| Abstract
| - Melting is analyzed dynamically as a problem of localization at a liquid−solid interface. A Lindemann-likecriterion of melting is derived in terms of particular vibrational amplitudes, which turn out to equal a universalquotient (about one-tenth) of the molecular spacing, at the interface. The near universality of the Lindemannratio apparently arises owing to strongly overdamped dynamics near melting, and despite the anharmonicinteractions being system-specific. A similar criterion is derived for structural displacements in the bulk ofthe solid, in particular the premelted layer; the criterion is no longer strictly universal, but still depends onlyon the harmonic properties of the solid. We further compute the dependence of the magnitude of the elementalmolecular translations, in deeply supercooled fluids, on the temperature and the high frequency elastic constants.We show explicitly that the surface tension between distinct liquid states, near the glass transition of asupercooled liquid, is nearly evenly split between entropic and energetic contributions.
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