Thermodynamics of freezing and melting.

Ulf R. Pedersen,Lorenzo Costigliola,Nicholas P. Bailey,Jeppe C. Dyre,Thomas B. Schrøder

doi:10.1038/ncomms12386

Ulf R. Pedersen, Lorenzo Costigliola + Show 3 more

Open Access

https://doi.org/10.1038/ncomms12386

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Journal: Nature Communications	Publication Date: Aug 17, 2016
Citations: 83	License type: CC BY 4.0

Affiliation: Roskilde University

Abstract

Although the freezing of liquids and melting of crystals are fundamental for many areas of the sciences, even simple properties like the temperature–pressure relation along the melting line cannot be predicted today. Here we present a theory in which properties of the coexisting crystal and liquid phases at a single thermodynamic state point provide the basis for calculating the pressure, density and entropy of fusion as functions of temperature along the melting line, as well as the variation along this line of the reduced crystalline vibrational mean-square displacement (the Lindemann ratio), and the liquid's diffusion constant and viscosity. The framework developed, which applies for the sizable class of systems characterized by hidden scale invariance, is validated by computer simulations of the standard 12-6 Lennard-Jones system.

Highlights

The freezing of liquids and melting of crystals are fundamental for many areas of the sciences, even simple properties like the temperature–pressure relation along the melting line cannot be predicted today
Since the hard-sphere system has only a single nontrivial thermodynamic state parameter, the packing fraction, the phase diagram is basically one-dimensional, which implies that the system has a unique freezing/melting transition
The theory presented above predicts the thermodynamics of freezing and melting from a single coexistence state point

Summary

Introduction

The freezing of liquids and melting of crystals are fundamental for many areas of the sciences, even simple properties like the temperature–pressure relation along the melting line cannot be predicted today. Other empirical rules, which are predicted by the hard-sphere picture and reasonably well obeyed by many systems, include the facts that in properly reduced units the liquid’s self-diffusion constant and viscosity are invariant along the freezing line[26,27], the Hansen–Verlet rule[17,28] that the amplitude of the first peak of the liquid static structure factor is about 2.85 at freezing, or Richard’s melting rule[3] that the entropy of fusion DSfus is about 1.1kB (which in a more modern and accurate version is the fact that the constant-volume entropy difference across the density–temperature coexistence region is close to 0.8kB (refs 23,29)). The theory is validated by computer simulations of the standard 12-6 LJ system

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Conclusion