Strain coupling as the dominant interaction in structural phase transitions

Abstract

A rigorous theory is developed for the ordering interaction J(R _ij) in a crystal having a structural phase transition when J(R _ij) is mediated by elastic relaxation in the material. The ordering process in cell i sets up a local stress field due to the sizes, shapes or displacements of atoms or atomic groups, which propagates elastically to a distant cell j. The atomistic theory for ferro-and antiferro-elastic transitions takes into account two types of singularity, one due to elastic anisotropy and the other to the Zener interaction J_z of infinite range in ferroelastic transitions, as well as the self-energy of relaxation around each cell. Four types of case are distinguished fora simple cubic model, which between them encompass the phenomena in much more complex situations. The interaction J_K in Fourier space is dominated by whether or not domain walls perpendicular to k have a low energy from their strain satisfying Sapriel's compatibility relations. Thus embryonic tweed texture in fluctuations above T_c is readily accounted 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 Zener 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 of metastable textures, including ‘tweed’.

Key Words:

• Strain coupling