Pressure- and Temperature-Coupling-Induced Structural Transition and Thermal Properties of Al3TM (TM = Ti, Zr, Hf)

Pressure-temperature-coupling-induced structural transition and thermal properties of Al3TM (TM = Ti, Zr, Hf) have been studied using the first-principles calculations combined with the quasi-harmonic approximation. The enthalpy indicates that Al3TM transitions to L12 structure at a specific pressure threshold (P=30+2.6x10-4T-1.1x10-6T2$P amp;amp;amp;amp;amp;amp;amp;amp;equals; 30 amp;amp;amp;amp;amp;amp;amp;amp;plus; 2.6 \times \left(10\right)<^>{- 4} T - 1.1 \times \left(10\right)<^>{- 6} T<^>{2}$ for Al3Ti, P=29-5.5x10-4T-1.0x10-6T2$P amp;amp;amp;amp;amp;amp;amp;amp;equals; 29 - 5.5 \times \left(10\right)<^>{amp;amp;amp;amp;amp;amp;amp;amp;hyphen; 4} T - 1.0 \times \left(10\right)<^>{- 6} T<^>{2}$ for Al3Zr, and P=47-1.2x10-3T-7.5x10-7T2$P amp;amp;amp;amp;amp;amp;amp;amp;equals; 47 - 1.2 \times \left(10\right)<^>{amp;amp;amp;amp;amp;amp;amp;amp;hyphen; 3} T - 7.5 \times \left(10\right)<^>{- 7} T<^>{2}$ for Al3Hf). The fundamental thermodynamic parameters, including thermal equilibrium volume V0$V_{0}$, thermal expansion coefficient alpha, and heat capacity CP$C_{\text{P}}$, do not abruptly change due to the structural transition. Whereas many elastic properties, including elastic constants, shear modulus, and Young's modulus, exhibit abrupt variations. Such as, at P=30+2.6x10-4T-1.1x10-6T2$P amp;amp;amp;amp;amp;amp;amp;amp;equals; 30 amp;amp;amp;amp;amp;amp;amp;amp;plus; 2.6 \times \left(10\right)<^>{- 4} T - 1.1 \times \left(10\right)<^>{- 6} T<^>{2}$ structural transition critical boundaries, V0=13+1.5x10-4T+1.5x10-7T2$V_{0} amp;amp;amp;amp;amp;amp;amp;amp;equals; 13 amp;amp;amp;amp;amp;amp;amp;amp;plus; 1.5 \times \left(10\right)<^>{- 4} T amp;amp;amp;amp;amp;amp;amp;amp;plus; 1.5 \times \left(10\right)<^>{- 7} T<^>{2}$, alpha=2.2x10-5-2.5x10-5e-4.7x10-3T$\alpha amp;amp;amp;amp;amp;amp;amp;amp;equals; 2.2 \times \left(10\right)<^>{- 5} - 2.5 \times \left(10\right)<^>{- 5} e<^>{- 4.7 \times \left(10\right)<^>{- 3} T}$, and Cp=102-119e-5.4x10-3T$C_{\text{p}} amp;amp;amp;amp;amp;amp;amp;amp;equals; 102 - 119 e<^>{- 5.4 \times \left(10\right)<^>{- 3} T}$ for Al3Ti. V0$V_{0}$ shows that Al3TM is difficult to oppose hydrostatic pressure, and alpha indicates that Al3TM maintains strong stability under high pressure and its volume expansion is expected to be linear at high temperature. Furthermore, CP$C_{\text{P}}$ shows that the absorbing capacity or heat-sinking capacity of Al3TM is strong at the low pressure and high temperature. The elastic properties exhibit an increasing trend with increasing pressure, whereas they exhibit a more or less decreasing trend with increasing temperature. Both numerical indicators and 3D images of the elastic anisotropy are derived, revealing that Al3TM possesses a high degree of anisotropy.