Symmetry breaking and transformation twinning

The investigation of microstructure is largely based on the knowledge of the transformation twins the are possible for a crystal undergoing a symmetry-breaking, di usionless phase transition. In order to have a complete description of this phenomenon, in this paper we review the subject of mechanical twinning from the point of view of nonlinear elasticity, and we examine the existence and genericity of all transformation twins, that is, all the rank-1 connections between the low-symmetry potential-wells occurring in a suitable neighborhood of the high-symmetry well for all the symmetry-breaking transitions that are possible in three-dimensional simple lattices. The analysis also shows that there are exceptions to the so-called \Mallard law", according to which the twins arise generically