Microstructure in the cubic to monoclinic transition in titanium-nickel shape memory alloys

Microstructure in the cubic to monoclinic transition in the technologically important Ti-Ni shape memory alloys is considered. Using a geometrically nonlinear theory of martensitic transformations, the twinned martensite, austenite-martensite, wedge, triangle, and diamond microstructures are studied. Specifically, compound, type I, and type II twins are possible for any choice of the lattice parameters; while, non-standard twins may exist with special lattice parameters only. In addition, 192 habit planes are found for a particular Ti-Ni alloy, but only 24 have been unambiguously observed in experiments. Further, the twinned wedge is possible in this alloy, but the triangle and diamond are not. These latter three are special microstructures, which provide a mechanism through which a specimen can easily transform and are possible only for alloys with specific lattice parameters. A complete enumeration of the various microstructures is given, and algorithms are presented so that the calculations can be repeated with different lattice parameters.