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 ferroelastic transitions with two-component vector order parameters (NOP = 2) in 2-spatial dimensions. The zero value pseudospin is the single high-temperature phase while the low-temperature phase has Nv variants. Thus the number of nonzero values of pseudospin are triangle-to-centered rectangle (Nv = 3), square-to-oblique (Nv = 4) and triangle-to-oblique (Nv = 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 (NOP = 1,Nv = 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. Systematic temperature quench experiments can look for martensite formation and growth during conversion-incubations, divergences, and distributions close to the transition.