2025/11/01 by Cayron, Cyril
#FOS: Physical sciences #Materials Science (cond-mat.mtrl-sci)
paper · doi:10.48550/arxiv.2511.00633
The phenomenological theory of martensite crystallography (PTMC) explains the main crystallographic and microstructural features of martensite in shape memory alloys, such as the transformation twins between the martensite variants, and the interfaces between austenite and martensite bi-variant laminates. It also permits to determine which austenite and martensite lattice parameters should be targeted to get supercompatibility, which has driven over the last decades important research and development of new shape memory alloys with low hysteresis and high cyclability. First, we show that the cofactor conditions generally used to define supercompatibility are not necessary because they are redundant with the invariant plane condition. Second, we develop an alternative to the PTMC, called correspondence theory (CT). The mathematical tools of the PTMC come from continuum mechanics (pole decompositions and stretch tensors); they are advantageously replaced here by pure crystallographic tools (metric tensors, group of symmetries and correspondence), which allow direct calculations of the transformation twins and their generic and non-generic characters. A new symmetric matrix, called compatibility of metrics by correspondence (CMC) is also introduced. The supercompatibility condition can now be understood and written as the degeneracy of a quadratic form of the CMC, or geometrically as the degeneracy of double-cone into a double-plane, a plane, or the full space.