] 0.21 X
[90Lee] 850, 900 0.21 X
[90Sch] 850 0.21 X
[90Shi] 0.21
[91Hol] 865 1
[92Maj] 0.21
[92Miil] 830 0.21 X X
[92Leo] 1000 0.21 X
[92Shii] 0.21
[93Cha2] 800 0.21 X
[93CM1] 1300 0.21 X
[94Nev] 840-880 0.21 X
[94Majl] 850 0.21 X
[95Ide] 850 0.21
[95Mac] 725-830 10""5-0.21 X
X
XX X
X X
t Studies related to the cation- and oxygen-uonstoichiometry of 2212 are
summarized in section II.1.5.
i In the tetrahedron
equilibria with 02x1 and CaO on the Ca rich side and with 11_905 and 014x24 on the
Sr rich side. 91150 and CuO are also often reported in equilibria on the Bi poor and
Bi rich side respectively.
The calculated equilibria with less experimental support are those between 2212 and
01x1. Equilibria between these two phases have been reported by only few authors
e.g. [95Mac]. In most studies, equilibria between 2212 and 014x24 or 02x1 are found
instead.
The equilibria with the liquid phase are rarely documented in experimental studies.
Some support the present calculations. For example, the 4-phase equilibrium between
2212, 11905, CuO, and the liquid (h) has been observed at 850T! in air [94Majl].
The calculated single-phase field of 2212 is smaller than reported in most experimental
studies (see section II.1.5). Whenever we want to compute diagrams where the single-
phase region can be seen instead of the several multiphase equilibria lying nearby, we
need a representative composition lying in the calculated single-phase field of 2212.
The composition Bi2os(Sr062Cao38)2.95Cu20I has proven to be quite useful with the
present thermodynamic description. This composition is used for calculations of phase
equilibria around 2212 throughout the rest of this chapter unless explicitely stated
otherwise.
182 PROCESSING
III.2.2 Melting relations and meltprocessing
The composition of the liquid phase, which is in equilibrium with 2212, is rich in
bismuth. This is illustrated by two isothermal sections in Fig. III.2.4.
BiOv
0.2'
0.4 0.6 0.8
xCu ' (XBi+xSr+xCa+xCu)
1.0
CuO
SrO
B
28.57 mol-% CuO,
-' 0 0.2 0.4 0.6 0.8 1.0
BiOx W^Bi+Xsr+Xca) Ca°
Figure III.2.4: Isothermal sections at 85VC in air: A) at constant Sr/Ca ration,B) at constant CuO content. The shaded area shows the liquid single-phase field. The
projections of the cuts A and B are indicated by dashed lines in B and A respectively.
For each composition, an overview of the phase relations as a function of temperature
BI-2212 SUPERCONDUCTORS 183
and oxygen partial pressure can be obtained by plotting the oxygen potential diagram.
For example, Fig. III.2.5.A shows the calculated oxygen potential diagram at the com¬
position Bi2 05(Sr062Ca038)2 95Cu2Oj.. For considerations on meltprocessing, the two
most important lines are the stability limits of the 2212 phase and of the liquid. These
are shown in Fig. III.2.5.B. The 2212 phase can be meltprocessed by starting in the
stability field of the liquid and ending in the 2212 single-phase field. Two major types
of processing routes are indicated by arrows in Fig. III.2.5.B. Most studies are made at
constant oxygen partial pressure e.g. [95Has, 95Shi, 95Yos, 95Zha, 96Buh] using similar
temperature programs (arrow A). The material is heated just above the decomposition
temperature of the 2212 phase for densification, then cooled down to an annealing step
to promote the formation of 2212 and minimize the fraction of secondary phases and
liquid. Another approach is to follow an isothermal meltprocessing [95Hol2, 95Holl].The material is first melted in Ar at a temperature where only CaO and the liquid
are stable. The oxygen partial pressure is then increased under isothermal conditions
(arrow B). There are two main aspects which influence the choice of an optimal tem¬
perature and oxygen partial pressure program.
Oxygen loss
The first aspect is that the oxygen content is larger in the superconducting phases than
in the liquid so that oxygen is released upon melting. In the oxide liquid, the oxidation
state of copper is between +1 and +2 and that of bismuth is equal to +3 or lower. In
2212, the oxidation state of copper can exceed +2 and that, of bismuth can exceed +3.
This oxygen loss plays an important role during solidification. If the cooling rate is
too rapid, the oxygen uptake will not be sufficient and the formation of other phases
(i.e. mainly the 1-layer compound H905) is observed instead of 2212 e.g. [92Hee].The amount of 2212 phase can be increased in a following annealing treatment, but a
significant fraction of secondary phases remain even after longer annealing periods.
The oxygen loss can be decreased if the oxygen partial pressure of the processing
program is increased. The reasons are twofold. On one hand, the oxygen content
in the liquid increases significantly with the oxygen partial pressure in comparison
to that of 2212 (see e.g. Figs. 1.2.2 and II.1.3). On the other hand, the 2212 phase
decomposes into compounds richer in oxygen (i.e. 91150 and 014x24) at higher oxygen
partial pressure. This is illustrated in Fig. III.2.6. Thermogravimetric measurements
show that the oxygen loss decreases significantly when Po2 changes from air to 1 bar
02. The measured weight change in 1 bar O2 decreases in two steps. The first step
corresponds to the decomposition of 2212, the second one to that of 014x24. Thus,
the presence of 014x24 as a decomposition product of 2212 considerably limits the
oxygen loss. This feature can be reproduced by the calculation. However, as the
calculated stability limit of 014x24 lies at higher oxygen partial pressure values than
experimentally observed, a calculation of the weight loss was made at 5 bar 02 to
increase the temperature range where 014x24 is stable and, thus, to amplify the effect.
Growth of secondary phases
The second aspect is that some of the secondary phases can grow rapidly in the partially
melted state and form large needles or platelets. The larger grains can only hardly be
redesolved during solidification and, as a result, the alignement of the superconducting
grains is locally hindered with drastieal affects on the transport properties.
184 PROCESSING
950
900
O 850-
800
750
700
650
950
900
Log(P0 [bar])
() 850•e-
(V
-I
a 800
0n
b
|S 750
700
650
1 1 1 1 i <
•
Partially Melted State
//A
B
2212 stable
i i ii i i
B
-4 -3 -2
Log(P0 [atm])
Figure III.2.5: A) Oxygen potential diagram at the composition
B12.05/^ro^Cao^J2.95C112O2. B) Stability limits of the 2212 phase and the liq¬uid. The arrows indicate the two current trends in meltprocessing routes. The shaded
area shows the region where the stability fields of the liquid and 2212 overlap.
An alternative possibility is thus to melt the material at low oxygen pai'tial pressure
where most secondary phases are no longer stable. Below a certain oxygen partialpressure and above a certain temperature, CaO is the only solid phase in the liquid.Densificatioii in that range can be achieved without the formation of large grains of
BI-2212 SUPERCONDUCTORS 185
0.5
B
8,-0.5c
caJCo
§,-1.0
-1.5-
-2.0
v* calculated in 5 bar 0~
,—TG in 0,\
calculated in air -*
800 850 900
Temperature [°C]
950 1000
1.0
at 930 °C
0.5 1.0
Log(P02 [bar])
Figure III.2.6: Influence of the oxygen partial pressure on the oxygen loss and the
fraction of phases: A) calculated oxygen losses at melting m air and 1 bar O2 compared
to thermogravimetnc data [9JfLan]. B) calculated fraction of phases at 930°C.
secondary phases. Since the oxygen loss is important, various secondary phases may
form during solidification. However, as the processing temperatures can be lowered
with the oxygen partial pressure, as the stable phases are different, etc., the grain size
of the secondary phases tends to remain smaller. A large amount of the 2212 phase
can be regained after an annealing step at higher oxygen partial pressures.
186 PROCESSING
Current trends
Most of the early meltprocessing studies were done in air. The improvements in critical
current densities reflect the two aspects mentioned above. Meltprocessing of 2212 in
air is now mainly used for bulk materials, current densities at 77 K are e.g. 450 A/cm2[94Gor], 1400 A/cm2 [95Pau]. Meltprocessing of thick films, wires, or tapes of 2212
is currently favoured at high oxygen partial pressure, in 1 bar 02 e.g. [93End, 95Mot,95Shi, 95Zha, 96Buh], or at low oxygen partial pressure, e.g. in 0.01 bar 02 [95Has,95Yos] or using isothermal processing [95Hol2, 95Holl]. Critical current densities in
thick films are strongly dependent on the sample thickness e.g. [95Lan2]. Values at 77
K have reached e.g. 18000 A/cm2 [94Buh] (20/mi thick), 13000 A/cm2 [95Has] (30,1mlthick), 6000 A/cm2 [96Buh] (130^m thick).
The shaded area in Fig. III.2.5.B represents the range where both the liquid and the
2212 phase are stable. The phase relations in this area and below are very sensitive to
small changes in composition and their understanding is especially important for the
optimization of the crystal growth of 2212. Slightly different starting compositions will
have different melting points and will lead to different composition of the 2212 solid
solution and to other secondary phases. Above the decomposition temperature of 2212,the phase relations are less sensitive to small changes in the starting composition. This
latter topic is discussed next, the former one follows in section III.2.4.
III.2.3 Stability of secondary solid phases in the partially meltedstate
The ranges of stability of the various solid phases in the partially melted state could be
shown in Fig. III.2.5.A. To facilitate the graphical representation, the stability limits
of these secondary phases are summarized in Fig. III.2.7 and III.2.8 for each phaseseparately. The major secondary phases observed in the meltprocessing of 2212 are
the Bi-free phases 014x24, 01x1, 02x1, 01x0 (CaO), and the Cu-free phases 9U50 and
23x0. Their stability limits are shown in Fig. III.2.7. A few other phases are calculated
to be stable close to the melting line or at lower oxygen partial pressure: H905, 2201,2302, Cu20, 01x2, 22x0. These results are shown in Fig. III.2.8. The stability limits
of H905, 2201, 2302, and 2212 are very sensitive to small energy changes between
these phases. The present calculations are subject to a large uncertainty. These phaseshave furthermore complex crystal structures and may exhibit large differences in their
formation kinetics. Of the compounds shown in Fig. III.2.8, U905, Cu20, and 22x0
have been observed in the meltprocessing of 2212. The following discussion concentrates
on the major secondary phases shown in Fig. III.2.7.
Some general statements can be made for the partially melted state (see Fig. III.2.7
and III.2.8):
BI-2212 SUPERCONDUCTORS 187
-6 -S -4 -3 -2 -1
Log(P0 [bar])
-6 -5 -4 -3 -2 -1
Log(P [bar])
Figure IH.2.7: Stability limits of the secondary phases 014?24_. 01x1. 02x1. CaO.
91150, and 23x0.
1. Starting from the melting point of 2212 in high oxygen partial pressure, the Bi-
free phases form in the order 014x24, 01x1. 02x1, and CaO either by increasing
the temperature or decreasing the oxygen partial pressure.
2. 02x1 is stable in a wide range of oxygen partial pressure. It is found in equi¬
librium with all the other Bi-free phases 014x24. 01x1, and CaO.
3. 014x24 and 01x1 have a common stability limit, indicating that one phase
decomposes when the other forms.
4. 91150 is stable only at high oxygen paitial pressures and 23x0 only at lower
ones.
5. The decomposition temperature of 23x0 does not depend significantly on the
oxygen partial pressure.
Besides these general observations on the stability ranges of the secondary phases, it
is of particular interest to have further information on the fraction of phases under
various conditions. In the following, we would like to compare some calculations with
188 PROCESSING
1000-
Liquid +.
950-
O 900-
ature otoa.
E
£ 800- /y750-
^^"11905 2212
700- 1 p-—,—j—,- 1.
-4 -3 -2 -1
Log(P0 [bar])
-6 -5 -4 -3 -2 -1
Log(P0 [bar])
-4 -3 -2 -1
Log(P02[bar])
-4 -3 -2 -1
L0g(Po [bar])
Figure III.2.8: Stability limits of the secondary phases U905, 2201, 2302, Cii^O,01x2 and 22x0.
experimental observations at conditions which have been favoured for the meltprocess-
ing of 2212. The fraction of phases in the partially melted state are discussed for four
cases: in air, hi 1 bar 02, in 0.01 bar 02, and under isothermal conditions.
The solid phases forming upon melting of 2212 have been studied at several oxy¬
gen partial pressures, mainly in air, in quenched samples [890ka2, 93Xu2, 94Yos,
95Has, 95Yos, 95Zha, 96Lan] or using high-temperature x-ray diffraction (HTXRD)[890kal, 92Has, 92Pol, 93Xu2, 93Pol, 94Has, 95Mis]. Most experimental investiga¬tions have been made on thick films or tapes processed on Ag or using Ag addition
in the oxide powder. The resulting phase evolution can show significant differences
depending wheather Ag was used as a substrate, as admixture to the oxide powder, or
both [94Has]. Experimental studies with conditions close to the equilibrium state in
the BSCCO system are rare and the results which are most consistent with calcula¬
tions are probably those obtained on MgO substrates. As there are few studies of the
phase evolution in the partially melted state, we have also included the results from
BI-2212 SUPERCONDUCTORS 189
the Ag/BSCCO system in the following tables.
In air
Experimental studies of the partially melted state in air are summarized in Table III.2.3.
The calculated phase fractions in air as a function of the temperature are shown in
Pig. III.2.9.
The calculated phase evolution is in general good agreement with the experimental
observations. The phases which form upon melting of 2212 are 02x1. 01x1, and 9U50.
The Bi-free phases 02x1 and 01x1 have been identified and reported by most authors.
A Cu-free phase is also reported in most studies, but only few authors have identified
it with certainty as 91150. From the present thermodynamic description, it seems
improbable that any other Cu-free phase than 91150 could be stable in the partially
melted state in air. The calculated stability ranges of 01x1 and 91150 are compatible
with the reported data. The major difference between calculated and experimental
values concerns the higher stability limit of 02x1, which is found more stable in the
calculation than in any experimental investigation. The decomposition of 014x24 is
observed below the melting point of 2212. The calculation is there in good agreement
with the experimental data.
850 900
Temperature [°C]
950
Figure III.2.9: Fraction of phases
Bl2 05 fSl'o 62Cao 38/2 95CU2OZ .
in air at the composition
reported.phase
Cu-free
unidentified
*
observed.
phase
x
respectively.limits
stabilityhigher
and
lower
the
are
Th
and
T\temperatures
The
|Ag.
on
(d)addition
Ag
with
MgO
on
(c)MgO,
on
(b)Pt,
on
(a)t
882-888
928-
880-989
875-915
-875
-882
work
This
*870-900
900-
880-930
870-910
—
-870
(c)HTXRD
*870-900
900-
880-930
870-920
—
-870
(b)HTXRD
[95Mis]869-900
905-
885-910
863-910
-863
-863
(d)quench
[95Zha]880-
905-
890-
880-900
—
-880
(d)quench
[95Has]X
——
XX
(d)quench
[94Yos]
*860-890
900-
880-900
860-880
—
-860
(d)HTXRD
*860-890
890-
880-890
——
-860
(c)HTXRD
*870-940
940-
910-940
880-910
870-880
-880
(b)HTXRD
[94Has]
—890-
870-890
870-880
—
-870
(a)HTXRD
[93Pol]
——
XX
—
(a)quench
[890ka2]
——
—X
—
(a)HTXRD
[890kal]
91150
CaO
02x1
01x1
014x24
2212
(Tt[X)}-Th[V})tstate
melted
partiallythe
in
phases
Solid
(f)Method
Exp.
Ref.
air.
in
state
melted
partiallythe
in
observed
Phases
III.2.3:
Table
BI-2212 SUPERCONDUCTORS 191
In 1 bar 02
Experimental studies of the partially melted state in 1 bar O2 are summarized in Table
III.2.4. The calculated fractions of phases as a function of the temperature are shown
in Fig. III.2.10.
In 1 bar 02, the 2212 phase is reported to decompose mainly in 014x24 and 9U50.
These phases are also calculated to be the main decomposition products. The calcula¬
tion predicts that the phase 02x1 should foim upon melting too. Experimentally, this
compound is observed to form at a temperature slightly above the melting point of
2212. The major difference between calculated and experimental values concerns the
temperature at which CaO forms. It has been observed at much lower temperature
than the calculation predicts. This point seems related to the discrepancy mentioned
above concerning the stability of 02x1 in air.
The phase 014x24 is the dominant Bi-free phase observed in meltprocessing studies in
1 bar 02. The calculated temperature interval, in which 014x24 is stable, is relatively
narrow. The temperature range where a significant amount of 014x24 is formed would
certainly increase with the addition of Ag to the system due to the decrease in the
melting temperature of 2212. However, it seems that the stability of 014x24 with
respect to 01x1 is slightly underestimated in the present description.
In 0.01 bar 02
Experimental studies of the partially melted state in 0.01 bar 02 are summarized in
Table III.2.5. The calculated fractions of phases as a function of the temperature are
shown in Fig. III.2.11.
In 0.01 bar 02, the observed decomposition products are 01x1, 02x1 and 23x0. CaO
is observed to form slightly above the melting point of 2212. The calculated phase
evolution is mainly in agreement with the experimental findings. The only differ¬
ence concerns the possible stability of the 1-layer compound 11905 above the melting
point of 2212. As mentioned previously, the oxygen content of 2212 with respect to
other phases is certainly overestimated in this preliminary description The calculated
equilibria between 2212 and U905 in low oxygen partial pressures are thus not very
accurate.
Under isothermal conditions
The calculated fractions of phases as a function of the oxygen partial pressure at several
temperatures aie shown in Fig. III.2.12.
In isothermal meltprocessing [95Hol2, 95Holl], the material is first melted in Ar and
then solidified in an oxidizing atmosphere. In 10~6 bar 02, the phases CaO, 23x0,
and the liquid are calculated to be in equilibrium above 1§0°C. 23x0 is calculated to
decompose above 830qC. This phase evolution is supported by the few experimental
results [93Hol, 93Hee2]. By increasing the oxygen partial pressure beyond the stability
limit of 2212. the calculations indicate that 02x1, 01x1 and U905 can be expected as
secondary phases besides 23x0 and CaO.
observed.
phase
x
respectively.limits
stabilityhigher
and
lower
the
are
Th
and
T;temperatures
The
I
Ag.
on
(d)addition
Ag
with
MgO
on
(c)MgO,
on
(b)Pt,
on
(a)f
827-836
837-849
845-
827-901
827-836
-827
work
This
—850-860
860-
-860
-840
-840
(d)quench
[95Zha]
—850-
855-
850-865
850-855
-850
(d)quench
[95Has]
—X
—
xx
(d)quench
[93Yos]
11905
23x0
CaO
02x1
01x1
2212
(Tj[QC]-rA['C])tstate
melted
partiallythe
in
phases
Solid
(f)Method
Exp.
Ref.
Obar
0.01
in
state
melt
partialthe
%n
observed
Phases
III.2.5:
Table
respectively.limits
stabilityhigher
and
lower
the
are
Th
and
T;temperatures
The
\
Ag.
on
(d)addition
Ag
with
MgO
on
(c)MgO,
on
(b)Pt,
on
(a)t
907-928
977-
907-
905-
——
888-
920-
920-
890-910
910-
920-
-909
-907
905-
-905
888-911
888
-920
-880
909-961
-909
-907work
This
(b)quench
920-930
888-911
-888(d)
quench
[96Lan](d)
quench
[95Zha]
91150
CaO
02x1
oixl
014x24
2212
{T,[°C\-Th[K}])%state
melted
partiallythe
in
phases
Solid
(f)Method
Exp.
Ref.
02.
bar
1in
state
melted
partiallythe
mobserved
Phases
III.2.4:
Table
BI-2212 SUPERCONDUCTORS 193
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
~~?11905
860
2212
9H50H
014x24H
1 bar O,
Liquid
02x1
880 900 920 940
Temperature [°C]
960
Figure III.2.10: Fraction of phases in 1 bar 02 at the composition
Bi2 osfSr0 62Cao 3^2 gsCuaO,
1.0
0.9
0.8
0.7
0.6
0.5
0.4 H
0.3
0.2
0.1
_l L.
2212
11905 -f
ln10"2barO,
800 820 840 860 880 900
Temperature [°C]
Figure III.2.11: Fraction of phases in 0.01 bar O2 at the composition
Bi2 05 fSro 62Cao 38^2 95Cii20z.
194 PROCESSING
1 0-
09-at 860 °C
08- "
a, 07-tn
foe¬'s
05-
o
S 04-
Liquid
2212
"-03-
02-
-11905
-01x1
01-CaO ^v
0- 1 1 r^ LT
1 0
09-
08
, 07i
[06
! °5
; 04i
:03
02-
01
0
Log(P02[bar])1 pJ
at 820 °C
^-01x1
-3 2
Log(P0 [bar])
-3 -2
Log(P0 [bar])
1 OH
09-at 780 °C
r
08- /o, 07- /foe-\ 05-
Liquid
-11905 2212
B 04-
"03-
/< -01x1
23xo y\
X101- < Oi
CaO \0- r-^—V r ,
Figure III.2.12: Fraction of phases, under isothermal conditions at A) 86BPC, B)82(PC, and C) 78ff>C
BI-2212 SUPERCONDUCTORS 195
III.2.4 Composition dependence, crystal growth and precipi¬
tates
The influence of the starting composition on the meltprocessing of 2212 has been
studied by only few authors e.g. [93Wul, 95Guo, 96Zha]. Due to the complexity of the
reactions in the Bi-Sr-Ca-Cu-0 system, most groups studying meltprocessing have
selected an appropriate starting composition from early results, and then optimize the
temperature program and the annealing atmosphere. All these starting composition
lie on the Bi-rich, Sr-rich side. The starting composition is usually choosen Bi-rich to
compensate for losses of bismuth due to evaporation. The Sr-rich side is preferred since
the critical temperature of 2212 has been found to decrease when the solid solution
extends towards the Ca-side e.g. [94Maj3]. Most of the information on the influence of
the composition for the crystal growth of 2212 comes from synthesis studies of single-
crystals.
Crystal growth and the 2-phase field 2212+liquid
For crystal growth, the phase diagram domain of interest is where the stability field of
2212 and the liquid overlap (shaded area in Fig. III.2.5.B). Ideally, one is interested in
a 2-phase field between 2212 and the liquid. A two-phase field 2212+liquid is expected
at Bi-rich, Ca-rich compositions [94Majl, 94Nev]. The search for such an equilibrium
is illustrated in Fig. III.2.13. The composition dependence of the phase relations is
scanned at a fixed oxygen partial pressure (air) at several temperatures. At &§§°C
(Fig. III.2.13.A), the 2212 phase is not stable in air. The ideal stoichiometry 2212 lies
in the 4-phase equilibrium L+02xl+01xl+911_50. At 880^0 (Fig. III.2.13.B), the 2212
phase has formed. At 870«C (Fig. III.2.13.C), a two-phase field between 2212 and the
liquid has appeared on the Bi-rich side. A composition lying in this two-phase field
is of special interest. We chose the stoichiometry Bi228Sri.72Cai 06Cui9,4OiE which is
indicated by a cross in Fig. III.2.13.C. A composition temperature diagram joining this
point to the BiO„ corner is shown in Fig. III.2.13.D
The existence of a two-phase field between 2212 and the liquid is of interest for the
crystal growth of the 2212 phase. The relevance of this two-phase field for a new
meltprocessing route depends on several factors. First, the amount of liquid which can
be produced must be sufficient for densification. Second, the fraction of phases which
is obtained at the end of the solidification process must consist mainly of the 2212
phase. Third, the obtained composition of the 2212 solid solution must exhibit the
appropriate superconducting properties. Finally, the processing window must be large
enough in order for the process to be reproducible in practice.
The fraction of phases at the composition Bi2 2sSri72Caio6Cui94Oit in air is shown in
Fig. III.2.14.
Fig. III.2.14 shows that a significant amount of liquid phase may be expected to be
produced below the decomposition temperature of the 2212 phase. The amount of
liquid which is produced is however related to the amount of secondary phases which
will form upon solidification. The two-phase field 2212+liquid lies above the equilibrum
between 2212,11905. and CuO. The more the composition is shifted towards the liquid,
the larger the amount of H905 and CuO which will result. The fraction of secondary
phases can be expected to consist mainly of 11905. A relatively large fraction of this
196 PROCESSING
0 26
03 04 05
Xcu/<x&+xSr+xC+xcJ
03 04 05
xCu/(XB,+XSr+xCa+XCu>
03 04 05
xCu/(*B,+XS,+xCa+XCu>
c
9S0-
^\\y \ \ liquid
900-\Ns\ \850-
800-
/ : FT2212 +11905+ CuO L_
750- 1
I 1
15 2 0 2.5 3 0
2+x in Bi2tx(Sr062Ca038)295Cu205
D
Figure III.2.13: The search for the 2-phase field 2212+hquid. The composition
dependence is scanned at several temperature by isothermal sections: A) 89WC, B)88CPC, and C) 87CPC The 2-phase field 2212+hquid appears at 870°C. A composition
of interest is indicated by a cross. The composition-temperature diagram along the line
of Hi-content including the composition of interest is shown m D). The fraction ofphases along the dashed line shown in D) is plotted in Fig III.2.H
phase in the resulting material may be nevertheless acceptable if the detrimental Bi-
free or Cu-free phases can be avoided. U905 has the advantage to be closely related to
2212 and a better texture on a large scale might be obtained than with few remaininggrains of Bi-free and Cu-free phases. For low temperature applications, the presenceof 11905 may be less problematic since this compound has a Tc value around 20 K.
The resulting composition of the 2212 solid solution will be Bi-rich and Ca-rich. In
that region, the critical temperature of 2212 is certainly much lower than 95 K, but
BI-2212 SUPERCONDUCTORS 197
1.0--
0.9-
0.8-
<d 0.7-
to.6-° 0.5-
o
•G 0.4-CO
"- 0.3-
0.2- =
0.1-
0--
Figure III.2.14: Fraction of phase at the composition Bi228Sri72Cai 060111940, in
air.
can be expected to lie above 80 K [930ka, 94Maj3]. For a comparison, a few compo¬
sitions of flux or solvent used in various experimental studies on the growth of single-
crystals of 2212 are shown in Fig. III.2.15. Single-crystals have been obtained by slow
cooling e.g. [95Hual], top-seeded solution growth (TSSG) e.g. [930ka], and travelling
solvent floating zone (TSFZ) e.g. [930ka. 94Li, 95Hua2]. Several reviews have been
given e.g. [93Ass, 94Kho]. The 2212 phase resulting from the starting composition
Bi22sSr1.72Ca106Cu1.94OT can be expected to have properties close to those measured
by Oka et al. [930ka] on their single-crystal. Oka et al. [930ka] used the starting
composition Bi24Sri5CaioCui8Oa! for TSSG and TSFZ growth. In both cases, the
resulting 2212 composition was Bi22Sri8CaioCui90I with a Tc value around 85 K.
The processing window can be expected to be relatively narrow, but large enough for
practical applications. In conclusion, this possibility of meltprocessing the 2212 phase
should be investigated further.
Growth of precipitates
The inclusion of small grains of secondary phases in the superconducting material may
have a positive influence on the superconducting or the mechanical properties. This
is particularly of interest for the BSCCO superconductors since they have a relatively
weak pinning potential and are very brittle. In order to improve the critical current
density of superconducting materials, it is necessary to introduce defects in the ma¬
terial, which create dips in the order parameter of the superconducting state. The
potential dips, the so-called "pinning" centers, are energetically more favourable for
magnetic flux vortices penetrating the material. The pinning centers allow thus to
preserve the superconducting properties even when a magnetic field gradient is present
iO 800 850
Temperature [°C]
900 950
198 PROCESSING
Sr0 62Ca0 38°0.55-
\ -f-Bi228Sr172CaI06Cu1s4Ox
*
**
-> 0.50 4<
0-45/ D\/ 0 >
A [930ka]
0 [94Li]
O [95Hua]
[95Kis]
X3 0.40/^y^l
/— 2212 +liquid \
V* 0.35/<!>
0.20 0.25 0.30A
0.35 0.40 0.45
BiOx XCu / (xBl+xSr+xCa+Xi \ CuO
Figure III.2.15: Some starting compositions used in crystal growth of 2212 are com-
with the calculated isothermal section at 87CPC in air.
inside the material. High critical current densities are therefore dependent on the pin¬ning potential of the material. Defects can serve as pinning centers if their size is
comparable to the coherence length of the superconductor. This means, for BSCCO
superconductors, that pinning centers should not exceed about 10 nm.
Precipitation of secondary phases have recently been reported by Majewski et al.
[95Majl] to increase the critical current density in Bi-2212 superconductors. These
results brings a further interest for the phase equilibria around the superconductingphase. The phase relations around the 2212 phase as a function of the temperature in
air are shown in Pig. III.2.16. Both cuts lie in the plane of constant 28.57% CuO. The
first one shows the influence of the Bi content, the second one shows the influence of
the Sr/Ca ratio.
The growth of precipitates has been tested in both sections by annealing the 2212 phaseslightly above the single-phase field [94Maj2]. Majewski et al. [95Maj2] could increase
the critical cuirent density of their sample by a factor 5 after a short heat treatment
of about 20 min in the 3-phase field 2212+02xl+L. Longer annealing times result in
a decrease of jc probably due to an increase in the grain size of the precipitates. At
the ideal time, the size of precipitates was about 100 nm, so that the possible influence
of the precipitates on the pinning behaviour is still unclear. These results are however
promising and various types of precipitates will have to be tried, which will requirea more precise knowledge of the single-phase domain of 2212, especially at various
oxygen partial pressures.
BI-2212 SUPERCONDUCTORS 199
2.00 2.05 2.10 2.15
2+x in Bi2+x(Sr06Ca04)3.xCu2O8
2.20
0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4
y in Bi21Sr29.yCayCu208+8
Figure III.2.16: Phase relations around the smgle phase field of 2212 m air.
200 PROCESSING
III.2.5 Solidification cases
The phase evolution during solidification of 2212 materials has been studied by many
authors e.g. [89Boc, 92Has, 92Hee, 93Hol, 93Pol, 94Has, 95Kis, 95Zha, 96Lan]. The
fraction of phases obtained in the partially melted state as a function of the composi¬tion, temperature, or oxygen partial pressure has been briefly discussed in the previoussections. The fraction of phase resulting from the solidification process is influenced bytwo furthei processing parameters which are the maximum temperature of the melt-
processing and the cooling rate. For example, the influence of these two parameters
on the phase assemblage of bulk 2212 meltprocessed in air has been studied by Heeb
et al. [92Hee]. These results are shown in Fig. III.2.17.
The kind and the amount of Bi-free phases which form during solidification dependon the maximum temperature. In air, 01x1 has been the only Bi-free phase found byseveral authors e.g. [890kal, 89Boc, 92Hee]. In other studies, large amounts of 02x1
and 01x1 have been simultaneously observed e.g. [92Has, 93Pol, 94Has, 95Zha]. Other
secondary phases, which have been reported to form during solidification in air, are
CuO, Cu20, and the Cu-free phases 9U50, 23x0 and 22x0.
The increase of the H905/2212 ratio with the cooling rate or the maximum temperatureis a general trend observed in all studies. In early investigations, 11905 was alwaysfound at the beginning of the solidification process and it has been proposed that the
2212 phase forms only via an intermediate reaction with U905 e.g. [89Boc, 93Hol].The 2212 phase, however, could be observed to form directly from the melt duringsolidification of thick films [95Lanl] or tapes [92Has]. The latter results suggest that
the resulting H905/2212 ratio is mainly dependant on the composition of the liquid.Two factors are therefore expected to control the formation of the 2212 phase duringsolidification, namely the rate of oxygen uptake by the liquid and the redistribution of
the cations via the dissolution of secondary phases in the liquid. In the following, we
present some first calculations made to simulate the influence of these two factors.
Oxygen uptake during solidification
The melting of the 2212 phase is characterized by a loss of oxygen (see Fig. III.2.6).During solidification, only part of the oxygen lost to the surrounding atmosphere will
be re-absorbed by the condensed phases. The effective oxygen content in the material
during solidification always lies between two extreme values: the maximum value is
given by the oxygen content of the system in equilibrium with the surrounding at¬
mosphere, the minimum value is given by the oxygen content in the system at the
maximum temperature of the meltprocessing. These two extreme cases can be simu¬
lated by equilibrium calculations made under the appopriate conditions.
Let us consider the solidification of 2212 in air as an example. The equilibrium fraction
of phase in air was shown in Fig.III.2.9. The 2212 phase is calculated to be stable below
882qC. The solidification without oxygen uptake is simulated as follow. The equilibriumstate is first calculated in air, at the maximum temperature of the meltprocessing, e.g.
choosen here at 900tC. The condition on the oxygen partial pressure is then released
and the oxygen content in the system at 900^0 is taken as a new condition and keptfix. The result of the calculation is shown in Fig. III.2.18.A.
BI-2212 SUPERCONDUCTORS 201
Cu-free phases
1 10 100
Cooling rate [K/min]
1000
100
B
r-^ anM*—»
c
r>
60o
to
*•—
V 40
F=3
O
20
\ *Jk Cu-free
1 v\V---—
>hases
Cu p/Non-crystatline Phases
" \ v.
01x1
- \\
2212 \
\\
\
\
\
\
V1905
1,1,
900 950 1000 1050 1100
Melting Temperature I*C]
Figure III.2.17: Experimental fraction of phase [92Hee]: A) as a function of the
cooling rate from a maximum temperature of 96ITC, B) as a function of the maximum
temperature for a cooling rate of 7 K/min.
The calculated fraction of phase shows 2201 and 2302 as important solidification prod¬
ucts and U905 appearing only below TSO'C. In experimental studies, only the 1-layer
compound U905 was reported. The phases 2201 and 2302 are strongly related to 11905
202 PROCESSING
both in structure and composition and may have a slower kinetic of formation. If we
assume that the formation of H905 is favoured over that of 2201 and 2302, we can
remove these two phases from the system and performe the same calculation again.The resulting fraction of phase is shown in Fig. III.2.18.B.
B
650 700 750 800 850
Temperature [°C]
900 950
650 700 750 800 850
Temperature [°C]
900 950
Figure III.2.18: Solidification with no oxygen uptake: A) considering all phases, B)assuming that 11905 forms instead of 2201 and 2302.
This calculation represents a limiting case of infinitely fast cooling rate with respect to
oxygen. Looking at the calculated fraction of phase at 750%}, it can be expected that
BI-2212 SUPERCONDUCTORS 203
about half the material will consist of a glass phase for fast cooling rates. A limitation
of the oxygen uptake results in the formation of U905 (possibly also 2201 or 2302)
instead of 2212. This is well supported by the experimental observations.
The above calculation is a limiting case. To simulate the influence of the cooling
rate on the fraction of phase, without applying an extensive kinetic treatment, we can
make equilibrium calculations for various oxygen contents lying between the minimum
and maximum values mentioned above. The largest oxygen loss occurs at the melting
point of 2212. We have thus simulated the influence of the oxygen diffusing back into
the system by considering only the variation in oxygen content at the melting point.
The oxygen content corresponding to various cooling rates are described here by the
expression :
x0{T) = x'0 + {xe0-x'0)exp{-{T-Tm)/a] (III.2.1)
where Xq and Xq are the oxygen contents at the beginning and at the end of the melting
reaction respectively. Tm is the melting temperature of 2212, taken here as 882^0. a
is a parameter simulating various cooling rates. The equilibrium oxygen content in
air and the oxygen contents corresponding to the values of a equal to 10, 50, 100,
200, and 500 are shown in Fig. III.2.19.A. The calculated fractions of phase along the
respective curves are shown in Fig. III.2.19.B to III.2.19.F. These calculations are also
made without the phases 2201 and 2302 which form instead of U905 even at the slowest
rate.
The compound H905 obtained during solidification is often observed as intergrowth in
the 2212 phase e.g. [93Hei]. In a typical temperature program of meltprocessing, the
cooling step is followed by an annealing treatment usually around 800^ to increase the
content of 2212 formed from 11905 and the remaining phases e.g. [93Heel]. It is thus
of interest, for example, to know the fraction of phase obtained at the beginning of the
annealing treatment as a function of the cooling rate. This information, obtained from
the calculations shown in Fig. III.2.19, is plotted in Fig. III.2.20.
This result can be compared with the experimental data shown in Fig. III.2.17. The
present simple treatment does not allow to make reliable quantitative predictions. Nev¬
ertheless, these calculations show a promising potential in the use of the theimodynamic
description.
204 PROCESSING
750
E
700 750 800 850 900
Temperature [°C]
800 850
Temperature [°CJ
900
800 850
Temperature [°C]
800 850
Temperature [°C]
800 850
Temperature [°C]
900
D
1 0-
09- Lqud .
08-I
07-
06-
05-
04-11905
03- ____JS!=b 91150 -
02-02x1
01-""
01x1
1 i
800 850
Temperature [°C]
900
Figure III.2.19: A) Simulated oxygen contents corresponding to various cooling rates
in air B)-F) Calculated fraction of phases obtained for oxygen contents correspondingto values of a equal to B) 10, C) 50 D) 100 E) 200, and F) 500
BI-2212 SUPERCONDUCTORS 205
log(coohng rate) [a. u ]
Figure III.2.20: Simulation of the fraction of phase at 80CPC as a function of the
cooling rate
206 PROCESSING
Redissolution of secondary phases during solidification
We mentioned above that the redissolution of secondary phases plays an important role
in the formation of the 2212 phase during solidification. During meltprocessing of thick
films in 1 bar 02, for example, the oxygen uptake is close to the equilibrium conditions
and 2212 forms directly from the melt [95Lanl]. Grains of U905 are first observed
when the fraction of 2212 is already relatively large and the Cu-free and Bi-free phasesare separated from each other by plates of 2212 [96Lan]. The diffusion of cations is
much slower in the solid phases than in the liciuid, so that it can be assumed that the
formation of U905 in a later stage of the solidification process is due to a change of
the liquid composition during solidification.
To test this, a solidification without redissolution of secondary phases is simulated. The
equilibrium state is first calculated in 1 bar 02 at the maximum temperature of the
meltprocessing as before. The conditions on the total composition of the system are
then modified. The composition of the liquid at the maximum temperature is taken as
the new total composition and kept fix. The calculated fraction of phase in equilibriumwith 1 bar 02 was shown in Fig. III.2.10. The fraction of phase obtained in 1 bar 02if there are no ledissolution of secondary phases is illustrated in Fig. III.2.21. The
calculation supports the previous interpretation of experimental data.
650 700 750 800 850 900 950
Temperature, °C
Figure III.2.21: Solidification with no redissolution of secondary phases.
BI-2223 SUPERCONDUCTORS 207
III.3 Bi-2223 Superconductors
III.3.1 Domain of stability
Very little is known on the phase relations around the undoped 2223 phase. Pb ad¬
dition was used in the great majority of studies since it was found that Pb facilitates
the formation of 2223 [88Tak]. The 2223 phase is approximated here as a stoichio¬
metric compound and its thermodynamic description is based on a measurement of
the enthalpy of formation [93Ide] and on melting point data. The latter are discussed
below.
The stability of Bi-2223 as a function of temperature and oxygen partial pressure has
been studied by a few authors [88End, 89Tsu, 92Rub. 94Mac]. These experimental
results are compared with the calculated stability limit of 2223 in Fig. III.3.1.
-4 -3 -2 -1
Log(P02 [bar])
Figure III.3.1: Range of stability of the 2223 phase as function of temperature and
oxygen partial pressure. The melting line %s indicated by a thick line.
The experimental data, based on XRD analysis of annealed samples [88End], DTA/TG
[89Tsu]. and coulometric titration [92Rub, 94Mac], are in excellent agreement with
each other. The measurements based on coulometric titration extend in a wide range
of oxygen partial pressure and show a change in slope at about 10-3 bar 02.
Below 10"3 bar 02. 2223 decomposes into 2212. 02x1. aud Cu20 [92Rub, 94Mac].The T vs. Pq2 dependence of this solid state decomposition was observed to coincide
208 PROCESSING
with the C112O-CUO phase boundary. The calculated equilibria are in close agreementwith these observations. The major difference is that phases such as 11905 or 2302 are
calculated to be more stable than 2212 at low oxygen partial pressure. This problemhas been discussed in section III.2.1. The addition of Pb has been found to increase the
stability limit of 2223 to lower oxygen partial pressure than those of the Cu20-CuOline [94Mac]. Other data [95Tet] suggest that the decomposition line of 2223 may lie
at higher oxygen partial pressure than the Cu20-CuO line even for Pb-doped samples.
Above 10~3 bar 02, 2223 melts peritectically. For a comparison, the melting of 2223 in
air has been observed at about 870<C [91Hor, 92Kim], 875< [88End, 89Tsu, 94Mac],and 885qC [94Ber]. The kind of solid phases present with the liquid phase as a function
of the temperature and the oxygen partial pressure is not well documented. MacManus-
Driscoll et al. [94Mac] reports the presence of 02x1 between 10~3 and 10_1 bar 02,and of 02x1 and 01x1 at higher oxygen partial pressures. In air, several phases have
been found in equilibrium with the liquid upon melting of Pb-doped 2223. These are
2212 [90Lo. 90Str, 94Ber. 95Kae, 95Zha], 11905 [90Lo, 90Str, 91Hor, 910h, 94Ber],02x1 [90Str, 91Hor, 910h, 94Ber, 95Kae], 01x1 [91 Oh], 014x24 [94Ber, 95Kae],and CuO [91Hor, 910h, 94Ber]. The calculated stability limits of the solid phasesin the partially melted state are comparable at the 2223 and the 2212 compositions.In view of the relatively good agreement between calculations and experimental data
at the 2212 composition (see section III.2.3), it can be expected that the equilibriapredicted at the 2223 composition are close to reality. The stability limits of 2223,2212, 11905, and CuO differ only slightly from one another. The equilibria in a small
temperature band along the decomposition line of 2223 are rather uncertain. With
the present thermodynamic description, only 2212 is calculated to be stable above the
decomposition temperature of 2223. The calculated stability limits of 11905 and CuO
lie below that of 2223. The addition of Pb was found to lower the melting point of
2223 by about 10 to 20 K [92Kim, 94Ber, 94Mac].
The stability limit of undoped 2223 at high oxygen partial pressure is practically un¬
known, but lies, according to the results of Endo et at [88End], probably slightly abovethe air atmosphere. The stability limit of Pb-doped 2223 has been studied by Allemeh
and Sandhage [95A11] between 500 and WSV,. They also found the 2223 phase to
decompose at oxygen partial pressures slightly above 0.2 bar 02 almost independentlyof the temperature. The calculated stability limit at high oxygen partial pressures is
consistent with these observations.
The stability limit of 2223 at low temperature is unknown. It has been reportedthat the 2223 phase forms only in a narrow temperature interval below its meltingline e.g. [88End]. Thermodynamic considerations about this domain of formation are
presented in the next section.
III.3.2 Domain of formation
The 2223 phase has been found difficult to form. The presence of a liquid phase seems
necessary to the formation of 2223 and has been explained by kinetic reasons, i.e.
because the transport of cations and thus the reaction kinetic is increased with the helpof the liquid. The positive influence of Ag and Pb in the processing of 2223 materials
BI-2223 SUPERCONDUCTORS 209
has also been attributed to some extend to their lowering of the melting reactions,
which may increase the processing window. The phase equilibria involving 2223 and
the liquid are thus of particular interest as a domain favourable to the formation of
2223.
The phase relations around the 2223 composition in air have been studied by a few
authors at different temperatures. The 2223 phase was not found by Miiller et al.
[92Miil] at &S0V and by Nevfiva et al. [94Nev] at 860^!. but it was obtained by
Majewski et al. [91Maj, 94Majl] at 8501C.
The calculated phase relations in air in isothermal sections of Sr/Ca ratio equal to 1 are
shown in Fig. III.3.2. The phase relations around the 2223 phase observed by Majewski
et al. [91Maj, 94Majl] at 850^ are to a large extend similar to those calculated at
8700C. They observed the very flat 4-phase equilibrium between 2223, 2212. 02x1.
and 014x24 at the Sr-rich, Ca-rich side of the 2223 phase, whereas they found the
Bi-rich, Cu-rich compositions to lie in the 4-phase equilibria 2223-L-02xl-2212 or
2223-L-02xl-CuO. The calculated equilibria at STOX! agree with these experimental
data to the exception of those between 2223 and CuO, which appear at oxygen partial
pressures lower than air in the calculations. In air, the 2223 phase is calculated to be
in equilibrium with 014x24 instead of CuO. Below the temperature at which 2223 gets
in contact with the liquid, the 2223 phase is predicted to be "'squized" between two
very flat equilibria with 2212, 02x1, and 014x24-
The most important feature of the phase equilibria around 2223 is probably that the
phase fields are very flat. This means, as already mentioned by Majewski et al. [91Maj,
94Majl], that a small deviation from the 2223 stoichiometry results in a drastic decrease
of the 2223 phase fraction. From their phase diagram, Majewski et al. [91Maj. 94Majl]
suggested to use Bi-rich. Cu-rich compositions in order to avoid the very flat 4-phase
equilibrium between 2223, 2212, 02x1, and 014x24. The present calculations suggest
that very flat equilibria surround the 2223 phase up to the temperature at which
equilibria with the liquid occur.
The calculated phase relations along the line joining the 2223 stoichiometry to the
(Sr,Ca)0 corner are shown m Fig. III.3.3.A. Fig. III.3.3.A shows that the composition
range lying inside the stability domain of 2223 is drastically increased with the appear¬
ance of equilibria with the liquid. This opens the processing window in composition.
The 2223 phase fraction is shown in Fig. III.3.3.B for two different temperatures lying
below and above the first melting reaction.
This shows that equilibria between 2223 and the liquid are probably also necessary from
a thermodynamic point of view in order to obtain a large amount of the 2223 phase.
The region of temperatures and oxygen partial pressures where 2223 and the liquid
can be expected to be in equilibria is shown by the shaded area in Fig. III.3.4.A. This
calculated narrow temperature band where the formation of 2223 should be favoured is
in good agreement with the experimental observations shown in Fig. III.3.4.B [88End].
210 PROCESSING
850°C
0.2 0.4 0.6 0.8
W <xB,+xSr+XC«+xCU>
1.0
CuO
BiO„
0.2 0.4 0.6 0.8
><CU/(xDi+x&+X&+xCu>
1.0
CuO
850°C
0.25
BiOv
0.30 0.35 0.40
W<x&+xS,+xC.+xCu>
0.45
CuO
0.25
BiO„
0.30 0.35 0.40
xCu' (xBi+xSr+xCa+XcJ
0.45
CuO
Figure III.3.2: Isothermal sections at Sr/Ca ratio equal to 1 in air: A) and B) at
850PC, C) and D) at 870°C. B) and Dj show an enlarged area around the 2223 phase.
BI-2223 SUPERCONDUCTORS 211
950
B
0.35 0.40 0.45
XSr+XfiJ(XB,+XSr+XCa+Xr.„)
BrASrT"CaTACu'
0.35 0.40 0.45
xSr+xCa/(XB,+xSr+XCa+xCu>
0.50
0.50
Figure III.3.3: A) Phase relations in air as a function of the (Sr,Ca,)-content. B)
Fraction of the 2223 phase as a function of the (Sv,Cn)-content,
212 PROCESSING
-4.0 -3.5 -3.0 -2.5 -2.0 -1.5 -1.0 -0.5 0
Log(P0 [bar])
Figure III.3.4: A) The shaded area shows the calculated region where both the liquidand the 2223 phase are stable. B) The shaded area shows the experimental phase
diagram region favourable to the formation of 2223 [88Endj.
OUTLOOK 213
III.4 Outlook
After several years marked by the discovery of many new superconducting compounds
and by a rapid increase of the maximum reported ciitical temperatme, the pace of
discovery and the improvement of the superconducting properties has slowed down.
The current favourite materials, among them the BSCCO phases 2212 and 2223, have
established themselves as '"good enough" for a whole series of new applications and
will probably remain subject of research for some years. The research effort now
concentrates on the optimization of the piocessing methods in order to optimaly use the
potential of these materials and in order to achieve a better reproducibility. This means
that much more precise phase diagram knowledges will be required than currently
available. Where considerable uncertainties remain in different systems could be shown
well in the optimization work (see e.g. Chap. II.5 and II.6). The thermodynamic
description presented in this work forms an ideal basis foi any further study of the
phase relations in the BSCCO system.
Some preliminary calculations have shown that a probable 2-phase field between the
liquid and the 2212 phase might be of interest for meltprocessing. A starting compo¬
sition and processing window have been suggested. Further experimental work in that
part of the phase diagram are now needed to clarify the phase relations.
Equilibrium calculations have been used foi testing extreme cases and making simple
simulations of the solidification of 2212 materials. Reliable quantitative predictions
cannot be presented at this stage. The calculations were mainly intended as a way
to demonstrate the potential of the approach. The thermodynamic database resulting
from this modelling work of the BSCCO system offers an excellent starting point for
kinetic treatments. Further work should be directed towards the modelling of the
solidification process.
The comparison of first calculations with experimental results obtained under process¬
ing conditions has clearly shown that further elements should be included in the model
description. Possible extensions of the thermodynamic description are for example: the
inclusion of Ag to consider the influence of substrate or additives, the inclusion of Pb
for the processing of 2223, the inclusion of Y and Ba for the processing of the newly
reported 1212 phase which shows less anisotropy.
Finally, the research on the superconducting systems has given a great impulse for
a better understanding of oxide systems. Many phases discovered in the BSCCO or
related systems may exhibit other interesting properties than superconductivity. The
thermodynamic modelling presented here may also find valuable applications and new
extensions, for example towards systems of Bi-based ionic conductors.
214 PROCESSING
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[95Hua2] Y. Huang, M.-H. Huang, K.-W. Yeh, and M.-Y. Hong, "Controlled Growth
of Bi2Sr2CaCu20„ Superconductor Single Crystals", Mater. Chem. Phys.,41, 290-294 (1995).
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Oxides of the Bi-2212 Phase", Physica C, 249, 123-132 (1995).
[95Kae] S. Kaesche, P. Majewski, and F. Aldinger, "Phase Relations and
Homogeneity Region of the High Temperature Superconducting Phase
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the Ca-Cu-0 System", J. Am. Ceram. Soc, 78(10), 2655-61 (1995).
[95Ris2] D. Risold, B. Hallstedt, and L. J. Gauckler, "Thermodynamic Assessment of
the Sr-Cu-0 System", J. Am. Ceram. Soc. (1995). submitted.
[95Ris3] D. Risold, B. Hallstedt, and L. J. Gauckler, "Thermodynamic Modelling and
Calculation of Phase Equilibria in Sr-Ca-Cu-0 System at Ambient Pres¬
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222 PROCESSING
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(1996).
[96Hall] B. Hallstedt, D. Risold, and L. J. Gauckler, "Thermodynamic Assessment of
the Bi-Ca-0 Oxide System", J. Am. Ceram. Soc. (1996). submitted.
[96Hal2] B. Hallstedt, D. Risold, and L. J Gauckler, "Thermodynamic Assessment of
the Bi-Sr-0 Oxide System", J. Am. Ceram. Soc. (1996). submitted.
[96Lan] T. Lang, D. Buhl, B. Hallstedt, D. Risold, and L. J. Gauckler, "Microstruc-
tural Evolution during Partial Melt processing of Bi-2212", J. Mat. Res.
(1996). submitted.
[96Zha] W. Zhang, E. A. Goodilin, and E. E. Hellstrom, "Composition Studies for Ag-Sheathed Bi2Sr2CaCu208 Conductors Processed in 100% 02", Supercond.Sci. Technol, 0(3), 211-217 (1996).
Curriculum vitae
I was born on Is' May 1966 in Boudevilliers (NE) as the son of Josiane and Michel
Risold. I followed the Primary and Secondary School in Chezard and Cernier (NE)
and entered High School in La Chaux-de-Fonds in 1981. In 1983-84, I had the chance
to spend one year as an exchange student in Annapolis (MD), USA, where I discovered
the benefits of cross-cultural experiences. Back in La Chaux-de-Fonds, I obtained the
Diploma of Maturite Federate Type C in 1985.
After a period of military service, I started my studies at the Physics Department of
the ETH Ziirich in Autumn 1986. I laid the emphasis on lectures of optoelectronics
and solid state physics, and graduated in 1991 as Dipl. Phys. ETH with a diploma
work on the magnetic properties of type II superconductors.
Since 1992, I have been working as a research associate and PhD student in the De¬
partment of Materials, Institute for Nonmetallic Materials at the ETH Ziirich. This
thesis was performed under the supervision of Prof. L. J. Gauckler.
I am married since 1994 and the proud father of a cute little girl since 1995.
223
Publications
The results of this study have been presented in the following articles and oral presen¬
tations :
Articles :
B. Hallstedt, D. Risold and L. J. Gauckler, "Thermodynamic Assessment of the
Copper-Oxygen System", J. Phase Equilibria 15 [5] (1994) 483-499.
B. Hallstedt, D. Risold and L. J. Gauckler, "'Modelling of Thermodynamics and
Phase Equilibria in Subsystems of the Bi-Sr-Ca-Cu-0 System", in Electroce-
ramics IV, Vol. II, Augustinus Buchhandlung Aachen, Proc. Conf. Sep. 5-7,1994, Aachen, Germany, pp. 911-916 (1994).
B. Hallstedt, D. Risold, R. Miiller and L. J. Gauckler, "Modelling of Thermo¬
dynamics and Phase Equilibria in Selected Subsystems of the Bi-Sr-Ca-Cu-0
System", in Advances m Superconductivity VII, Springer-Verlag, Tokyo, Proc.
7th Int. Symp. on Superconductivity (ISS '94), Nov. 8-11, 1994, Kitakyushu,Japan, pp.' 361-364 (1994).
D. Risold, B. Hallstedt, L. J. Gauckler, H. L. Lukas and S. G. Fries, "The
Bismuth-Oxygen System", J. Phase Equilibria 16 [3] (1995) 1-12.
D. Risold, B. Hallstedt and L. J. Gauckler, "Thermodynamic Assessment of the
Ca-Cu-0 System", J. Am. Ceram. Soc. 78 [10] (1995) 2655-61.
B. Hallstedt, D. Risold and L. J. Gauckler, "Modelling of Thermodynamics and
Phase Equilibria in the Bi-Sr-Ca-Cu-0 System", in Controlled Processing ofHigh-Temperature Superconductors: Fundamentals and Applications, Proc. Int.
Workshop on Superconductivity (ISTEC and MRS), June. 18-21, 1995, Maui,Hawaii", pp. 48-50 (1995).
D. Buhl, T. Lang, M. Cantoni, B. Hallstedt, D. Risold and L. J. Gauckler,"Critical current densities in Bi-2212 thick films", Physica C 257 (1996) 151-
159.
B. Hallstedt, D. Risold and L. J. Gauckler, "Thermodynamic Evaluation of the
Bi-Cu-0 System", J. Am. Ceram. Soc. 79 [2] (1996) 353-358.
224
D. Risold, B. Hallstedt, L. J. Gauckler, H. L. Lukas and S. G. Pries, "Thermo¬
dynamic Optimization of the Ca-Cu and Sr-Cu Systems", Calphad 20 (1996)
to be published.
D. Risold, B. Hallstedt and L. J. Gauckler, "The Sr-0 System", Calphad (1996)
accepted for publication.
D. Risold, B. Hallstedt and L. J. Gauckler, "Thermodynamic Assessment of the
Sr-Cu-0 System", J. Am. Ceram. Soc. (1996) accepted for publication.
D. Risold, B. Hallstedt and L. J. Gauckler, "Theimodynamic Modelling and
Calculation of Phase Equilibria in Sr-Ca-Cu-0 System at Ambient Pressure",
J. Am. Ceram. Soc. (1996) accepted for publication.
B. Hallstedt, D. Risold and L. J. Gauckler, "Thermodynamic Assessment of the
Bi-Sr-0 Oxide System", J. Am. Ceram. Soc. (1996) submitted.
B. Hallstedt, D. Risold and L. J. Gauckler, "Thermodynamic Assessment of the
Bi-Ca-0 Oxide System", J. Am. Ceram. Soc. (1996) submitted.
T. Lang, D. Buhl, B. Hallstedt, D. Risold and L. J. Gauckler, "Microstructural
Evolution during Partial Melt processing of Bi-2212", J. Mat. Res. (1996)submitted.
Presentations :
D. Risold, B. Hallstedt and L.J. Gauckler, "Thermodynamic Evaluation of the
Sr-Ca-Cu-0 System", ACerS 96th Annual Meeting, Apr. 24-28, 1994, Indi¬
anapolis IN, USA
D. Risold, B. Hallstedt and L.J. Gauckler Thermodynamische Berechnungen
des Systems Sr-Ca-Cu-0 DGM Hauptversammlung 1994, May 24-27, 1994,
Gottingen, Germany
D. Risold, B. Hallstedt and L.J. Gauckler Thermodynamic Evaluation of the
Sr-Ca-Cu-0 System Calphad XXIII, Jim. 12-17, 1994, Madison WI, USA
D. Risold, B. Hallstedt and L.J. Gauckler Melt Processing of Bi-Sr-Ca-Cu-0
(BSCCO) Superconductois: a Thermodynamic Approach. Calphad XXIV, May
21-26, 1995, Kyoto, Japan
D. Risold, B. Hallstedt and L.J. Gauckler Modelling of Thermodynam¬
ics and Phase Equilibria in the Bi-Sr-Ca-Cu-0 System. Workshop NFP30
"Hochtemperatur-Supraleitung", Oct. 12-13, 1995, Baden-Dattwil, Switzerland
225
Appendix
The following thermodynamic description of the Bi-Sr-Ca-Cu-0 system is a prelim¬inary version which has been used to test the compatibility between the parametersof the various subsystems and to calculate the diagrams shown in Part III. It should
be paid attention to the fact that the parameters shown below e.g. for the subsystemsBi-O, Sr-O, Sr-Cu-O, Ca-Cu-O, and Sr-Ca-Cu-0 differ from those shown in Part II.
The ones given in Part II are more recent and offer a more accurate description of the
corresponding subsystems, they cannot however be included in the following database
without adjusting parameters in other subsystems.
CuO
GCuO = _172735 + 291.777T - 49.03 Tln(T) - 0.00347 T2 + 390000 T"1
Cu20
GCu2o = _193230 + 360.057T - 66.26Tln(T) - 0.00796T2 + 374000T"1
a - Bi203
Ga"B,2°3 = -606870.23 + 576.2797T - 105.952269 Tln(T) - 0.016929576 T2
5 phase
sublattice model :
(Bi+3,Sr+2,Ca+2)2(0-2,Va)4
parameters :
G*i+3 0_2= 1<3*-B'J°* + 24.93622 T
Gt+'K)-» = Glr2o2 + 1gs-b"°> - l-AGsr + 35.52083T
GL+> o- = GCa2o2 + \g6-^0' - ±AGf + 35.52083T
GBi+3 Va= °
<&«.v. = GL2o2 " 2-Gs-^°* + l-AGsr + 10.58461 T
GCa« va= GCa2o2 - \ GS~Bli°3 + \aGst + 10.58461 T
4.+',s.+'(J-' = -30400- 28 T
4.+»,Ca^.o-» = -123700 +62.4T
226
4l+3sr+^va=-3°400-28T
4,+3,ca+; va= "123700 + 62.4T
where :
Gs-B"°° = -604157.47 + 859.25796 T- 149.748312 Tln(T)
Gsr2o2 = 2GSr0 + 100000
GCa2o2 = 2GCa0 +100000
AG* = 0
/3 phase
stiblattice model :
(Bi+3,Si+2,Ca+2)(Bi+3)2(0-2)2(Cr2,Va)4
parameters :
Gl+,0 2= 1.6 Gi + 35.20367 T
Gl+2 Q_2= G£ + 0 8G^, - 0.5AG? + 40.65455 T
G^a+2 Q_2= G^a + 0.8 Gi, - 0.5A G? + 40.65455 T
GB.+3 Va= °
G£+2 Va= g£ - 0.8 Gi + 0.5A G? + 5.450879 T
G^a+2 Va= G^a - 0.8G|, + 0 5AG? + 5.450879T
iB,+3,Sr+2 o-o=-30400-28 T
j{U»,c+»o-'=-123700 + 624:r
iB,+3iS^Va=-30400-28T
£B,+3ca«va = -123700 + 62.4T
where.
G^ = 1.5GQ"B,2°3 + 45000 - 36.3T
G|r = GSr0 + G°-B,2°' - 67350 + LIT
G£a = GCa0 + Ga~Bl2°3 + 30500 - 46 8T
AG? = 0
7 phase
sublattice model •
(Bi+3,Sr+2,Ca+2)2(0-2,Va)3
227
parameters :
n~l_
nl
"^B^3 O-2~~
°Bi
Gs>-o- = Gl + \Gl- \AG" + 15.87691 T
Gca« o^ = Gca + I Gl -
iA G? + 15.87691 T
GB,+3 Va= °
G&« va= Gl ~ l Gb. + \A G? + 15.87691 T
G3a+2 va= <& - f (& + fA G? + 15.87691 T
^1+3)Sl+20-2 =-339260 +61T
ia+«,c.+>o-» = -214100
^.C^ 0-2= +50000
£Bi+3,S^Va=-339260 + 6l
£B1+3,Ca«Va = -214100
isr«,ca«va =+50000
u;/»ere :
G^ = 2Ga-B'2°3+20000
GJr = 2GSr0 +57000
Gja = 2GCa° +85500
AG,7 = 0
Bii4Ca5026
GiillcSoZ = 7GQ-B,2°3 + 5GCa0 - 137000 - 45.74T
Bi2Ca205
Gillcllol = G°-B'2°3 + 2GCa0 - 40000 + 1.04T
Bi2Ca04
Gb^So, = G"-B'203 + GCa0 - 30000 - 0.94 T
Bi6Ca4013
GBi'66Caa44o,'33 = 3G"-Bl2°3 + 4GCa0 - 101000 - 6.66T
Bi4Sr6015
GbuS^o" = 2G'V-B,2°3 + 6GSr0 + 1.5G°2 - 397000+ 175 T
228
2310
-.2310
22x0
sublattice model :
(Bi+3)2(Sr+2,Ca+2)2(Cr2)5
GB?2fI2o5 = Ga-B,2°3 + 2GSr0 - 113000 + 17 64T
,02210 /-ia-Bl2Oj,or'CaO
CrBi2Ca205- U + ZLr
23x0
sublattice model :
(Bi+3)2(Sr+2,Ca+2)3(0-2)6
GlvLos = GQ-Bl2°3 + 3GS,° - 105000 - 2.56 T
Gn^Lo„
= Ga~B,2°3 + 3GCa° - 32000JBi2Ca205
-23i0
IySr+2,CaI23?»„+2 =+10000
13x0
sublattice model :
(Bi+3)2(S1+2.Ca+2)e(0-2)1l
GbSbOh = Ga-B,2°3 + 6GS,° + G°2 - 316000+ 154.7T
Gb^Ou = GQ-Bl2°3 + 6GCa0 + G°2 + 20800
21x0
sublattice model •
(Bi+3)2(Sr+2,Ca+2)(0-2)4
G^loi = GQ-Bl2°3 + GSr0 - 70000 - 0 05 T
Gl«ca04 = G"-B,2°3 + GCa0 - 21000
91150
sublattice model :
(Bi+3)12(Bi+3)6(Sr+2,Ca+2)32(0-2)65
Gg"50 = 9Ga-B,2°3 + 32GSr0 + 3G°2 - 1470000 + 400 T
Gmw = 9G,a-Bi2o3 + 32GCa0 + 3G°2 - 415000 + 400 T
£p°ca+2 = "750000
229
2110
sublathce model :
(Bi+3)14(Sr+2,Ca+2)12(0-2)33
Gfr110 = 7<3°-b.203 + i2G,s'° - 559000
G2iio = 7G.a-B,2o3 + 12<3CaO _ 1872oo - 49.4T
iSi",Ca+^ = -50000
CaCu2Os
Gclcntol = G°a° + 2G0u0 - 3193.3 + 1.983 T
Ca1_xCu02
Gcl\Zlclol = 15GCa0 + 18GCu0 + G°2 - 226044 + 190.98 T
OlxO
sublattice model :
(Sr+2,Ca+2)(0-2)
GSrO°= GSr° = -603900 + 251T- 45.45T\n(T) - 0.003642T2
4^,Ca« = +22167.5 - 3801 (ter// - 2/c//)
01x2
sublathce model :
(Sr+2,Ca+2)(Cu+2)2(0-2)2
GSr2c2u03 = C3'0 + gCu2° - 16000 - 1-3 T
G&ScuO, = GCa0 + Gc^° + 15550
02x1
sublathce model :
(Sr+2,Ca+2)2(Cu+2)(0-2)3
Gs£c»o3 = 2gS'° + G°"° " 31500 + 3-1 T
Gca2cu03 = 2GCa° + gCu° " 7565 + 11-255T - 0.89Tln(T)
£g?W' = +20000
230
Olxl
sublaiiice model :
(Sr+2,Ca+2)(Cu+2)(0-2)2
GsrCuOj = <?Sr0 + GCu0 - 21800 + 2T
Gc1aCu02 = G°a° + gCu° + 1200 + 0.416 r
£sr« Ca«= +3800
014x24
sublathce model.
(Sr+2,Ca+2)14(Cu+2)18(Cu+3)6(0-2)41
G2-*P„
= 14GSr0 + 24GCu0 + 1.5G°2 + 149600- 70.5T0114VjU24'j4i
Gc^s,24o41 = 14GCa° + 24GC"° + 1.5G°2 - 612000 + 250T
I^.« = "80500
IL compound
<?£ = 7GS,° + 40G°8° + 47GCu0
Bi2Cu04
gb,22Cu044 = GQ-B,2°3 + GCu0 - 13100 + 4.37T
2201
Gfloi = G°"-B,2°3 + 2GSl° + G0u0 + 5(-19000 - 1.8T)
2302
Glial = GQ-B'2°3 + 3GSr° + 2GCu0 + 7(-27000 + 8.1 T)
4805
Glial = 2G°"B,2°3 + 8GSr0 + 5GCu0 + 17(-25000 + 7.5 T)
11905
sublattice model
(Bi+3, Bi+5)2(Sr+2, Bi+3, Ca+2)2(Cu+2, Cu+3)1(0-2)6(0-2, Va)0 2
parameters :
^,11905_ ^,11905
"B^3 Sr+2 Cu+2 O-2 Va~~
^905
^11905 _
,-,11905 , 1nA ^U905 , r.U905
^B,+5 Sr+2 Cu+2 0_2 Va- (JU905 + lui*UBi+3-Bi+5
+ °d
231
232
511905+
t>ACfCu+2_Cu+3^+i<(+10AG-Bi+3_Bi+5+b—+
.-,11905nA,cll905,^il9"^AAi,C11905,
Bi+35AGs^9f+4G°20-2GSl°-Ga-B'2°3+Grrws5Je+CrCu+2_Cu+3OflZ+^)c+C1W05_l_A>U905AKo.011905,
Bi+35AGs^9f+4G°30-2GSr0-G°-B'2°3+Gjjgot5p05+5AG^9+025_Cu+3+2
S?905+lOAG^S8.^.+G°210+Gff90056SP°5+
Cu+3G^+°255A2+G°210+Glfoos
5f905++10AG^f_Bi+5AGs%fCa+2+1G°20+2GSr°-2GCa0+Gao°55
0a«AG^f+1G°20+2GS'°-2GC*°+(?S
SfM+Gii9f_B_+5A1Q++5ii905
5AG£??iBl+,+4G°20-2GSr0-G°-Bl2°3+G§o!
CU905i
5AG^fBi+!+4G0i0-2GSr0-G"-B'2°3+S
S?+10AG^5_Bi+5+1G°20+G^
1G°2Grf90°5+05AG^9+025_c2++Sf0S
Bi+5G^f10A+Ca+2G^l?A+GSr02-G2+G^0°55be++2oAGCii+2_Cu+3
<?22124-CA^119059,
+flV!-C»+iZLr-
Z<J'-'11905+r>il905a,r<StOo--.CaO0,-,11905
tjCu+2-Cu+3°nZ+ad+'Bi+3-B.+5-oil905Aro,CU905,11905
5AG^+rBi+3+
5G°20-
2Gbr°_03
"*«+-Cu+3e22121
>
52212+
10AGBf?05I++S,P05
5AGS^2°!.E+
5G0i
0-
2GS'°
-Ga-B'*°3+Grf9o°55P05+5AG^9+°25_Cu+32++S"905
HbGg?,^,+5G°20-2GS'°-Ga~B^+GS
5p05+
(jCu+2-Cu+3bAZ+ad+iUAtrB,+3-Bi+J+C,U905-,11905Ap0,CU905,-,11905An,.,,11905
°~+t,A(jCu+2-Cu+3A+^11905,,11905./-rll905ar0,--,11905
ad+CH905.
lOAG^+AGS^+TCa+2+2GSr0-2Gcm+GtS°0!Z\OrSr+2_Ca+2+ZL,-Or+2!^11905
/"H905A,riSrO
o-^CaO0,-,11905
i>d+10AtrBi+3_Bl+5++a—
eW05L/-<il806Aa1,11905c,
5AG^205_+5G°20-2GS'°-G°-B»°°+GJ$£
511905+
5AGs^f+5G0i0-2GSl°-Ga-B"°*+Gff9o°55
,Bi+3-Bi+5
3rSr+2-B.+,U905
?S.+2-B.+3
0-22OCu+3Bi+3tjB1+5--,11905
200-2Cu+3Bi+3^B^3,,11905
200-2Cu+2Si+2<J'Bi+5,,11905
0-2o-2Cu+2Sr+2^Bl*3-,11905
0-20_2Cu+2Ca+2^Bl*5,-,11905
2O0-2Cu+2Ca+2^B^3-,11905
o-2oCu+2Bi+3JBi+5
—
2o20Cu+2Bi+3JBi+3_
-,11905
—
0-220Cu+2Sr+2-TBl+5_
,,11905
—
2o20Cu+2Sr+2Bi+3G,
:
Va20Cu+3Ca+2tTBi+5-,11905
Va0-2Cu+3Ca+2B.+3
-
Va0-2Cu+3Bi+3JBi+5
:
Va2OCu+3Bi+3B.+3G
:
Va2oCu+2Sr+'Bi+5^,11905
!
Va0-2C+2S.+2°B,+3,,11905
Va0-2Cu+2Ca+2tzBi+5
0-2\atrBi+3Ca+2Cu+2-,U905
^-,11905:
Va0-2Ou+2Bi+3Bi+5
,11905
:
Va0-2Cu+2B!+3Bi+3
„11905
^B^5 Ca+2 (
_11905 ,,11905 , 9 ,-,CaO 9 (oSrO , n 1 <7°2 + A (^i1905G£7+3 Ca+2 Cu+3 0-2 o 2
= Gii905 +2G -2G +U1L, + AUSr+2_Ca+2
, ^cA/jli905 i C2212+2.5AGCu+2_Cu+3 + Z>e
„11905 . or,CaO 0,-,SrO , n -, pOi , A /,A1905
2 C,,+3 0"= 0-2=
G11905+2G-2G +V-M* + AGSi+2-Ca+2
, , n A ,,11905 e11905 , 9 c A ,"AA905 -I- ?221:+10AGBi+3_Bl+5
+ i>d +2 5AGCu+2_Cu+3 + ie
where :
G^0°55 = G«-B'2°3 + 2GSr0 + GCu0 + AG^SS
5po5 = _4i.606T
5ii905 = _54,05811T
511905 = _i3.9894T
coefficients :
AGjgos = -90000 -8.1 T
AG^+f Bi+3= -24000 + 34.7T-
AGiT+25_Ca+2 =+94000
AGgf+f Bi+5= -30000 + 32.9 T
AG^f+°?_Cu+3 = -30000 + 38.3 T
2212
sublathce model :
(Bi+3, Bi+5)2(Sr+2, Bi+3, Ca+2)2(Ca+2)1(Cu+2, Cu+3)2(0-2)8(0-2. Va).
,-,2212
^B^3 St*2 Ca+2 Cu+2 0 2 Va
parameters .
,2212
IBl+3
,2212
7Br+5
,-,2212
= G2212
2212
^2212 _ /,22121 fi A n2212 4-
<?2:
GBr+5 Sr+2 Co+2 Cu+2 0-2 Va~
°2212 "+" 0iiLrBi+3-Bi+5 ^ °<i
12212
T2212
_
^,2212
Bi+5 B1+3 Ca+2 Cu+2 0_2 Va~ "2212
, c2212
Qc.-B.2O3 _ 2GSrO _ iG02 + 3AG|212_Bi+3
JBl+5 Bi+3 Ca+2 Cu+2 0-2 Va
,-,2212(jBi+3 Ca+2 Ca+2 Cu+2 0-2 Vb
= G2212 + Ga-Bl>°° - 2 GSr0 -
i G°2 + 3AG22+i
+Sf12 + 6AG22+2_R,+5 + S'-2B
Sr+2-Bi+3
,-,2212 , 9,-iCaO 9^,SrO , a ,"2212=
G2212+2G-2G + ACrSr+2_Ca+2
-,2212 ,-.2212 , 0 /,CaO 9 ,-,SiO , A ,"2212 ifiAfi3B.+ ' Ca+2 Ca+2 Cu+2 0-2 va
=G2212 + 2G
~ 2G + AGSr+2-Ca+2+ bA
GB,+3-Bi+5
,"2212 _ ,-,2212 , nj ^,2212 , c2212
(jBi+3 S.+2 Ca+2 Cu+2 0-2 Va-
Cr2212 +6A ^Cu+2-Cu+3 + be
,"2212LrBi+5 Sr+2 Ca+2 Cu+2 0-2 Va
*Bi+3 B1+3 Ca+2 Cu+3 0-2 Va
,-,2212LrB1+5 B1+3 Ca+2 Cu+3 0-2 Va
^2212 ,RA ,"2212 , c2212 , oa/^212 , (,2212=
G2212 + bAGBi+3-Bi+5 + bd + JA<JCu+2-Cu+3 + °e
= GlIU + G"-^0' - 2 GSr0 -
i G°2 + 3A Gs22+12„Bl+3
+52212 + 3AG221+22_Cu+3 + 52a2
= Gffif + G°-B'2°3 - 2G&0 - 1G02 + 3A Gs2r2+1I_Bl+31 C2212 , r A ,"2212 , (;22(2 , o A p2212 , c.2212
+ 6,. + t)AtBl+3_Bl+i t ij +3^<JCu+2-Cu+3 + Oc
233
CrBi+3 Ca+2 Ca+2 Cu+2 o 2 Va
LrB.+5 Ca+2 Ca+2 Cu+2 O 2^a-
^B^3 Sr+2 Ca+2 Cu+2 0 2 0 2
,-12212^Bl+S Sr+2 Ca+2 Cu+2 0-2 0-2
,-i2212^B^3 Bi+3 Ca+2 Cu+2 0-2 o 2
^2212tjBi+5 Bi+3 Ca+2 Cu+2 0-2 0-2
,-12212CrB.+3 Ca+2 Ca+2 Cu+2 o 2 o 2
,-12212tjBi+5 Ca+2 Ca+2 Gu+2 0-2 o-2
,-12212^Bi+S Sr+2 Ca+2 Cu+2 o-2 0-2
"
,-12212<J'Bl+5 Si+2 Ca+2 Cu+2 0-2 0 2 -
,-i2212UBi+3 Bi+3 Ca+2 Cu+3 Q-2 o 2
"
,-12212<J'Bi+5 Bi+3 Ca+2 Gu+3 o 2 Q-2
,-12212CrBi+3 Ca+2 Ca+2 Cu+2 Q-2 0 2
,-12212 , 0^iCaO o^SrO, A /12212
(j"2212+Z(j-^(jt + zi(j"Si+2-Ca+2
,o* ,12212 . r.2212
+>>ACjGu+2-Cu+3 + be
,-12212 , 0 ,-iCaO ti ,-iSiO . A n2212Cr2212 + ^^
— ZCj + AtjSr+2-Ca+2
+6AG^LBl+5 + Sf12 + 3AG^2_Cu+3,-12212
i
1
•^2212G°2
= Gill + iG^+eAGSr6
Bi+3-Bi+5r.2212
G%\1 + Ga-B"°3 - 2GSr0 - ^G°2 + 3AGS22+12_+
C2212
G221f + Ga-Bl2°3 - 2GSr0 - \g°> +3AG22+f
+Sf12 + 6AG|2i2_Bl+5+S,H21
Si+2-B.+3
= G,221,2 + 2 GCa0 - 2 GSr0 + ^ G°2 + AGS22.
+6AG|2+-2_Bl+5 + S2
Sr+2-Ca+2
G222x12 + 2GC»° - 2GSr0 + \g°> + AGs22+12_Ca+2r.2212
^12212 1
X,-i02 1 0 A /i2212 . c2212
'-'2212+ g"+ >jAljCu+2-Cu+3 + ^e
,-12212 ,
*,-i02 , RA Ci2212 . c2212
"2212 +p" + DA<JBi+3-Bi+5 + ^d
1 o A /i2212 1 c2212+dA<j-f,+2_r„+3 + A.
-B12O3- 2GSl° - ^G°2 + 3AGf2+12_Bl+3
, c2212 1 9 a /12212 , c2212+ bc + ^AtiCu+2_Cu+3 + ie
= Ggftf + Ga-Bl2°3 - 2 Gs'° - i G°2 + 3A G|2+122_B>+3+S2212 + 6AG22S_Bl+5 + S22*2 + 3AG22122_Cu+3 + Sf12
GlUI + 2GCM - 2GS'° + ^G02 + AGs2r2+12_ca+2, o A ,"2212 1 C2212+dA CjGu+2-Cu+3 + be
,-12212"B1+5 Ca+2 Ca+2 Cu+2 O"2 0~2
^2212 j_ 0 ,-iCaO
I /? A ,-12212 1 C2212
,QA ,-12212
,Q
+t>Z\GBl+3_Bl+5 + i>d + 3AltCu+2_Cu+3 + *«
2GSl0 + -G°2 +AG2212
Sr+2-Ca+2
2212 , c-22121
oA ,-12212
. r.2212
where
G22|11|=Ga-Bl2°3+2GSr0 +
52212 = -31 75382 T
GGa° + 2Gc
adjustable coefficients
-*2212
12212
AG|2«_Bl+3= +90000
52212 = _31 75382 r AG2:
!l+5= -26000 + 32 9 T
-,„«= -25000 + 38 3 T
234
2223
GllH = Ga-Bl2°s + 2GSr0 + 2GCa0 + 3GCu0 + 0 1G°2 + 9(-13000 + 0 052T)
Liquid
sublathce model
(Bi+3, Si+2, Ca+2, Cu+\ Cu+2)P(0-2, Va-^g
parameters
G['*+,0 2
= -575811 33 + 757 4207T - 138 89Tln( T)
GZ+> 0-2= 2(-563950 + 446 T - 73 lTln(T))
UCa+20-2 - ^CaOn^i
_ o/^l>qLrCu+1 O"2
~
0tjrCu2O
<&' o-»=4G&o -44058 + 25T
fWq _
^rliq
L'Bi+3 Va-<1_ ^Bi
USx+2 Va '_ ^Sr
r<"1 _/^!iq
°Ca+2 Va 1_
^Ca
^"q _
/-|llt'
UCu+I Va-l_
^Cu
GCu+2Va-<,= Gcqu + 600000
OiB^Cu+1va, = +20747 5-5 85T
liB^Cu+1Va_q = -4925 + 2 55T
2iB?+3Cu+1Va, = +4387 5-2 3T
°Ll> Cu+> va-,= "16711 89 + 16 0545r
1l'^+2 Cu+1 Va q= -12157 32 + 5 8061T
2£srW'Va-=, = -887243-4 5571T
04qa«Cu+^a-, = -27966 7
licqa+2c„-va<, = +9737 92
2icqa+2Cu-Va<, = -4993 82
04q+3 0-2 Va ,
= +201258 5-75 13125 T
0iCqa+2 O 2 Va-= +17331
°£cq+2o-2Va, = +27004 + 2 6T
liS,u+.o.v., = -9894 + 5 73T
2icq„+2o-2Va ,
= +20462-9 8T
icu+1 c..+2 o-2= -6879
2icq«cu+2o2 = +800°
0iBq+3 sr+2 o-2= "260000
0£b?+3 ca+2 o-2= -160000
£Bi+3Cu+2o 2= -700
0iBq+3Cu+io2 = +4300
235
°£B^iCu+10-,iVatl =+79300
^.«o^ = +146000
iB.+3,C..+1 0~2,Va <= +2500
•lg+.iCa«0-» =+94844
£Sr+i,Cu+i 0~>= -23700
°4'rq+2Cu+10_2 =-189500 +50 T
^cWu^o-^-iogesis0l£+1Cu+lo_, = -87197 8 + 37 8T
0icqa-,Cu«o-,Va-, = "396000
0£B?«,s^,Ca«o2 = -100000
0iB^,sr«,Cu^o- = "200000
0-C+3Sl+2Cu+lo_2 =-200000
°^+.'c.Wo-» = -100000
0o*3,Ca+,iGu+10-. = -100000
iB?+3,Si+i,ca+2 Cu+2 o ^= -700000
iBi+3,Sr+2 Ca+2,Cu^1 0~*= -70°000
G'bI, Ggrq, G^, and G^q are from [91Din] (iJe/ m Part I)
Gcao " /m [93Sell (Ref m chaP H.l)
GCu2o = -47734 + 148 463 T - 28Tln( T)
236
