Relationship between crystalline order and melting mechanisms of solids

The mechanism for homogeneous nucleation of the liquid phase in Lennard-Jones solids is studied by combining the Landau free energy approach with some of the methodology developed to characterise transition path ensembles. The second-order bond orientational order parameter, Q ₆ which indexes the overall degree of crystalline order, is shown to provide a dynamically significant collective coordinate describing the melting process. Trajectories generated from configurations sampled in the vicinity of the maximum in the Landau free energy curve, F(Q ₆), are shown to have equal likelihood of teminating in either the solid or liquid-like free energy minima. It is also demonstrated that Q ₆ is necessary but not sufficient as a dynamical coordinate to describe melting and it is necessary to explore possiblities for additional coordinates which are critical for initiating melting. Our sudy suggests that the additional coordinates for describing the melting process would be some type of localised defect, much smaller in spatial extent than the size of the critical nucleus predicted by classical nucleation theory.