Microstructure in the cubic to trigonal transition

Microstructures for the cubic to trigonal transition are constructed using a geometrically non-linear theory of martensitic transformations. Specifically, the twinned martensite, parallelogram, austenite-martensite, wedge, triangle, and diamond microstructures are studied. In particular, the twins are found to be compound twins, and a parallelogram microstructure is constructed which is observed during twin crossings. All habit plane solutions, the shape strains and the habit plane normals, are enumerated; also, the special value of the trigonal angle at which the wedge microstructure exists is found. The predictions agree with available experimental data for a Au-Cd alloy and the R-phase in several Ti-Ni shape memory alloys. These calculations are the first complete analysis of microstructures in this transformation.