Effect of alloying on elastic properties of ZrN based transition metal nitride alloys

Surface & Coatings Technology xxx (2014) xxx–xxx

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Effect of alloying on elastic properties of ZrN based transition metalnitride alloys

Mohammed Benali Kanoun, Souraya Goumri-SaidPhysical Science & Engineering Division, King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia

E-mail addresses: [email protected] ([email protected] (S. Goumri-Said).

http://dx.doi.org/10.1016/j.surfcoat.2014.03.0480257-8972/© 2014 Elsevier B.V. All rights reserved.

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Keywords:NitridesTernary alloysZr\M\NElastic propertiesDuctilityAb initio calculations

We report the effect of composition and metal sublattice substitutional element on the structural, elastic andelectronic properties of ternary transition metal nitrides Zr1 − xMxN with M = Al, Ti, Hf, V, Nb, W and Mo. Theanalysis of the elastic constants, bulk modulus, shear modulus, Young's modulus, and Poisson's ratio providesinsights regarding the mechanical behavior of Zr1 − xMxN. We predict that ternary alloys are more ductilecompared to their parent binary compounds. The revealed trend in the mechanical behavior might help forexperimentalists on the ability of tuning the mechanical properties during the alloying process by varying theconcentration of the transition metal.

© 2014 Elsevier B.V. All rights reserved.

1. Introduction

Hard coatings based on transition metal nitrides are well establishedand routinely used for various industrial applications due to theiroutstanding properties like high hardness, wear and corrosion resistance[1]. Besides binary nitride materials, ternary and higher order materialsystems are exploited in search of advantageous combination of intrinsicand structure relatedmaterial properties [1,2]. In order to further improvethe functional properties of these materials, the current research strategyis driven by the prospects of synthesizing new ternary or multinarysystems, by means of alloying different metal or non-metal elements [3].

Among the ternary M1\M2\N (M = transition metal) systems,Ti\M\N coatings have been the most widely investigated, whereasvery few studies have been devoted to the Zr\M\N systems. It isknown that ZrN has a lower coefficient of friction than TiN and othertransition metal nitrides, and is relatively hard [4,5]. However, its pooroxidation resistance hampers a broader range of applications. Therefore,alloying ZrN with transition metal was suggested in order to improvethe oxidation resistance and possibly also themechanical properties [6].Recently, various ZrAlN and ZrTiN ternary coatings have received lots ofattention due to their excellent properties [7–12]. No experimental datais available at present for Zr1 − xMxN (M= Hf, V, Mo and W), and onlyfew studies on Zr1 − xNbxN have been reported in the literature [13].

In this work, we report a comprehensive overview of structural andelastic properties of the binary transition metal nitrides and cubic AlN.Thus, we extend our calculation to study the effect of substitutionaltransition metal nitride element alloying on the elastic properties ofZrN at the atomic level. We therefore concentrate on the effectscharacteristic of a solid solution. It is our ambition to contribute towards

Kanoun),

umri-Said, Surf. Coat. Techno

relying on the phenomenological correlation between ductility and cer-tain elastic properties of the solution phases.We use first-principle-basedmethods to investigate the structure, mechanical and electronic proper-ties of Zr1 − xMxN, where M= Al, Ti, Hf, V, Nb, W and Mo ternary alloysto identify the candidate alloys for potentially hard coatings with en-hanced ductility. The elastic properties are of particular interest as theydetermine the mechanical stability of the material and some importantmacroscopic properties. In addition, the density of sates and chemicalbonding are used to provide insight into the bonding between nitrogenand transition metals.

2. Computational details

Total energy calculationshavebeenperformedusing the density func-tional theory based on the generalized gradient approximation (GGA) ofPerdew–Burke–Ernzerhof (PBE) [14], as implemented in the Vienna Abinitio Simulation Package (VASP) [15]. The electron and core interactionsare included using the projector augmented wave (PAW) method [16].The electronic wave functions were expanded with a basic set of planewaves with kinetic energies of up to 500 eV. Atomic positions wereoptimized until the residual forces were smaller than 0.01 eV A−1 forour calculations. Structure relaxations were carried out with 8 × 8 × 8k-point grids, while the density of states (DOS) and charge density distri-bution were computed with 16 × 16 × 16 on thick k-point grids in theMonkhorst–Pack scheme [17]. In order to investigate the chemical bond-ing between Zr and transition metal atoms on the metal sublattice of thecubic sodium chloride (B1) structure, we have constructed a 2 × 2 × 2supercell consisting of 64 atomswith aminimumnumber of intermetallicbonds (clustered configuration C#3) [18,19]. This structure closelymatches the CuPt-type atomic ordering observed experimentally inTixW1 − xN films [20]. The Zr1− xMxN were investigated with substitu-tional transition metal compositions x = 0, 0.25, 0.5 0.75 and 1. For

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Fig. 1. The calculated lattice constants a as a function of the composition x in the ternaryZr1 − xMxN with M = Al, Ti, Hf, V, Nb, W and Mo.

2 M.B. Kanoun, S. Goumri-Said / Surface & Coatings Technology xxx (2014) xxx–xxx

Zr1 − xAlxN solid solution, the experimental and theoretical studiesreported that the face-centered cubic (fcc, NaCl-type) exists and is stablefor 0b x b 0.50, and the hardness increases from21 to 28GPawhen theAlfractions increase from x = 0 to 0.43 [12,21]. Furthermore, with furtheraddition of Al, hexagonal close packed (hcp, ZnS-type) AlN appears andthe hardness of the coatings decreases. In this case, we have consideredin this paper the AlN and ZrAlN in NaCl structure.

For the calculation of the elastic coefficients, we employed thesymmetry-general least-squares extraction approach proposed by LePage and Saxe [22]. The calculated variation of the total energy withthe strain applied to induce deformation in the lattice is used to deter-mine the elastic properties of the crystal. For example, the diagonal elas-tic coefficients Cii can be determined from just the energy U(ϵ) of thestate deformed with the single-component strain ϵi using the relation-ship 2[U(ϵ) − U0] = ∑ i ∑ jCijϵiϵj where U0 corresponds to theminimum energy [22]. For cubic crystal, the elastic constants are com-puted by determining three independent parameters: C11, C12 and C44.In that case, we applied the strains: ± ϵ1, ϵ1 = ϵ2 and ± ϵ4. For eachset of strains ± ϵi three different magnitudes 0.25%, 0.5%, and 0.75%were used.

3. Results and discussion

The optimized lattice constants a, formation energies Ef, and massdensities ρ of binary compounds are summarized in Table 1. Sincethere is a vast amount of existing data for the equilibrium lattice param-eters in the literature, we refer to some experimental [23] and theoret-ical results [24–27] for comparison. Our results are slightly larger thanthe experimental values, except for VN. It is well known that the gener-alized gradient approximation functional tends to underestimate thebinding of the crystals and to give lattice parameter larger than theexperimental values. The predicted lattice constant values of MoN andWN are also listed in Table 1. It should be noticed that the experimentaland theoretical lattice constants of cubic B1 MoN and WN denote thelattice constants of their substoichiometric N-deficient configurations,as the stoichiometric configurations are mechanically unstable [28,29].

The formation energy, ΔEf, was calculated using the followingformulation [30]:

ΔE f Zr1−xMxNð Þ ¼ Etot Zr1−xMxNð Þ−12

xEtot Mð Þ þ 1−xð ÞEtot Zrð Þ þ 12Etot N2ð Þ

� �:

Here Etot(Zr1 − xMxN) is the total energy of the Zr1 − xMxN alloysand, Etot(M(Zr)) and Etot(N2) represent the isolated atomic energies ofthe individual metal species in crystalline form and molecular nitrogenN2, respectively. Our calculated formation energy values are also report-ed in Table 1. The values of formation energy are negative showing theirintrinsic stability. The positive energies of formation of MoN and WNfurther illustrate their instability. For this reason, in our DFT-calculations, we have considered the Zr1 − xMoxN, and Zr1 − xWxN at50% concentrations.

Table 1Calculated structural parameters, formation energy, ΔEf, andmass density of binary metalnitrides. The reported experimental lattice constants, aexp, refer to the experimental data[23].

a (Å) aexp (Å) ΔEf (eV/atom) Density (g/cm3)

AlN 4.068 4.045 −2.488 4.04TiN 4.242 4.241 −3.461 5.35ZrN 4.607 4.578 −3.381 7.10HfN 4.537 4.525 −3.523 13.69VN 4.125 4.139 −1.954 6.14NbN 4.454 4.389 −1.733 8.04MoN 4.357 – 0.064 8.83WN 4.367 – 0.661 15.78

Please cite this article as: M.B. Kanoun, S. Goumri-Said, Surf. Coat. Techno

In the case of alloys, each system and each composition x, theequilibrium properties were obtained by optimization of the supercellvolume and shape. The resulting lattice parameters are shown inFig. 1. As expected when transition metal atoms substitute for Zratoms, a decrease in the lattice parameter is observed with increasingM content. However, deviations are obtained from the linear interpola-tion. It can be seen that the Zr1 − xHfxN, Zr1 − xNbxN, Zr1 − xMoxN, andZr1 − xWxN exhibit the most linear behavior out of Zr1 − xTixN, Zr1 −

xVxN, and Zr1 − xAlxN. This is however a consequence of a smallermismatch of the lattice parameter between ZrN and other consideredcompounds. The calculated lattice parameters of Zr1 − xAlxN and Zr1 −

xTixN agree with the experimentally observed values and theoreticalcalculations [8,21,29,30], aside from the fact that the calculated valuesshow slightly larger values than the experimental ones. From ourknowledge, no experimental data is available for the lattice parametersof ternary Zr1 − xMxN (M=Hf, V,W andMo) solid solutions, which wereport here for the first time. Our results can provide useful informationfor designing coatings and for interpretation of experimental results.Fig. 2 shows ΔEf of ternary metal nitrides from all the systems consid-ered. We find that the values of ΔEf are always negative and very closein energy for all concentrations, indicating Zr1− xMxN where M = Al,Ti, Hf, V, Nb, W and Mo solid solutions with cubic structure to be stable.

The calculated stiffness constants are reported in Table 2, and theysatisfy the Born–Huang mechanical stability [31] expected for cubicstructures. In general, our calculated elastic constants are in good agree-ment with available data [32,33] and theoretical results [24,25,32–35],except with those reported in Ref. [36] for ZrN, where the followingvalues: 304, 114 and 511 GPa for the elastic constants C11, C12 and C44,respectively, are reported. The computed tendency of the elasticconstants of ZrN and HfN (C11 N C44 N C12) and NbN (C11 N C12 N C44)is in accordance with the neutron scattering measurements [33], andthe results are in better agreement with experiments than the availableab-initio calculations [24,25,27]. Furthermore, the elastic constant C11 issignificantly stiffer than the other two elastic constants. It should benoted that our calculated elastic constants of cubic B1 AlN are in goodagreement with those reported in Refs. [24,25], who mentioned theparticularly high value of C44 compared to the transition metal nitrides.

The computed Cij values of Zr1 − xMxN alloys are listed in Table 3,where a fair agreement is observed for ZrTiN compared to the calculatedvalues published in the literature [8]. Our results show that all Cij grad-ually increase with x fraction from ZrN to TiN and VN (see Table 2).Upon alloying with Al, however, the opposite situation occurs, the C11and C12 decrease and the C44 increaseswith the increases of x.Wenotice



Table 3The calculated elastic tensor C11, C12, C44 (in GPa), bulkmodulus B (in GPa), shearmodulusG (in GPa), Young'smodulus E (in GPa), and Poisson's ratio ν of ZrxM1 − xN (M = Ti, Hf, V,Nb, Mo, W and Al) alloys.

C11 C12 C44 C12 − C44 B G E ν G/B

Zr0.75Ti0.25N 533 109 122 −13 250 152 380 0.247 0.610Zr0.50Ti0.50N 531 115 134 −19 254 160 396 0.240 0.630Zr0.25Ti0.75N 571 109 142 −33 263 173 425 0.231 0.658Zr0.75Hf0.25N 545 104 113 −9 251 148 372 0.253 0.590Zr0.50Hf0.50N 560 108 118 −10 259 153 384 0.252 0.591Zr0.25Hf0.75N 579 104 116 −12 263 155 389 0.253 0.589Zr0.75V0.25N 507 114 119 −5 245 145 364 0.253 0.592Zr0.50V0.50N 546 128 132 −4 268 159 397 0.253 0.593Zr0.25V0.75N 580 130 123 7 280 157 396 0.264 0.560Zr0.75Nb0.25N 534 112 113 −1 253 145 366 0.259 0.573Zr0.50Nb0.50N 594 114 108 6 274 150 380 0.269 0.547Zr0.25Nb0.75N 614 125 91 34 288 137 355 0.294 0.476Zr0.75Al0.25N 476 114 90 24 235 119 306 0.283 0.506Zr0.50Al0.50N 397 158 138 20 237 130 331 0.268 0.549Zr0.25Al0.75N 403 125 130 −5 218 134 333 0.245 0.615Zr0.50Mo0.50N 571 134 78 56 280 120 315 0.312 0.429Zr0.50W0.50N 631 133 67 66 299 117 310 0.326 0.391

Fig. 2. Formation energy (Ef) of Zr1 − xMxN ternary metal nitrides.

3M.B. Kanoun, S. Goumri-Said / Surface & Coatings Technology xxx (2014) xxx–xxx

also, that from the Zr-rich to Nb, Hf, Mo andW-rich nitrides, C11 and C12increase whereas C44 decreases. However, their elastic constants arevarying monotonically with composition. This is attributed to the simi-larity of the electronic properties of ZrN\(Ti,Hf,V,Nb,Mo,W)N wherethe transition metal nitrides contain a significant part of the covalentbonding stronger than the ionic one [24].

After obtaining elastic constants, the polycrystalline bulk modulus(B) and shear modulus (G) are calculated from the Voigt–Reuss–Hill(VRH) approximations [37] (following the procedure detailed in Ref.[38]). The Young'smodulus E and Poisson's ratio ν are calculatedwithinE=9BG / (3B+G) and ν=(3B− 2G) / 2(3B+G). The calculated poly-crystalline elastic constants of binary nitrides are summarized inTable 2. We notice that NbN exhibits a large value of C11 and a smallvalue of C44, implying a low G and E despite diving a relatively large Bcompared to the other binary transition metal nitrides. For alloys, thegeneral trends of bulk modulus, shear modulus, and Young's modulusare shown in Fig. 3 (see Table 3). They fit well with the few accessibleexperimental data for parent compounds. It can be observed thatZrWN exhibits the largest bulk moduli of 299 GPa for x = 0.5, while237 GPa is obtained for ZrAlN, so that ZrWN possesses 20% larger bulkmoduli than ZrAlN. Moreover, for all transition metal additions investi-gated the bulk moduli increase with an increase in transition metalcontent (i.e., a linear interpolation of the binaries) except for ZrAlN,where our results suggest the existence of a large downward bowingof the bulk modulus curve. For example, Fig. 3 indicates that the bulkmoduli of ZrVN are actually well below the linear interpolation (in atleast qualitative agreement with literature — see e.g. negative ΔB[27]). The corresponding configurationally averaged values of theisothermal bulk modulus are found not to be linear as a function ofthe alloy composition and hence bowing occurs.

Table 2The calculated elastic tensor C11, C12, C44 (in GPa), bulkmodulus B (in GPa), shearmodulusG (in GPa), Young's modulus E (in GPa), and Poisson's ratio ν of binary metal nitrides.

C11 C12 C44 C12 − C44 B G E ν G/B

ZrN 524 107 118 −11 246 149 372 0.248 0.606TiN 586 126 165 −39 280 188 461 0.225 0.671HfN 582 113 117 −4 270 155 391 0.258 0.574VN 626 161 137 24 316 170 432 0.272 0.538NbN 643 134 72 62 304 123 325 0.322 0.405AlN 421 168 297 −129 253 211 494 0.174 0.834


For shear modulus and Young's modulus, we observe the samebehaviour like bulk modulus for all ternary except for ZrNbN whosequantities decrease with an increase in Nb content from 149 and372 GPa to 123 and 324 GPa, respectively. Furthermore, Fig. 3 showsthat G and E of ZrNbN are above the linear interpolation (again, in atleast qualitative agreement with positive ΔG in Ref. [27]). Generally,Poisson's ratio is connectedwith the volume change in amaterial duringuniaxial deformation and the nature of interatomic forces. If ν is 0.5, novolume change occurs,whereasν lower than 0.5means that the volumechange is associated with elastic deformation [39]. In our calculation, νvaries between 0.17 and 0.32, which shows that a considerable volumechange can be associated with the deformation in binaries and theiralloys.

Interestingly, the ductile to brittle mechanism is further supportedby both classical criteria of Cauchy pressure C12 − C44 (as proposed byPettifor in 1992 [40]) and of Pugh's modulus ratio G/B (as proposed byPugh [41]). From Table 2, the C12 − C44 values of NbN and VN are

Fig. 3. Calculated bulkmodulus, B, shear, G, and Young's, E, moduli for Zr1 − xMxN alloys asfunction of composition x.




positive, implying a metallic bonding framework in terms of Pettifor'ssuggestion [40]. Their G/B values are smaller than 0.571, suggestingtheir ductile mechanical properties based on Pugh's criterion of modu-lus ratio.

While for ZrN, TiN and HfN, the C12 − C44 values are negativerevealing a directional (covalent) bonding framework from Pettifor'scriterion of Cauchy pressure. In AlN, Cauchy pressure is largely negative,representing amore directional (ionic) characteristic. However, their G/B values are all larger than 0.571, suggesting their brittle mechanicalproperties based on Pugh's criterion ofmodulus ratio. In order to furtherassess the influence of Pugh's modulus ratio (G/B) and Cauchy pressure(C12− C44) on themechanical properties of cubicmaterials, we show inFig. 4, C12 − C44 against G/B for these Zr1 − xMxN alloys. As indicated bythe arrow in Fig. 4, the closer to the upper left corner, the more ductileand stronger the metallic bonding; inversely, the closer to the bottomright corner, the more brittle and stronger the covalent bonding. Asshown in Fig. 4, we can see that brittle ZrN and TiN are located in theupper bottom right corner in relationship of (C12 − C44) against G/B,while the AlN almost lie in the bottom right corner. Unlikely, HfN isalmost close to the vertical dashed line of the critical value defined byPugh [41] and exactly corresponds to the critical zero value of C12 −C44 proposed by Pettifor [34]. VN and NbN are located in the upperleft corner. Zr1 − xTixN alloys are located in the right corner betweenpure ZrN and TiN, indicating an increased brittleness with additionalTi in ZrN. Unlike for Zr1 − xHfxN, it shows a diminishing brittlenesswith increasing Hf concentration. It is also noted that alloying ZrNwith V, Nb, W and Mo improves ductility and move to the upper leftcorner. Surprisingly, Zr0.75Al0.25N and Zr0.5Al0.5N compounds aredramatically moved to the upper left corner, resulting in a ductilebehavior, while the Zr0.25Al0.75N is located in the upper bottom rightcorner.

It is well known that the bonding in ZrN as well as in the relatedtransitionmetal nitride compounds TiN, HfN, VN, and NbN is exhibitinga mixed character of covalent, ionic, and metallic bonds [19,42]. Thecalculated total and partial densities of state (DOS) curves at thepredicted equilibrium lattice constants for ZrN and ZrMN are shown inFig. 5, where the vertical line is the Fermi level (EF). Three main regionscan be observed in the total DOS: one around−15 eV due to N 2s states,another below the Fermi level due to N 2p states hybridizing with Zr 4dstates,which is in the origin of the covalent-like bonding in thismaterialand the last one from−2 eV to 4 eV up to the Fermi levelmainly consistof the Zr d states with a small contribution of the N p states. A finite

Fig. 4. Correlation between the Cauchy pressure (C12− C44) and the Pugh's modulus ratioG/B for Zr1 − xMxN alloys with M = Al, Ti, Hf, V, Nb, W and Mo.

Fig. 5. (a) Total and (b) partial densities of states for Zr1 − xMxN alloys. Vertical dashed linedenotes the Fermi level. The black, red, blue and green lines represent the LDOS of Zr d, Zrp, Ti d and N p states, respectively. (For interpretation of the references to color in this fig-ure legend, the reader is referred to the web version of this article.)


value of DOS at the Fermi level indicates metallic character for B1 ZrN.The occupied states, due to theN 2p\Zr 4d hybridizations, are indicatedby peaks in the range from −8 eV to −3 eV, separated from theunoccupied states located just above the Fermi level by a pseudo-gap ~ −3 eV. Similar behavior is observed for TiN, HfN, VN and NbN(not shown in the present paper). Due to the difference in electronega-tivities a large charge transfer occurs from transition metal to N leadingto an ionic admixture to the bonding. In cubic AlN, on the other hand,the ionic bonds have been shown to dominate [43], and the N 2p stateshybridize strongly with the Al p states.

When gradually increasing the Ti, Hf, V, Nb, W, Mo and Al contentin Zr1− xMxN, it can be seen that up to x = 0.50 there is a gradual,smooth change in the density of states (DOS). However, for thecomposition x= 0.75, it can be seen that the DOS shows clear similarities



Fig. 6. Charge density contours in the (100) plane (color scale units are electrons/Å3): (a) ZrN, (b) Zr0.50Ti0.50N, and (c) Zr0.50Al0.50N. (For interpretation of the references to color in thisfigure legend, the reader is referred to the web version of this article.)

5M.B. Kanoun, S. Goumri-Said / Surface & Coatings Technology xxx (2014) xxx–xxx

with the one for pure MN and AlN. For the ZrMNwith M= Ti, Hf, V, Nb,W, and Mo, the occupied states corresponding to hybridized s–p–d arelocated at around −10 eV to −4 eV or −10 to −3 eV, separated fromthe unoccupied states by a pseudo-gap ~ −3 or −4 eV (see Fig. 5b).From the DOS analysis in Fig. 5b, it follows that the pseudogapat ≈−2 eV below the Fermi level separates the hybridized orbitals ofthe (Zr,Al)\N bonds from the (predominantly) Zr\Zr d–d metallicbonds. This result can be explained by the fact that the substitution ofZr by Al is destroying the hybridization between next-nearest-neighbormetal atoms, as in Al there are no d states which could participate inthe bonding. This localizes the nonbonding Zr d states in the regionbetween −2 and 0 eV below the Femi level with predominantly ionicbonds. The present results for ZrAlN are well consistent with previoustheoretical calculations [30,44].

To gain a more detailed insight into the bonding characters of ZrNand related alloys, we plotted the charge density distribution andcharge density difference maps of ZrN, Zr0.5Ti0.5N and Zr0.5Al0.5N. Thecharge density and charge difference contours for a cut in the (100)plane of these materials are displayed in Figs. 6 and 7. It is clearly seenthat ZrN is characterized by a strong ionic character with a high concen-tration of electrons surrounding the N, as well as a covalent nature, dueto the strongly hybridized energy states of the Zr 4d and N 2p. In theZr0.50Ti0.50N composition, the N p electrons form directional bondingwith the Zr d electrons as well as with the Ti d states, translating intoa significantly more pronounced covalent character of the Ti\N bondscompared to Zr\N bonds. Moreover, the charge density differencemap also shows that the charge accumulation in the middle of Ti\Nbonds is slightly higher than those within the Zr\N (see Fig. 7). Theionic bonding character is reflected mainly by the charge accumulationon the N sites, the neighboring metallic sites are charge depleted. Note

Fig. 7.Charge density differencemap in the (100) plane shown for (a) ZrN, (b) Zr0.50Ti0.50N, andcolor in this figure legend, the reader is referred to the web version of this article.)


also that the charge density difference contours indicate an increase ofthe metallic bonds by addition of Ti, due to the interaction betweend(Zr) and d(Ti) states (see Fig. 5). For Zr0.5Al0.5N alloy, the charge densi-ty difference map exhibits enhanced directional bonding compared toZrN due to the additional p–p orbital interactions and no chargeaccumulation between Al and N atoms, suggesting the preferred ioniccharacter.

4. Conclusion

In summary, thepresentwork has involved a computational study ofthe structural, elastic and electronic properties of ZrN based transition-metal nitride alloys. Trends in the atomic volume, elastic constants andformation energies of Zr1− xMxN alloys were investigated for Ti, Hf, V,Nb, W, Mo and Al solute species x. Our results reveal that the ZrN TiN,HfN, VN, NbN and AlN compounds and Zr1− xMxN alloys in B1 structuralphase are thermodynamically and mechanically stable. Mixing Ti, Hf, V,Nb, W, and Mo into ZrN enhances the elastic moduli while mixing Alinto ZrN reduces the elasticmoduli. Their electronic structures highlightthat metal-mixing affects the M\N bond strengths of the compoundsand leads to the change of the elastic properties. Thus, the key-findingof the present work shows the relation between the solute additionimpact on the polycrystalline moduli and the intrinsic ductility param-eter G/B. Our results show that all solid solutions improve their B andductility (G/B) except for ZrAlN. Indeed, ductility decreases as Al con-tent is increased in ZrAlN, but on the other hand, ductility of ZrAlNwith x = 0.25 and 0.5 is much better than pure ZrN. Furthermore, thepresence of N has stabilized the rock salt structure. In particular, theZrxM1− xN bonding is characterized by the N preference to bond andgain charge mainly from Zr atoms, resulting in stronger covalent and

(c) Zr0.50Al0.50N (color scale units are electrons/Å3). (For interpretation of the references to




ionic features for the metal rich systems, while preserving its metalliccharacter. The revealed trendmight be interesting and useful in design-ing future coatings.

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