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

TL;DR

This paper uses Monte Carlo simulations on a vector pseudospin model to study microstructural evolution and martensitic transformation times in 2D ferroelastic materials with various variants, revealing generic behaviors and entropy barrier effects.

Contribution

It introduces a comprehensive pseudospin Hamiltonian model for 2D ferroelastic transitions with multiple variants, capturing both athermal and isothermal martensite regimes.

Findings

Rich microstructural behaviors are generic across different variants.

Conversion delays exhibit Vogel-Fulcher divergence, indicating entropy barriers.

The model explains temperature-time-transformation diagrams and incubation behaviors.

Abstract

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.