Quasi-harmonic thermoelasticity of palladium, platinum, copper, and gold from first principles

TL;DR

This study uses first-principles calculations within the quasi-harmonic approximation to determine the temperature-dependent elastic constants of palladium, platinum, copper, and gold, comparing results with experimental data and exploring electronic effects.

Contribution

It provides a comprehensive first-principles analysis of thermoelastic properties of these metals, including electronic contributions and the impact of exchange-correlation functionals.

Findings

Good agreement with experimental elastic constants at high temperatures.

Electronic excitations significantly affect certain elastic constants.

Anomalies in palladium and platinum at room temperature are not captured.

Abstract

We calculate the temperature-dependent elastic constants of palladium, platinum, copper and gold within the quasi-harmonic approximation using a first-principles approach and evaluating numerically the second derivatives of the Helmholtz free-energy with respect to strain at the minimum of the free-energy itself. We find an overall good agreement with the experimental data although the anomalies of palladium and platinum reported at room temperature are not reproduced. The contribution of electronic excitations is also investigated: we find that it is non-negligible for the $C_{44}$ elastic constants of palladium and platinum while it is irrelevant in the other cases. Its effect is not sufficient to explain the details of the anomalies found by experiments, not even when, in the case of platinum, we take into account the electron-phonon interaction. Lastly, the effect of the exchange and correlation functional is addressed and it is found that it is important at T=0 K, while all functionals give similar temperature dependencies.