Generic and non-generic cubic-to-monoclinic transitions and their

The analysis of microstructure, for instance in shape-memory alloys, is largely based on the knowledge of the twins that arise from a symmetry-breaking phase transition. Such ‘transformation twins’ can be determined by analysing the kinematic compatibility conditions between the variants of the low-symmetry product phase. In this paper we report on the remarkable properties of twinning in the two cubic-to-monoclinic transitions that are possible. Not all these twins are conventional of Type 1 or Type 2. Indeed, our aim is to underline a peculiarity of the cubic-to-monoclinic transitions: if the lattice parameters of the monoclinic phase satisfy certain relations that we give explicitly, there exist many more twins than in the generic case. This is important because an abundance of twins implies that the material can form, in connection with the phase change, a wider variety of microstructures to accommodate imposed displacements or loads. In turn, this should noticeably influence the macroscopic behavior of the crystal, for instance enhancing its memory characteristics. This theoretical analysis may thus assist in the search of new and interesting materials. We propose to the experimental community toinvestigate the non-generic twins here described, and to check whether the non-generic monoclinicmaterials do indeed exhibit the remarkable properties that are expected due to the existence of the extra twinning modes.