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

TL;DR

This paper models microstructure formation in ferroelastic transitions using strain pseudospin clock models within a local mean-field framework, capturing domain patterns and elastic textures in 2D and 3D.

Contribution

It introduces a novel pseudospin Hamiltonian approach for ferroelastic transitions, linking structural variants to discrete clock models and analyzing their microstructure formation.

Findings

Discrete pseudospin models replicate domain wall patterns.

Elastic textures are captured by local mean-field solutions.

Models connect ferroelastic transitions to spin systems in statistical mechanics.

Abstract

We show how microstructure can arise in first-order ferroelastic structural transitions, in two and three spatial dimensions, through a local meanfield approximation of their pseudospin hamiltonians, that include anisotropic elastic interactions. Such transitions have symmetry-selected physical strains as their $N_{OP}$-component order parameters, with Landau free energies that have a single zero-strain 'austenite' minimum at high temperatures, and spontaneous-strain 'martensite' minima of $N_V$ structural variants at low temperatures. In a reduced description, the strains at Landau minima induce temperature-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 such first-order structural transitions through a local meanfield approximation of their pseudospin hamiltonians, that include the powerlaw interactions. As a prototype, we consider the two-variant square/rectangle transition, with a one-component, pseudospin taking $N_V +1 =3$ values of $S= 0, \pm 1$, as in a generalized 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$). The local meanfield solutions in 2D and 3D yield oriented domain-walls patterns as from continuous-variable strain dynamics, showing the discrete-variable models capture the essential ferroelastic texturings. Other related hamiltonians illustrate that structural-transitions in materials science can be the source of interesting spin models in statistical mechanics.