Quasi-Spin Ising Model and Monte Carlo Simulation of Ferroelastic Phase Transition: 3D Diffuse Scattering and Displacement Short-Range Ordering in Pre-Martensitic State

TL;DR

This paper develops a quasi-spin Ising model and uses Monte Carlo simulations to study the atomic-scale behaviors and diffuse scattering in ferroelastic martensitic transformations, revealing how elastic properties influence phase stability.

Contribution

It introduces a novel quasi-spin Ising model for ferroelastic transitions and demonstrates its effectiveness through atomic-scale Monte Carlo simulations aligned with experimental data.

Findings

Diffuse scattering arises from displacement short-range order in pre-martensitic state.

Elastic softening promotes displacement waves that stabilize the austenite phase.

Simulation results agree with synchrotron X-ray diffuse scattering experiments.

Abstract

A quasi-spin Ising model of ferroelastic phase transition is developed and employed to perform atomic-scale Monte Carlo simulation of thermoelastic martensitic transformation. The quasi-spin variable associated with the lattice sites characterizes the local unit cells of the orientation variants of the ground-state martensite phase, which interact with each other through long-range elastic interactions. The simulation study focuses on the intrinsic behaviors of a defect-free crystal that undergoes cubic-to-tetragonal martensitic transformation. It is shown that the diffuse scattering in the pre-martensitic austenite state results from the spatial correlation of the atomic-scale heterogeneous lattice displacements and manifests the displacement short-range ordering. The effects of temperature, elastic anisotropy, and shear modulus softening on the diffuse scattering and displacement short-range ordering are investigated. It is found that elastic softening in the shear modulus C'=(C11-C12)/2 promotes <110>|<1-10> displacement plane waves that stabilize the cubic austenite phase through increased entropy, decreasing the martensitic transformation temperature. The simulated diffuse scattering is compared and agrees with the complementary synchrotron X-ray single-crystal diffuse scattering experiment.