Monte Carlo simulations of strain pseudospins: Athermal martensites, incubation times, and entropy barriers

We study martensitic transition kinetics through temperature-quench Monte Carlo simulations for a square/rectangle ferroelastic transition, described by a Hamiltonian of three-state pseudospins S, without extrinsic disorder. Here S=0 for high-temperature austenite, and S=±1 for the two martensite variants. The temperature-dependent pseudospin Hamiltonian comes from the total scaled free energy functional, evaluated at the three minima of Landau polynomials in order-parameter strains. It includes power-law anisotropic interactions from the St. Venant compatibility constraint, which orient the elastic domain walls in a symmetry-breaking diagonal direction. We find that temperature-time- transformation (TTT) plots for domain-wall phase evolution have phase crossover temperatures, which are understood through an effective-droplet energy parametrization. For temperature cycling through the phases, there are hysteretic peaks in physical quantities. For temperature quenches, a "vapor" of martensitic droplets converts at a time t_m(T) to a vibrating "liquid" of bidiagonal domain walls, which then orient at a time t_C(T) to a static "crystal" of single-diagonal martensitic twins, which can have bound residual austenite. Focusing on the conversion time t_m, we find a material-parameter phase diagram, which has regions of nonactivated "athermal" and activated "isothermal" martensites. In an athermal, nonactivated regime, there are explosive austenite-martensite conversions at temperatures below a residual-austenite spinodal in the TTT diagram, while above it, there are conversion tails, as in experiment. We find t_m(T) has a quasi-universal Vogel-Fulcher divergence at transition, with a log-normal conversion-rate distribution. The incubation times t_m,t_C are attributed to entropy barriers, with signatures of flat energies, during pathway searches for finite-scale transition textures, which are explicitly identified through textural and internal-stress snapshots. In a glasslike energy landscape picture, these entropic pathways to many locked-twin states dominate those to a single-variant martensite state, of almost the same energy density. Other transitions in 2D and 3D can be similarly studied. More generally, the models could be used to explore conceptual issues of how systems equilibrate after a deep quench.