Despite the fast development of computational material modeling, the theoretical description of macroscopic elastic properties of textured polycrystalline aggregates starting from basic principles remains a challenging task. In this study we use a supercell-based approach to obtain the elastic properties of a random solid solution cubic ${\mathrm{Zr}}_{1-x}{\mathrm{Al}}_x\mathrm{N}$ system as a function of the metallic sublattice composition and texture descriptors. The employed special quasirandom structures are optimized not only with respect to short-range-order parameters, but also to make the three cubic directions $\left[100\right]$, $\left[010\right]$, and $\left[001\right]$ as similar as possible. In this way, only a small spread of elastic constant tensor components is achieved and an optimum trade-off between modeling of chemical disorder and computational limits regarding the supercell size and calculational time is proposed. The single-crystal elastic constants are shown to vary smoothly with composition, yielding $x\approx 0.5$ an alloy constitution with an almost isotropic response. Consequently, polycrystals with this composition are suggested to have Young's modulus independent of the actual microstructure. This is indeed confirmed by explicit calculations of polycrystal elastic properties, both within the isotropic aggregate limit and with fiber textures with various orientations and sharpness. It turns out that for low AlN mole fractions, the spread of the possible Young's modulus data caused by the texture variation can be larger than 100 GPa. Consequently, our discussion of Young's modulus data of cubic ${\mathrm{Zr}}_{1-x}{\mathrm{Al}}_x\mathrm{N}$ contains also the evaluation of the texture typical for thin films.

• Received 10 July 2014
• Revised 1 September 2014

DOI:https://doi.org/10.1103/PhysRevB.90.184106

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Published by the American Physical Society