Dynamics of domain walls in ferrodistortive materials. I. Theory

A theoretical study of domain walls in uniaxial displacive ferrodistortive systems is presented. We start from a generalized Langevin equation of motion for the movements of the ions, which includes dissipative terms and external fields, in addition to anharmonic and strain-force terms. We obtain large- and small-amplitude solutions corresponding to domain walls and the usual soft-mode phonons, respectively. We show that apart from translation the domain walls are absolutely stable solutions of our equation and that in external fields they reach a unique terminal velocity. The linear dependence of the velocity on the field allows us to define a temperature-dependent mobility which is related to the diffusion coefficient for the wall. Furthermore, we calculate analytically the dynamic structure factor due to domain walls and soft-mode phonons. We find that the Brownian motion of the domain walls leads to a very narrow Rayleigh peak. As we show in the second paper of this series, our model is useful in correlating and interpreting experiments in this field.