In this letter we obtain the finite-temperature structure
of 180^o domain walls in PbTiO_3 using a quasi-harmonic
lattice dynamics approach. We obtain the temperature dependence of
the atomic structure of domain walls from 0 K up to room
temperature. We also show that both Pb-centered and Ti-centered
180^o domain walls are thicker at room temperature; domain
wall thickness at T=300 K is about three times larger than that of
T=0 K. Our calculations show that Ti-centered domain walls have a
lower free energy than Pb-centered domain walls and hence are more
likely to be seen at finite temperatures.

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.

In this paper, we study the effect of normal and shear strains and
oxygen vacancies on the structure of 180^o ferroelectric
domain walls in PbTiO_3.