Lindemann measures for the solid-liquid phase transition

A set of Lindemann measures, based on positional deviations or return distances, defined with respect to mechanically stable inherent structure configurations, is applied to understand the solid-liquid phase transition in a Lennard-Jones-type system. The key quantity is shown to be the single-particle return distance-squared distribution. The first moment of this distribution is related to the Lindemann parameter which is widely used to predict the melting temperature of a variety of solids. The correlation of the single-particle return distance and local bond orientational order parameter in the liquid phase provides insights into mechanisms for melting. These generalized Lindemann measures, especially the lower order moments of the single-particle return distance distribution, show clear signatures of the transition of the liquid from the stable to the metastable, supercooled regime and serve as landscape-based indicators of the thermodynamic freezing transition for the Lennard-Jones-type system investigated.