Modeling of metastable phase formation for sputtered Ti1 ...

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 -


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


- 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


- 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


- 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 -


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


- 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


- 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


- 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


- 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.


- 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.


- 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.


- 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


- 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


- 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)


- 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].


- 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.


- 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


- 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


- 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


- 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


- 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.


- 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


- 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.


- 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


- 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.


- 37 -

Fig. 3.8 Selected area electron diffraction patterns for Ti1-xAlxN samples with (a) x =


- 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


- 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


- 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.


- 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


- 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.


- 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


- 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.


- 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.


- 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.


- 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


- 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.


- 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


- 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.


- 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


- 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)


- 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.


- 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


- 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


- 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,


- 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.


- 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,


- 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.


- 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


- 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].


- 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.


- 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


- 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].


- 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.


- 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


- 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.


- 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


- 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 -


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


- 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.


- 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


- 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


- 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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Modeling of metastable phase formation for sputtered Ti1 ...

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