A mesoscopic model of a two-dimensional solid state structural transformation: statics and dynamics

We study the equilibrium properties of a system of particles in two dimensions, interacting via pair and three-body potentials. This system undergoes a structural transition from a square to a rhombic lattice and thus constitutes a simple model for a generic tetragonal to orthorhombic transition. We aim at an intermediate level of description lying in between that of coarse grained elastic strain Hamiltonians and microscopic ab initio approaches. We obtain macroscopic thermodynamic properties and the phase diagram at zero and finite temperatures as a function of the density and the relative strengths of the pair and three-body energies using lattice sums, an approximate 'cell model' theory and molecular dynamics simulations in the NVT ensemble. In addition, we study the dynamics of nucleation following a quench from the square to the triangular phase (Rao and Sengupta 2003 Phys. Rev. Lett. 91045502). As in real solids, the final microstructure depends sensitively on the depth of the quench-a shallow quench results in an equilibrium ferrite while a deep quench gives rise to a metastable twinned martensite., We find, in accordance with experiments, that the twinned martensite is associated with a diffusionless transformation. We propose that this model solid may be used as a test bed for studies of the statics and dynamics of structural transitions.