Structure of Defective Crystals at Finite Temperatures: A Quasi-Harmonic Lattice Dynamics Approach

TL;DR

This paper develops a quasi-harmonic lattice dynamics method to analyze the finite-temperature structure of defective crystals, enabling semi-analytical studies of defect behavior at non-zero temperatures.

Contribution

It extends classical lattice dynamics to defective crystals with partial symmetries, allowing finite-temperature defect structure analysis without molecular dynamics.

Findings

Domain wall thickness increases with temperature

Method accurately predicts defect structures at low temperatures

Applicable to systems where molecular dynamics is infeasible

Abstract

In this paper we extend the classical method of lattice dynamics to defective crystals with partial symmetries. We start by a nominal defect configuration and first relax it statically. Having the static equilibrium configuration, we use a quasiharmonic lattice dynamics approach to approximate the free energy. Finally, the defect structure at a finite temperature is obtained by minimizing the approximate Helmholtz free energy. For higher temperatures we take the relaxed configuration at a lower temperature as the reference configuration. This method can be used to semi-analytically study the structure of defects at low but non-zero temperatures, where molecular dynamics cannot be used. As an example, we obtain the finite temperature structure of two 180^o domain walls in a 2-D lattice of interacting dipoles. We dynamically relax both the position and polarization vectors. In particular, we show that increasing temperature the domain wall thicknesses increase.