Time evolution of tetragonal-orthorhombic ferroelastics

We study numerically the time evolution of two-dimensional (2D) domain patterns in proper tetragonal-orthorhombic (T-O) ferroelastics. Our results, found by solving equations of motion derived from classical elasticity theory, disagree with those found by other methods. We study first the growth of the 2D nucleus resulting from homogeneous nucleation events. The later shape of the nucleus is largely independent of how it was nucleated. In soft systems, the nucleus forms a flower-like pattern. In stiff systems, which seem to be more realistic, it forms an X shape with twinned arms in the 110 and \110 directions. Second, we study the relaxation that follows completion of the phase transition; at these times, the T phase has disappeared and both O variants are present, segregated into domains separated by domain walls. We observe a variety of coarsening mechanisms, most of them counterintuitive.