Structural transformations in crystalline solids are increasingly the basis of the functional behavior of materials. Recently, in diverse alloy systems, both low hysteresis and reversibility of phase transformations have been linked to the satisfaction of the nongeneric conditions of compatibility between phases. According to the Cauchy–Born rule, these conditions are expressed as properties of transformation stretch tensor. The transformation stretch tensor is difficult to measure directly due to the lack of knowledge about the exact transforming pathway during the structural change, and the complicating effects of microstructure. In this paper we give a rigorous algorithmic approach for determining the transformation stretch tensor from X-ray measurements of structure and lattice parameters. For some traditional and emerging phase transformations, the results given by the algorithm suggest unexpected transformation mechanisms.

The alloy Cu25Au30Zn45 undergoes a huge first-order phase transformation (6% strain) and shows a high reversibility under thermal cycling and an unusual martensitc microstructure in sharp contrast to its nearby compositions. This alloy was discovered by systematically tuning the composition so that its lattice parameters satisfy the cofactor conditions (i.e., the kinematic conditions of compatibility between phases). It was conjectured that satisfaction of these conditions is responsible for the enhanced reversibility as well as the observed unusual fluid-like microstructure during transformation, but so far, there has been no direct evidence confirming that these observed microstructures are those predicted by the cofactor conditions. To verify this hypothesis, we use synchrotron X-ray Laue microdiffraction to measure the orientations and structural parameters of variants and phases near the austenite/martensite interface. The areas consisting of both austenite and multi-variants of martensite are scanned by microLaue diffraction. The cofactor conditions have been examined from the kinematic relation of lattice vectors across the interface. The continuity condition of the interface is precisely verified from the correspondent lattice vectors between two phases.

The near equiatomic NiTi alloy is the most successful shape memory alloy by a large margin. It is widely and increasingly used in biomedical devices. Yet, despite having a repeatable superelastic effect and excellent shape-memory, NiTi is very far from satisfying the conditions that characterize the most reversible phase-transforming materials. Thus, the scientific reasons underlying its vast success present an enigma. In this paper, we perform rigorous mathematical derivations and accurate density-functional theory calculations of transformation mechanisms to seek previously unrecognized twinlike defects that we term involution domains, and we observe them in real space in NiTi by aberration-corrected scanning transmission electron microscopy. Involution domains lead to an additional 216 compatible interfaces between phases in NiTi, and we theorize that this feature contributes importantly to its reliability. They are expected to arise in other transformations and to alter the conventional interpretation of the mechanism of the martensitic transformation.