# First-principles prediction of the stacking fault energy of gold at finite temperature

## TL;DR

This study uses first-principles calculations to analyze how the stacking fault energy of gold decreases significantly with temperature, mainly due to vibrational entropy effects, impacting plasticity modeling.

## Contribution

It provides a detailed first-principles analysis of the temperature dependence of gold's stacking fault energy, highlighting vibrational entropy's role and comparing modeling approaches.

## Key findings

- ISFE decreases by 36-39% from 0 to 890 K
- Vibrational entropy at the stacking fault layer drives the decrease
- Debye model underestimates vibrational contribution

## Abstract

The intrinsic stacking fault energy (ISFE) $\gamma$ is a material parameter fundamental to the discussion of plastic deformation mechanisms in metals. Here, we scrutinize the temperature dependence of the ISFE of Au through accurate first-principles derived Helmholtz free energies employing both the super cell approach and the axial Ising model (AIM). A significant decrease of the ISFE with temperature, $-(36$-$39)$\,\% from 0 to 890\,K depending on the treatment of thermal expansion, is revealed, which matches the estimate based on the experimental temperature coefficient $d \gamma / d T $ closely. We make evident that this decrease predominantly originates from the excess vibrational entropy at the stacking fault layer, although the contribution arising from the static lattice expansion compensates it by approximately 60\,\%. Electronic excitations are found to be of minor importance for the ISFE change with temperature. We show that the Debye model in combination with the AIM captures the correct sign but significantly underestimates the magnitude of the vibrational contribution to $\gamma(T)$. The hexagonal close-packed (hcp) and double hcp structures are established as metastable phases of Au. Our results demonstrate that quantitative agreement with experiments can be obtained if all relevant temperature-induced excitations are considered in first-principles modeling and that the temperature dependence of the ISFE is substantial enough to be taken into account in crystal plasticity modeling.