A review of the intrinsic ductility and toughness of hard ...

A review of the intrinsic ductility and toughness

of hard transition-metal nitride alloy thin films H. Kindlund, Davide Sangiovanni, Ivan Petrov, Joseph E Greene and Lars Hultman

The self-archived postprint version of this journal article is available at Linköping

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N.B.: When citing this work, cite the original publication. Kindlund, H., Sangiovanni, D., Petrov, I., Greene, J. E, Hultman, L., (2019), A review of the intrinsic ductility and toughness of hard transition-metal nitride alloy thin films, Thin Solid Films, 688, 137479. https://doi.org/10.1016/j.tsf.2019.137479

Original publication available at: https://doi.org/10.1016/j.tsf.2019.137479

Copyright: Elsevier http://www.elsevier.com/

A review of the intrinsic ductility and toughness of hard transition-metal nitride alloy thin films

H. Kindlund,1 D. G. Sangiovanni,2,3 I. Petrov,2,4 J. E. Greene,2,4 and L. Hultman2

1Department of Mechanical and Aerospace Engineering, University of California, Los Angeles, CA 90095, USA 2Thin Film Physics Division, Department of Physics (IFM), Linköping University SE-58183, Linköping, Sweden

3Interdisciplinary Centre for Advanced Materials Simulation (ICAMS), Ruhr-Universität Bochum, D-44801 Bochum, Germany

4Department of Materials Science and the Fredrick Seitz Materials Research Laboratory University of Illinois, 104 South Goodwin, Urbana, IL 61801, USA

Abstract

Over the past decades, enormous effort has been dedicated to enhancing the hardness of

refractory ceramic materials. Typically, however, an increase in hardness is accompanied by an

increase in brittleness, which can result in intergranular decohesion when materials are exposed to

high stresses. In order to avoid brittle failure, in addition to providing high strength, films should

also be ductile, i.e., tough. However, fundamental progress in obtaining hard-yet-ductile ceramics

has been slow since most toughening approaches are based on empirical trial-and-error methods

focusing on increasing the strength and ductility extrinsically, with a limited focus on

understanding thin-film toughness as an inherent physical property of the material. Thus,

electronic structure investigations focusing on the origins of ductility vs. brittleness are essential

in understanding the physics behind obtaining both high strength and high plastic strain in ceramics

films. Here, we review recent progress in experimental validation of density functional theory

predictions on toughness enhancement in hard ceramic films, by increasing the valence electron

concentration, using examples from the V1-xWxN and V1-xMoxN alloy systems.

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1. Introduction

Transition-metal (TM) nitrides are refractory ceramics, which exhibit high hardness and

moduli, good electrical and thermal conductivities, high melting points, and excellent wear-,

ablation-, and corrosion- resistance [1-22]. Due to a mixture of ionic, covalent, and metallic

bonding, these hard refractory ceramics have been widely used as protective coatings on cutting

tools and structural components operating in extreme environments [23-25]. Moreover, they have

also been shown to be useful as diffusion barriers in electronic devices [26-31], as plasmonic

materials [32] in photo-thermal therapies [33], as well as for energy storage and conversion

applications [34-37].

The development of ceramic materials with enhanced mechanical properties for a wide

variety of applications has been a major goal in materials science [3, 38-43]. Historically, alloying

was a very common approach for tailoring the mechanical properties of materials. Over the past

decades, enormous efforts have been dedicated to enhancing hardness in ceramic materials [25,

44-52]. The insights gained from metal alloys transferred to ceramics, in which the introduction of

the alloying element in the substitutional sites of the crystal lattice alters the bonding, leading, in

some cases, to improved mechanical strength [24, 53, 54]. Particularly successful examples in the

TM nitride family include TiCN and TiAlN, which exhibit substantial hardness increase compared

to the parent compound TiN [55, 56]. However, in contrast to pure metals, the mixed bonding

nature (covalent, ionic, and metallic) of ceramics has rendered the ability to predict and design TM

nitride alloys with desired mechanical properties a challenge. Other strengthening mechanisms, in

which defects act as obstacles for dislocation glide, thus enhancing hardness, include phase-

stability tuning in polytype mixtures [57, 58], hardening via the growth of artificial superlattices

[3, 59], nanocomposites [44, 47], and vacancy-induced hardening [43, 60-62]. Each of these

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approaches, designed to enhance hardness by hindering dislocation movement and grain boundary

sliding, typically results in a corresponding loss in ductility, leading to crack formation,

propagation, and, ultimately, reducing the coating performance [63]. In order to avoid brittle

failure due to cracking, films must, in addition to possessing high strength, also be ductile, i.e. one

has to focus on increasing hardness and ductility simultaneously. This combination of properties

is referred to as toughness, which is a measure of a material’s resistance to crack formation.

TM nitrides, as most ceramics, generally exhibit low ductility and hence poor toughness.

Enhanced toughness requires hindering crack formation and propagation. In polycrystalline

nitrides, used in applications, cracks are more likely to propagate along the grain boundaries.

Therefore, most approaches to toughening ceramics have focused on strengthening the grain

boundaries [64, 65]. This led to the development of nanoscale composites [44, 66, 67]. Existing

literature based on this approach includes the incorporation of ductile phases into the ceramic

matrix to hinder crack propagation [46, 68-71], ductile phases at nanocolumn boundaries [72],

multilayer and nanocomposite structures to control crack propagation by deflection [63, 73-81],

phase transformations [82-85], and carbon-nanotubes [86-88]. Other toughening methods include

the introduction of compressive stresses to inhibit crack growth [63, 89-91], hierarchical

nano/microstructures [92], crack deflection toughening using tilted interfaces [93], and grain-

boundary sliding [52, 94, 95]. However, most of these approaches [64, 65] were developed for

bulk materials and are not optimal for use in coatings, often leading to film delamination or a

reduction in hardness [96].

Overall, fundamental progress in this area has been slow because most of these toughening

approaches are based on empirical trial-and-error methods that aim at increasing strength and

ductility extrinsically, but with a limited focus on understanding thin-film toughness as an inherent

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physical property of the material. Clearly, electronic structure investigations devoted to identifying

the origins of ductility vs. brittleness [97-101] are essential for understanding the physics behind

the long-standing challenge of realizing both high strength and high ductility/plastic-strain, i.e.

toughness, in ceramics films.

2. The quest for high toughness in ceramic films

Density functional theory (DFT) is useful for designing new materials and predicting their

physical properties, which depend, primarily, on the bond type and configuration. B1-structure

TM nitrides possess strong directional covalent p(N) – d-eg(TM) first-neighbor bonds, responsible

for the material's strength, and relatively weaker metallic d-t2g second-neighbor interactions [53,

54, 98]. The latter bonds, consisting of more delocalized electrons, control the material's resistance

to shear deformation which is, in turn, related to their ability to plastically deform. Therefore,

increasing the metallic d-d interactions should enhance the material’s ductility. For the B1-

structure TM nitrides, several reports [24, 54, 98, 101-107] have provided guidance as to how

mechanical stability and mechanical properties such as moduli, hardness, and shear strength are

expected to vary with the electron density in d-t2g orbitals. Since the d-t2g orbital occupancy is

related to the valence-electron concentration (VEC), several computational studies have used VEC

to compare and contrast the mechanical properties of different TM nitride alloys [54, 101, 105,

107].

Experimental results collected by Holleck demonstrated the correlation between VEC and the

trends in mechanical properties of cubic carbonitrides [24]. Subsequently, based upon DFT-

calculations, Jhi et al. [54, 60, 108] reported that the maximum hardness in cubic TM nitrides is

achieved at a VEC of ∼8.4 electrons per formula unit, due to complete filling of the shear-resistive

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p – d-eg orbitals, while shear-sensitive d-t2g TM/TM states remained unoccupied. At higher VEC,

the shear sensitive d-t2g orbitals begin to be filled, thus reducing the shear-resistance of the material

and, in turn, reducing its hardness. Hugosson et al. [57, 58] used VEC tuning as a criterion for

designing cubic TM carbonitrides with a high concentration of stacking faults, which increase

hardness by impeding dislocation motion across the fault. Sangiovanni et al. [100] have shown

that energetically-favored formation of 111 stacking faults in metastable cubic TM nitride solid

solutions — formed upon mixing cubic and hexagonal parent binary nitrides — is also beneficial

for ductility, as it promotes {111}⟨1 1 0⟩ lattice slip. Wu et al. [105] used first-principles

calculations to predict the variation in mechanical properties of TM nitrides with VEC based upon

the shear modulus G (C44) as an indicator of the material’s resistance to plastic deformation. They

found that alloys with VEC between 8 and 9 exhibit large G values, while G, and thus the resistance

to plastic deformation, reached a minimum at a VEC slightly above 10. More recent DFT results

obtained for a wide range of pseudobinary TM nitrides, carbides, and carbonitrides [107] showed

that the B1-structure is mechanically stable if VEC is < 10.6; hardness decreases, while ductility

increases, with increasing VEC, and maximum toughness is predicted for alloys with VEC

between 9.5 and 10.5.

Other useful criteria for classifying cubic materials as brittle or ductile were proposed by Pugh

[109] and Pettifor [110] based upon shear-to-bulk-moduli (G/B) ratios and Cauchy pressures (C12-

C44). A material is considered ductile if it has a positive Cauchy pressures with G/B < 0.5. Zhao et

al. [111] used this approach to predict hard-yet-ductile TM nitride coatings by alloying with Group

5 or 6 TM nitrides. Similarly, Chen et al. [112] confirmed the effects of alloying on the ductility

of TiN-based nitrides based upon DFT-calculated G/B ratios and Cauchy pressures and found that

alloying TiN (a Group 4 TM nitride) with MoN and WN (Group 6) increases the Cauchy pressure

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and reduces G/B, i.e. the alloy ductility is enhanced with respect to the parent binary compound

TiN. Table I lists elastic constant (C11, C12, C44) values; bulk (B), elastic (E), and shear (G) moduli;

Cauchy pressures (C12-C44); G/B ratios; and hardnesses of Group 4, 5, and 6 binary and

pseudobinary TM nitride alloys. More detailed electronic-structure studies by Sangiovanni et al.

[98, 101] suggested that the addition of MoN and WN (Group 6 nitrides) in Group 5 TM nitrides

leads to toughness enhancement due to increased VEC. The higher VEC of these pseudobinary

alloys optimizes the occupancy of d-t2g – d-t2g metallic bonding states which, upon shearing,

promote electron delocalization along TM/TM lattice interfacial directions, irrespective of the

degree of ordering in the TM sublattice [113]. Until recently, experimental validation of these DFT

predictions was lacking.

Abadias et al. [114] carried out electronic-structure calculations using DFT, and experiments

on cubic Zr1-xTaxN (0 ≤ x ≤ 1) alloys, for which the VEC varies from 9 (ZrN) to 10 (TaN). They

found that Ta-rich Zr1-xTaxN alloys (0.51 ≤ x ≤ 0.78, with VEC ∼ 9.5-9.8), exhibit enhanced

toughness, compared to the binary compound ZrN, as a result of enhanced d-d interactions due to

an increased VEC.

For Group-6 CrN-based TM nitride alloys, Zhou et. al [115, 116] have shown, using DFT

calculations, that small additions of Groups 5 and 6 TMs (V, Nb, Ta, Mo or W) increase film

ductility as a result of increasing the metal–metal d–d orbital hybridization.

An alternative approach to increasing toughness, but also based upon VEC, was proposed

by Glechner et al. [117]. In this DFT-based work, instead of tuning the number of valence electrons

by alloying the TM sublattice, they used TaC1-xNx as a model system to investigate alloying on the

non-metal anion sublattice and found that both the hardness and elastic modulus of cubic TaC1-

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xNx decreases with increasing N content (i.e., with increasing VEC), which they attributed

primarily to changes in bonding leading toward a more metallic character.

To date, the only systematic studies linking theoretical predictions with experimental results

on enhanced toughness in single-crystal TM nitrides via alloying have been based upon cubic B1

NaCl-structure (space group Fm3̅m) V1-xMoxNy and V1-xWxNy alloys. Toughness in these alloys

was evaluated based upon material pile-up or crack formation following nanoindentation

experiments and calculated elasticity/plasticity parameters which are empirically related to

toughness. Recently, H. Kindlund et. al [refs. [118] and [119]] have demonstrated that

polycrystalline, columnar-structure VMoN films grown at Ts = 100 and 300 C also exhibt

enhanced toughness and good mechanical properties. In the next sections, we first provide an

overview of the structural, electronic, and bonding properties of TM nitrides (2.1); then discuss

the effects of alloying (2.2), anion vacancy concentration (2.3), and crystallinity/orientation (2.4)

on the mechanical properties of single-crystal pseudobinary TM nitride alloys.

2.1. Groups 4, 5, and 6 TM nitrides: an overview of fundamental properties

Titanium nitride (TiN, in mineral form (osbornite), was first isolated in a meteorite found

by George Osborne in the mid-1800s near Gorakhpur, Uttar Pradesh, India [120]) is the most

widely investigated and the most widely used refractory nitride coating material in technological

applications [38, 39]. The Group 4, TM nitrides, TiN, ZrN, and HfN, with VEC = 9, crystallize in

the B1 NaCl-structure with wide single-phase TM/N fields [121, 122] with melting points above

3000 K. The Group 5 TM nitrides VN, NbN, and TaN (VEC = 10) are dynamically unstable (i.e.,

exhibit imaginary phonon frequencies at zone Brillouin boundaries) in the B1 phase at 0 K [123,

124]. Nevertheless, the B1 structure is stabilized by lattice vacancies [125, 126] and/or by lattice

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vibrations at room temperature [124, 127, 128]. More complex is the case of Group 6 nitrides, with

VEC = 11. The ground state of CrN (CrN (carlsbergite) and VN (uakitite) are members of the

osbornite mineral group, and like TiN, found in meteorites. Uakitite, obtained from a meteorite

found in the Baunt Evenk district, Republic of Buryatia, near Zabaykalsky Krai (Eastern Siberia),

Russia, was recently reported at the Annual Meeting of the Meteoritical Society in Moscow, July

22-27 (2018) [129] is an antiferromagnetic orthorhombic phase, which becomes paramagnetic B1

at room temperature [130]. MoN and WN, both mechanically unstable in defect-free B1 structures

[123], can be stabilized in the NaCl phase by lattice vacancies [131-135]. Furthermore, the

occurrence of an antiferromagnetic (0 K) → paramagnetic (room temperature) transition has

recently been found in understoichiometric B1 MoNx [136].

In the B1 lattice, TM and nitrogen atoms occupy two interpenetrated fcc sublattices, with

each TM (N) atom octahedrally coordinated along ⟨100⟩ directions with six N (TM) atoms (nearest

neighbor shell) and surrounded by 12 TM (N) atoms along ⟨110⟩ directions in the second-neighbor

shell. The understanding of B1 TM nitride electronic properties is facilitated by the use of a

“TMN” cluster model and ligand-field theory. The discussion below is focused on p(N) –d(TM)

and d(TM) – d(TM) interactions, primarily responsible for the mechanical behavior of TM nitrides.

The d-orbitals of a transition-metal atom, perturbed by the electron clouds of six N ligands

along <100> directions, split into two energy-degenerate groups: d orbitals with eg symmetry (dx2-

y2 and dz2), which point directly toward N first-neighbors, and have higher energies than orbitals

with t2g symmetry (dxy, dxz, and dyz) due to stronger repulsion from N electrons (Fig. 1).

The d-eg orbitals hybridize with TM s and p orbitals to form sp3d2 electron-waves, which

possess optimal geometry to overlap with px, py, and pz orbitals of the neighboring N atoms. Thus,

constructive and destructive electron-wave interference leads to formation of σ bonding (low

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energy) and σ* anti-bonding (high-energy) sp3d2(TM) – p(N) states (labeled as d-eg – p in Fig.

2(a)) of the TM-N6 cluster. d-t2g orbitals, non-bonding in the TM-N6 cluster of Fig. 2(a), participate

in metal/metal bonds when the cluster is expanded to include the second-neighbor shell (TM13-

N6), Fig. 2(b). Since the distance between nearest-neighbor metal atoms is ×√2 larger than the

TM/N distance, the d(TM) – d(TM) wave interference is relatively weak in comparison to that of

d(TM) – p(N). This results in a small energy gap between σ bonding and σ* anti-bonding d-d

states (Fig. 2(b)).

For progressively larger clusters, the interaction between discrete energy states gives rise

to bands with a continuum energy spectrum. The cluster orbitals become wavefunctions in a

periodic three-dimensional lattice. A qualitative relationship between the TM13N6 orbitals and the

electronic density of states (DOS) of the B1 TM-N crystal is schematically illustrated in Fig. 2(c).

Fermi level energy EF (highest energy occupied state for electrical conductors) depends upon the

valence of the TM element. Note that the DOS shown on the right side of Fig. 2(c) was calculated

via DFT for B1 TiN [101].

Due to the large energy separation, bonding vs. anti-bonding p(N) – d(TM) states are easily

identifiable in B1 TM nitride DOS (σ in blue at the bottom vs. σ* in red at the top of Fig. 2(c)). In

contrast, an analysis of the DOS is unsuited for unambiguously locating bonding vs. anti-bonding

d-d metallic states on the energy scale. The DOS provides no clear indication of whether all, or

only some of, σ bonding d-d metallic states are occupied, in Fig. 2(c). It is, however, necessary for

enabling rational design of B1 TM nitrides with improved ductility, given that d-d interactions

control the metallic character of the material.

Analysis of the crystal orbital overlap population (COOP) [137], a projection of the

electronic density of states into bonding (positive COOP) vs. antibonding (negative COOP) states,

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provides the solution to the above conundrum. COOP calculations for TiN reveal that σ bonding

d-d metallic states are only partially populated [98], see schematic representation in Fig. 3(a).

Based upon a rigid-band model, the Fermi level can be shifted to higher energy upon alloying TiN

with TM nitrides of higher VEC to optimize the occupation of bonding shear-sensitive d-d states

[98, 101]. DFT calculations show that full population of bonding d-d states is achieved for B1 TM-

N alloys with VEC = 10.5, e.g., V0.5Mo0.5N and V0.5W0.5N (Fig. 3(b)). A further increase in VEC

would result in the destabilization of the B1 structure.

2.2. Effect of alloying on mechanical properties: VN-MoN and VN-WN alloys

DFT-calculated Cauchy pressures (C12-C44) and G/B ratios for V1-xWxN alloys with

0.125 ≤ x < 0.625 were found to increase and decrease, respectively, with the addition of cubic-

WN [104]. The Cauchy pressure and G/B ratio for VN are 1 GPa, and 0.60, respectively. However,

the Cauchy pressure becomes more positive, ranging from 83 GPa with x = 0.125 to ~139 GPa

with x = 0.375-0.625, while G/B decreases to 0.44 for x = 0.125 and ~0.33 with x = 0.375-0.625.

These theoretical results provided an initial indication that V1-xWxN alloys, irrespective of WN

concentration over the range 0.125 ≤ x < 0.625 [104], are more ductile than the binary parent

compound VN.

Cubic B1-phase single-crystal V1-xWxN alloys have been grown on MgO(001) substrates with

W fractions x from 0 to 0.6 [104, 138]. Toughness was first characterized empirically using

measured hardness-to-elastic-modulus ratio [139, 140]. For example, increasing H3/E2 has been

proposed [141] as an indicator of a material’s increasing resistance to plastic deformation.

Nanoindentation results showed that alloying VN with c-WN leads to an increase in hardness and

a reduction in the elastic modulus [104]. Nanoindentation data obtained using a Berkovich

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diamond tip indicated that V1-xWxN hardnesses increase continuously with the addition of WN,

from 16±1 GPa with x = 0 (i.e. VN), to 18±2 GPa with x = 0.14, to 25±2 GPa with x = 0.60.

Moreover, E initially decreases from 404±20 GPa (for VN) to 335±30 GPa with x = 0.14, and then

increases to 376±40 GPa with x = 0.60. The elastic modulus behavior vs. x was explained in terms

of a change in chemical bonding: in VN, the strong directional ionic/covalent V-N bonds (as shown

in Ref. [98]), result in a high elastic modulus value (and relatively low ductility). The addition of

cubic WN into the VN lattice enhances the metallic character of the chemical bonds by forming

stronger W-W and weaker W-N bonds compared to V-N bonds [98]. These results provided an

initial indication of enhanced toughness in V1-xWxN [101, 104].

Similar experiments were carried out alloying VN with MoN with Mo/V = 1. V0.5Mo0.5N(001)

hardnesses H and elastic moduli E obtained from nanoindentation results using a Berkovich

diamond tip are HVMoN = 20±1 and EVMoN = 376±30 GPa [102]. The single-crystal parent nitride

VN(001) and the most commonly studied nitride, TiN(001), were used as references;

HVN = 16±1 GPa, EVN = 386±20 GPa, HTiN = 23±2 GPa, and ETiN = 421±40 GPa [102]. That is,

the hardness of VMoN is 25% higher than that of VN and comparable with that of single-crystal

TiN. However, the addition of MoN in VN does not significantly affect the elastic modulus.

Complementary DFT-calculated Cauchy pressures and G/B ratios indicate that V0.5Mo0.5N,

with (C12-C44) = 95 GPa and G/B = 0.411, is more ductile than both VN (with (C12-C44) = 1 GPa

and G/B = 0.597) and TiN ((C12-C44) = -44 GPa and G/B = 0.690). That is, V0.5Mo0.5N has a more

positive Cauchy pressure and a lower G/B ratio than the two binary compounds. The combined

results — increased hardness with essentially constant elastic modulus together with a positive

Cauchy pressure and low G/B — argue that the toughness of Group 5 VN is enhanced by alloying

with Group 6 MoN.

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The relative ductilities of 3000-Å-thick VN, TiN, and V0.5Mo0.5N were also assessed by

nanoindentation using cube-corner diamond tips, which are sharper and produce much higher

stresses in the contact area than the Berkovich tip, based upon the observation of material pile-up

around the nanoindents [102]. At least ten indents were produced in each sample with a sharp

cube-corner diamond tip to a constant depth of 4000 Å to assure that the penetration depth extends

through the films and into the substrates in order to provide massive deformation as a severe test

of film toughness. Results were evaluated using scanning electron microscopy (SEM) and

scanning probe microscopy (SPM) and typical images are presented in Fig. 4. While the binary

reference compounds VN(001) and TiN(001) exhibit severe cracking along ⟨110⟩ directions

around the nanoindents (see Figs. 4(a) and 4(b)) cracks were never observed in V0.5Mo0.5N(001)

(Fig. 4(c)). Instead, indented V0.5Mo0.5N films exhibited material pile-up around indent edges (Fig.

4(d)), which is typical for ductile materials and indicative of plastic flow. Comparison of

nanoindentation results carried out in VN and V0.5Mo0.5N samples [102], demonstrated that the

introduction of MoN in VN increases the ductility, while retaining the strength (hardness), i.e.

these alloys exhibited enhanced toughness. V0.5Mo0.5N (with VEC ~ 10.5) is tougher than the

parent binary compound VN (VEC ~ 10) and the reference Group 4 nitride, TiN (VEC ~ 9). These

experiments are consistent with the results of electronic-structure calculations discussed earlier.

To provide additional insights into plastic deformation behavior in V0.5Mo0.5N, Ref. [103]

included high-resolution cross-sectional transmission electron microscopy (HR-XTEM) images of

indents demonstrating that, despite severe indenter penetration, V0.5Mo0.5N deformed without

rupture or internal cracking. Instead, the films deformed via material pile-up around the indent

edges while maintaining an epitaxial relationship with the substrate. Complementary selected-area

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electron diffraction patterns and Fourier transforms showed that the deformed regions around the

indented area consisted of continuous tilted and/or rotated planes [103].

DFT COOP [98, 99, 137, 142] calculations were also carried out [103]. COOP, the DOS

resolved into bonding and antibonding states, is used to quantify the strength of the covalent part

of chemical bonds. COOP and charge-transfer maps results revealed that the VEC of V0.5Mo0.5N

optimizes the occupancy of metallic d-t2g bonding states, without filling antibonding states, leading

to the formation of stronger TM/TM bonds within the slip plane and weaker TM/N bonds parallel

to the applied strain, which allows for easier slip. More recent molecular-dynamic simulations of

V0.5Mo0.5N alloys at room–temperature [143] attributed the intrinsic ductility of this alloy to its

ability to isotropically redistribute the stresses and dissipate the strain, preventing brittle failure,

by undergoing local structural transformations.

2.3. Effect of anion vacancies on mechanical properties of V0.5Mo0.5N alloys

Early theoretical studies had indicated that an increased concentration of N vacancies in

TiNy [60] and VNy [144, 145] increases the electron density of the metal-metal d-t2g orbitals which,

in turn, reduces the shear modulus [60]. These results provided an indication that ductility may

also be further increased in tough cubic TM nitride alloys by decreasing the nitrogen-to-metal ratio

[60, 98]. Experimental studies on the effect of N anion vacancies on the mechanical properties of

single-crystal TiNx/MgO(001) [43, 61] showed that hardness increases with increasing N vacancy

concentration (vacancy hardening) due to dislocation pinning at vacancy sites. Motivated by the

above results, the effect of N vacancies on the mechanical properties of epitaxial

V0.5Mo0.5Ny/MgO(001), with varying stoichiometries (0.55 ≤ y ≤ 1.03), was investigated

experimentally [103].

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Fig. 5 shows H and E values for single-crystal V0.5Mo0.5Ny/MgO(001) layers as a function

of the N concentration y. For comparison, H and E values for epitaxial VNy and TiNy are also

shown. The V0.5Mo0.5Ny nanoindentation hardness H, measured with a Berkovich tip, was found

to increase linearly with increasing N vacancy concentration from 17±1 GPa with y = 1.03 to 26±1

GPa for V0.5Mo0.5N0.55 (see Fig. 5(a)). The nanoindentation elastic modulus E (Fig. 5(b)) remains

essentially constant at ∼370 GPa for under-stoichiometric alloys with y = 0.55 - 0.94, and then

decreases to E = 265±10 GPa for over-stoichiometric alloys with y = 1.03.

To assess the ductility of the 3000-Å-thick V0.5Mo0.5Ny layers, cube-corner

nanoindentation experiments were performed to a constant penetration depth of 4000 Å. SEM

images of nanoindents on both under-stoichiometric and slightly over-stoichiometric alloy layers

revealed prominent material pile-up around the indents, indicating plastic flow. Cracks were rarely

observed in V0.5Mo0.5Nx alloys, in contrast to epitaxial VN and TiN films which exhibited severe

cracking. The material accumulation (plastic flow) observed around the indent edges, with

essentially no cracking upon severe nanoindentation, demonstrates that all V0.5Mo0.5Ny layers —

understoichiometric, stoichiometric, and overstoichiometric — are ductile compared to the parent

binary compound VN and TiN reference layers. Combining the ductility results with the hardness

data, increasing H values with increasing N vacancy concentration (Fig. 5(a)), provided the first

evidence of vacancy-induced toughening in TM nitrides [103].

DFT-calculated Cauchy pressures and G/B ratios [103] are consistent with the experimental

results showing that V0.5Mo0.5Ny alloys are ductile, irrespective of the N concentration. Cauchy

pressures ranged from 76 to 97 GPa, indicating a strong metallic bonding character typical of

ductile materials, while G/B ratios were between 0.404 and 0.444 (VN, has a calculated Cauchy

pressure of 1 GPa with G/B = 0.597 (Ref. [98])).

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Valence-band x-ray photoelectron spectroscopy (XPS) measurements [118, 146, 147] provide

additional clues as to the origins of enhanced toughness. The valence-band spectra of TM nitrides

consists of 2s(N) states, followed by a band which arises from the interaction of p(N) and the metal

d-eg(TM) orbitals, and the metallic d-t2g interaction band situated closer to the Fermi level [98,

148, 149]. Results on XPS valence-band spectra experiments carried out on a series of

V0.5Mo0.5Ny/MgO(001) samples deposited at different partial pressures are shown in Fig. 6(b) for

N concentrations y = 0.55 (red circles), y = 0.72 (green triangles), and y = 1.03 (blue squares). For

comparison, the XPS valence-band spectrum of single-crystal VN0.89 [118] is also shown in Fig.

6(a). The peaks situated at ~17.5 eV are primarily due to the s(N)-s(TM) σ interactions. The

features located at ~6.5 eV are due to interactions between p(N) and d-eg(TM) orbitals, while

spectral contributions at binding energies near 2 eV are due to d-t2g(TM) – d-t2g(TM) metallic

states [118]. These results indicate that the volume density of both the metallic d-t2g and p – d-eg

orbitals increase compared to the parent binary compound VN (Fig. 6(a)), and that the metallic

d-t2g interactions are enhanced with increasing N vacancies (Fig. 6(b)). However, the volume

density of the p(N) – d-eg(TM) states does not change significantly with N concentration.

XPS core-level studies of V0.5Mo0.5Ny films [118, 150-152] revealed that the N(1s)

photoelectron peaks shift to lower binding energies with decreasing N vacancy concentrations,

while the Mo(3p3/2) peaks shift to higher binding energies. This indicates decreasing electron

transfer from TM atoms to N atoms with increasing N vacancies; that is, V0.5Mo0.5Ny alloys

become less ionic. The combined XPS results — decreased ionicity and increased metallic

character with increasing N vacancy concentration — together with the hardness results and cube-

corner indentation data demonstrate that toughness in V0.5Mo0.5Ny is enhanced with increasing N

vacancy concentration.

16

2.4. Effects of orientation and crystallinity on V0.5Mo0.5Ny mechanical properties

001- and 111-oriented V0.5Mo0.5Ny films were grown on MgO(001) and Al2O3(0001)

substrates, respectively, as a function of temperature Ts from 100 to 900 oC [118, 119] and their

ductility assessed (material pile-up vs. crack formation) via severe cube-corner indentations. SEM

and SPM analyses of the indents showed that polycrystalline (Ts < 500 oC ) and single-crystal (Ts

≥ 700 oC) V0.5Mo0.5Ny(001)/MgO(001) and V0.5Mo0.5Ny(111)/Al2O3(0001) alloys are more ductile

than VN(001).

Hardnesses and elastic moduli for both 001- and 111-oriented V0.5Mo0.5Ny films, based upon

nanoindentation results using a Berkovich diamond tip, are summarized in Figs. 7(a) and 7(b).

Hardness values for the 001-oriented V0.5Mo0.5Ny layers increase from 17±3 for polycrystalline

films grown at Ts = 100 oC (y = 1.02) to 20±1 GPa for epitaxial films grown at 700 oC (y = 0.94),

and 26±1 GPa for layers grown at Ts = 900 °C (y = 0.64) [102, 118]. Increasing the growth

temperature from 700 to 900 oC, for films grown at constant N2 partial pressures, results in a 30%

increase in hardness due to the introduction of N vacancies. For the 111-oriented layers, hardness

values increase from 15±1 GPa for films grown at Ts = 100 °C (y = 0.90) to 19±2 GPa for films

grown at temperatures between 300 and 700 oC, and then to 23±2 GPa for films deposited at

Ts = 900 °C (y = 0.40) [119]. Thus, for both 001- and 111-oriented layers, hardness increases with

increasing growth temperatures (i.e. with increasing N vacancy concentrations).

For polycrystalline and highly-002-textured V0.5Mo0.5Ny/MgO(001) films, E values range from

323±30 GPa (Ts = 100 °C, y = 1.02), to 298±10 GPa (Ts = 300 °C, y = 1.02), and 319±10 GPa

(Ts = 500 °C, y = 1.02). For the single-crystal 001-oriented layers, E ranges from 376±30 (Ts =

700 oC, y = 0.94) to 370±10 GPa (Ts = 900 °C, y = 0.64) [102, 118]. Thus, E follows the same

trend as for the 001-oriented films, but the absolute values are slightly lower, ranging from 198±5

17

GPa for films grown at Ts = 100 °C to ~310±25 GPa at Ts = 300-700 oC, and then increasing to

381±11 GPa at Ts = 900 °C [119].

Both hardness and elastic modulus values are larger for the 001-oriented V0.5Mo0.5Ny layers

than for the 111-oriented films [118, 119]. This is the opposite of what was previously reported

for TiN [6, 153], and can be explained if the operating room-temperature slip systems are different

for V0.5Mo0.5N and TiN. The primary room-temperature slip system for TiN is {110}⟨1 1 0⟩ [154].

Nanoindentation experiments with pyramidal indenters sample all possible crystallographic

orientations, but are more heavily weighted in the forward direction. Since the indentation loading

direction is primarily along ⟨100⟩ for 100-oriented films and ⟨111⟩ for 111-oriented films, and

assuming a Burgers’ vector direction of ⟨1 1 0⟩, the resolved shear stresses τ for V0.5Mo0.5N loading

along [100] are τ = 0, 0.50σ, and 0.41σ for slip on {100}, {110}, and {111} planes, respectively,

for which σ is the applied stress. For loading along [111], τ = 0.47σ, 0, and 0.27σ for slip on {100},

{110}, and {111} (Ref. [155]). Thus, for [100] loading, τ is maximum for the {110}⟨1 1 0⟩ slip

system, and zero for the {100}⟨1 1 0⟩ system, while for [111] loading, τ for the {110}⟨1 1 0⟩ slip

system is zero, while it is maximum for the {100}⟨1 1 0⟩ system. Thus, for [001] loading, the most

likely active slip system will be {110}⟨1 1 0⟩, while for [111], it is {100}⟨1 1 0⟩. Given that 111-

oriented V0.5Mo0.5Nx is softer than corresponding 100-oriented films, we rule out {110}⟨1 1 0⟩ and

{111}⟨1 1 0⟩ as the primary slip systems for V0.5Mo0.5Nx(111). Thus, we propose that {100}⟨1 1

0⟩ is the preferred slip system for V0.5Mo0.5N(111) at room temperature in this alloy.

3. Conclusions and outlook

Two important and highly desirable properties for structural materials are hardness and

ductility. However, refractory ceramics typically possess only one or the other. In investigations

18

designed to address the physics behind the long-standing challenge of realizing simultaneously

high strength and high ductility in ceramics films, electronic structure results have shown that VEC

is an important parameter for predicting mechanical properties in TM nitride alloys [54, 60, 98,

101, 105, 107, 108, 117]. The overall results demonstrate that hardness decreases (maximum

hardness is expected at VEC ~ 8.4), while ductility increases with increasing VEC; and optimum

toughness is predicted for alloys with VEC ~ 10.5. DFT-inspired experimental work on VWN and

VMoN alloys (both with VEC = 10.5) demonstrated that, indeed, these alloys are tougher than the

binary parent compound VN (VEC = 10).

A review of experimental results on epitaxial V1-xWxNy(001) and V1-xMoxNy(001) alloys,

based on a combination of Berkovich nanoindentation hardness and elastic modulus data, together

with analyses of cube-corner nanoindentation results, reveal that these alloys exhibit enhanced

toughness compared to the parent compound single-crystal VN(001) and reference TiN(001)

layers.

In addition to stoichiometric alloy films, epitaxial N-deficient V0.5Mo0.5Ny(001) alloys were

analyzed [103]. V0.5Mo0.5Ny hardnesses were found to increase with increasing N vacancy

concentration from 17 GPa with y = 1.03 to 25 GPa with y = 0.55 (vacancy hardening), while the

elastic modulus remained essentially constant at ~370 GPa. Epitaxial VN(001) (H = 16 GPa) and

TiN(001) (H = 23 GPa) reference samples were shown to exhibit severe cracking under cube-

corner indentation, which is typical of brittle ceramics. In contrast, SEM and SPM images of cube-

corner indentations on epitaxial V0.5Mo0.5Ny layers showed essentially no cracking. Instead, the

indented V0.5Mo0.5Ny alloys exhibited material pile up, due to plastic flow, characteristic of ductile

materials. This, combined with the higher hardness inherent to V0.5Mo0.5Ny alloys, irrespective of

N content, renders the alloys tougher than VN. Similar results were obtained for polycrystalline

19

V0.5Mo0.5Ny alloys. DFT calculations attribute the increased toughness in V0.5Mo0.5Ny to an

optimal filling of the metallic d-t2g states resulting from a higher VEC in the nitrides.

Correspondingly, XPS valence-band spectra show an increase in the density of d-t2g states of

V0.5Mo0.5Ny compared to VN. For N-deficient V0.5Mo0.5Ny alloys, XPS results reveal that the d-t2g

orbital occupancy increases with increasing N-vacancy concentration. Thus, DFT predictions of

toughness enhancement in these alloys have been verified by experiment.

Additional experiments comparing the mechanical properties of epitaxial 001- and 111-

oriented V0.5Mo0.5Ny films indicate that 001-oriented alloys exhibit higher hardness than

corresponding 111-oriented layers grown at the same Ts and with similar N concentrations y [118,

119]. This is in contrast to what is reported for TiN. Based upon nanoindentation results, we

propose that this behavior is due to different preferred room-temperature slip systems in TiN and

VMoN. However, additional experiments, such as compression tests of nanopilars fabricated from

alloy films with different orientations, are required to isolate the active slip systems in these alloys

in addition to determining yield strength and other mechanical properties.

Based on experimental and DFT studies [102-104], we expect other combinations of Groups

4, 5, and 6 TM nitride alloys with VEC ~10.5 to show mechanical properties similar to those of

VMoN and VWN. Examples include VCrN, NbMoN, NbWN, TaMoN, and TaWN. Additional

potentially tough TM nitride alloys with VEC ~10.5 can be achieved by higher-order Groups 4, 5,

and 6 pseudoternary, pseudoquaternary, etc. TM nitride alloys. The field of hard and ductile

(tough) TM nitride alloys has an exciting future!

20

Acknowledgements

The authors acknowledge the financial support of the Knut and Alice Wallenberg Foundation

(KAW 2011-0094), the Swedish Research Council (VR 2014-5790), and the Swedish Government

Strategic Research Area Grant in Materials Science (SFO Mat-LiU) on Advanced Functional

Materials. D.G.S. gratefully acknowledges access to supercomputer resources provided by the

Swedish National Infrastructure for Computing (SNIC), and financial support from the Olle

Engkvist Foundation and the VINN Excellence Center Functional Nanoscale Materials (FunMat-

2) Grant 2016–05156. The authors are grateful to Esteban Broitman, L. Martínez-de-Olcoz, G.

Greczinsky, J. Birch, and Valeriu Chirita for fruitful discussions.

Table I: Elastic constants (C11, C12, C44), bulk B; elastic E and shear moduli G, Poisson’s ratios,

ν, Cauchy pressures (C12-C44), shear-to-bulk moduli ratios (G/B), and hardnesses H of Groups 4,

5, and 6 compound and pseudobinary TM nitrides. Valence electron concentrations VEC are

shown in brackets beside each alloy.

Alloy [VEC] C11

[GPa] C12

[GPa] C44

[GPa] B [GPa] E [GPa] G [GPa] 𝜈𝜈 C12-C44

[GPa] G/B H [GPa] Ref.

TiN [9]

TiN1 [9]

640

671

625

626

590

115

106

165

206

169

159

166

163

156

164

290

295

318

346

309

489

514

475

455

463

200

213

190

178

0.22

0.209

0.25

0.28

0.22

-44

-60

5

0.69

0.69

25

20.2

[101]

[156]

[157]

[62]

[107]

[61]

21

TiN1,2 [9] 20-24 [6]

ZrN [9]

ZrN1 [9]

546

611

164

117

126

129

291 403

0.25 38 0.59 19

12-19.5

[107]

[158]

HfN [9]

HfN1 [9]

602

694

163

112

120

611

309 392

0.24 43 0.63 20

16-19.5

[107]

[158]

VN [10]

VN [10]

680

533

585

623

140

135

178

251

139

133

126

122

320

375

478

406

191

0.251

0.29

0.28

1

129

0.59

0.50

15

[98]

[157]

[159]

[107]

NbN [10]

NbN1 [10]

639

692

739

556

164

113

161

152

78

84

76

125

322

306

335

660

187

0.32 86 0.41

0.14

10

17-201

[107]

[160]

[158]

[157]

TaN [10] 719 195 59 369 319

0.33 135 0.36 8 [107]

CrN [11] 582 270 8 373 45

0.44 262 0.14 2 [107]

MoN2[11] 582 248 -40 359 -55 - - 288 - - [107]

WN2 [11] 680 202 -86 361 -285 - - 288 - - [107]

Ti0.75Zr0.25N [9]

Ti0.50Zr0.50N [9]

Ti0.50Zr0.50N [9]

Ti0.45Zr0.55N1 [9]

594

531

526

85

115

120

147

134

133

254

254

252

456

396

391

190

160

157

0.201

0.24

0.24

-62

-19

-15

0.75

0.63

0.62

25

[156]

[161]

[162]

[163]

Ti0.50V0.50N [9.5]

Ti0.50V0.50N1 [9.5]

511

183

153

288

388

152

0.28

0.53

20

[164]

[3]

22

Ti0.75V0.25N [9.25] 574 124 159 274 454 186 0.223 -35 0.68 [156]

Ti0.50Nb0.50N [9.5]

Ti0.75Nb0.25N [9.25]

623

591

131

103

121

146

292

266

577

452

153

186

0.217

-43

0.52

0.70

16 [165]

[156]

Ti0.50Ta0.50N [9.5]

Ti0.50Ta0.50N [9.5]

Ti0.50Ta0.50N1 [9.5]

763

568

118

158

124

120

342

293

461

381

182

149

0.269

0.28

37

0.51

30

[166]

[162]

[163]

Ti0.50V0.50N [9.5] 520 156 143 283 397 157 0.27 20 0.55 [162]

Ti0.50Hf0.50N [9] 552 120 138 262 410 165 0.24 -19 0.63 [162]

Ti0.75Cr0.25N [9.5]

Ti0.50Cr0.50N1 [10]

649 124 160 299 493 201 0.225 -36 0.67

14

[156]

[167]

Ti0.50Mo0.50N [10]

Ti0.75Mo0.25N [9.5]

Ti0.50Mo0.50N1 [10]

655

573

153

191

77

145

321

318

382

419

147

163

0.302

0.281

76

46

0.458

0.513

34

[101]

[156]

[168]

Ti0.50W0.50N [10]

Ti0.75W0.25N [9.5]

Ti0.50W0.50N [10]

720

574

145

154

60

134

336

286

394

413

151

164

0.305

0.258

85

20

0.449

0.576

[101]

[156]

Zr0.50Hf0.50N [9] 560 108 118 259 384 153 0.252 -10 0.591 [161]

Zr0.50V0.50N [9.5] 546 128 132 268 397 159 0.253 -4 0.593

[161]

Zr0.50Nb0.50N [9.5] 594 114 108 274 380 150 0.269 6 0.547

[161]

Zr0.50Ta0.50N [9.5]

Zr0.50Ta0.50N4 [9.5]

Zr0.59Ta0.41N1.091 [∼9.8]

645

443

127

197

94

159

300

278

370

353

143

137

0.294

0.288

33

38

0.48

0.49

15-26

[114]

[114]

[169]

Zr0.48Cr0.52N1 [10]

21 [170]

Zr0.50Mo0.50N [10] 571 134 78 280 315 120 0.312 56 0.492

[161]

Zr0.50W0.50N [10] 631 133 67 299 310 117 0.326 66 0.391

[161]

23

Cr0.50Nb0.50N1 [10.5] 20 [167]

V0.50Nb0.50N [10]

V0.5Nb0.5N1 [10]

621 141 100 301 399 156 0.279 41 0.518

18.5

[98]

[59]

V0.50Ta0.50N [10] 653 143 73 313 379 146 0.298 70 0.466 [98]

V0.50Mo0.50N [10.5]

V0.50Mo0.50N4 [10.5]

V0.5Mo0.5Ny5 [10.5]

617

465

191

212

71

90

333

296

340

278

128

103

0.330

0.396

120

121

0.384

0.349

17-26

[98]

[113]

[103]

V0.50W0.50N [10.5]

V0.50W0.50N4 [10.5]

V0.50W0.50N6 [10.5]

V1-x WxN (0.14≤x≤0.6) [10.14-10.6]

690

526

506

166

207

220

61

96

80

340

313

315

372

315

283

141

118

105

0.318

0.388

0.350

105

110

140

0.415

0.377

0.33

21-25

[98]

[113]

[104]

[104]

Cr0.50Mo0.50N [11] 13.5 [167]

Cr0.50W0.50N [11] 25.5 [167]

1Experimental. 2 For single-crystal TiN, depending on orientation. 3Mechanically unstable in B1 structure. 4Special quasirandom structure disordered configuration. 5With varying N stoichiometries. 6Metal atoms randomly placed on cation sublattice.

24

Figure 1: Schematic representation of d-orbital energy splitting due to TM/N electrostatic

repulsion in a TM-N6 octahedral cluster.

25

Figure 2: Ligand-field theory model of the electronic properties of TM nitrides. (a) Bonding and

antibonding nearest-neighbor TM-N interactions in a TM-N6 cluster. (b) A relatively small energy

gap separates σ bonding and σ* anti-bonding d-d TM/TM orbitals in a TM13-N6 cluster. (c) The

discrete energy spectrum of the cluster becomes continuous (electronic density of states) in a 3D

periodic B1 TM-N lattice.

26

27

Figure 3: Schematic representation of the rationale for enhancing toughness in B1 TM nitrides via

electronic-structure manipulation. Crystal orbital overlap population (COOP) analysis is used to

project the electronic densities of states (DOS) onto bonding and anti-bonding states. Valence

electrons in, for example, TiN, with a valence electron concentration (VEC) of 9, occupy only a

small fraction of bonding d-d states. However, the valence electrons in alloys with VEC = 10.5

(e.g., V0.5Mo0.5N) completely fill the bonding metallic d-d states while retaining strong p(N)-

deg(TM) bonds; thus, rendering the alloy more compliant to shearing.

Figure 4: SEM images of nanoindentations in epitaxial (a) TiN(001) and (b) VN(001). (c) SEM

micrograph and (d) SPM image of nanoindentations in epitaxial V0.5Mo0.5N(001). Figure adapted

from Ref. [102].

Figure 5: (a) Hardness and (b) elastic modulus values for B1-structure single-crystal

V0.5Mo0.5Ny(001) thin films as a function of the N concentration y. For comparison, the hardness

28

and elastic modulus of epitaxial VNy(001) and TiNy(001) reference samples are also shown. Data

from Refs. [102] and [103].

Figure 6: XPS valence band spectra from (a) VN0.89 (blue squares) and V0.5Mo0.5N0.94 (orange

triangles), and (b) V0.5Mo0.5Ny, with y = 0.55 (red circles), y = 0.72 (green triangles), and y = 1.03

(blue squares). Data adapted from Ref. [118] and Ref. [171].

Figure 7: (a) Hardness and (b) elastic modulus values for single-crystal (SC) and polycrystalline

(PC) 001-and 111-oriented V0.5Mo0.5Ny films (y values are listed beside the data bars). Data from

Refs. [118] and [119]. H and E values include experimental uncertainties.

29

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