Quasi-harmonic temperature dependent elastic constants: applications to silicon, aluminum, and silver

TL;DR

This paper introduces a computational method to calculate temperature-dependent elastic constants of cubic solids using ab-initio techniques, validated on silicon, aluminum, and silver, and compares results with experimental data.

Contribution

The study develops a new implementation within the thermo_pw code for calculating quasi-harmonic elastic constants of cubic materials at finite temperatures.

Findings

Calculated elastic constants agree with experimental measurements.

Method effectively captures temperature effects on elastic properties.

Validated approach applied successfully to silicon, aluminum, and silver.

Abstract

We present ab-initio calculations of the quasi-harmonic temperature dependent elastic constants. The isothermal elastic constants are calculated at each temperature as second derivatives of the Helmholtz free energy with respect to strain and corrected for finite pressure effects. This calculation is repeated for a grid of geometries and the results interpolated at the minimum of the Helmholtz free energy. The results are compared with the quasi-static elastic constants. Thermodynamic relationships are used to derive the adiabatic elastic constants that are compared with the experimental measurements. These approaches are implemented for cubic solids in the $\texttt{thermo_pw}$ code and are validated by applications to silicon, aluminum, and silver.