Energy barriers and hysteresis in martensitic phase transformations

We report results from a systematic program of changing composition of alloys in the system TiNiX, X= Cu, Pt, Pd, Au, to pursue certain special lattice parameters that have been identified previously with low hysteresis. We achieve λ2 = 1, where λ2 is the middle eigenvalue of the transformation strain matrix, for alloys with X = Pt, Pd, Au. In all cases there is a sharp drop of the graph of hysteresis vs. composition at the composition where λ2 = 1. When the size of the hysteresis is replotted vs. λ2 we obtain an universal graph for these alloys, which also agrees with trends in an earlier combinatorial study of alloys in the system TiNiCu. Motivated by these experimental results, we present a new theory for the size of the hysteresis based on the growth from a small scale of fully developed austenite martensite needles. In this theory the energy of the transition layer plays a critical role. New methods for calculation the optimal layer are developed that rely on Γ-convergence arguments, the small parameter being |λ2 − 1|. The limiting energy of the transition layer is found to be governed by a nonstandard linear elasticity problem. Overall, the results point to a simple systematic method of achieving low hysteresis and a high degree of reversibility in transforming materials.