Dynamically strained ferroelastics: Statistical behavior in elastic and plastic regimes

The dynamic evolution in ferroelastic crystals under external shear is explored by computer simulation of a two-dimensional model. The characteristic geometrical patterns obtained during shear deformation include dynamic tweed in the elastic regime as well as interpenetrating needle domains in the plastic regime. The geometrical mechanisms for the evolution of the ferroelastic micro-structure under strain deformation remain similar in all thermal regimes, whereas their thermodynamic behavior differs dramatically: on heating, from power-law statistics via the Kohlrausch law to a Vogel-Fulcher law. There is hence no simple way to predict the local evolution of the twin micro-structure from just the observed statistical behavior of a ferroelastic crystal. It is shown that the Poisson distribution is a convenient way to describe the crossover behavior contained in all the experimental data without recourse to specific scaling functions or temperature-dependent cutoff lengths.