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We show how microstructure can arise in first-order ferroelastic structuraltransitions, in two and three spatial dimensions, through a local meanfieldapproximation of their pseudospin hamiltonians, that include anisotropicelastic interactions. Such transitions have symmetry-selected physical strainsas their $N_{OP}$-component order parameters, with Landau free energies thathave a single zero-strain 'austenite' minimum at high temperatures, andspontaneous-strain 'martensite' minima of $N_V$ structural variants at lowtemperatures. In a reduced description, the strains at Landau minima inducetemperature-dependent, clock-like $\mathbb{Z}_{N_V +1}$ hamiltonians, with$N_{OP}$-component strain-pseudospin vectors ${\vec S}$ pointing to $N_V + 1$discrete values (including zero). We study elastic texturing in five suchfirst-order structural transitions through a local meanfield approximation oftheir pseudospin hamiltonians, that include the powerlaw interactions. As aprototype, we consider the two-variant square/rectangle transition, with aone-component, pseudospin taking $N_V +1 =3$ values of $S= 0, \pm 1$, as in ageneralized Blume-Capel model. We then consider transitions with two-component($N_{OP} = 2$) pseudospins: the equilateral to centred-rectangle ($N_V =3$);the square to oblique polygon ($N_V =4$); the triangle to oblique ($N_V =6$)transitions; and finally the 3D cubic to tetragonal transition ($ N_V =3$). Thelocal meanfield solutions in 2D and 3D yield oriented domain-walls patterns asfrom continuous-variable strain dynamics, showing the discrete-variable modelscapture the essential ferroelastic texturings. Other related hamiltoniansillustrate that structural-transitions in materials science can be the sourceof interesting spin models in statistical mechanics.

Microstructure from ferroelastic transitions using strain pseudospin clock models in two and three dimensions: a local mean-field analysis