Stability of crystalline solids—II: Application to temperature-induced martensitic phase transformations in a bi-atomic crystal

Abstract

This paper applies the stability theory of crystalline solids presented in the companion paper (Part I) to the study of martensitic transformations found in shape memory alloys (SMA's). The focus here is on temperature-induced martensitic transformations of bi-atomic crystals under stress-free loading conditions. A set of temperature-dependent atomic potentials and a multilattice description are employed to derive the energy density of a prototypical SMA ( B 2 cubic austenite crystal). The bifurcation and stability behavior are then investigated with respect to two stability criteria (Cauchy–Born (CB) and phonon). Using a 4-lattice description five different equilibrium crystal structures are predicted: B 2 cubic, L 1 0 tetragonal, B 19 orthorhombic, Cmmm orthorhombic, and B 19 ′ monoclinic. For our chosen model only the B 2 and B 19 equilibrium paths have stable segments which satisfy both the CB- and phonon-stability criteria. These stable segments overlap in temperature indicating the possibility of a hysteretic temperature-induced proper martensitic transformation. The B 2 and B 19 crystal structures are common in SMA's and therefore the simulated jump in the deformation gradient at a temperature for which both crystals are stable is compared to experimental values for NiTi, AuCd, and CuAlNi. Good agreement is found for the two SMA's which have cubic to orthorhombic transformations (AuCd and CuAlNi).