Computational modeling of softening in a structural phase transformation

We develop a free energy density to model a structural first-order phase transformation from a high-temperature cubic phase to a low-temperature tetragonal phase. The free energy density models the softening of the elastic modulus controlling the low-energy path from the cubic to the tetragonal lattice, the loss of stability of the tetragonal phase at high temperatures, the loss of stability of the cubic phase at low temperatures, and the effect of compositional fluctuation on the transformation temperature. Numerical experiments are given for the qua si-static cooling and heating of a single crystal thin film through the transformation. Tweed-like oscillations are obtained as precursors to the structural phase transformation.