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A quasi-spin Ising model of ferroelastic phase transition is developed andemployed to perform atomic-scale Monte Carlo simulation of thermoelasticmartensitic transformation. The quasi-spin variable associated with the latticesites characterizes the local unit cells of the orientation variants of theground-state martensite phase, which interact with each other throughlong-range elastic interactions. The simulation study focuses on the intrinsicbehaviors of a defect-free crystal that undergoes cubic-to-tetragonalmartensitic transformation. It is shown that the diffuse scattering in thepre-martensitic austenite state results from the spatial correlation of theatomic-scale heterogeneous lattice displacements and manifests the displacementshort-range ordering. The effects of temperature, elastic anisotropy, and shearmodulus softening on the diffuse scattering and displacement short-rangeordering are investigated. It is found that elastic softening in the shearmodulus C'=(C11-C12)/2 promotes <110>|<1-10> displacement plane waves thatstabilize the cubic austenite phase through increased entropy, decreasing themartensitic transformation temperature. The simulated diffuse scattering iscompared and agrees with the complementary synchrotron X-ray single-crystaldiffuse scattering experiment.

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