Theoretical Insights into Non-Arrhenius Behaviors of Thermal Vacancies in Anharmonic Crystals

TL;DR

This paper develops a theoretical model to explain the non-Arrhenius behavior of vacancies in anharmonic crystals during heating, highlighting the importance of anharmonic effects and vibrational excitations.

Contribution

It introduces a simple theoretical framework incorporating quantum vibrational analysis to better understand vacancy proliferation beyond Arrhenius law.

Findings

Vacancy formation exhibits strong nonlinearity due to anharmonic effects.

The model aligns with previous simulations and experimental observations.

Arrhenius law is insufficient for describing vacancy behavior in anharmonic crystals.

Abstract

Vacancies are prevalent point defects in crystals, but their thermal responses are elusive. Herein, we formulate a simple theoretical model to shed light on the vacancy evolution during heating. Vibrational excitations are thoroughly investigated via moment recurrence techniques in quantum statistical mechanics. On that basis, we carry out numerical analyses for Ag, Cu, and Ni with the Sutton-Chen many-body potential. Our results reveal that the well-known Arrhenius law is insufficient to describe the proliferation of vacancies. Specifically, anharmonic effects lead to a strong nonlinearity in the Gibbs energy of vacancy formation. Our physical picture is well supported by previous simulations and experiments.