Multidimensional geometric aspects of the solid–liquid transition in simple substances

Any molecular system explores significantly different regions of the potential-energy hypersurface as the system is found, respectively, in the solid and liquid phases. We study in detail the multidimensional geometry of these different regions with molecular-dynamics calculations for 256 simple atoms in a fixed volume. The atomic interactions are chosen to represent the noble gases. The stable crystal for this model displays a face-centered cubic structure. We evaluate the local gradient and curvatures of the regions of the hypersurface sampled by the system for a wide range of temperatures. We observe that a significant fraction of the curvatures become negative in the region sampled by the system at temperatures even as low as one-fourth the melting temperature. Further, the curvature distribution changes dramatically with respect to temperature at the melting point. We also construct and evaluate a new distribution for the distance between the atoms in their instantaneous dynamical configurations and those in their corresponding ‘‘quenched’’ configuration (i.e., the configuration found at the corresponding potential-energy minimum). With the help of this new distribution, we conclude that the quenched configurations which are encountered during the melting process are structures which contain vacancy-interstitial defect pairs.