Elastic anisotropy and thermal properties of Zr-Al-N ternary nitrides using first-principles explorations

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First-principles calculations based on density functional theory (DFT) were employed to explore the anisotropies in elastic and thermal properties of six Zr-Al-N ternary nitrides (Zr2AlN, Zr5Al3N, ZrAlN2, Zr3AlN4, ZrAl3N4 and Zr3AlN). The single-crystal elastic constants and poly-crystalline elastic moduli were acquired by using Voigt-Reuss-Hill approximations. The elastic anisotropies of the above six Zr-Al-N ternary nitrides were characterized by a three-dimensional (3D) surface constructions and two-dimensional (2D) plane projections. The elastic modulus anisotropy is in the order of ZrAlN2 > Zr3AlN > ZrAl3N4 > Zr3AlN4 >Zr2AlN > Zr5Al3N. Furthermore, these six Zr-Al-N ternary nitrides have the hardness ranging from 12.7 to 18.7 GPa. Moreover, these six ternary nitrides all meet the brittleness criteria in terms of Poisson's ratio, GH/BH and Cauchy pressure. Finally, the sound velocities, Debye temperature, thermal conductivity and their anisotropies of these Zr-Al-N ternary nitrides are discussed, showing that the sound velocities and Debye temperature are anisotropic in the [001] and [100] directions.