Ginzburg-Landau modelling of precursor nanoscale textures in ferroelastic materials

Abstract

A Ginzburg–Landau free-energy model is proposed to study spatially inhomogeneous states that often occur as precursors of ferroelastic/martensitic transitions. Disorder is included in the harmonic coefficient of the free-energy density which gives rise to a spatial distribution of transition temperatures, and lattice integrity is imposed through Saint-Vénant compatibility conditions which lead to a long-range anisotropic elastic interaction. We show that precursor textures are a result of the competition between elastic anisotropy and disorder. Cross-hatched modulations (tweed patterns) take place for temperatures above the martensitic phase in the limit of high anisotropy and/or low disorder while a nano-cluster phase-separated state occurs at low anisotropies or high disorder. In the latter case, nanoscale inhomogeneities give rise to glassy behaviour while the structural transition is inhibited. Interestingly, in this case, the ferroelastic system also displays a large thermo-mechanical response so that the low-symmetry structure can be easily induced by the application of relatively small stresses within a broad temperature range.