Stability of thermally-induced martensitic transformations in Bi-atomic lattices

A well-known feature of some metallic alloys, such as NiTi, is their thermally induced, stress-dependent shape memory behavior. These alloys' remarkable properties are due to one or more martensitic transformations near room temperature, in which the crystalline configuration changes from a higher symmetry austenite (cubic lattice), to a lower symmetry martensite (rhombohedral, orthorhombic, tetragonal or monoclinic lattice) with decreasing temperature. In contrast to existing phenomenological approaches, the present work constructs a continuum energy density function W(F;θ) (as a function of a uniform deformation gradient and temperature) of a perfect periodic bi-atomic lattice from temperature dependent atomic potentials. Of interest in this work are the equilibrium solutions and their stability as functions of temperature for crystals under an applied pressure. Although the full problem is solved numerically, a post-bifurcation asymptotic analysis is necessary to guide the numerical solution near multiple bifurcation points. For the particular choice of a Morse-type pair potential, two stable cubic phases are predicted, one that corresponds to austentite (CsCl structure), which is stable at higher temperatures, and one that has a denser packing (NaCl structure), which is stable at lower temperatures. Theses stable portions oerlap at intermediate temperatures, which is suggestive of a hysteretic temperature-induced martensitic transformation. Lower symmetry crystals, such as orthorhombic, monoclinic, and rhombohedral structures, are also predicted.