A cubic-to-tetragonal martensitic transition was modelled in terms of a Ginzburg-Landau free energy in the symmetrical strain tensor. It was shown that, in 3 dimensions, solving the St Venant compatibility relationships for strain (treated as independent field equations) generated 3 anisotropic long-range potentials between the 2 order parameter components. These potentials encoded 3-dimensional discrete symmetries, expressed the energetics of lattice integrity and determined 3-dimensional textures. The predictions of the simulation included twins with a temperature-varying orientation, helical twins, competing metastable states and compatibility-induced elastic frustration.

Three-Dimensional Elastic Compatibility and Varieties of Twins in Martensites. K.O.Rasmussen, T.Lookman, A.Saxena, A.R.Bishop, R.C.Albers, S.R.Shenoy: Physical Review Letters, 2001, 87[5], 055704 (4pp)