In this work, the thermodynamic properties of TMAl (TM = Ni, Fe, Ti) compounds were studied at a temperature of 0–1000 K and a pressure of 0–40 GPa through first principles based on density functional theory. The thermal expansion coefficient α and Debye temperature (θD) is sensitive to temperature and pressure. The single crystal elastic constants and polycrystalline elastic properties were calculated by the stress–strain method and Voigt–Reuss–Hill approximation. By analyzing the elastic anisotropy index (AU, Acomp, Ashear, and A1, A2, A3) and the surface structure and projection of Young’s modulus, the anisotropy of TMAl compounds was discussed. In addition, the sound velocities, anisotropy of the sound velocities and the electronic structures were also discussed.

中文翻译：

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TMAl（TM = Ni、Fe、Ti）的热力学和机械性能的理论预测

在这项工作中，通过基于密度泛函理论的第一性原理，在 0-1000 K 的温度和 0-40 GPa 的压力下研究了 TMAl（TM = Ni、Fe、Ti）化合物的热力学性质。热膨胀系数 α 和德拜温度 (θD) 对温度和压力很敏感。通过应力-应变法和 Voigt-Reuss-Hill 近似计算单晶弹性常数和多晶弹性特性。通过分析弹性各向异性指数(AU、Acomp、Ashear和A1、A2、A3)和杨氏模量的表面结构和投影，讨论了TMAl化合物的各向异性。此外，还讨论了声速、声速的各向异性和电子结构。