Classical isotropic two-body potentials generating martensitic transformations

An isotropic interaction potential for classical particles is devised in such a way that the crystalline ground state of the system changes discontinuously when some parameter of the potential is varied. Using this potential we model martensitic transformations, and are able to study in detail the processes that are usually associated with them: the shape memory effect and superelasticity, as well as many details concerning the dynamics of the transformations, particularly the characteristics of the martensitic texture obtained as a function of parameters affecting the transformation rate. Here we introduce the interaction potentials and present some basic results concerning the transformations that they can be used to describe, for the particular cases of two-dimensional triangular rhombohedral and triangular-square transformations.