Viscosity and Thermodynamics 2004

7/28/2019 Viscosity and Thermodynamics 2004

1/14

HARMONIZATION OF VISCOSIMETRIC AND THERMODYNAMIC DATA FOR

INDUSTRIAL MULTI-COMPONENT GLASSES AND GLASS MELTS

Reinhard Conradt

Aachen University

Institute of Mineral Engineering andDepartment of Glass and Ceramic Composites

Mauerstrasse 5

52064 Aachen

Germany

ABSTRACT

A thermodynamic model used earlier with success for the prediction of glass properties is

applied to nine industrial multi-component glasses, comprising E fibre, C fibre, stone wool, float,

TV panel, and low expansion glasses. Data for the zero Kelvin entropy (vitrification entropy) Svit

and the jump cP of the heat capacity at the glass transition temperature are derived. The samedata are derived by an evaluation of the viscosity-temperature relation by means of the Adam-

Gibbs equation. In general, the data derived by both approaches agree very well. However, in

individual cases (Svit of the E fibre; cP of the float glass), larger deviations are found, which areexploited to identify shortcomings in the thermodynamic data base.

INTRODUCTION

Thermodynamic data of multi-component glass-forming systems have been successfully

modeled in the past (see, e.g., [1-2] for geochemically relevant systems, and [3] for metallurgical

slags). Calculated integral and partial molar properties, such as standard heats and Gibbs energies

of formation, or chemical potentials of individual oxides agreed well with experimental data. By

an own model which was designed for the composition of commercial glasses, the energy

consumption of the batch-to-melt conversion or the hydrolytic stability of glasses was predicted

in a reliable way [4-6]. However, experimental thermodynamic data for multi-component systems

relevant to the glass industry are scant. Therefore, the verification and improvement of the model

proceeds at a slow pace. The lack of thermodynamic data can be compensated, at least to a

certain extent, by a systematic evaluation of viscosity data. This is the focus of the present paper.

The scientific basis of this approach is not new. It dates back to the work by Adam and Gibbs [7]

and has been applied with success to broaden the data base of one- and multi-component

magmatic systems, see [8-9] and [10], respectively, and of nuclear waste glasses [11]. In the

present paper, the approach is extended to viscosity data of industrial glasses, thereby exploiting

the advantage that the glass industry possesses a host of reliable data of this type. The scope ofthis investigation comprises nine industrial glasses, among which are different man-made mineral

fibre glasses, a float glass, a TV panel and a low expansion (Pyrex or Duran type) glass.

THEORY

Brief sketch of a thermodynamic model

The model outlined below has been used with success to predict the properties of rigid glasses

and glass melts from their chemical composition. The model consists of two parts, (1) an


2/14

appropriate thermodynamic description of glass-forming one-component systems, and (2) an

extension of this description to multi-component systems.

The thermodynamics of a one-component system in its stable liquid, metastable undercooled,

glassy, and crystalline state at an ambient pressure of P = 1 bar is described by the following

seven quantities in a comprehensive way. These are:

H = the standard enthalpy at 298 K, for the crystalline solid, stable at T = Tg,

S = the standard entropy at 298 K, for the crystalline solid, stable at T = Tg,

Hfus = the enthalpy of fusion,

Tliq = the liquidus temperature,

cP(T) = the heat capacity of the crystalline solid as a function of temperature;

represented by the polynomial cP(T) = A + BT + C/T2,

Hvit = the vitrification enthalpy,

Svit = the vitrification entropy (zero Kelvin entropy of the glass),

cP = the jump of the heat capacity at the glass transition temperature,Tg = the glass transition temperature.

In principle, all quantities referring to the glassy state depend on the cooling rate at which this

state is reached. With the cooling rate defined, they assume unambiguous values. The details are

not elaborated here. The set of quantities Hfus, Sfus, Tliq, Hvit, Svit, cP, and Tg is redundant. It is

linked by the relations given in eqs. 1 to 3 a-c as specified in figure 1 a-b. Hc(T) and Sc(T) denote

the configurational enthalpy and entropy, respectively.

liqfusfus THS /= (1)

( ) ( )

( )gliqPfusvit

liqPfus

gPvit

crystPliqPfus

crystPliqPvit

C

TTcHH

TTcHTTcH

dTccHdTccH(T)H

liqT

T

T

gT

+

=+=

)()( ,,,,

(2 a-c)

and

.

,,,,

g

liq

Pfusvit

liq

Pfusg

Pvit

crystPliqPfuscrystPliqPvit

C

T

TlncSS

T

TlncS

T

TlncS

dTT

cc

SdTT

cc

S(T)S

liqT

T

T

gT

=

+=

(3 a-c)


3/14

The knowledge of any four of the above redundant set of quantities is sufficient to derive the rest.

As shown by a large number of calorimetric experiments [9], the error introduced by the

approximation of the real shape of the cP jump by a constant value is insignificant; vitrificationenthalpy values Hvit derived from the approximated cP(T) curves agree well with H

vit values

directly measured. Thus HC(T) and SC(T) may be calculated as suggested by eqs. 2 c and 3 c.

Fig. 1 a-b. Illustration of equations 2 a-c and 3 a-c; arbitrary units; the assumption thatbelow Tg, cP(glass) cP(cryst), is valid in good approximation if the crystallinephase stable at Tg is taken into consideration

The identification of the crystalline reference state of a one-component system is simple. It is

usually polycrystalline but contains chemically identical phases. The crystalline reference state of

a multi-component system, by contrast, is chemically heterogeneous. The thermodynamic

description of a multi-component system in terms of crystalline reference states is a challenging

task requiring strategies to identify the coexisting phases and to quantify their amounts. Once this

problem is solved, a multi-component system is treated the very same way as outlined above, i.e.,

by assessing the enthalpy and entropy differences between the crystalline state and the

corresponding glass or melt, respectively. An adequate strategy is developed by exploiting three

fundamental principles found to be valid in the mineral world. These are:

the principle of majority partition.By experience, even complicated multi-component systems, such as magmatic and igneous

rock melts, metallurgical slags, commercial glasses, etc., can be represented by a predominant

quaternary typically comprising more than 85 95 % of the oxides on a molar basis.

Tliq

cryst.,

glass

meltundercooled melt

cryst.

Tg

298 K

area =

Hfus

- Hvit

heatc

apacitycP

temperature T

area = Sfus

- Svit

cryst.

melt

undercooled

melt

cryst.,

glass

Tliq

Tg

298 K

c

P/

T

temperature T


4/14

the principle of parsimony.The very large number of combinatorial possibilities of compound formation is not exploited

by nature. Rather, a quite limited set of binary and ternary compounds is found. The

constitutional relations in a given multi-component system are therefore approximated in the

following way: First, the minority oxides are allotted to a set of normative phases as suggested by

the CIPW norm calculation (see e.g. [12]). The remaining four majority oxides are allotted to therespective constitutional sub-range in the predominant quaternary identified and reconstructed by

the evaluation of existing phase diagrams.

the principle of medium-range order mixing.Systems with a strong tendency to compound formation do not mix on a scale equivalent to

61023 per g-atom, not even in the liquid state way above T liq. Therefore, when a system is ex-

pressed in terms of stoichiometric entities k with compositions identical to the co-existing

mineral phases, then the contributions of mixing are minimized to an extent that they may be

neglected. This has been formulated in detail before [13] and is well in line with experimental

findings [14]. Consequently, a thermodynamic quantity Z, where Z may denote an enthalpy H,entropy S, or Gibbs energy G, of a multi-component system is obtained from the molar amounts

nkand the quantities Zkof the pure compounds by a relation as simple as

Z = nkZk. (4)

Eq. 4 is valid for the crystalline as well as for the liquid and glassy state if the k are taken in the

respective state.

Recently, the model was submitted to a stringent test: By own work, Gibbs energies of

formation were calculated for four different mineral fibre glasses (alumina rich alkali + alkaline

earth alumosilicate glasses containing iron oxide and further minor additions). The values were

checked by calorimetry by an independent laboratory [15], yielding the following experimental

vs. calculated values for the standard Gibbs energies of formation from the elements (in kJ per

mol of oxides): -852.0 vs. -849.6; -865.0 vs. -867.2; -880.8 vs. -881.8; -855.4 vs. -852.7. The

standard Gibbs energies of formation from the oxides read: -12.9 vs. -10.6; -35.4 vs. -37.7;

-34.0 vs. -35.0; -44.1 vs. -41.4.

Adam-Gibbs analysis of industrial glasses

The model, as successful as it may have been in individual cases as above, suffers from a

general lack of opportunities to be put to the test. This is simply because thermodynamic data,

specifically, data for Svit

, Hvit

and cP, are rarely available for industrial products. Thusverification of the model and its data base proceeds very slowly. Therefore, use is made of thefact that glass producers need to have a good command of workability and cooling. In other

words: They usually know the chemical composition and viscosity-temperature relation of their

glasses well. Such data can be submitted to an analysis by the Adam-Gibbs equation [7], yielding

information on Svit andcP. There is a host of data available for this approach, which have hardlyever been exploited. The method, however, has been used in the past to confirm thermodynamic

data of glasses of predominantly scientific interest [9].


5/14

The Adam-Gibbs relation predicts a linear relationship between log and the reciprocal valueof the product of configurational entropy SC(T) (see eq. 3 a-c) and absolute temperature:

)(log

TST

TDA

C

g

+= . (5)

Employing eq. 3 b yields

)(log TfDA += (6)

with

T

T

S

cST

TTf

g

vit

Pvit

g

ln1

1)(

= . (7)

For a set of experimentally determined viscosity data, eqs. 6-7 generate a linear relationship

versus Tg/(TSC) for one distinct ratio of the so-called structure parametera = cP/Svit only. After

determining a by an incremental approach to optimal linearity (as, e.g., reflected by a maximum

regression coefficient r2), optimal values for the intercept A and slope D in eq. 6 are obtained

which are, in turn, converted to estimates of Svit andcP by

AL

DS

g

vit

= (8)

and

vitP Sac = . (9)

In eq. (8), Lg denotes the decadic logarithm of the viscosity at Tg: Lg = log (T=Tg).

Thermodynamic modeling of vitrification entropies and jumps of the heat capacities

In parallel to the above analysis, Svit andcP values are calculated from the glass compositionby means of the constitutional model. The database used stems from various sources and is

compiled in [16]. For glasses from the system Na2O-B2O3-SiO2, a revision of the database wasimplemented. The author has been noticing that for some reason, the constitutional model

generated grossly erroneous results in the silica rich corner of the system. Existing phase

diagrams do not seem to reflect the structural relations in the glasses well. Compounds of the type

Na2OB2O3nSiO2 are often ignored, in spite of experimental and theoretical evidence [17, 18].

Polyakova [18] states that in lithium and sodium borosilicate systems, the structural groupings

which exist in the vitreous state cannot form any corresponding crystalline structures for steric

reasons. In the homologous sequence of potassium, rubidium, and cesium borosilicates, however,

crystalline compounds isostructural to leucite, i.e., R2OB2O34SiO2, are formed, leading to the


6/14

suggestion [18] that lithium and sodium borosilicate glasses should be described in reference to

such a compound as well.

In order to implement a latent sodium boroleucite compound in the constitutional model, data

for a hypothetical crystalline compound Na2OB2O34SiO2 are estimated from tabulated data for

leucite Na2OAl2O34SiO2, NaBO2, NaAlO2, Al2O3, and B2O3. This is done under the assumption

that

H(Na2OB2O34SiO2) H(Na2OAl2O34SiO2) + 2H(NaBO2) 2H(NaAlO2),

S(Na2OB2O34SiO2) S(Na2OAl2O34SiO2) + S(B2O3) S(Al2O3).

The set of data thus obtained is refined against calorimetric data for the Gibbs energy of

formation (from the oxides) of a glass with a composition (by wt.) of 14.21 Na2O, 20.21 B2O3,

65.58 SiO2, yielding -(45.300.81) kJ/mol [11]. The thermodynamic data obtained as described

above are compiled in table 1. Figure 2 illustrates the constitutional relations allowing for the

formation of a latent boroleucite compound.

Tab. 1. Thermodynamic data for compounds k from the system Na2O-B2O3-SiO2; N = Na2O,

B = B2O3, S = SiO2; M = molar mass in g/mol; H = enthalpy in kJ/mol, G = Gibbs

energy in kJ/mol, T = temperature in in K; A, B, C = constants for the calculation of

the heat capacity cP in J/(molK), by the polynomial cP = A + BT + C/T2; superscripts:

= standard state at 298 K, 1 bar; = formation from the elements; vit = vitrification;

tr = transition; data for the hypothetical compoundNBS4: own estimates; the rest after

data compiled in [16, 19]

k state M -H S -G Hvit Svit Ttr Htr A B10+3 C-5

NB4 s 340.455 5902.8 276.1 5543.0 58.3 40.1 298 345.18 226.35 -95.81

liq 1085 130.4 704.28

NB2 s 201.217 3284.9 189.5 3089.7 48.8 18.5 298 206.10 77.11 -37.49

liq 1016 81.2 444.88

NB s 131.598 1958.1 147.1 1838.8 43.6 19.5 298 101.21 107.34 0.00

liq 1239 72.5 292.88

NBS4 s 371.934 5710.9 270.0 5367.9 42.7 21.1 298 325.89 172.36 -63.47

liq 1123 71.1 540.97

RESULTS

Table 2 shows the oxide compositions of six industrial glasses submitted to an Adam-Gibbs

analysis. Experimental viscosity data are shown in figure 3 in terms of a Vogel-Fulcher-

Tammann plot. The glasses depicted cover a wide range of industrial products. In table 3, the

same glasses are presented in terms of their constitutional compounds k. This presentation is the

basis for the thermodynamic calculation of Svit andcP. The set of glasses is complemented byfour stone wool type mineral fibre compositions, i.e., three recent ones and a former one melted

from natural basaltic rock. The compositions of the latter glasses are given in terms of

compounds k in table 4.


7/14

Fig. 2. Constitutional relations in the ternary system Na2O-B2O3-SiO2; the open

circle marks the composition of a glass investigated by calorimetry [11]

Tab. 2. Composition of glasses DGG-1 [20], JM-753C [21], E fibre [22], low expansion

(low ) [22], and TV panel [22], given as wt. % of oxides j

oxide j float

DGG-1

C fibre

JM-753C

E fibre low TV panel

SiO2 71.7 63.4 55.15 80.99 61.76

TiO2 0.1 0.57 0.43

ZrO2 1.40

Al2O3 1.2 5.1 14.42 2.19 2.07

B2O3 - 4.8 6.86 12.60

Fe2O3 0.2 - 0.44 0.04 0.04

MgO 4.2 3.1 4.22 0.01

CaO 6.7 6.2 17.73 0.02 0.05

SrO 9.22

BaO 9.26

ZnO 0.51

Li2O 0.01 0.01

Na2O 15.0 15.6 0.61 4.09 7.67

K2O 0.4 1.0 0.05 7.58

SO3 0.4 0.2

NBS4NS

N2S

NS2

N3BN2BNBNB2NB4 Na2O

SiO2

B2O3


8/14

Tab. 3. Composition of five industrial glasses (see table 2), given in terms of normative

compounds k in g per 100 g glass; for the C fibre glass (wool) and the low glass, thespeciation using the compound Na2OB2O34SiO2 is shown; for DGG-1 (float glass),

the thermodynamically correct speciation requiring the compound Na2OMgO4SiO2

[23] was approximated by a speciation using MgOSiO2

compound k float [20]

DGG 1

C fibre [21]

JM-753C

E fibre [22] low [22] TV panel[22]

FeOFe2O3 0.17 0.04 0.43 0.04 0.04

FeOSiO2 0.03

ZnO2SiO2 0.70

ZrO2SiO2 2.08

TiO2 0.14 0.57 0.43

Li2OSiO2 0.03 0.03

SrOSiO2 14.57

BaO2SiO2 16.52K2OAl2O36SiO2 2.26 5.95 0.32 11.29

K2O2SiO2 12.90

Na2OAl2O36SiO2 4.23 20.82 5.19 10.96

B2O3 6.86 9.46

Na2OB2O34SiO2 25.84 16.77

MgOSiO2 10.46

CaOAl2O32SiO2 36.59

CaOMgO2SiO2 16.78 22.67 0.04

Na2OMgO4SiO2 *)

CaOSiO2 3.94 9.30 0.02 0.10

Na2O3CaO6SiO2 23.75

Na2O2SiO2 35.36 26.31 22.54

SiO2 23.61 18.39 62.38 18.80

*) no thermodynamic data available for this compound

For the stone wool type fibre glasses, viscosity data can be measured at temperatures above

Tliq only. Due to their poor stability against crystallization, a major part of the viscosity

temperature curve is hidden behind the crystallization curtain.

Figure 4 shows that all industrial glasses yield straight lines in the Adam-Gibbs plot. For

reasons of comparison, data for glassy anorthite are added. For anorthite glass, the following

values have been measured [9]: cP = 34.1 J/(100 gK) and Svit = 13.1 1.4 J/(100 gK).The quality of the viscosity data analyzed in the present paper and the achieved linearity form

an excellent basis to calculate cP and Svit. The high-T viscosity data of the stone wool type

glasses (see figure 5) accumulate around the so-called fibrization level of log = 1.5 ( in dPas).For these glasses, the linear regression analysis was performed on the high-T data alone. As the

resulting straight lines match the respective data points at Tg (for basalt less well than for the

rest), they may be considered a sufficiently reliable basis for a determination of cP and Svit as

well.


9/14

Fig. 3. Viscosity-temperature relation of five different industrial glasses; lines: calculated

from eqs. 6-7; symbols: experimental data (float glass [20]; C glass wool [21]; E

fibre, low , TV panel glass [22];)

Tab. 4. Composition of four stone wool type fibre glasses, given in terms of normative

compounds k in g per 100 g glass

compound k fibre 1 fibre 2 fibre 3 basalt

P2O53CaO 2.10

FeOFe2O3 2.88 5.67 6.98 7.43

FeOSiO2 0.55 1.08 1.33 7.89

MnOSiO2 0.28 0.31 0.37 0.34

CaOTiO2 0.34 0.58 0.58 4.64

K2OAl2O36SiO2 2.37 1.78 1.60 4.27

K2OAl2O32SiO2 2.20

Na2OAl2O36SiO2 5.51 7.61 8.56 12.96Na2OAl2O32SiO2 6.35

MgOSiO2 2.24 3.82 19.40 16.44

CaOAl2O32SiO2 15.84

CaOMgO2SiO2 41.58 41.86 41.70 18.76

Na2O3CaO6SiO2 40.70 28.71

Na2O2SiO2 7.05

SiO2 3.40 8.32 12.10

400 600 800 1000 1200 1400 1600

1

3

5

7

9

11

13

glass wool JM-753C

low glass

TV panel glass

float glass

DGG-1

E fibre glass

log

,i

ndPas

Tg/T


10/14

Fig. 4. Adam-Gibbs plot for six different glasses; lines: calculated from eqs. 6-7; symbols:

experimental viscosity data (float glass [20]; C glass wool [21]; E fibre, low , TVpanel glass [22]; anorthite [9])

Fig. 5. Adam-Gibbs plot for four different mineral wool glasses; lines: calculated from eqs.

6-7; symbols: experimental viscosity data

0 2 4 6 8 10 12 14-2

0

2

4

6

8

10

12

14

16

glass wool JM-753C

glassy

anorthite

float glass DGG-1

TV panel glass

low glassE fibre glass

log

,i

n

dPas

Tg/(TSC) in (gK)/J

0 2 4 6 8 10 12 14-2

0

2

4

6

8

10

12

14

16

fibre 1

fibre 2

fibre 3

basalt wool from

quarry "Westerwald"

2 3

1

2

log

,i

n

dPas

Tg/(TSC) in (gK)/J


11/14

In table 5, the results obtained from the thermodynamic model and the Adam-Gibbs analysis

are contrasted. In addition to the values for Svit andcP, the structure parametera and the slope f(fragility slope) at which the viscosity value at Tg is approached in the Angell plot [24] are given,

too. The fragility slope f is calculated from the first derivative (log ) / (Tg/T), eqs. 6-7, forT Tg. The precision of the data generated by the Adam-Gibbs analysis and by the

constitutional model is 0.3 J per mol and 100 g glass. The precision is taken as the basis toassess the match of the two approaches. The accuracy of the data is much lower: Based on a

previous comparison of experimental and modeled results [6], the error in cP is estimated as 5 %. The error of Svit typically amounts to 10 to 15 % [9].

Tab. 5. Vitrification entropy Svit, jump of the heat capacity cP in the glass transition,structure parametera = cP/S

vit, and fragility slope f for different types of glass; AG:

derived from an Adam-Gibbs analysis of viscosity data; MOD: calculated by the

constitutional model

glass Svit in J per mol and

100 g glasscP in J per mol and

100 g glass

structure

parameter

a = cP/Svit

fragility slope

f =

(Lg-A)(1-a)

MOD AG MOD AG AG AG

fibre 1 8.2 8.3 30.2 29.2 3.5 64.6

fibre 2 9.1 9.0 29.5 28.3 3.1 59.3

fibre 3 11.8 11.8 29.6 32.4 2.8 56.7

basalt 12.1 12.1 19.9 33.7 2.8 63.5

DGG-1 7.7 7.9 18.8 14.2 1.8 38.9

glass wool 8.3 8.3 18.5 20.0 2.4 46.7

E fibre 13.6 18.1 24.3 23.7 1.3 37.7

low 11.2 12.0 14.5 11.2 0.9 26.7TV panel 8.2 7.4 12.4 12.4 1.7 36.7

DISCUSSION

As a general result, vitrification entropies Svit from the thermodynamic model and the analysis

of viscosity data match well. It is only in one case (E fibre glass) that a deviation is found which

is worth being discussed. The deviation is attributed to the fact that no Ca borate phases were

taken into account for the E fibre glass composition. With CaO being the only high-basicity oxide

in the composition, the coexistence of wollastonite CaOSiO2 with pure B2O3 is most unlikely.Consequently, the data base for alkali free boron containing glasses has to be adjusted

accordingly. As an especially appreciated result, the Svit value of the low glass is predictedwell. It may be concluded that, with the introduction of the latent boroleucite compound in the

database, the former problems encountered in modeling this type of glasses have been solved.

This is expected to have an impact on the prediction of hydrolytic stability of pharmaceutical

glasses and their theory-guided improvement.

The modeling ofcP is more difficult. This is due to the fact that the heat capacities of high-Tliquids are often less well know than the formation properties of mineral compounds. Again, the


12/14

data match well for most glass types. The mismatch for the basalt should not be taken too serious,

as the Adam-Gibbs evaluation is based on a relatively poor linear correlation of only three

viscosity points (see figure 5). For some glasses (low ; glass wool), cP could be modeledsuccessfully only if the latent boroleucite compound was taken into account. Here, the Adam-

Gibbs analysis provided a most valuable incentive for a meanwhile accomplished improvement

of the database.The obvious mismatch in cP for the float glass (DGG-1) comes as an unpleasant surprise.

There is ample experimental proof that enthalpies, Gibbs energies and sodium oxide activities of

typical float and container glasses can be modeled with satisfactory accuracy, which is obviously

not the case forcP. The reason could not yet be identified in an unambiguous way. However, acomparison of the speciations of all glasses compiled in tables 3 and 4 shows that DGG-1 and

fibre 3 are the only cases where Na2O2SiO2 and MgOSiO2 are supposed to coexist. According

to the phase diagram [23], MgO should rather be allotted to a compound Na2OMgO4SiO2, thus

allowing for the coexistence of Na2O2SiO2 and Na2OMgO4SiO2. As no data were available for

this compound, a speciation using MgOSiO2 was adopted as an approximation. This

approximation seems to have only a minor effect on the calculation of enthalpies etc., but it is

unacceptable for the modeling of cP (even though the comparatively small amount ofNa2O2SiO2 in the case of fibre 3 keeps the cP mismatch low). It is thus suggested that animprovement of the database for float and container glasses should focus on an assessment of

data for Na2OMgO4SiO2.

SUMMARY

Viscosity data of glass forming systems have been exploited before with success to derive or

confirm thermodynamic data of glass melts. Such work was, however, focused on melts with

primarily scientific interest, or on melts relevant to geoscience. In the present paper, this

approach was extended to industrial glasses of different compositional families. The studycomprised the stone wool type fibre glasses which differ from natural systems in so far as they

are atypically rich in MgO or alkali oxides. It also comprised traditional soda lime silicate

glasses, different borosilicate systems (high silica; moderately high silica; alkali free) and

systems with heavy alkali and alkaline earth elements (TV panel). The problem was tackled from

two sides:

Viscosity data were submitted to an Adam-Gibbs analysis, and data for the vitrification

entropy Svit and the jump of the heat capacity cP were derived via a regression analysis. It isworth mentioning that the viscosity data of all glasses could be linearized. This confirms the

assumption that the Adam-Gibbs analysis is a general tool applicable to multi-component glasses.

In parallel to the Adam-Gibbs analysis, the quantities Svit andcP were calculated by the

constitutional model. For this purpose, a new compound, i.e., the sodium boroleuciteNa2OB2O34SiO2 was implemented in the database.

The results of both approaches agree well. In a few individual cases, the comparison yields

valuable incentives to improve the thermodynamic database. In order to improve the modeling of

float and container glasses, the thermodynamic data of the compound Na2OMgO4SiO2 should

be assessed.


13/14

REFERENCES1M. S. Ghiorso, Modelling magmatic systems: Thermodynamic relations, in:

Thermodynamic Modelling of Geological Materials: Minerals, Fluids, and Melts. I. S. E.

Carmichael and H. P. Eugster, eds. Mineralogical Society of America, Short Course Notes 1987,

443-465.2

M. S. Ghiorso, R. O. Sack, Chemical mass transfer in magmatic processes IV. A revisedand internally consistent thermodynamic model for the interpolation and extrapolation of liquid-

solid equilibra in magmatic systems at elevated temperatures and pressures, Contrib. Mineral.

Petrol. 119 (1995), 197-212.3Slag atlas. Allibert, M. et al., eds. Verlag Stahleisen GmbH, Dsseldorf, (1995)4R. Conradt, Modeling of the thermochemical properties of multicomponent oxide melts,Z.

Metallkd. 92 (2001), 1158-1162.5R. Conradt, A proposition for an improved theoretical treatment of the corrosion of multi-

component glasses,J. Nucl. Mat. 298 (2001), 19-26.6C. Madivate, F. Mueller, W. Wilsmann, Thermochemistry of the glass melting process

Energy requirement in melting soda-lime-silica glasses from cullet-containing batches Glastech.

Ber. Glass Sci. Technol. 69 (1996), 167-177.7G. Adam, J. H. Gibbs, On the temperature dependence of cooperative relaxation properties

in glass-forming liquids,J. Chem. Phys. 43 (1965), 136-146.8P. Richet, Low-temperature heat capacity of diopside glass (CaMgSi2O6): A calorimetric

test of the configurational-entropy theory applied to the viscosity of liquid silicates, Geochimica

et Cosmochimica Acta Vol. 50 (1986), 1521-1533.9P. Richet, Y. Bottinga, Rheology and configurational entropy of silicate melts, Reviews in

Mineralogy 32 (1995), 65-93.10D. R. Neuville, P. Richet, Viscosity and mixing in molten (Ca, Mg) pyroxenes and

garnets, Geochimica et Cosmochimica Acta Vol. 55 (1991), 1011-1019.11Y. Linard, I. Yamashita, T. Atake, J. Rogez, P. Richet, Thermochemistry of nuclear waste

glasses: an experimental determination,J. Non-Cryst. Solid286 (2001), 200-209.12A. R. Philpotts, Principles of igneous and metamorphic petrology. Chapter 6:

Classification of igneous rocks,Prenctice Hall, Englewood Cliffs, 1990.13R. Conradt, A thermodynamic approach to the structure of oxide glasses, in:

Fundamentals of Glass Science and Technology. Glafo, Vxj, Sweden 1997.14A. Navrotsky, R. Hon, D. F. Weill, D. J. Henry, Thermochemistry of glasses and liquids in

the system CaMgSi2O6-CaAl2Si2O8-NaAlSi3O8, SiO2-CaAl2Si2O8-NaAlSi3O8 and SiO2-Al2O3-

CaO-Na2O, Geochim. Cosmochim. Acta 44 (1980), 1409-1432.15P. Richet, private communication.16R. Conradt, Thermochemistry and structrure of oxide glasses, in: Analysis of the

composition and structure of glass and glass ceramics. H. Bach and D. Krause, eds. SpringerVerlag, Berlin 1999.17G.W. Morey, The ternary system Na2O-B2O3-SiO2, J. Soc. Glass Technol. 35 (1951),

270-283.18I. G. Polyakova, Alkali borosilicate systems: phase diagrams and properties of glasses,

Phys. Chem. Glasses 41 (2000), 247-258.19O. Kubaschewski, E. B. Alcock, P. J. Spencer, Materials thermochemistry, Pergamon

Press, Oxford 1993.


14/14

20Standard glass I of the German Society of Glass Technology, Offenbach (Germany). Data

tables. 1974.21Marble glass no. 753-C byManville-Schuller Co., Denver, CO (U.S.A.) 1994.22T. P. Seward (principal investigator), Modeling of glass making processes for improved

efficiency. High temperature glass melt property database for modeling, work conducted under

U.S. DOE grant no. DE-FG07-96EE41262. Alfred University 2003.23PK. A. Shahid, F. P. Glasser, Phase equilibriums in the glass forming region of the system

sodium oxide-calcium oxide-magnesium oxide-silicon dioxide, Phys. Chem. Glasses 13 (1972),

27-42. See also: Phase diagram no. 5457 in: Phase Equilibria Diagrams. CD-ROM database

Ver. 2.1. The American Ceramic Society, Westerville, Ohio 1998.24C. A. Angell: Strong and fragile liquids, in: Relaxations in complex systems. K. Ngai and

G. B. Wright, eds. National Technical Information Service, U.S. Dept. of Commerce, Springfield

(VA) 1985.

Documents

Viscosity and Thermodynamics 2004