Theoretical insights on elastic anisotropy and thermal anisotropy of TM5Al3C (TM= Zr, Hf, and Ta) carbides

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Structural, elastic, and thermal properties of the hexagonal TM5Al3C (TM = Zr, Hf, and Ta) carbides were investigated using first-principles calculations based on density functional theory (DFT). The calculated formation enthalpies and phonon dispersions indicate that these carbides are thermodynamically and dynamically stable. The calculated hardness values of TM5Al3C carbides are less than 20 GPa. The obtained Poisson's ratio, GH/BH, and Cauchy pressure indicate that these carbides are brittle. Elastic anisotropy indexes, three-dimensional (3D) surface construction, and two-dimensional (2D) planar projection were used to quantify the elastic anisotropy of these carbides, and the elastic anisotropy is in the order of Zr5Al3C > Ta5Al3C > Hf5Al3C. Finally, sound velocity, Debye temperature, and thermal conductivity were calculated based on the elastic constants and moduli. The calculated sound velocities and Debye temperatures of these carbides are found to be anisotropic. The minimum thermal conductivity has the same anisotropy order as elastic modulus.