Microstructure from ferroelastic transitions using strain pseudospin clock models in two and three dimensions

We show how microstructure can arise in first-order ferroelastic structural transitions, in two and three spatial dimensions, through a local mean-field approximation of their pseudospin Hamiltonians, that include anisotropic elastic interactions. Such transitions have symmetry-selected physical strains as their order parameters, with Landau free energies that have a single zero-strain ``austenite'' minimum at high temperatures, and spontaneous-strain ``martensite'' minima of structural variants at low temperatures. The total free energy also has gradient terms, and power-law anisotropic effective interactions, induced by ``no-dislocation'' St Venant compatibility constraints. In a reduced description, the strains at Landau minima induce temperature dependent, clocklike Hamiltonians, with strain- pseudospin vectors S pointing to discrete values including zero. We study elastic texturing in five such first-order structural transitions through a local mean-field approximation of their pseudospin Hamiltonians, that include the power-law interactions. The local mean-field solutions in 2D and 3D yield or oriented domain- wall patterns as from continuous-variable strain dynamics, showing the discrete- variable models capture the essential ferroelastic texturings.