A microstructure of martensite which is not a minimiser of energy: the X-interface

In this paper we investigate the X-interface, a microstructure observed in Indium-Thallium byBasinski &Christian 5].Ball &James 3] have shown howsimple martensitic microstructures can be represented by sequences of elastic deformations which minimise a free-energy functional. In contrast we show that the X-interfacecannot be represented by such a sequence. In an attempt to understand this result we develop a less restrictive theory based onEricksen's ideas about low-energy modes of deformation for martensitic materials. This theory has some interesting conclusions for the X-interface and Indium-Thallium, for the wedge-like microstructures analysed recently byBhattacharya 6], and for the general problem of microstructures which cannot be represented by minimising sequences. The calculations in this paper apply only to cubic-to-tetragonal transformations.