Abstract

Melting is a phase transition with which we all become familiar early on in our lives, and is also among the generally better understood ones, on basic grounds of statistical thermodynamics. At a sufficiently low temperature, the equilibrium phase of a generic condensed matter system is predicted by classical mechanics to be a crystalline solid, with atoms or molecules arranged in orderly, periodic arrays, typically referred to as lattices. This arrangement is that in which the potential energy of the system is minimum. In a crystal, particles (atoms or molecules) are bound to lattice positions, held in place by restoring forces that, for small displacements, can be regarded as harmonic, i.e., “spring-like”; particles only make small excursions away from their equilibrium positions, with a mean square amplitude proportional to the temperature T. As T is raised, thermal agitation increases, displacements away from equilibrium positions become significant, and, eventually, particles are no longer localized at lattice sites. A transition occurs to a disordered, isotropic phase, i.e., the liquid.