Structure of defective crystals at finite temperatures: A quasi-harmonic lattice dynamics approach

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 quasi-harmonic 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° domain walls in a 2D 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.