Thermodynamic Limit of the Transition Rate of a Crystalline Defect

TL;DR

This paper proves that, under harmonic approximation, the supercell approximation of defect transition rates in crystals converges to the true value as the cell size increases, with explicit convergence rates.

Contribution

It provides a rigorous analysis of the convergence of supercell approximations for defect transition rates, including sharp convergence rates and a renormalisation approach.

Findings

Supercell approximation converges to the true transition rate as cell size increases.

Explicit convergence rates are established for the approximation.

A spatial decomposition technique is used to analyse vibrational entropy differences.

Abstract

We consider an isolated point defect embedded in a homogeneous crystalline solid. We show that, in the harmonic approximation, a periodic supercell approximation of the formation free energy as well as of the transition rate between two stable configurations converge as the cell size tends to infinity. We characterise the limits and establish sharp convergence rates. Both cases can be reduced to a careful renormalisation analysis of the vibrational entropy difference, which is achieved by identifying an underlying spatial decomposition.