Transformation twinning and Mallard's law

The analysis of microstructure is largely based on the knowledge of the transformation twins in a crystal undergoing a symmetry-breaking phase transition. According to a conjecture referred to as "Mallard's law", the transformation twins generically arise from the lost symmetry planes in the parent phase, and correspond to the conventional Type-1 twins, with their conjugate Type-a twins. The analysis of the generic rank-one connections between potential wells occurring in any of the symmetry-breaking transitions that are possible for simple lattices shows that actually Mallard's law does not hold, because there do exist generic non-conventional twins. The law holds if at least one of the twins in a conjugate pair is required to have a material interface, or if twin genericity is interpreted in a particularly restrictive way.