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Modeling of metastable phase formation for sputtered
Ti1-xAlxN and V1-xAlxN thin films
Von der Fakultät für Georessourcen und Materialtechnik der
Rheinisch - Westfälischen Technischen Hochschule Aachen
zur Erlangung des akademischen Grades eines
Doktors der Ingenieurwissenschaften
genehmigte Dissertation
vorgelegt von
Herrn Sida Liu, M. Sc.
aus Shandong Province, China
Berichter: Herr Univ.-Prof. Jochen M. Schneider, Ph. D.
Herr Univ.-Prof. Keke Chang
Tag der mündlichen Prüfung: 01. 10. 2020
Diese Dissertation ist auf den Internetseiten der Universitätsbibliothek
online verfügbar
- I -
Abstract
The metastable transition metal aluminum nitride (TMAlN) coatings are widely
applied in cutting and forming applications. In this thesis, the metastable phase
formation of sputtered TM1−xAlxN (TM = Ti, V) thin films was studied by
thermodynamic calculations, ab initio calculations, and experiments. The addition of
Al to TMN, resulting in the formation of metastable TMAlN improves the oxidation
resistance compared to TMN. The modeling of the effect of energetic and kinetic
factors on phase formation allows for quantum-mechanically guided design of
face-centered cubic (fcc) TMAlN thin films with increased Al concentration.
In the first part, the metastable phase formation of TiAlN is predicted based on
one combinatorial magnetron sputtering experiment, the activation energy for surface
diffusion, the critical diffusion distance, as well as thermodynamic calculations.
Although it is generally accepted that the phase formation of metastable TiAlN is
governed by kinetic factors, modeling attempts today are based solely on energetics.
The phase formation data obtained from further combinatorial growth experiments
varying chemical composition, deposition temperature, and deposition rate are in
good agreement with the model. Furthermore, it is demonstrated that a significant
extension of the predicted critical solubility range is enabled by taking kinetic factors
into account. Explicit consideration of kinetics extends the Al solubility limit to lower
values, previously unobtainable by energetics, but accessible experimentally.
TMAlN (TM = Ti, V) thin films are today deposited utilizing ionized vapor phase
- II -
condensation techniques where variations in ion flux and ion energy cause
compressive film stress, in turn affecting Al solubility. While the metastable phase
formation of TiAlN has been modeled, the influence of film stresses on phase
formation has so far been overlooked. In the second part, using combinatorial
deposition via magnetron sputtering, thermodynamic modeling, and density functional
theory calculations, the phase formation of V1−xAlxN and Ti1−xAlxN thin films at
various substrate temperatures and deposition rates is investigated. Ab initio
calculations indicate that the maximum solid solubility of Al in fcc-V1−xAlxN or
fcc-Ti1−xAlxN shows a linear trend as a function of the magnitude of compressive
stress. Here, the influence of film stresses on the metastable phase formation of
fcc-V1−xAlxN and fcc-Ti1−xAlxN is considered for the first time. Specifically,
experimental data from a single combinatorial deposition is utilized to predict the
stress-dependent formation of metastable phases based on thermodynamic and ab
initio data. Explicit consideration of stress extends the Al solubility limit to higher
values for both Ti1-xAlxN and V1-xAlxN thin films, previously unobtainable by
energetics, but accessible experimentally. These predictions are experimentally
verified and thus provide guidance for experimental efforts with the goal of increasing
the Al concentration in fcc-TMAlN thin films.
The present work shows that CALPHAD modeling and ab initio calculations can
be used successfully to predict the metastable phase formation of TMAlN thin films.
This enables future knowledge-based design of face-centered cubic TMAlN thin films
- III -
with increased Al concentration.
- IV -
Zusammenfassung
In dieser Arbeit wird die metastabile Phasenbildung von mittels
Magnetronsputtern hergestellten TM1−xAlxN (TM = Ti, V)-Dünnschichten anhand von
thermodynamischen Berechnungen, ab initio-Berechnungen und
Syntheseexperimenten untersucht. Die Zugabe von Al zu TMN-Dünnschichten
resultiert in der Bildung von metastabilem TMAlN mit erhöhtem
Oxidationswiderstand gegenüber TMN. Die Modellierung des Einflusses
energetischer und kinetischer Faktoren auf die Phasenbildung ermöglicht das
quantenmechanisch geführte Design von flächenzentrierten
(fcc)-TMAlN-Dünnschichten mit erhöhter Al-Konzentration.
Trotz der gesicherten Erkenntnis, dass die metastabile Phasenbildung von TiAlN
von kinetischen Faktoren bestimmt wird, basieren aktuelle Modellierungsansätze
ausschließlich auf Energetik. Im ersten Teil der Arbeit wird daher die metastabile
Phasenbildung von TiAlN-Dünnschichten auf der Grundlage eines kombinatorischen
Magnetronsputter-Syntheseexperiments und begleitender thermodynamischer
Berechnung u. a. der Aktivierungsenergie für Oberflächendiffusion und der kritischen
Diffusionslänge modelliert. Syntheseexperimente mit Variation der chemischen
Zusammensetzung, der Abscheidetemperatur und Schichtrate zeigen gute
Übereinstimmung mit den Modellierungsergebnissen. Weiterhin zeigen die
Berechnungen, dass kritische Lösungsbereiche durch die Berücksichtigung
kinetischer Faktoren signifikant erweitert werden können. So sinkt die
- V -
Löslichkeitsgrenze von Al durch explizite Berücksichtigung kinetischer Faktoren in
Übereinstimmung mit experimentellen Ergebnissen auf niedrigere Werte als mittels
energetischer Berechnungen darstellbar.
TMAlN (TM = Ti, V)-Dünnschichten werden heute überwiegend mittels
ionisierte Plasmaabscheideprozesse hergestellt, in denen Variationen des Ionenflusses
und der Ionenenergie Druckspannungen in der wachsenden Schicht erzeugen, die
wiederum die Al-Löslichkeit beeinflussen. Die metastabile Phasenbildung von TiAlN
wurde bereits umfassend beschrieben, allerdings wurde der Einfluss der
Schichteigenspannungen auf die Phasenbildung bisher nicht berücksichtigt. Im
zweiten Teil der Arbeit wird deshalb die Phasenbildung in den Systemen V1−xAlxN
and Ti1−xAlxN in kombinatorischen Magnetronsputterprozessen unter Zuhilfenahme
thermodynamischer Berechnungen und Berechnungen mittels der
Dichtefunktionaltheorie bei unterschiedlichen Substrattemperaturen und
Abscheideraten untersucht. Ab initio-Berechnungen zeigen damit erstmals, dass die
maximale Festkörperlöslichkeit von Al in fcc-V1−xAlxN or fcc-Ti1−xAlxN einer
linearen Funktion in Abhängigkeit der Druckeigenspannungen folgt. Auf der
Grundlage eines kombinatorischen Syntheseexperiments wird anhand
thermodynamischer und ab initio-Berechnungen die spannungsabhängige Bildung
metastabiler Phasen vorhergesagt. Aufgrund der Berücksichtigung der
Eigenspannungen wird der Al-Löslichkeitsbereich in den untersuchten Systemen
V1−xAlxN and Ti1−xAlxN in Übereinstimmung mit den experimentellen Daten
- VI -
gegenüber rein energetischen Modellierungen nach oben hin erweitert. Diese
experimentell bestätigten Vorhersagen liefern einen Beitrag zur verständnisbasierten
Erhöhung der Al-Konzentration in fcc-TMAlN-Dünnschichten.
Die vorliegende Arbeit zeigt, dass die thermochemische Modellierung nach der
CALPHAD-Methode in Kombination mit ab initio-Berechnungen erfolgreich zur
Vorhersage der Phasenbildung in TMAlN-Dünnschichten eingesetzt werden kann und
liefert somit einen Beitrag zur zukünftigen Entwicklung von
fcc-TMAlN-Dünnschichten mit erhöhter Al-Löslichkeit.
- VII -
Preface
Papers contributing to this thesis:
Paper I
Modeling of metastable phase formation for sputtered Ti1−xAlxN thin films
S. Liu, K. Chang, S. Mráz, X. Chen, M. Hans, D. Music, D. Primetzhofer, J.M.
Schneider, Acta Materialia 165 (2019) 615-625.
Paper II
Stress-dependent prediction of metastable phase formation for
magnetron-sputtered V1−xAlxN and Ti1−xAlxN thin films
S. Liu, K. Chang, D. Music, X. Chen, S. Mráz, D. Bogdanovski, M. Hans, D.
Primetzhofer, J.M. Schneider, Acta Materialia 196 (2020) 313-324.
The calculations and model development in the paper I to paper II were done by S.
Liu with the help of D. Music. The samples for the paper I to paper II were deposited
by S. Liu with the help of S. Mráz. For all papers, goals were discussed, and strategies
were developed with J.M. Schneider, and K. Chang. All co-authors took part in the
discussion of the results, and editing the manuscript.
Contents
Abstract ......................................................................................................................... I
Zusammenfassung..................................................................................................... IV
Preface ....................................................................................................................... VII
Chapter 1 Introduction ................................................................................................ 1
Chapter 2 Methods ...................................................................................................... 5
2.1 Ab initio calculations......................................................................................... 5
2.1.1 Activation energy for surface diffusion .................................................. 5
2.1.2 Enthalpy as a function of pressure .......................................................... 7
2.2 CALPHAD approaches ..................................................................................... 8
2.2.1 TiN-AlN system ...................................................................................... 8
2.2.2 VN-AlN system .................................................................................... 11
2.3 Experimental methods .................................................................................... 13
2.3.1 Magnetron Sputterings .......................................................................... 13
2.3.2 Characterizations................................................................................... 14
Chapter 3 Results and discussion ............................................................................. 16
3.1 Modeling of metastable phase formation for Ti1-xAlxN thin films .................. 16
3.1.1 Introduction ........................................................................................... 16
3.1.2 Calculations........................................................................................... 18
3.1.3 Experiments .......................................................................................... 22
3.1.4 Modeling: Metastable phase formation of Ti1-xAlxN ............................ 29
3.1.5 Summary ............................................................................................... 42
3.2 Modeling of stress-dependent metastable phase formation for Ti1-xAlxN and
V1-xAlxN thin films ................................................................................................ 43
3.2.1 Introduction ........................................................................................... 43
3.2.2 Calculations........................................................................................... 47
3.2.3 Experiments .......................................................................................... 53
3.2.4 Modeling: Metastable phase formation of V1-xAlxN............................. 56
3.2.5 Modeling: Stress-dependent metastable phase formation of Ti1-xAlxN
and V1-xAlxN .................................................................................................. 63
3.2.6 Summary ............................................................................................... 69
Chapter 4 Conclusions and outlook ......................................................................... 70
4.1 Conclusions ..................................................................................................... 70
4.2 Outlook: suggestions for future work ............................................................. 71
References ................................................................................................................... 75
Chapter 1 Introduction
- 1 -
Chapter 1 Introduction
Transition metal aluminum nitrides are of particular interest as coatings for
forming and cutting tools [1-3], with TiAlN being one of the benchmark materials for
the last 20 years [2, 4-6]. VAlN, isostructural to TiAlN, was reported to exhibit a
lower coefficient of friction of μ < 0.085 [7], compared to a value of 0.35 ≤ μ ≤ 0.40
in TiAlN coatings [8], and the elastic modulus of VAlN can reach 488 GPa [9], which
is comparable to that of TiAlN coatings at around 410 GPa [10]. Both TiAlN and
VAlN form metastable solid solutions [6, 11-17] and are readily obtained by
direct-current magnetron sputtering (DCMS) [12, 18-20] as well as by high-power
impulse magnetron sputtering (HIPIMS) [13-15, 21]. Generally, the incorporation of
Al into fcc-TiN and fcc-VN results in the formation of metastable fcc-TiAlN and
fcc-VAlN solid solutions, both crystallizing in the space group with NaCl as
the prototype. This causes a significant enhancement of both hardness [10, 18] and
oxidation resistance [14, 22] compared to the binary TiN and VN compounds. In light
of these properties, investigating the metastable phase formation and increasing the
maximum solubility of Al (xmax) in metastable fcc-TM1−xAlxN (TM = Ti, V) are vital,
application-relevant research goals, and multiple experimental studies have been
performed to that effect.
Several attempts have been made to study the metastable phase formation and
specifically the critical solubility of Al in Ti1-xAlxN. In contrast to the published
experimental xmax range from 0.40 to 0.90 [23-35], the xmax range predicted by
thermodynamic calculations is 0.60 to 0.72, and the ab initio predicted xmax range is
Chapter 1 Introduction
- 2 -
0.50 to 0.79, hence covering only 24% and 58% of the experimentally reported
critical solubilities, respectively. Even including anharmonic phonon free energy
effects, the experimental low solubility boundary is not covered in the theoretical
predictions [36]. It is evident that modeling attempts regarding the metastable solid
solubility solely based on energetic considerations cannot predict the full range of the
experimentally obtained solubility data. Although Sangiovanni et al. introduced
surface diffusion and adsorption energies to model the growth of stable TiN [37-39],
and Alling et al. [40] considered the effect of configurational disorder on surface
diffusion on TiAlN(001) surfaces, no modeling attempts including both energetic
(thermodynamic) and kinetic considerations have been reported for predicting the Al
solubility limit in metastable TiAlN. For the first part of this thesis (chapter 3.1), we
include for the first time kinetics in a predictive model based on the work of Chang et
al. [41, 42] for metallic thin films to describe the metastable phase formation of
Ti1-xAlxN where the low Al solubility limit range, covering 0.42 ≤ x ≤ 0.50, is
accessible providing a metastable ternary phase region that is consistent with
experiments for this technologically important benchmark system.
While the calculated solubility range agrees well with phase boundaries
determined from experiments [12], the aforementioned model failed to predict the
application-relevant and experimentally reported Al solubility range from 0.68 to 0.90
for Ti1−xAlxN. It is well known that the phase formation and hence xmax in
fcc-TM1−xAlxN is dependent on the film stress [43]. In 2009, in an ab initio study,
Alling et al. calculated the mixing enthalpies of the Ti1−xAlxN system, and showed a
Chapter 1 Introduction
- 3 -
clear pressure dependence of the phase stability [44]. In 2010, Holec et al. used ab
initio methods to demonstrate a pressure dependence of xmax in fcc-Ti1−xAlxN and
fcc-Cr1−xAlxN, where an increase in xmax of approx. 0.1 was observed under
compression of −4 GPa for both the Ti1−xAlxN and the Cr1−xAlxN systems [45]. No
kinetics were considered. As for V1-xAlxN, the maximum solubility of Al in
metastable fcc-V1−xAlxN reported in the literature ranges from 0.52 to 0.62 for DCMS
[18, 19], and between 0.59 and 0.75 for DCMS/HIPIMS [13-15]. In contrast to the
plethora of experimental studies, there are very few theoretical and computational
works focusing on xmax in fcc-V1−xAlxN. Using density functional theory (DFT)
calculations, Greczynski et al. in 2017 observed that xmax increases with increasing
hydrostatic pressure and that the resulting compressive stress is a partial, but not the
dominant contribution to explaining the enhanced Al solubility [15]. However, though
pressure-dependent, these values were calculated for the ground state of the respective
systems at T = 0 K, excluding kinetic effects, and are not consistent with the
experimentally observed xmax range in fcc-V1−xAlxN, as discussed above. Up to now,
no models considering energetic and kinetic factors simultaneously were used for
prediction of the stress-dependent xmax in metastable V1−xAlxN or Ti1−xAlxN thin films.
For the second part of this thesis (chapter 3.2), we extend our model [12] to predict
the stress-dependent metastable phase formation of V1−xAlxN and Ti1−xAlxN. The
predictions were critically appraised by experiments.
The metastable phase formation diagrams of sputtered TM1−xAlxN thin films
have been predicted and experimentally verified [12, 20]. The stress factor was then
Chapter 1 Introduction
- 4 -
introduced into the model to predict the stress-dependent metastable phase formation
of TM1−xAlxN [20], the calculation results clearly showed a broadening of the
predicted solubility range, and thus significantly improved agreement with
experimental data.
Chapter 2 Methods
- 5 -
Chapter 2 Methods
2.1 Ab initio calculations
2.1.1 Activation energy for surface diffusion
The atomic surface diffusion energies in Ti1−xAlxN and V1−xAlxN were obtained
via ab initio calculations using a density functional theory (DFT) approach as
implemented in the Vienna ab initio Simulation Package (VASP) code [46, 47]. The
projector-augmented wave (PAW) method [48, 49] was used for basis set
representation within the framework of the generalized-gradient approximation
(GGA), while exchange and correlation effects were described using the established
Perdew-Burke-Ernzerhof (PBE) functional [50]. A k-point grid of 5×5×5 was chosen
to ensure energetic convergence for all supercells containing 64 atoms. All systems
were treated without spin polarization. The C#3 structure [51] was applied to study
fcc structures, and the w#2 structure [52] was employed for hexagonal close-packed
structures, in order to determine the lattice parameter of Ti1-xAlxN, and the atomic
migration for both Ti1-xAlxN and V1-xAlxN. For the calculation of activation barriers
for surface diffusion in the fcc and hcp (hexagonal close-packed structures, also
denoted as the wurtzite structure structures) phases, the following scheme was
employed: Instead of adatoms, TM (Ti, V), Al, or N surface atoms located on an initial
atomic position in equilibrium were sequentially moved to the closest neighboring
vacant site at the thermodynamically stable (100) (fcc) mixed and (0001) (hcp) metal
Chapter 2 Methods
- 6 -
and non-metal terminated surfaces of the supercell. Qs describes the atomic migration
in the surface layer, rather than on the surface layer, as depicted in Fig. 2.1. This
migration occurred stepwise in a series of calculations with identical parameters,
differing only in the position of said atom. An additional vacancy was introduced into
the system in the immediate vicinity. The lattice parameters and the positions of the
atoms at the bottom layer of the supercell and at the surface were fixed, with 4 atomic
layers constituting the immobile slab, and a vacuum region with an extent of 10 Å
was placed adjacent to the surface. The size of the vacuum region was shown to be
sufficient to remove all periodic image interactions in energetic convergence studies
considering vacuum regions with extents of 8 and 12 Å for comparison. The vacuum
thickness of 10 Å is commonly employed in theoretical treatments of NaCl-structured
surfaces [53]. All other atomic positions underwent full relaxation. This simulation
methodology is described in detail in previous works [12, 20, 41, 42].
Chapter 2 Methods
- 7 -
Fig. 2.1 The respective atomic diffusion processes of Ti (or V), Al, and N atoms on an
fcc (100) surface in the [110] direction as indicated by the arrows.
2.1.2 Enthalpy as a function of pressure
Ab initio simulations of unperturbed bulk systems (with no atomic movement
and lacking a vacuum region) with varying cell volumes were also used for the
calculation of the enthalpy as a function of pressure [45]. The enthalpy, as defined in
equation (2.1), must be taken as the correct thermodynamic potential instead of the
internal energy U, when the pressure p is considered:
(2.1)
The Murnaghan equation of state is provided below [54]:
(2.2)
Chapter 2 Methods
- 8 -
It involves the bulk modulus B0 and its first derivative with respect to pressure B0’. V
is the volume, and the V0 represents the equilibrium volume. E designates the total
energy (at T = 0 K), and E0 is the value of E when p = 0 GPa. The Murnaghan
equation of state [54] provides an expression for the equilibrium volume as a function
of p (p=∂E/∂V):
(2.3)
Combining equations (2.2) and (2.3), an analytical expression (2.4) for the enthalpy as
a function of p is obtained:
(2.4)
Further details can be found in the literature [45].
2.2 CALPHAD approach
2.2.1 TiN-AlN system
The CALPHAD (CALculation of PHAse Diagrams) method was utilized to
calculate stable phase diagrams of the TiN-AlN system considering the phase
equilibria and provide thermodynamic data to study metastable phase formation [12].
The FactSage software was utilized for the simulations. The Gibbs energy expressions
and calculated parameters for pure components [55], binary (Ti-Al [56], Ti-N [57],
Al-N [58]), and ternary Ti-Al-N [59] phases in the Ti1-xAlxN system are provided [12].
Chapter 2 Methods
- 9 -
The thermodynamically stable TiN-AlN pseudo-binary phase diagram, calculated
with CALPHAD, is shown in Fig. 2.2(a). It is evident that Al has almost no solid
solubility in the fcc phase; the same is observed for Ti in the hcp phase. In Fig. 2.2(b),
the crossover of the Gibbs free energy for hcp and fcc solid solution phases indicates
the metastable solid solubility limit (Al in fcc-Ti1-xAlxN) at x = 0.68 at 0 °C. Hence,
the maximum critical solubility (xmax) of Al in the fcc structure based on the current
model is 0.68 as diffusion can only reduce this value.
Chapter 2 Methods
- 10 -
Fig. 2.2 (a) Thermodynamic values using the CALPHAD approach: stable TiN-AlN
pseudo binary phase diagrams; (b) thermodynamic values using the CALPHAD
approach: the calculated Gibbs free energy of the fcc and hcp solid solution phases in
the Ti1-xAlxN system.
Chapter 2 Methods
- 11 -
2.2.2 VN-AlN system
The stable phase diagrams of the VN-AlN system were calculated by the
CALPHAD approach, describing the phase boundaries and equilibria of the system
and serving as an initial dataset to investigate the formation of metastable phases [20].
The Gibbs energy expressions in literature were adopted from pure components [55],
binary (V-Al [60], V-N [61], Al-N [62]), and ternary V-Al-N [62] systems. The stable
pseudo-binary VN-AlN phase diagram at thermodynamic equilibrium, calculated with
the CALPHAD method, is depicted in Fig. 2.3(a), clearly demonstrating that Al and V
each exhibit negligible solid solubility in the “host” phase (fcc and hcp, respectively).
Therefore, the minimum solid solubility xmin is 0. Fig. 2.3(b) shows the crossover of
the Gibbs free energy for the hcp and fcc solid solution phases at 0 °C, indicating an
xmax of 0.62. While N under-stoichiometry causes an increase of the Gibbs free
energies for both the fcc and hcp phases, its effect on the crossover of the
corresponding G(x) curves is marginal, with x = 0.62 for 50 at.% nitrogen and x =
0.63 for 46 at.% nitrogen. Hence, it was not considered.
Chapter 2 Methods
- 12 -
Fig. 2.3 (a) VN-AlN pseudo-binary phase diagrams calculated via the CALPHAD
approach; (b) the calculated Gibbs free energies of the fcc and hcp solid solution
phases in V1−xAlxN at 0 °C.
Chapter 2 Methods
- 13 -
2.3 Experimental methods
2.3.1 Magnetron Sputterings
All the Ti1-xAlxN and V1-xAlxN thin films were synthesized in an industrial
CemeCon 800/9 system using DC magnetron sputtering. The experimental setup is
sketched schematically in Fig. 2.4 and shows that the thin films with an Al
compositional gradient are deposited from the split Al and Ti (or V) targets at a
target-to-substrate distance of 10 cm. Such a setup enables an efficient determination
of phase boundaries and is commonly referred to as combinatorial synthesis [63].
Ti1-xAlxN and V1-xAlxN thin films were synthesized at various substrate temperatures
ranging from 100 to 550 °C, which were measured with two thermocouples clamped
to the substrate holder (without rotation) in the vicinity of the Si (100) substrates. Five
different power densities (0.2, 1.2, 2.3, 4.6, and 6.8 W cm-2) in total were applied to
study the effect of the deposition rate on the phase formation for all thin films. The
partial pressures of Ar and N2 were 0.35 and 0.18 Pa, respectively. The DC bias
voltage values of −60, −120, −180, and −240 V were applied to the substrates for all
the depositions.
Chapter 2 Methods
- 14 -
Fig. 2.4 Schematic representation of the deposition setup showing the split targets, the
substrate holder, and the compositional gradient for combinatorial growth of Ti1-xAlxN
and V1-xAlxN. Using this setup, all thin films were synthesized.
2.3.2 Characterizations
Thin film chemical compositions were determined by energy dispersive X-ray
spectroscopy (EDX) in a JEOL JSM-6480 scanning electron microscope with an
EDAX Genesis 2000 detection system at 10 kV acceleration voltage calibrated with
reference samples. The chemical compositions of these reference samples were
quantified by time-of-flight elastic recoil detection analysis (ERDA) at the Tandem
Chapter 2 Methods
- 15 -
Accelerator Laboratory of Uppsala University. Recoils were generated with 36 MeV
127I8+ primary ions and recorded with a gas ionization detection system [64]. Average
Ti, Al, N, and O concentration values were obtained from depth profiles, which were
evaluated with the CONTES program package [65].
For phase identification, X-ray diffraction (XRD) was used employing a Bruker
AXS D8 Discover General Area Diffraction Detection System (GADDS) with =
15° and operated at 40 kV and 40 mA. The sin2Ψ method [66, 67] was applied to
obtain the stress-free lattice parameters of Ti1-xAlxN thin films.
Spatially-resolved chemical composition analysis was carried out by
three-dimensional atom probe tomography (APT) on selected samples. The APT tips
were extracted parallel to the growth direction of the film utilizing a dual-beam
focused ion beam microscope (FIB) FEI Helios NanoLab 660. APT measurements
were conducted in a Cameca LEAP 4000X HR employing laser-assisted pulse mode
with 30 pJ energy at 250 kHz frequency, 60 K temperature, and 0.5% detection rate.
Reconstructions and data analysis were carried out using the Cameca IVAS 3.8.0
software.
Transmission electron microscopy (TEM) analysis was applied for
spatially-resolved phase identification of selected samples. Site-specific lift-outs were
done by FIB in order to prepare cross-sectional TEM foils. A thin layer of platinum
was deposited on the film surface for protection against ion beam damage before
cutting. Structural TEM characterization of the thin films was carried out using a
Tecnai F20 TEM operated at a voltage of 200 kV.
Chapter 3 Results and discussion
- 16 -
Chapter 3 Results and discussion
3.1 Modeling of metastable phase formation for Ti1-xAlxN thin
films
3.1.1 Introduction
TiAlN is the benchmark coating material for metal cutting and forming
applications [2, 4, 5, 68-70]. The metastable solid solution can be formed by physical
vapor deposition techniques such as magnetron sputtering [71, 72] and cathodic arc
evaporation [73]. Additions of Al to TiN, resulting in the formation of metastable
TiAlN, were reported by Münz in 1986 to improve the oxidation resistance compared
to TiN [74].
One major research focus is to increase the Al concentration in fcc-TiAlN (space
group Fm m, prototype NaCl). To this end, several attempts have been made to study
the metastable phase formation and specifically the critical solubility of Al (xmax) in
Ti1-xAlxN. The critical Al solubilities in the fcc phase obtained by growth experiments
were recently reviewed in Ref. [23] covering the xmax range of 0.40 to 0.90. As for
thermodynamic attempts, the Al solubility limit in the metastable TiAlN was first
reported by Spencer et al. [75] in 1990 and Stolten et al. [76] in 1993, where xmax was
estimated to range between 0.70 and 0.72. CALPHAD calculations by Zeng and
Schmid-Fetzer [77] in 1997 were reassessed by Chen and Sundman [59] in 1998,
reporting an xmax range from 0.60 to 0.70. Spencer et al. [78] introduced the
Chapter 3 Results and discussion
- 17 -
stable-to-metastable structural transformation energies into their Gibbs free energy (G
vs. x) model in 2001, yielding an xmax of 0.71.
As for density functional theory (DFT) calculations, Hugosson et al. [79] studied
the phase stability of Ti1-xAlxN in 2003 and obtained an xmax = 0.60. Mayrhofer et al.
[51] reported an xmax range from 0.64 to 0.74, depending on the Al distribution on the
metal sublattice in 2006. Holec et al. [45] reported the influence of compressive
stresses on the critical Al solubility rendering an xmax range of 0.70 to 0.79 in 2010.
Euchner et al. [16] considered vacancies on the metal and non-metal sublattices (xmax
= 0.65 to 0.72) in 2015, while Hans et al. [23] reported an xmax range from 0.50 to
0.75 based on crystallite size effects in 2017.
In contrast to the published experimental xmax range extending from 0.4 to 0.9
[23-35], the xmax range predicted by thermodynamic calculations is 0.60 to 0.72, and
the ab initio predicted xmax range is 0.50 to 0.79, hence covering only 24% and 58% of
the experimentally reported critical solubilities, respectively. Even including
anharmonic phonon free energy effects, the experimental low solubility boundary is
not covered in the theoretical predictions [36]. It is evident that modeling attempts
regarding the metastable solid solubility solely based on energetic considerations
cannot predict the full range of the experimentally obtained solubility data.
A model describing the metastable phase formation during thin film growth
based on both thermodynamic and kinetic data was recently reported by Chang et al.
[41, 42] for Cu-W and Cu-V thin films, extending the Saunders and Miodownik
approach from 1987 [80]. The calculated solubility limits show very good agreement
Chapter 3 Results and discussion
- 18 -
with experimentally determined phase boundaries [81]. While Sangiovanni et al.
introduced surface diffusion and adsorption energies to model the growth of stable
TiN [37-39] and Alling et al. [40] considered the effect of configurational disorder on
surface diffusion on TiAlN(001) surfaces, no modeling attempts including both
energetic (thermodynamic) and kinetic considerations have been reported for
predicting the Al solubility limit in metastable TiAlN.
Here, we include for the first time kinetics in a predictive model based on the
work of Chang et al. [41, 42] for metallic thin films to describe the metastable phase
formation of Ti1-xAlxN where the low Al solubility limit range, covering 0.42 ≤ x ≤
0.50, is accessible providing a metastable ternary phase region that is consistent with
experiments for this technologically important benchmark system.
3.1.2 Calculations
From references [41, 42], it can be inferred that the activation energy for surface
diffusion (Qs) is essential for predicting the metastable solid solubility. In this work,
Qs values of fcc-Ti1-xAlxN are obtained for x = 0, 0.25, 0.5 and of hcp-Ti1−xAlxN for x
= 0.75, 1.0. The [110] direction was selected based on Oshcherin’s observations for
isostructural systems [82]. Surface diffusion activation energies of Ti, Al, and N atoms
are calculated, and the arithmetic average values for each composition are
summarized in Fig. 3.1. We employ averaged activation energies for surface diffusion
because the diffusion of individual species cannot be treated within the computational
framework [41, 42]. The magnitude of Qs obtained here is between the barrier for an
Chapter 3 Results and discussion
- 19 -
adatom (one atom moves on the surface) [40] and the bulk diffusion barrier [37].
Fig. 3.1 Calculated diffusion activation energies (Qs) of fcc phase on a (100) surface
and hcp phase on a (0001) surface.
Fig. 3.2(a) shows the calculated and experimental stress-free lattice parameters
versus x for fcc phases compared to published calculated [51] and experimental data
[26, 27, 31-35, 83]. For the comparison of here presented experimental data with
respect to reported lattice parameter values, the trend is consistent with the
incorporation of Al in the fcc lattice in the whole x range. The maximum deviation of
experimental data with respect to experimental literature data is 1.5%, which may be
explained by residual stresses affecting the reported lattice parameter values. Our
Chapter 3 Results and discussion
- 20 -
experimental data and ab initio predictions [32, 83] are in very good agreement with a
deviation of < 0.5%, as common deviations between theoretically and experimentally
obtained lattice parameters are within 2% [84]. In terms of the calculation of hcp
structures in the whole composition range, the comparison between here obtained ab
initio and reference data [85] is also shown in Fig. 3.2(b). Good agreement between
predictions and reference data is obtained with < 0.5% for the lattice parameter a and
approximately 1% for the lattice parameter c. The above results demonstrate the
successful prediction of the lattice parameters for both fcc and hcp phases in the
Ti1-xAlxN thin film system by means of ab initio calculations. Achieving consistency
between the experimental phase boundary within the complex process parameter
space (5 substrate temperatures and 3 target power densities) and density functional
theory data, required as input for the extension of the energetics solubility model with
kinetic factors (activation energy), enables the crucial validation of the model.
Chapter 3 Results and discussion
- 21 -
Fig. 3.2 Ab initio and experimental lattice parameters of (a) fcc and (b) hcp structures
in Ti1-xAlxN system compared to published theoretical and experimental data.
Chapter 3 Results and discussion
- 22 -
3.1.3 Experiments
Ti1-xAlxN thin films were synthesized in an industrial CemeCon 800/9 system
using DC magnetron sputtering. The thin films with an Al compositional gradient are
deposited from the split Al and Ti targets at a target-to-substrate distance of 10 cm.
Such a setup enables an efficient determination of phase boundaries and is commonly
referred to as combinatorial synthesis [63]. Ti1-xAlxN thin films were synthesized at
various substrate temperatures ranging from 100 to 550 °C, which were measured
with two thermocouples clamped to the substrate holder (without rotation) in the
vicinity of the Si (100) substrates. Three different power densities (2.3, 4.6, and 6.8 W
cm-2) were applied to study the effect of the deposition rate on the phase formation.
The partial pressures of Ar and N2 were 0.35 and 0.18 Pa, respectively. A DC bias
voltage of −60 V was applied to the substrates. The deposition parameters are
summarized in Table 3.1.
Chapter 3 Results and discussion
- 23 -
Table 3.1 Experimental synthesis parameters for metastable Ti1-xAlxN employing
combinatorial DC magnetron sputtering.
The combinatorial Al concentration gradient x in Ti1-xAlxN was determined by
EDX and for selected samples by ERDA, serving as calibration standards for EDX.
The EDX results show that the Al concentration of all thin films were varied from 7 ±
2 at.% to 44 ± 2 at.%. The O concentration, most likely caused by the incorporation of
residual gas [86] during growth was 2 at.%. The average N content in the range of
48 ± 3 at.% was obtained by ERDA-calibrated EDX, averaging the composition for
all samples obtained at different target power densities and substrate temperatures.
There is no functional dependence between the N content, mostly induced by
vacancies on the non-metal sublattice, and the target power density or the substrate
temperature. According to Euchner and Mayrhofer [16], vacancies on the metal and
Chapter 3 Results and discussion
- 24 -
non-metal sublattice in Ti1-xAlxN affect the physical properties, whereas their effect
on the phase transition region is too small to be validated experimentally. Even for a
vacancy concentration of 6.25% on the non-metal sublattice, the Al solubility limit is
essentially unaffected [16]. Since the N content variations in this work are within the
range probed by Euchner and Mayrhofer [16], no detectable N induced variation of
the phase formation is expected.
To identify the relationship between Al concentration and phase formation,
diffractograms of Ti1-xAlxN thin films deposited at a temperature of 550 °C and a
power density of 4.6 W cm-2 are shown in Fig. 3.3. For x ≤ 0.60, the formation of an
fcc single phase region is observed. As x increases from 0.60 to 0.61 the formation of
the hcp phase is observed at 2θ = 64°. Hence, the phase boundary between the fcc and
mixed phase region lies between 0.60 to 0.61 as x = 0.60 is located in pure fcc region,
while at x = 0.61, the presence of the hcp phase can be observed in addition to the fcc
phase. The mixed phase region (containing fcc and hcp phases) is observed for the x
range of 0.61 ≤ x ≤ 0.70. As the Al concentration is increased to x ≥ 0.71, all
diffraction signals are associated with the formation of the hcp phase. Hence, the
phase boundary between hcp and the mixed phase region lies between 0.70 < x < 0.71.
The region, where only the hcp phase is formed, extends over an x range of 0.71 ≤ x ≤
1. Even though the composition-constitution correlation in Fig. 3.3 (550 °C, 4.6 W
cm-2) is consistent with previous reports [23-35], it provides, together with all other
process parameter combinations (5 substrate temperatures and 3 target power
densities), a unique and comprehensive data set obtained under the same experimental
Chapter 3 Results and discussion
- 25 -
conditions (base pressure, working pressure, substrate selection, target-to-substrate
distance, etc.), which is required to critically appraise and validate the here proposed
model.
Fig. 3.3 Diffractograms of Ti1-xAlxN thin films (0.11 ≤ x ≤ 0.92) deposited at a
temperature of 550 °C and a target power density of 4.6 W cm-2.
In order to reveal compositional changes at the nanometer scale, APT was
employed. The local compositions of single phase fcc-Ti0.46Al0.54N were compared to
the film with the nominal composition of Ti0.37Al0.63N, which exhibits a phase mixture
of fcc + hcp. The compositions are based on EDX measurements, and both films were
deposited at 550 °C substrate temperature and at a target power density of 4.6 W cm-2.
The reconstruction of Ti0.46Al0.54N and Ti0.37Al0.63N films is presented in Fig. 3.4(a)
Chapter 3 Results and discussion
- 26 -
and Fig. 3.4(b), respectively. Regions with ≥ 50 at.% Al are highlighted by
isoconcentration surfaces and only visible in the case of Ti0.37Al0.63N, see Fig. 3.4(b).
The notion of clustering or chemical segregations is confirmed by the frequency
distribution analysis, which is shown for Ti0.46Al0.54N in Fig. 3.4(c) and for
Ti0.37Al0.63N in Fig. 3.4(d). Here, the measured distributions of constitutional elements
(squares for Ti, circles for Al, diamonds for N) are compared to random, binomial
distributions (solid lines). While the measured local distribution of Ti, Al, and N is in
accordance with the binomial distribution for Ti0.46Al0.54N, Fig. 3.4(c), a significant
deviation is evident for Ti0.37Al0.63N, Fig. 3.4(d). Furthermore, the Pearson correlation
coefficient μ was obtained from the distribution analysis. Values close to zero (μTi =
0.04, μAl = 0.06, and μN = 0.04) indicate a random distribution for Ti0.46Al0.54N. In
contrast, significantly higher correlation coefficients (μTi = 0.19, μAl = 0.48, and μN =
0.10) emphasize local clustering or segregations for Ti0.37Al0.63N. Finally, the
chemical composition profile of Ti0.37Al0.63N (see Fig. 3.4(f)) in a cylindrical region of
10×10×140 nm (indicated in Fig. 3.4(b) by dotted lines) is consistent with the
formation of an Al rich and a Ti deficient region. Hence, the comparison of APT
results indicates the presence of a phase mixture in case of the higher Al concentration,
which agrees well with the structure evolution presented in Fig. 3.3 and with APT
data in a previous report on the decomposition pathway in TiAlN by Rachbauer et al.
[72].
Chapter 3 Results and discussion
- 27 -
Fig. 3.4 Spatially-resolved local chemical composition distribution of thin films
deposited at 550 °C with a power density of 4.6 W cm-2 obtained by atom probe
tomography. Reconstruction of (a) Ti0.46Al0.54N and (b) Ti0.37Al0.63N films showing the
position of Al atoms as well as isoconcentration surfaces with ≥ 50 at.% Al.
Chapter 3 Results and discussion
- 28 -
Frequency distribution analysis of (c) Ti0.46Al0.54N and (d) Ti0.37Al0.63N films
comparing the measured distributions of constitutional elements (squares for Ti,
circles for Al, diamonds for N) to random, binomial distributions (solid lines). μ
values are the Pearson correlation coefficients. Chemical composition profiles of (e)
Ti0.46Al0.54N and (f) Ti0.37Al0.63N films from a cylindrical region of 10x10x140 nm
(indicated by dotted lines in (a) and (b), respectively) in the growth direction.
Fig. 3.5 depicts the experimental metastable TiN–AlN phase formation diagram
with an Al concentration range from 0.11 to 0.92, which is obtained from composition
and structure data of magnetron sputtered thin films grown at three different target
power densities. At 550 °C, it is observed that a mixed phase region containing fcc
and hcp phases forms for Al concentrations ranging from 0.57 ≤ x ≤ 0.70 at the target
power density of 2.3 W cm-2, which is wider than the range at 4.6 W cm-2 (0.61 ≤ x ≤
0.70) indicating that the increase in power density increases the metastable solubility
of Al. It is found that the Al concentration range for the two phase region is reduced as
the deposition temperature is reduced. This trend can be extrapolated to 0°C resulting
in a phase boundary at 0.68. The above results clearly show that the maximum
metastable solubilities of Ti in hcp and Al in fcc, as well as the extension of the mixed
phase region, is determined by processing parameters. The results also underline that
predictions of the solid solubility based on thermodynamic or ab initio models that do
not account for process parameter induced changes in kinetics show limited
agreement with experimental data. The composition-constitution-process parameter
Chapter 3 Results and discussion
- 29 -
correlations in Fig. 3.5 are required to validate the here proposed model based on both
energetics and kinetics, as detailed below.
Fig. 3.5 Experimental metastable TiN-AlN phase formation diagram obtained from
composition and structure data of magnetron sputtered thin films grown at three
different power densities (2.3, 4.6, and 6.8 W cm-2). The symbols correspond to the
experimental phase formation data for the different metastable phases.
3.1.4 Modeling: Metastable phase formation of Ti1-xAlxN
For low temperature deposited thin films, surface diffusion often predominates
the metastable phase formation [87, 88]. It was shown by Chang et al. [41, 42] that
Chapter 3 Results and discussion
- 30 -
the activation energy of surface diffusion processes is critical for predicting the
metastable phase formation of Cu-W and Cu-V thin films [41, 42]. The atomic
mobility can be described by the temporal dependence of the surface diffusion
distance of a single atom from Einstein [89]:
, (3.1)
where X is the diffusion distance, Ds is surface diffusivity, and t is the time. Based on
equation (3.1), Cantor and Cahn [90] proposed the following relationship to describe
the surface diffusion, deposition rate, and temperature dependence of the diffusion
distance during deposition and thin film growth:
, (3.2)
where ν is the atomic vibrational frequency (1013 s-1) [91], a is the distance of an
individual atomic jump based on lattice parameter data for Ti1-xAlxN [12], rD is the
deposition rate, Qs is the atomic activation energy for surface diffusion, k is the
Boltzmann constant, and T is the substrate temperature. The Qs values were
determined based on the migration energy landscape calculation for Ti, Al, and N
atoms, which is provided by Fig. 3.1. When the atomic diffusion distance reaches a
critical value (Xc), the second phase is formed [41, 42]. Based on the above reasoning,
equation (3.3) can be obtained from equation (3.2):
, (3.3)
where Tc is the critical temperature for each Ti1-xAlxN composition at a certain
deposition rate. When the substrate temperature is lower than Tc, the diffusion
Chapter 3 Results and discussion
- 31 -
distance of atoms on fcc or hcp surfaces is smaller than Xc, meaning that the formation
of a second phase is prevented by kinetic limitations due to insufficient atomic
mobility. When the temperature is equal to or larger than Tc, a second phase is formed
due to the enhanced atomic mobility.
From equation (3.3), it is found that the activation energy for surface diffusion
(Qs) is essential for predicting the metastable phase formation of sputtered Cu-W and
Cu-V thin films [41, 42]. In order to model the metastable phase formation diagram, it
is necessary to know the relationship between Tc and x [41, 42]. Independent of
crystal structure, the relationship of Xc and Al solubility can be fitted using the
following function [41, 42]:
, (3.4)
where xmin is the Al solubility in the equilibrium TiN-AlN phase diagram, and xmax is
the maximum solubility of Al in metastable fcc-Ti1−xAlxN. Xc/2 is the critical diffusion
distance at half metastable solid solubility, i.e. at x = (xmax + xmin) / 2. According to the
CALPHAD results, the value of xmin can be regarded as 0, and xmax = 0.68, as shown
in Fig. 2.2 for Ti1−xAlxN. This model defines the surface diffusion required for the
formation of a second phase and describes the relationship between the critical
diffusion distance and solubility. The outlined methodology is described in greater
detail in the literature [12, 20, 41, 42].
The composition dependence of Xc at the fcc and hcp surfaces is calculated by
equation (3.3), as shown in Fig. 3.6(a). The constant Xc/2 was calculated based on
experimental data obtained at a substrate temperature of 550°C and a target power
Chapter 3 Results and discussion
- 32 -
density of 2.3 W cm-2 by using the equations (3.3) and (3.4), and is further used for
the calculation of other Xc values, shown in Fig. 3.6(b). Then, the relationship
between Tc and x, which is used to calculate the metastable phase formation diagram
for the whole composition range based on the input of the phase formation data
obtained from only one combinatorial deposition experiment, is obtained.
Chapter 3 Results and discussion
- 33 -
Fig. 3.6 (a) Composition dependence of Xc at the fcc and hcp surfaces; (b) Xc vs. x plot:
experimental data and fitted curves for both fcc and hcp phases in the Ti1−xAlxN
Chapter 3 Results and discussion
- 34 -
system. The Xc value obtained for a deposition temperature of 550°C and a target
power density of 2.3 W cm-2 (solid symbols) is used for the calculation of other Xc
values for the target power densities of 4.6 and 6.8 W cm-2.
The metastable phase formation data obtained from one combinatorial deposition
performed at a temperature of 550 °C and a target power density of 2.3 W cm-2 have
been selected to model the Ti1-xAlxN system for the whole composition range. Based
on this model, the positions of the phase boundaries have been predicted for the target
power densities of 4.6 and 6.8 W cm-2, as shown in Fig. 3.7(a). Furthermore,
additional experimental data obtained at a power density of 2.3 W cm-2 and substrate
temperatures of 100, 250, 350, and 450 °C are also consistent with the model, as
shown in Fig. 3.7 (b). The predicted phase formation diagrams for power densities of
4.6 and 6.8 W cm-2 agree very well with the experimental phase formation data
depicted in Fig. 3.7(c) and Fig. 3.7(d), respectively. Therefore, a research strategy
proposed for predicting the metastable solid solubility of Cu-W and Cu-V [41, 42] has
successfully been adapted for modeling and predicting the metastable phase formation
of magnetron sputtered Ti1-xAlxN thin films. The evaluation criteria are the positions
of the predicted metastable phase boundaries compared to the experimental data. The
correlative experimental and theoretical research strategy proposed here for modeling
the metastable phase formation during magnetron sputtering is not limited to fcc and
hcp solid solutions and may be expanded to other metastable phases such as
amorphous phases.
Chapter 3 Results and discussion
- 35 -
Fig. 3.7 Metastable TiN-AlN phase formation diagrams: (a) calculated diagrams using
experimental data at a temperature of 550 °C and a power density of 2.3 W cm-2;
validation using experimental data at the power densities of (b) 2.3 W cm-2, (c) 4.6 W
cm-2, and (d) 6.8 W cm-2. The points correspond to the experimental values in Fig. 3.5.
The solid curves represent the calculated values with the experimental verification,
while the dashed ones represent the predicted phase boundaries above the highest
deposition temperature of 550 °C and below the lowest temperature of 100 °C
employed in this work.
To critically appraise the integral phase formation data obtained by XRD,
selected area electron diffraction (SAED) studies were carried out on samples with
Chapter 3 Results and discussion
- 36 -
compositions close to the predicted phase boundaries. Figs. 3.8(a) and (b) show
SAED patterns of Ti1-xAlxN with x = 0.49 (550°C, 4.6 W cm-2) and x = 0.64 (100°C,
4.6 W cm-2), respectively, which were based on XRD classified as single phase fcc.
Consistent with XRD, also the SAED data show the formation of a single phase fcc
structure. Furthermore, for the Ti1-xAlxN sample with x = 0.62 (550°C, 4.6 W cm-2),
again consistent with XRD, hcp and fcc diffraction patterns are observed (Fig. 3.8(c)),
while for x = 0.74 (550°C, 4.6 W cm-2) single phase hcp is identified, see Fig. 3.8(d).
Hence, for all here investigated samples, the XRD data are consistent with the SAED
data. Finally, in Fig. 3.8(e), the SAED data are compared to the above described
model. The predicted phase boundaries are consistent with the phase formation data
obtained from SAED.
Chapter 3 Results and discussion
- 37 -
Fig. 3.8 Selected area electron diffraction patterns for Ti1-xAlxN samples with (a) x =
Chapter 3 Results and discussion
- 38 -
0.49 (550°C, 4.6 W cm-2), (b) x = 0.64 (100°C, 4.6 W cm-2), (c) x = 0.62 (550°C, 4.6
W cm-2), (d) x = 0.74, (550°C, 4.6 W cm-2), (e) comparison between selected area
electron diffraction patterns and the above described model. The solid lines represent
the experimentally verified temperature region, while the dashed lines mark the
predicted phase boundaries.
Reviewing the attempts to study the Al solubility limit values of metastable
fcc-TiAlN in the past 28 years [75], experimental data (0.40 ≤ xmax ≤ 0.90) [23-35] are
compared to predictions based on energetics (0.50 ≤ xmax ≤ 0.79) [16, 23, 45, 51, 59,
75-79] in Fig. 3.9. The xmax range predicted by energetic calculations covers only 58%
of the experimentally reported critical solubilities, which indicates that modeling
attempts regarding the metastable solid solubility solely based on energetic
considerations cannot predict the full range of the experimentally obtained solubility
data. Based on the experimentally verified model (for power densities of 4.6 and 6.8
W cm-2) yielding an Al xmax range from 0.58 to 0.68 (0°C ≤ T ≤ 550°C), we predict
xmax values for the power densities of 0.1 and 100 W cm-2 (without experimental
verification) assuming a linear dependence of the deposition rate on the target power
density [41]. Compared with the lowest experimentally reported xmax = 0.40 from
Wahlström in 1993 [35], the here predicted xmax is 0.42. The corresponding predicted
Al solubility limit range is 0.42 ≤ xmax ≤ 0.68 at 0.1 W cm-2 for the deposition
temperature range of 0°C ≤ T ≤ 550°C. This prediction is consistent with
experimentally reported xmax values < 0.5, and it is important to note that this range
Chapter 3 Results and discussion
- 39 -
was previously unobtainable by modeling attempts. Hence, the experimentally
verified model yields accurate predictions regarding the critical solubility of Al in
fcc-TiAlN in the application relevant growth temperature range of 100 °C to 550 °C.
The original energetics-based model for metastable Ti1-xAlxN, introduced by
Hugosson et al. in 2003 [79] yielding a single-point Al solubility limit, was
significantly improved by adding additional factors: (i) the Al distribution on the
metal sublattice [51], (ii) compressive stress [45], (iii) vacancies on the metal and
non-metal sublattices [16], and (iv) crystallite size effects [23]. Even though kinetics
was considered to investigate the effect of configurational disorder on surface
diffusion on TiAlN(001), no explicit inclusion of the kinetic factors into the solubility
model was attempted prior to this work. Low solubility limits, known experimentally
[23-35], are not obtainable unless both kinetic and energetic effects are taken into
account in the unified model formulated herein. Using the calculated activation
energies (Fig. 3.1), the Al solubility limit can be obtained based on equation (3.3).
Hence, Fig. 3.9 does not only contain the previously obtainable solubility range, but it
also broadens the accessible range to lower values and covers the full solubility
window established experimentally in this work and the literature [23-35].
Alling et al. [40] compared the surface diffusion of Ti and Al on Ti0.5Al0.5N (001)
and TiN (001) and thereby probed the effect of configurational disorder (local
chemistry). They show that Ti adatoms exhibit two stable surface adsorption sites,
while Al always prefers a single site (atop N) [40]. This gives rise to a multiple
surface activation energies for Ti in the <110> direction (variation < 0.2 eV) where
Chapter 3 Results and discussion
- 40 -
the absolute difference for the maximum activation energy of Ti and Al is 0.2 eV [40].
To critically appraise the influence of an assumed variation in surface diffusion
activation energies we have recalculated the critical solubility for surface diffusion
activation energies being 0.2 eV larger and 0.2 eV smaller than the above employed
(averaged) value (see Fig. 3.1) for the power density of 2.3 W cm-2 at 500°C. The
position of the phase boundary at x = 0.59 obtained for the averaged activation energy
for surface diffusion does not change as a consequence of the 0.2 eV variation. This
indicates that the critical solubility of Al in fcc-TiAlN at this temperature and power
density is primarily affected by quenching of the deposited adatoms that diffuse over
the surface by the subsequently deposited flux restricting the adatoms.
Chapter 3 Results and discussion
- 41 -
Fig. 3.9 Metastable TiN-AlN phase formation diagrams in varying temperatures and
power densities compared with previous Al solubility limit values in Ti1-xAlxN
through thermodynamic models, DFT calculations, and experiments. The solid lines
represent the experimentally verified temperature region, while the dashed lines mark
the predicted phase boundaries.
Hence, we have proposed a novel predictive model verified by experiment,
which introduces kinetic contributions into energetic calculations to describe the
metastable phase formation of the nitride thin films for the first time. The model is
Chapter 3 Results and discussion
- 42 -
based on the work of Chang et al. for metallic thin films [41, 42].
3.1.5 Summary
Based on one combinatorial magnetron sputtering experiment, CALPHAD, and
ab initio calculations (activation energy), a model to predict metastable phase
formation of TiAlN thin films considering kinetic effects is proposed. The model was
validated for the application relevant growth temperature range of 100 °C to 550 °C.
Experimental data from magnetron sputtered Ti1-xAlxN thin films are in good
agreement with the model, which describes the effect of composition, deposition
temperature, and kinetic factors on the metastable phase formation of Ti1-xAlxN
systematically. Furthermore, compared to the lowest experimentally reported xmax
value of 0.40, the here predicted xmax value is 0.42 consistent with the experiment. The
here reported model allows for the prediction of the experimentally reported xmax
range of 0.42 ≤ xmax < 0.50, which was previously unobtainable by energetics-based
models. This significant extension of the predicted critical solubility range is enabled
by taking the effect of the activation energy for surface diffusion and the critical
diffusion distance on the metastable phase formation into account.
Chapter 3 Results and discussion
- 43 -
3.2 Modeling of stress-dependent metastable phase formation for
Ti1-xAlxN and V1-xAlxN thin films
3.2.1 Introduction
TMAlN (TM = Ti, V) are of particular interest as coatings for forming and
cutting tools [1-3], with TiAlN being one of the benchmark materials for the last 20
years [2, 4-6]. VAlN, isostructural to TiAlN, was reported to exhibit a lower
coefficient of friction of μ < 0.085 [7], compared to a value of 0.35 ≤ μ ≤ 0.40 in
TiAlN coatings [8], and the elastic modulus of VAlN can reach 488 GPa [9], which is
comparable to that of TiAlN coatings at around 410 GPa [10]. Both TiAlN and VAlN
form metastable solid solutions [6, 11-17] and are readily obtained by direct-current
magnetron sputtering [12, 18-20] as well as by high-power impulse magnetron
sputtering [13-15, 21]. Generally, the incorporation of Al into fcc-TiN and fcc-VN
results in the formation of metastable fcc-TiAlN and fcc-VAlN solid solutions, both
crystallizing in the space group with NaCl as the prototype. This causes a
significant enhancement of both hardness [10, 18] and oxidation resistance [14, 22]
compared to the binary TiN and VN compounds.
In light of these properties, investigating the metastable phase formation and
increasing the maximum solubility of Al in metastable fcc-TM1−xAlxN are vital,
application-relevant research goals, and multiple experimental studies have been
performed to that effect. For instance, by applying DCMS, Rovere et al. obtained an
xmax value of 0.54 in 2010 [19], while Zhu et al. reported the range 0.52 ≤ xmax ≤ 0.62
Chapter 3 Results and discussion
- 44 -
in 2013 [18]. An effective strategy to further increase xmax in fcc-V1−xAlxN is to use an
advanced sputtering technique such as HIPIMS [13-15]. In this regard, it is worth
mentioning that Greczynski et al. obtained fcc-V1−xAlxN films with an unprecedented
xmax of up to 0.75 by employing hybrid co-sputtering, powering the Al target with a
HIPIMS generator and the V target with a DCMS generator (Al-HIPIMS/V-DCMS in
shorthand nomenclature), in 2017 [13-15]. This processing strategy allowed for
separating fluxes from the DCMS and HIPIMS sources into time and energy domains
via utilization of substrate bias pulses that are synchronized with the HIPIMS source
[13-15, 21]. In contrast to the plethora of experimental studies, there are very few
theoretical and computational works focusing on xmax in fcc-V1−xAlxN. Using density
functional theory (DFT) calculations, Greczynski et al. in 2017 observed that xmax
increases with increasing hydrostatic pressure and that the resulting compressive
stress is a partial, but not the dominant contribution to explaining the enhanced Al
solubility [15]. However, though pressure-dependent, these values were calculated for
the ground state of the respective systems at T = 0 K, excluding kinetic effects, and
are not consistent with the experimentally observed xmax range in fcc-V1−xAlxN, as
discussed above. Furthermore, a metastable phase formation diagram for V1−xAlxN
thin films is unavailable.
For Ti1−xAlxN thin films, the experimental xmax range extends from 0.40 to 0.90,
in a deposition temperature range from no intentional heating to 800 °C, as described
in numerous studies reviewed in the literature [23]. As for thermodynamic attempts,
the Al solubility limits in the metastable TiAlN were first reported by Spencer et al.
Chapter 3 Results and discussion
- 45 -
[75] in 1989, and Stolten et al. [76] in 1993, where xmax was estimated to range
between 0.70 and 0.72 at a temperature of 500 K. CALPHAD calculations by Zeng
and Schmid-Fetzer [77] in 1997 were reassessed by Chen and Sundman [59] in 1998,
reporting an xmax range from 0.60 to 0.70, likewise at a temperature of 500 K. Spencer
et al. [78] introduced the stable-to-metastable structural transformation energies into
their Gibbs free energy (G vs. x) model in 2001, yielding an xmax of 0.71 in a
temperature range from 200 to 800 °C. Thus, in contrast to these experimental values,
predictions of xmax yield a range between 0.60 and 0.72 according to thermodynamic
calculations, and between 0.50 and 0.79 as given by ab initio results at a temperature
of 0 K [16, 23, 45, 51, 79]. Thus, the ranges of these calculated values cover only
24% and 58% of the critical solubility range determined via experiments, respectively.
In 2019, we proposed a model that predicts the solubility range of 0.42 ≤ xmax ≤ 0.50
in fcc-Ti1−xAlxN obtained from experiments, previously outside the capabilities of
purely energetics-based models [12]. This significant gain in prediction accuracy
stems from a consideration of both surface diffusion activation energies and critical
diffusion distances as factors impacting metastable phase formation [12]. Thus, both
thermodynamic and kinetic contributions are explicitly considered, extending both the
model described by Saunders and Miodownik [80], itself based on the work of Cantor
and Cahn in 1976 [90], and the model suggested by Chang et al. [41, 42]. While the
calculated solubility range agrees well with phase boundaries determined from
experiments [12], the model failed to predict the application-relevant and
experimentally reported Al solubility range from 0.68 to 0.90 for Ti1−xAlxN.
Chapter 3 Results and discussion
- 46 -
It is well known that the phase formation and hence xmax in fcc-TM1−xAlxN is
dependent on the film stress [43]. In 2009, in an ab initio study, Alling et al.
calculated the mixing enthalpies of the Ti1−xAlxN system and showed a clear pressure
dependence of the phase stability, with the enthalpy crossover points indicating higher
stability of the hexagonal phase vs. the fcc phase shifting from x = 0.71 at 0 GPa to x
= 0.83 and x = 0.94 at 5 and 10 GPa, respectively [44]. In 2010, Holec et al. used ab
initio methods to demonstrate a pressure dependence of xmax in fcc-Ti1−xAlxN and
fcc-Cr1−xAlxN, where an increase in xmax of approx. 0.1 was observed under
compression of −4 GPa for both the Ti1−xAlxN and the Cr1−xAlxN system [45]. No
kinetics were considered. Besides the study mentioned above discussing a relationship
between xmax and compressive stress [15], Greczynski et al. also illustrated that a
coating synthesis strategy based on tuning the incident energy of the bombarding ions
in magnetron sputtering techniques could be utilized to control the incorporation of
these ions into subsurface regions of the substrate [14]. This allows for unprecedented
enhancements of the metastable Al solid solubility in fcc-V1−xAlxN at low or moderate
compressive stress levels, varying from −1.6 GPa with xmax = 0.53 to −3.8 GPa for
xmax = 0.74 [14]. Up to now, no models considering energetic and kinetic factors
simultaneously were used for prediction of the stress-dependent xmax in metastable
V1−xAlxN or Ti1−xAlxN thin films.
Here, we extend our model [12] to predict the stress-dependent metastable phase
formation of V1−xAlxN and Ti1−xAlxN. The predictions were critically appraised by
experiments.
Chapter 3 Results and discussion
- 47 -
3.2.2 Calculations
Accurate predictions of metastable solid solubility values require consideration
of the surface diffusion activation energy Qs, as clearly seen from equation (3.3) and
prior work [12, 41, 42]. In the present study, Qs values are obtained for x = 0, 0.25, 0.5
in the fcc-V1−xAlxN system and for x = 0.75, 1.0 in hcp-V1−xAlxN. Based on prior
findings for isostructural systems by Oshcherin [82], the [110] direction was chosen
for modeling diffusion. Qs pertains to atomic migration in the surface layer, rather
than on it [12], consistent with observations in isostructural systems which suggest
that ion irradiation during growth not only generates mobility on the surface but also
in and below it [92, 93]. The activation energies were calculated for atoms of each
species (V, Al, and N), with the corresponding arithmetic averages shown in Fig. 3.10
for each composition. This averaging of the Qs values is a necessity because the
diffusion of individual species cannot be treated within the computational framework
[12, 41, 42]. For the atomic diffusion in the pure fcc-VN phase (x = 0), according to
the work of Sangiovanni in 2019 [94], ab initio molecular dynamics simulations at
temperatures in excess of 1500 K yield N vacancy activation energies of 3.1 ± 0.3 eV,
which is consistent with the diffusion activation energy for N of 3.3 eV provided in
Fig. 3.10. For the diffusion of N vacancies in the pure hcp-AlN phase (x = 1), based
on the work of Almyras et al. in 2019 [95], semi-empirical force-field calculations for
N vacancy diffusion within the B4-AlN (0001) plane at 0 K yield activation energy of
1.97 eV. This corresponds well to the activation energy value of 2.2 eV for N
diffusion on the hcp-AlN (0001) surface, shown in Fig. 3.10. In terms of Al diffusion
Chapter 3 Results and discussion
- 48 -
in the hcp-AlN phase, a value of 2.72 eV is reported for the activation energy of the
in-plane diffusion [95], comparable to the value of 3.1 eV from this work. The
magnitude of the calculated Qs values lies between the energetic barrier for diffusion
of an adatom (moving on the surface) [40] and the diffusion barrier in bulk [37] of
isostructural TiAlN. As for the aforementioned other parameters, the surface diffusion
activation energies of the Ti1−xAlxN system were also reported in our previous work
[12].
Fig. 3.10 Diffusion activation energies of the fcc-V1−xAlxN (diffusion on (100) surface)
and hcp-V1−xAlxN phases (diffusion on (0001) surface) calculated via density
functional theory.
Chapter 3 Results and discussion
- 49 -
Ab initio simulations of unperturbed bulk systems (with no atomic movement
and lacking a vacuum region) with varying cell volumes were also used for the
calculation of the enthalpy as a function of pressure [45]. Based on equation (2.2), the
bulk modulus of Ti0.5Al0.5N and V0.5Al0.5N is 261 and 276 GPa, respectively, while
the pressure derivative for both compounds is 4.2. This is consistent with the literature
[9, 96]. The 6% larger bulk modulus of V0.5Al0.5N relative to Ti0.5Al0.5N implies
stronger bonding in V0.5Al0.5N, which may hence be less susceptible to pressure
changes. This is relevant for the phase stability data. A comparison of the ab
initio-derived enthalpies H of the fcc and hcp phases as a function of x with varying
compressive pressure p is depicted in Fig. 3.11 for the V1−xAlxN system. It is
important to note that ground-state enthalpies at a temperature of 0 K are shown, as
usual for DFT results, and thus cannot be directly compared with the Gibbs energy
data at 0 °C from CALPHAD modeling, as provided in Fig. 2.3. However, for the
purposes of identifying the crossover points of the H(x) curves, this is entirely
appropriate as long as an identical temperature is used in one dataset. With the change
of compressive pressure (p) from 0 to −5 GPa for the V1−xAlxN system, the value of x
at the energetic crossover between the fcc and hcp phases increases from 0.62 to 0.77;
compare Figs. 3.11(a) and (b), respectively. Thus xmax increases by 0.15 (~24%) with
the change of compressive pressure from 0 to −5 GPa. It is worth noting that
compressive stresses are commonly observed in sputtered thin films [45, 97], and for
V1−xAlxN and Ti1−xAlxN thin films, they are reported to range from 0 to −5 GPa
[13-15, 45]. With the further change of compressive stress from −5 to −10 GPa, xmax
Chapter 3 Results and discussion
- 50 -
increases to 0.94 in Fig. 3.11(c). Based on the calculation of nine different p values
from 0 to −10 GPa, the dependence of xmax in fcc-V1−xAlxN as a function of p is
shown in Fig. 3.11(d). The fcc phase can be stabilized under a certain compressive
pressure across the entire Al compositional range [45]. Based on the linear fitting
result in Fig. 3.11(d), the relationship between the maximum Al solubility and
compressive pressure (p, absolute value) in V1−xAlxN thin films at a substrate
temperature of 0 °C is given below:
(3.5)
Since xmin designates the equilibrium solubility of Al in fcc-V1−xAlxN, which is zero,
the influence of pressure on xmin is expected to be negligible. Other parameters, such
as diffusion length, are, in principle, expected to be affected by pressure. However,
additional degrees of freedom imposed by surfaces (atoms can relax out of a surface
plane) are assumed to minimize the pressure dependence. Hence, only energetics are
treated as pressure-dependent in the current model, and the very good agreement
between theory and experiment obtained here justifies this computational approach.
Chapter 3 Results and discussion
- 51 -
Fig. 3.11 Ground-state enthalpies (T = 0 K) of the fcc and hcp phases of the V1−xAlxN
system from ab initio calculations: (a) at equilibrium, (b) under a load of −5 GPa
compressive pressure, (c) under a load of −10 GPa compressive pressure, (d)
calculated maximum Al solubilities in fcc-V1−xAlxN across the whole compressive
pressure range.
For Ti1−xAlxN, as the magnitude of the compressive pressure increases from 0 to
−5 GPa, the value of xmax at the enthalpic crossover between the fcc and hcp phases
increases from 0.69 to 0.82; compare Figs. 3.12(a) and 8(b), respectively. Thus the
xmax increases by 0.13 (~19%) within the described pressure change, which represents
a common residual stress range for deposited thin films, as outlined above [45, 97].
With a further change in compressive pressure from −5 to −10 GPa, xmax increases to
Chapter 3 Results and discussion
- 52 -
0.90 in Fig. 3.12(c). Based on the calculation of nine different p values from 0 to −10
GPa, the dependence of xmax in fcc-Ti1−xAlxN as a function of p is shown in Fig.
3.12(d). Analogous to equation (3.5) as previously given for V1−xAlxN, the linear
relationship between xmax and compressive pressure (p, absolute value) in Ti1−xAlxN
thin films at a substrate temperature of 0 °C, based on the linear fit in Fig. 3.12(d), is
given by:
(3.6)
Fig. 3.12 Ground-state enthalpies (T = 0 K) of the fcc and hcp phases of the Ti1−xAlxN
system from ab initio calculations: (a) at equilibrium, (b) under a load of −5 GPa
compressive pressure, (c) under a load of −10 GPa compressive pressure, (d)
Chapter 3 Results and discussion
- 53 -
calculated maximum Al solubilities in fcc-Ti1−xAlxN across the whole compressive
pressure range.
3.2.3 Experiments
V1−xAlxN thin films were prepared using DCMS in an industrial CemeCon 800/9
system, and a high-throughput route was chosen to obtain the phase formation data
efficiently. Thin films exhibiting an Al compositional gradient were deposited from a
split Al/V target in a gas atmosphere of Ar (pressure: 0.35 Pa) and N2 (pressure: 0.18
Pa), and the target-to-substrate distance was 10 cm. The synthesis was conducted at
substrate temperatures of 100, 250, 450, and 550 °C, measured using a thermocouple
clamped to the surface of the substrate holder next to the Si (100) substrates. Five
distinct power densities, namely 0.2, 1.2, 2.3, 4.6 and 6.8 W cm-2, were utilized to
study the effect of deposition rate on the phase formation, while the substrates were
biased with a DCMS voltage of −60 V. A summarized listing of key deposition
parameters is given in Table 1.
Chapter 3 Results and discussion
- 54 -
Table 3.2. Experimental parameters for the synthesis of metastable V1−xAlxN via
combinatorial DCMS.
As alluded to in the experimental section, the combinatorial Al concentration
gradient x in the deposited V1−xAlxN thin films was determined by EDX, while
calibration standards were obtained via ToF-ERDA analysis of selected samples. The
Al concentration of the VAlN thin films varied from 9 ± 2 at.% to 44 ± 2 at.% as
determined by EDX. Oxygen impurities in the range of 2 to 5 at.% were measured in
the reference samples by ToF-ERDA and likely result from residual gas incorporation
[86] during thin film growth. The N concentration is approximately 46 ± 1 at.% for all
samples as analyzed by EDX, irrespective of different substrate temperatures and
target power densities. There is no functional dependence between the N content,
mostly caused by vacancies on the non-metal sublattice, target power density, and
Chapter 3 Results and discussion
- 55 -
substrate temperature. The effect of vacancies (on the metal and non-metal sublattice)
on the phase transition is too small to be validated experimentally in Ti1−xAlxN,
according to Euchner and Mayrhofer [16]. The Al solubility limit is essentially
unaffected for a vacancy concentration of 6.25% on the non-metal sublattice [16].
Since the N content variations in this work are within the range mentioned above [16],
no detectable N-induced variation of the phase formation is expected.
The relationship between Al solubility in the fcc phase (xmax) and phase
formation follows from Fig. 3.13, showing diffractograms of V1−xAlxN thin films
deposited at a power density of 2.3 W cm−2 and a deposition temperature of 550 °C. It
is clearly evident that a single fcc phase forms for x ≤ 0.50. Upon an increase of x
from 0.50 to 0.51, the incipient formation of the hcp phase is indicated by the
diffraction peak at 2θ = 33°. As x = 0.50 is still located in the single-phase fcc region,
while at x = 0.51 both the hcp phase and the dominant fcc phase are readily
observable, it follows that the phase boundary between pure fcc and the fcc + hcp
mixed-phase region lies between 0.50 and 0.51. The aforementioned mixed phase
region extends throughout the range of 0.51 ≤ x ≤ 0.62. At Al concentrations of x ≥
0.65, all diffraction signals pertain to the hcp phase solely, so that the single-phase hcp
/ mixed-phase fcc + hcp phase boundary is located between 0.62 < x < 0.65, with
solely the hcp phase forming above 0.65. The entirety of obtained compositional and
structural data for the deposited V1−xAlxN thin films is provided later, while the data
for the corresponding Ti1−xAlxN thin films are given in our previous work [12] and
were shown to be consistent with previous reports [12-15, 18, 19]. Thus, a
Chapter 3 Results and discussion
- 56 -
comprehensive data set obtained under constant process parameters (base and
working pressure, substrate type, target-to-substrate distance, etc.) has been generated.
This data set is necessary for critical evaluation and validation of the model developed
herein for all other combinations of process parameters (four substrate temperatures
and five power densities).
Fig. 3.13. X-ray diffractograms of V1−xAlxN thin films of varying compositions (0.11
x 0.91), synthesized at a deposition temperature of 550 °C and a target power
density of 2.3 W cm-2.
3.2.4 Modeling: Metastable phase formation of V1-xAlxN
From the thermodynamic calculations performed for the VN-AlN pseudo-binary
phase, as shown in Fig 2.3(a), both the hcp and the fcc case clearly exhibit a value of
xmin = 0. From the critical crossover point of the Gibbs energy data for both phases,
Chapter 3 Results and discussion
- 57 -
depicted in Fig. 2.3(b), the maximum solubilities are xmax (Al) = 0.62 and xmax (V) =
0.38 for the fcc and hcp phases, respectively. As surface diffusion is a key factor
enabling the formation of a second phase, the relationship between the critical
diffusion distance Xc and the solubility can be characterized via the utilized model,
taking into account the dependence of Xc at the surfaces of both phases upon the
chemical composition, given in equation (3.3). For the calculation of Xc/2, as defined
in the context of equation (3.4), data resulting from a deposition experiment using a
target power density of 2.3 W cm-2 at a substrate temperature of 550 °C was employed.
The obtained Xc/2 was then used to calculate critical diffusion distances for other
solubilities per equation (3.3). This enables the quantification of the T(x) relationship,
in turn allowing the calculation of a metastable phase formation diagram covering the
entire compositional range, while using experimental data from a single combinatorial
deposition as input.
Chapter 3 Results and discussion
- 58 -
Fig. 3.14 Relationship between Xc and x for both fcc and hcp phases in V1−xAlxN,
showing both experimental data and the predicted curves. From the Xc value
calculated for the combinatorial experiment (deposition temperature 550 °C, target
power density 2.3 W cm-2, solid green square), Xc values for other target power
densities were calculated per equation (3.3).
To model the V1−xAlxN system under varying deposition rates (rD), a single
combinatorial deposition experiment was performed, with a substrate temperature (T)
of 550 °C, a bias voltage (Vbias) of −60 V, and a target power density of 2.3 W cm-2 as
the deposition parameters, yielding experimental metastable phase formation data. As
shown in Fig. 3.15, metastable phase boundaries have been predicted for target power
densities of 0.2, 1.2, 4.6, and 6.8 W cm-2. For a power density of 2.3 W cm-2,
additional data were experimentally obtained for substrate temperatures of 100, 250,
Chapter 3 Results and discussion
- 59 -
and 450 °C, and are quantitatively consistent with the model predictions as well, as
depicted in Fig. 3.15. This consistency holds true for the other four power densities as
well, evident from a comparison with experimental phase formation data presented in
Fig. 3.15(c) to Fig. 3.15(f), respectively. It should be noted that at lower temperatures,
the two-phase fcc + hcp region does not form, with all compositions with x < xmax
crystallizing in a single fcc phase, while x > xmax correspondingly results in the
formation of a single hcp phase. This is a general result for lower temperatures,
independent of the chosen reference temperature, and occurs in other metallic systems
as well [41, 42]. In Fig. 3.15, the symbols signify experimental values, solid lines
represent values given by the model and verified by experimental values at three
different temperatures (100, 250, and 450 °C), while dashed lines depict the predicted
phase boundaries given by the model, verified by experimental values at 550 °C and
100 °C (or only 550 °C). In summary, it is evident that the research strategy
previously employed for predicting the metastable solid solubilities of the Cu-W,
Cu-V [41, 42], and Ti1−xAlxN [12] systems is entirely transferable to magnetron
sputtered V1−xAlxN thin films as well, yielding predictions of metastable phase
boundaries in good agreement with experiments.
Chapter 3 Results and discussion
- 60 -
Fig. 3.15 Metastable VN-AlN phase formation diagrams for varying power densities:
calculated diagrams compared to experimental data at T = 550 °C, Vbias = −60 V, and a
power density of 2.3 W cm-2 (a); comparison with experimental data at the power
densities of 2.3 W cm-2 (b), 4.6 W cm-2 (c), 6.8 W cm-2 (d), 1.2 W cm-2 (e), and 0.2 W
cm-2 (f).
Selected area electron diffraction (SAED) analysis was performed on the sample
Chapter 3 Results and discussion
- 61 -
with the lowest deposition rate (rD = 0.02 nm s-1, T = 550 °C, Vbias = −60 V, a power
density of 0.2 W cm-2), with an Al composition of x = 0.50 close to the predicted
phase boundary to appraise the phase formation data obtained by XRD. Based on the
cross-sectional TEM image in Fig. 3.16(a), columnar crystals with an average
crystallite size of 43 nm are formed. Fig. 3.16(b) shows the SAED pattern of the
sample, which was previously classified as the fcc + hcp mixture phase based on XRD
results (see Fig. 3.13). Consistent with these results, the SAED data show the
emergence of the characteristic hcp and fcc diffraction patterns and suggest the
formation of a phase mixture. Hence, for the sample investigated here, the XRD data
are consistent with the SAED data. Finally, in Fig. 3.16(c), a comparison between the
SAED data and the predicted phase boundary indicates consistency between model
and experiment. A good agreement between SAED data and predictive model was
also previously reported by us in the case of Ti1−xAlxN thin films [12].
Chapter 3 Results and discussion
- 62 -
Fig. 3.16 (a) Cross-sectional TEM images of the V0.5Al0.5N sample at T = 550 °C,
Vbias = −60 V, and a power density of 0.2 W cm-2. The white arrow indicates the
growth direction of the as-deposited thin film. (b) Selected area electron diffraction
patterns of the V0.5Al0.5N sample. (c) Comparison with the above-described model.
The dashed line is the predicted phase boundary with a power density of 0.2 W cm-2.
Chapter 3 Results and discussion
- 63 -
3.2.5 Modeling: Stress-dependent metastable phase formation of
Ti1-xAlxN and V1-xAlxN
As seen in Fig. 3.17, the maximum solubility of Al in metastable fcc-V1−xAlxN
reported in the literature ranges from 0.52 to 0.62 for DCMS [18, 19] and between
0.59 and 0.75 for DCMS/HIPIMS [13-15]. The metastable phase formation during the
growth of Cu-W, Cu-V [41, 42], and Ti1−xAlxN [12] thin films was predicted based on
kinetic factors. One of these is the deposition rate, which is correlated with xmax as
evident from equations (3.2) and (3.3). Based on one combinatorial DC magnetron
sputtering experiment, the xmax range predicted by the model is 0.50 ≤ xmax ≤ 0.62 at a
power density of 2.3 W cm-2, which is comparable to the experimentally obtained
range given above for a pure DCMS setup [18, 19]. As the deposition rate is reduced
by one order of magnitude to rD = 0.02 nm s-1 (power density of 0.2 W cm-2), the
predicted xmax range is significantly extended towards an experimentally verified
lowest value of 0.42, compared with the previously known lowest experimental xmax
value of 0.52 given by Zhu et al. in 2013 [18]. The mechanistic explanation, as given
by Greczynski et al., is that in the comparatively low-energy DCMS setup, neutral Al
and V atoms are deposited on the substrate (only the gas species are ionized) [15]. If
limited surface diffusion of metal atoms occurs, the formation of a metastable solid
solution is observed [15]. However, if the chosen deposition conditions result in
enhanced surface diffusion, the thermodynamically stable hexagonal phase forms in
addition to the metastable solid solution [15]. Including the activation energy for the
surface diffusion into the model takes these kinetic phenomena into account and
Chapter 3 Results and discussion
- 64 -
improves the prediction accuracy and range [15].
A further important factor affecting solubility is stress. Based on the described
pressure-dependent model, as the absolute value of the compressive stress is increased
from 0 to −2, −4, and −5 GPa, xmax increases from 0.62 to 0.68, 0.74, and 0.77,
respectively, as shown in Fig. 3.17, yielding the prediction of a stress-dependent
extended Al solubility range of 0.42 ≤ xmax ≤ 0.77. While the largest experimentally
reported xmax is 0.75 [13], the largest reported xmax with a measured stress value is 0.74
for the compressive stress of −3.8 GPa [14]. Using equation (3.5) we compute a
critical Al solubility of 0.734 for this stress state. This is in very good agreement with
the here proposed model.
These findings clearly indicate that the predicted critical solubility range based
on kinetics in terms of surface diffusion as well as energetics, extended by the here
communicated pressure dependence, can predict all experimentally observed
solubility data where film stress data were reported. Upon comparison with prior
experimental studies, as seen in Fig. 3.17, the predicted critical solubility range is
consistent with experiments [13-15, 18, 19].
Chapter 3 Results and discussion
- 65 -
Fig. 3.17 The extended xmax range based on the metastable phase formation diagrams
with varying deposition rates and compressive pressures. For comparison, the
maximum Al solubility limit ranges in V1−xAlxN from references are given as well.
As in the case of fcc-V1−xAlxN, experimental data on xmax in metastable
fcc-Ti1−xAlxN from literature (0.40 ≤ xmax ≤ 0.90) [12] are compared to predictions
from thermodynamic modeling and DFT calculations (0.50 ≤ xmax ≤ 0.79) [12] in Fig.
Chapter 3 Results and discussion
- 66 -
3.18. Considering the deposition rate effects, there is an extension of xmax to a lower
value of 0.42 based on our previous modeling work of Ti1−xAlxN [12]. To increase the
xmax range, now we predict a higher xmax value of 0.90 according to the compression of
−10 GPa via DFT calculations. Comparing the pressure-dependent model with the
reported Ti1−xAlxN stress-related xmax values, ab initio calculations are employed to
demonstrate a strong pressure dependence of xmax in fcc-Ti1−xAlxN by Holec et al. in
2010 [45]. Under a compression of −4 GPa, an x increase by 0.10 is obtained in
fcc-Ti1−xAlxN [45], which is comparable to the xmax increase of 0.08 according to
equation (3.6). Based on our model, the pressure-dependent xmax value is 0.69 for the
stress-free Ti1−xAlxN thin film, and then increases to 0.90 at a high pressure of −10
GPa, which is comparable to the xmax values of 0.70 (p = 0 GPa) and 0.92 (p = −10
GPa) from the reference [45]. Based on the limited experimental pressure-dependent
xmax values for Ti1−xAlxN in literature, the xmax value of 0.64 with a stress value of
−0.8 GPa for the Al–HIPIMS/Ti–DCMS setup given by Greczynski et al. in 2014 [21],
is in reasonable agreement with the pressure-dependent xmax value of 0.70 for −0.8
GPa based on our model. In addition, the Al solubility reaches the maximum
limitation xmax = 1.0 (pure AlN) at a compressive pressure of −15 GPa according to the
model. The trend for an increasing xmax with increasing compressive stress is expected
since the AlN transformation from hcp to fcc occurs at ~−14 GPa, a value known from
both experiments and calculations [45, 98, 99], which agrees well with our results.
It is evident that high solubility limits of Al in Ti1−xAlxN (0.79 < xmax ≤ 0.90) [23]
and V1−xAlxN (0.62 < xmax ≤ 0.75) [15], known experimentally, are not obtainable
Chapter 3 Results and discussion
- 67 -
unless stress is taken into account in the unified model formulated herein. By
comparing Figs. 3.17 and 3.18, the solubility range resulting from prior experiments
and predictions is not only covered entirely, but also expanded towards lower and
higher values for both systems. Hence, the model proposed herein is able to predict
the full experimental solubility window reported in the literature [12-15, 18, 19, 45,
98, 99] as well as all experimental solubility data reported in this work.
Chapter 3 Results and discussion
- 68 -
Fig. 3.18 The extended xmax range based on the metastable phase formation diagrams
with varying deposition rates and compressive pressures, compared with previous
maximum Al solubility limit ranges in Ti1−xAlxN from references.
Summarizing, we applied a quantitative, predictive model, verified by
experiments, that, in addition to incorporating the kinetic effects of surface diffusion
Chapter 3 Results and discussion
- 69 -
[12, 41, 42], considers pressure dependence for energetic calculations for the first time.
The resulting prediction of the metastable phase formation of V1−xAlxN and Ti1−xAlxN
thin films exhibits a significantly widened range and improved accuracy compared to
previous studies.
3.2.6 Summary
We have predicted and experimentally verified the metastable phase formation
diagrams of sputtered V1−xAlxN thin films using a model based on one combinatorial
magnetron sputtering experiment, DFT calculations yielding activation energies for
surface diffusion, and thermodynamic calculations via the CALPHAD method. A
pressure-dependent theoretical model to describe TM1−xAlxN (TM = Ti, V) phase
formation is proposed, showing that xmax in fcc-TM1−xAlxN increases linearly with
compressive stress, where an increase in compression of 5 GPa increases xmax by 0.15
for fcc-V1−xAlxN and 0.13 for fcc-Ti1−xAlxN. The stress factor was introduced into the
modeling of metastable phase formation diagrams, and the calculation results clearly
showed a broadening of the predicted solubility range and thus significantly improved
agreement with experimental data from DCMS in comparison with previous
stress-free, purely energetics-based models. The predicted value of the maximum Al
solubility limit in V1−xAlxN can drop to as low as 0.42 and was verified by the
extremely low-rate deposition, which has not been reported before. The here proposed
model provides guidance for experimental efforts to control and extend the Al
solubility in fcc-TM1−xAlxN thin films.
Chapter 4 Conclusions and outlook
- 70 -
Chapter 4 Conclusions and outlook
4.1 Conclusions
In the present dissertation, the combinatorial magnetron sputtering,
characterization techniques, CALPHAD, and ab initio calculations have been carried
out to model the metastable phase formation of TM1−xAlxN (TM = Ti, V) thin films.
The following conclusions have been drawn.
(1) Based on the combinatorial magnetron sputtering experiment, CALPHAD,
and ab initio calculations (activation energy), a model to predict metastable phase
formations of TM1−xAlxN thin films considering kinetic effects is proposed. The
model was validated for the application relevant growth temperature range of 100 °C
to 550 °C. Experimental data from magnetron sputtered TM1−xAlxN thin films are in
good agreement with the model, which describes the effect of composition, deposition
temperature, and kinetic factors on the metastable phase formations of TM1−xAlxN
systematically.
(2) Compared to the lowest experimentally reported xmax value of 0.40 in
fcc-Ti1-xAlxN, the here predicted xmax value is 0.42 consistent with the experiment.
The here reported model allows for the prediction of the experimentally reported xmax
range of 0.42 ≤ xmax < 0.50, which was previously unobtainable by energetics-based
models. As for V1−xAlxN, the predicted value of xmax can drop to as low as 0.42 and
was verified by the extremely low-rate deposition, which has not been reported before.
This significant extension of the predicted critical solubility range is enabled by
Chapter 4 Conclusions and outlook
- 71 -
taking the effect of the activation energy for surface diffusion and the critical
diffusion distance on the metastable phase formation into account.
(3) A pressure-dependent theoretical model to describe TM1−xAlxN phase
formation is proposed, showing that xmax in fcc-TM1−xAlxN increases linearly with
compressive stress, where an increase in compression of 5 GPa increases xmax by 0.15
for fcc-V1−xAlxN, and 0.13 for fcc-Ti1−xAlxN. The stress factor was introduced into the
modeling of metastable phase formation diagrams, and the calculation results clearly
showed a broadening of the predicted solubility range and thus significantly improved
agreement with experimental data from DCMS in comparison with previous
stress-free, purely energetics-based models. The here proposed model provides
guidance for experimental efforts to control and extend the Al solubility in
fcc-TM1−xAlxN thin films.
4.2 Outlook: suggestions for future work
Currently, advanced protective hard coatings require improved phase stability,
longer lifetime, higher oxidation resistance, and higher wear resistance. Other
metastable transition metal aluminum nitrides than TiAlN are promising candidates
for future coatings. Thus, the substitution of other transition metals for Ti and V is of
interest. Also, in order to design new nitride coatings, it is essential to perform
experimental/theoretical investigations on the whole system, including energetics and
kinetics. The following topics can be suggested for future work.
Chapter 4 Conclusions and outlook
- 72 -
(1) It is possible to develop a model, including an additional bulk diffusion factor,
due to the increase of bias voltage to predict the Vbias-dependent metastable phase
formation of TM1−xAlxN (TM = Ti, V). The activation energy of bulk diffusion can be
calculated by ab initio calculations, and then introduced into the prediction of phase
formation, based on the current model. The bulk diffusion energy can be assumed to
be added to the activation energy for surface diffusion. In addition, the effect of bias
potential on other parameters in the model, such as atomic vibrational frequency,
deposition rate, and diffusion distance, can be studied.
(2) Verify the CALPHAD modeling and ab initio approaches proposed in
Chapter 2 by studying on Ta1-xAlxN and Nb1-xAlxN ternary systems. Consistent results
have been obtained to study the kinetics and energetics of Ti1-xAlxN and V1-xAlxN thin
films. It is important to verify the reliability of the approaches for other TMAlN
ternary systems. Due to a higher complexity than Ti–N as a variety of crystallographic
phases can be formed, Nb–N system has received much attention as potential coatings.
Taking the Nb1-xAlxN as an example, it can be studied using the same approaches like
that in the present dissertation. Also, TaN thin films have been studied widely due to
their relevance for many electronic and mechanical applications, so the Ta1-xAlxN can
be investigated.
(3) Experimental study on phase formation of higher-order Ti-V-Al-X-N (X = Nb
or Ta) systems. Recently compositionally complex materials, sometimes referred to as
high entropy alloys (HEAs), have been investigated as they have been suggested to
surpass the property limits of traditional materials. Hence, stabilization of the metallic
Chapter 4 Conclusions and outlook
- 73 -
solid solutions and prevention of intermetallic phase formation during crystallization
are expected based on the high mixing entropy. Compositionally complex nitride thin
films are of interest, but their phase formation has so far not been predicted. In the
case of TiAlN thin film, the addition of V improves friction performance. The
addition of Nb to the same system improves the hardness and thermal stability of the
coating, while the addition of Ta inhibits the formation of α-TiO2, thus effectively
improving oxidation resistance. These findings suggest tremendous
application-relevant potential in higher-order systems, yet the exploration of
multi-element coatings mainly focuses on ternary systems, rarely going beyond.
Hence, Thin films in the quaternary Ti-V-Al-N, the quinary Ti-V-Al-X-N (X = Nb or
Ta) and senary Ti-V-Al-Nb-Ta-N systems will be synthesized via magnetron
sputtering using a combinatorial approach.
(4) Thermodynamic and ab initio calculations of the higher-order Ti-V-Al-X-N
(X = Nb or Ta) systems. Ab initio calculations and experimental investigation suggest
that a B1 structured solid solution TixNbyAlzN can be grown. Theoretical analysis of
the thermodynamic driving force towards spinodal decomposition exhibits a
dependence on Nb content irrespective of thermodynamic stability, indicating that the
mechanism of decomposition should also be different. Since the TiN–AlN–NbN
quasi-ternary phase diagram has been reported, no theoretical method has been
suggested so far to calculate the metastable phase formation diagram of the
TiVAlNbN quinary system. As for adding Ta, several CALPHAD-type studies
evaluated both the binary TaN system and later, the ternary TaAlN system, providing
Chapter 4 Conclusions and outlook
- 74 -
a comprehensive thermodynamic model of the latter across the entire compositional
range. For the quinary TiVAlTaN system, neither CALPHAD-type investigation nor
metastable phase formation modeling has been reported to date. Taking the
TiN-VN-AlN, NbN-TiVN-AlN, TaN-TiVN-AlN, and NbTaN-TiVN-AlN as examples,
it can be studied using the same approaches as that in the present dissertation via
CALPHAD modeling and ab initio calculations.
(5) Modeling of the higher-order Ti-V-Al-X-N (X = Nb or Ta) systems. A purely
experimental exploration of the metastable phase formation of higher-order nitride
thin films would be both very time and resource-intensive. As thin film properties
mainly depend on the structure, a phase formation diagram of compositionally
complex nitrides enables understanding of the relationship between structure,
composition, and synthesis parameters. This understanding is essential for
rationally-guided materials design. The methodology already established for ternary
nitrides will be critically appraised for these highly complex systems, yielding
TiN-VN-AlN, NbN-TiVN-AlN, TaN-TiVN-AlN, and NbTaN-TiVN-AlN metastable
phase formation diagrams. We expect that these metastable phase formation diagrams
will provide a solid basis for future rationally-guided design efforts for
compositionally complex, face-centered cubic thin film materials.
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