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In this work, the elastic and thermodynamic properties of Pt$_{3}$Al underhigh pressure are investigated using density functional theory within thegeneralized gradient approximation. The results of bulk modulus and elasticconstants at zero pressure are in good agreement with the available theoreticaland experimental values. Under high pressure, all the elastic constants meetthe corresponding mechanical stability criteria, meaning that Pt$_{3}$Alpossesses mechanical stability. In addition, the elastic constants and elasticmodulus increase linearly with the applied pressure. According to the Poisson'sratio $\nu$ and elastic modulus ratio ($B/G$), Pt$_{3}$Al alloy is found to beductile, and higher pressure can significantly enhance the ductility. Thoseindicate that the elastic properties of Pt$_{3}$Al will be improved under highpressure. Through the quasi-harmonic Debye model, we first successfully reportthe variations of the Debye temperature $\Theta_\textrm{D}$, specific heats$C_{P}$, thermal expansion coefficient $\alpha$, and Gr\"{u}neisen parameter$\gamma$ under pressure range from 0 to 100 GPa and temperature range from 0 to1000 K.

Theoretical study of the elastic and thermodynamic properties of Pt$_{3}$Al with the L1$_{2}$ structure under high pressure