Stability of thermally-induced martensitic transformations in bi-atomic crystals

Abstract

Some of the most interesting, and technologically important solid–solid transformations are the first order diffusionless transformations that occur in certain equiatomic, ordered, bi-atomic crystals. These displacive transformations include thermally-induced, reversible, proper martensitic transformations as seen in shape memory alloys such as NiTi (where group–subgroup relationships exist between the symmetry groups of the crystal phases) and the reconstructive martensitic transformations seen in certain ionic compounds such as CsCl (where no group–subgroup relationship exists between the phases). In contrast to existing continuum mechanics 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 crystal from temperature-dependent atomic pair-potentials. Equilibrium solutions and their stability are examined as a function of temperature for crystals under no external stress. The full problem is solved numerically, and an asymptotic theory is employed to guide the numerical solution near multiple bifurcation points. Using pair-potentials and enforcing constrained kinematics (uniform deformation of a cubic CsCl-type crystal), lower symmetry crystals, such as orthorhombic, monoclinic, and rhombohedral structures are predicted. The first two of these are unstable within the chosen temperature window for our particular case, while the third is stable for higher temperatures. In addition, a hysteretic transformation was discovered in which the CsCl structure is stable at high temperatures and the NaCl structure is stable at low temperatures. These two cubic phases are connected by an unstable rhombohedral path corresponding to the transformation mechanism proposed by Buerger (1951). The CsCl–NaCl transformation suggested by the numerical results is a reconstructive transformation with a group–nonsubgroup relationship between the symmetry groups of the two phases.