Dynamically strained ferroelastics: Statistical behavior in elastic and plastic regimes

Abstract

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. As a result, the statistics of jerk energy differ in the elastic and plastic regimes. In the elastic regime the distributions of jerk energy are sensitive to temperature and initial configurations. However, in the plastic regime the jerk distributions are rather robust and do not depend much on the details of the configurations, although the geometrical pattern formed after yield is strongly influenced by the elastic constants of the materials and the configurations we used. Specifically, for all geometrical configurations we studied, the energy distribution of jerks shows a power-law noise pattern $P(E)\ensuremath{\sim}{E}^{\ensuremath{-}(\ensuremath{\gamma}\ensuremath{-}1)}(\ensuremath{\gamma}\ensuremath{-}1=1.3\ensuremath{-}2)$ at low temperatures and a Vogel-Fulcher distribution $P$($E$) \ensuremath{\sim} exp-($E/{E}_{0}$) at high temperatures. More complex behavior occurs at the crossover between these two regimes where our simulated jerk distributions are very well described by a generalized Poisson distributions $P(E)\ensuremath{\sim}{E}^{\ensuremath{-}(\ensuremath{\gamma}\ensuremath{-}1)}$ exp-($E/{E}_{0}$)${}^{n}$ with $n$ $=$ 0.4--0.5 and \ensuremath{\gamma}\ensuremath{-}1 \ensuremath{\approx} 0 (Kohlrausch law). The geometrical mechanisms for the evolution of the ferroelastic microstructure 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 microstructure 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.