Triplet condition: A new condition of supercompatibility between martensitic phases

Enhancing the compatibility of phases and hence reducing the introduction of plastic de-formations during phase transitions are crucial to improving the hysteresis and cycling perfor-mance of shape memory alloys. We focus here on a new condition of supercompatibility between martensitic variants (called the triplet condition, TC) that allows for the formation of three-fold microstructures and that we believe influences the reversibility of martensitic transformations. Most interesting of all, we show that in the case of cubic-to-orthorhombic phase transformations TC generalizes the cofactor conditions (Chen et al., 2013. Journal of the Mechanics and Physics of Solids 61, 2566-2587.), conditions of supercompatibility between phases that empirically seem to influence reversibility but are extremely difficult to achieve in the design of new materials. We then analyze the martensite microstructure in a sample of Ti-30Ni-20Cu (at%) alloy, which closely satisfies TC, revealing an unusual microstructure comprising two-fold (ordinary twin), three-fold (TC), and four-fold (crossing twin) building blocks connected to each other. We finally discuss the possibility of designing durable shape memory alloys based on TC.