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Macroscopic Elastic Properties of Textured ZrN--AlN Polycrystalline Aggregates: From Ab initio Calculations to Grain-Scale Interactions

Despite the fast development of computational materials modelling, theoretical description of macroscopic elastic properties of textured polycrystalline aggregates starting from basic principles remains a challenging task. In this communication we use a supercell-based approach to obtain the elastic properties of random solid solution cubic ZrAlN system as a function of the metallic sublattice composition and texture descriptors. The employed special quasi-random structures are optimised not only with respect to short range order parameters, but also to make the three cubic directions $[1\,0\,0]$, $[0\,1\,0]$, and $[0\,0\,1]$ as similar as possible. In this way, only a small spread of elastic constants tensor components is achieved and an optimum trade-off between modelling of chemical disorder and computational limits regarding the supercell size is achieved. The single crystal elastic constants are shown to vary smoothly with composition, yielding $x\approx0.4$-0.5 an alloy constitution with an almost isotropic response. Consequently, polycrystals with this composition are suggested to have Young's modulus independent on the actual microstructure. This is indeed confirmed by explicit calculations of polycrystal elastic properties, both within the isotropic aggregate limit, as well as with fibre textures with various orientations and sharpness. It turns out, that for low AlN mole fractions, the spread of the possible Young's moduli data caused by the texture variation can be larger than 100 GPa. Consequently, our discussion of Young's modulus data of cubic ZrAlN contains also the evaluation of the texture typical for thin films.