STRAIN COUPLING AS THE DOMINANT INTERACTION IN STRUCTURAL PHASE-TRANSITIONS

A rigorous theory is developed for the ordering interaction J(R(ij)) i n a crystal having a structural phase transition when J (R(ij)) is med iated by elastic relaxation in the material. The ordering process in c ell i sets up a local stress field due to the sizes, shapes or displac ements of atoms or atomic groups, which propagates elastically to a di stant cell j. The atomistic theory for ferro- and antiferro-elastic tr ansitions takes into account two types of singularity, one due to elas tic anisotropy and the other to the Zener interaction J(Z) of infinite range in ferroelastic transitions, as well as the self-energy of rela xation around each cell. Four types of case are distinguished for a si mple cubic model, which between them encompass the phenomena in much m ore complex situations. The interaction J(k) in Fourier space is domin ated by whether or not domain walls perpendicular to k have a low ener gy from their strain satisfying Sapriel's compatibility relations. Thu s embryonic tweed texture in fluctuations above T-c is readily account ed for. The asymptotic J(R) at large R is shown to be very anisotropic even in sign. The transition temperature T-c for ferro transitions in the mean-field (Bragg-Williams) approximation is dominated by the Zen er contribution. The long-range and anisotropic nature of the coupling has implications for the kinetics of phase transformations, critical fluctuations near T-c, the theory of domain walls, and the formation o f metastable textures, including 'tweed'.