Efficient first-principles approach to Gibbs free energy with thermal expansion

TL;DR

This paper introduces an efficient first-principles method to compute Gibbs free energy considering thermal expansion, validated on various materials, and compares favorably with traditional approaches in accuracy and computational cost.

Contribution

The authors develop a novel approach to evaluate Gibbs free energy from constant-volume phonon calculations, eliminating the need for volume variation in traditional methods.

Findings

Accurately predicts free energy changes due to thermal expansion.

Validated method against conventional quasiharmonic approximation.

Demonstrates computational efficiency for complex materials.

Abstract

We propose a method to evaluate the Gibbs free energy from constant-volume first-principles phonon calculations. The volume integral of the pressure is performed by determining the volume and the bulk modulus in equilibrium at finite temperatures, where the pressure and its volume derivative are evaluated utilizing first-principles calculations of the Gr\"{u}neisen parameter without varying the volume. We validate our method for fcc Al by comparing with the conventional quasiharmonic approximation. Furthermore, we integrate our method with self-consistent phonon theory and apply it to calculations for bcc Ti, hcp Ti, and tetragonal ZrO$_2$. We demonstrate the accuracy and computational efficiency of our method by comparing results with those obtained from directly volume-varied self-consistent phonon calculations. In all cases, our method accurately evaluates the free energy change due to thermal expansion using only constant-volume phonon calculations.