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

Abstract

We study the equilibrium properties of a system of particles in two dimensions, interactingvia pair and three-body potentials. This system undergoes a structural transition from asquare to a rhombic lattice and thus constitutes a simple model for a generic tetragonal toorthorhombic transition. We aim at an intermediate level of description lyingin between that of coarse grained elastic strain Hamiltonians and microscopicab initio approaches. We obtain macroscopic thermodynamic properties and thephase diagram at zero and finite temperatures as a function of the density andthe relative strengths of the pair and three-body energies using lattice sums,an approximate ‘cell model’ theory and molecular dynamics simulations in theNV T ensemble. In addition, we study the dynamics of nucleation following a quench from thesquare to the triangular phase (Rao and Sengupta 2003 Phys. Rev. Lett. 91 045502). As in realsolids, the final microstructure depends sensitively on the depth of the quench—a shallowquench results in an equilibrium ferrite while a deep quench gives rise to a metastabletwinned martensite. We find, in accordance with experiments, that the twinned martensiteis associated with a diffusionless transformation. We propose that this model solidmay be used as a test bed for studies of the statics and dynamics of structuraltransitions.