The Correspondence Theory and Its Application to NiTi Shape Memory Alloys

Abstract

Martensite crystallography is usually described by the phenomenological theory of martensite crystallography (PTMC). This theory relies on stretch matrices and compatibility equations, but it does not give a global view on the structures of variants, and it masks the relative roles of the symmetries and metrics. Here, we propose an alternative theory called correspondence theory (CT) based on correspondences and symmetries. The compatibility twins between the martensite variants are inherited by correspondence from the symmetry elements of austenite. We show that, for the B2 to B19′ transformation, there is a one-to-one relation between the specific misorientations and the specific inter-correspondences between the variants. For each type of misorientation, the twin of its junction plane can be predicted without calculating the stretch matrices, as in PTMC. The rational elements of the twins do not depend on the metrics; all the transformation twins are thus “generic”. We also introduce the concept of a weak plane that permits to explain the junction planes for polar pairs of variants for which the PTMC compatibility equations cannot be solved. The predictions are validated by comparison with experimental Transmission Kikuchi Diffraction (TKD) maps.