Ferroelastics:

Many solid-state phase transformations involve shape changes. For example, with decreasing temperature a cubic system can distort and become tetragonal by contracting (or expanding) along any of the three cubic axes; the three low-temperature states, called variants, are the eqivalent of domains in ferromagnets. Ideally, only one variant would occur in a sample at low temperature, real materials, however, usually contain all possible variants, because of multiple nucleation events or external constraints (such as neighbouring grains in polycrystalline materials). To describe the walls between the variants in these inhomogeneous systems, I use nonlinear elasticity theory (an expansion of the energy in powers of the strains and their gradients). The optimal structure is found by minimizing the energy, subject to the constraints. An example is a square with fixed boundaries; energy would be gained if the square could distort to either of two rectangles, but it cannot. The question is then: how does a system which gains energy by changing its shape gain energy if its shape cannot change? The answer is that it forms both variants, separated by twin walls. Research in progress looks at twin walls and their intersections (with applications for example to twin walls in the in the celebrated 92K superconductor YBa₂Cu₃O_7-delta) and the transformation front of the tegragonal -> orthorhombic transformation in a temperature gradient.