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Monte Carlo simulations of vector pseudospins for strains: Microstructures, and martensitic conversion times

We present systematic temperature-quench Monte Carlo simulations on discrete-strain pseudospin model Hamiltonians to study microstructural evolutions in 2D ferroelastic transitions with two-component vector order parameters ($N_{OP}=2$). The zero value pseudospin is the single high-temperature phase while the low-temperature phase has $N_v$ variants. Thus the number of nonzero values of pseudospin are triangle-to-centered rectangle ($N_v=3$), square-to-oblique ($N_v=4$) and triangle-to-oblique ($N_v=6$). The model Hamiltonians contain a transition-specific Landau energy term, a domain wall cost or Ginzburg term, and power-law anisotropic interaction potential, induced from a strain compatibility condition. On quenching below a transition temperature, we find behaviour similar to the previously studied square-to-rectangle transition ($N_{OP} =1, N_v = 2$), showing that the rich behaviour found, is generic. Thus we find for two-component order parameters, that the same Hamiltonian can describe both athermal and isothermal martensite regimes for different material parameters. The athermal/isothermal/austenite parameter regimes and temperature-time-transformation diagrams are understood, as previously, through parametrization of effective-droplet energies. In the athermal regime, we find rapid conversions below a spinodal like temperature and austenite-martensite conversion delays above it, as in the experiment. The delays show early incubation behaviour, and at the transition to austenite the delay times have Vogel-Fulcher divergences and are insensitive to Hamiltonian energy scales, suggesting that entropy barriers are dominant.