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We have investigated the phonon, elastic and thermodynamic properties ofL1$_{2}$ phase Al$_{3}$Ta by density functional theory approach combining withquasi-harmonic approximation model. The results of phonon band structure showsthat L1$_{2}$ phase Al$_{3}$Ta possesses dynamical stability in the pressurerange from 0 to 80 GPa due to the absence of imaginary frequencies. Thepressure dependences of the elastic constants $C_{ij}$, bulk modulus $B$, shearmodulus $G$, Young's modulus $Y$, $B/G$ and Poisson's ratio $\nu$ have beenanalysed. The elastic constants are satisfied with mechanical stabilitycriteria up to the external pressure of 80 GPa. The results of the elasticproperties studies show that Al$_{3}$Ta compound possesses a higher hardness,improved ductility and plasticity under higher pressures. Further, wesystematically investigate the thermodynamic properties, such as the Debyetemperature $\Theta$, heat capacity $C_{p}$, and thermal expansion coefficient$\alpha$, and provide the relationships between thermal parameters andpressure.

First-principles study of the structural, phonon, elastic, and thermodynamic properties of Al$_{3}$Ta compound under high pressure