  Motivated by experimental observations of H. Seiner et al., we study the
nucleation of austenite in a single crystal of a CuAlNi shape-memory alloy
stabilized as a single variant of martensite. In the experiments the nucleation
process was induced by localized heating and it was observed that, regardless
of where the localized heating was applied, the nucleation points were always
located at one of the corners of the sample - a rectangular parallelepiped in
the austenite. Using a simplified nonlinear elasticity model, we propose an
explanation for the location of the nucleation points by showing that the
martensite is a local minimizer of the energy with respect to localized
variations in the interior, on faces and edges of the sample, but not at some
corners, where a localized microstructure, involving austenite and a simple
laminate of martensite, can lower the energy. The result for the interior,
faces and edges is established by showing that the free-energy function
satisfies a set of quasiconvexity conditions at the stabilized variant in the
interior, faces and edges, respectively, provided the specimen is suitably cut.
