Weak Martensitic Transformations in Bravais Lattices

Abstract

Nonlinear thermoelasticity theory is being used, with some success, to analyze phenomena associated with phase transitions in some crystals, involving a change in crystal symmetry, what are often called Martensitic transformations. Roughly, these are the crystals which are, or at least behave as if they were Bravais lattices. For such lattices, molecular theories of thermoelasticity imply that the Helmholtz free energy should be invariant under an infinite discrete group. However, workers often use constitutive equations which are invariant only under a finite subgroup, to analyze behavior near transitions, Physicists are likely to use polynomials of as low degree as is feasible, what is sometimes called “Landau Theory”, to treat second-order or “weak” first-order transitions. I don’t know how to give a precise meaning to the notion of a weak transition. By one rather pragmatic interpretation a transition is weak if behavior near the transition of interest can be analyzed, satisfactorily, with a free energy function which is invariant only under some finite subgroup. Using this idea, one can deduce some properties which transitions must have, to be considered weak. My purpose is to elaborate this, to try to get some better understanding of what limits the ranges of applicability of what are, really, two versions of thermoelasticity theory.