A Universal Criterion of Melting

TL;DR

This paper proposes a universal vibrational criterion for melting based on molecular displacements, linking it to overdamped dynamics and deriving implications for supercooled liquids and glass transition phenomena.

Contribution

It introduces a universal Lindemann-like criterion for melting derived from vibrational amplitudes, applicable at the liquid-solid interface and in the bulk, connecting microscopic dynamics to macroscopic phase behavior.

Findings

The vibrational amplitude at melting is about one-tenth of the molecular spacing.

The criterion's universality stems from overdamped dynamics near melting.

Surface tension near the glass transition is nearly equally split between entropy and energy.

Abstract

Melting is analyzed dynamically as a problem of localization at a liquid-solid interface. A Lindemann-like criterion of melting is derived in terms of particular vibrational amplitudes, which turn out to equal a universal quotient (about one-tenth) of the molecular spacing, at the interface. The near universality of the Lindemann ratio apparently arises owing to strongly overdamped dynamics near melting, and despite the anharmonic interactions' being system-specific. A similar criterion is derived for structural displacements in the bulk of the {\em solid}, in particular the premelted layer; the criterion is no longer strictly universal, but still depends only on the harmonic properties of the solid. We further compute the dependence of the magnitude of the elemental molecular 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 a supercooled liquid, is nearly evenly split between entropic and energetic contributions.