Theory of melting lines with a variable enthalpy of fusion

TL;DR

This paper develops an analytical model for melting lines considering a variable enthalpy of fusion, linking thermophysical properties to the shape of melting curves and supporting their universal parabolic form.

Contribution

It introduces a modified Clausius-Clapeyron relation incorporating anharmonic effects and derives a second-order differential equation for melting lines based on fundamental thermophysical properties.

Findings

Derived approximate parabolic solutions for melting lines.

Parameters depend on bulk moduli, thermal expansion, and specific volumes.

Supports the universal parabolic shape of melting curves from a new theoretical perspective.

Abstract

Conventional derivations of phase boundaries from the Clausius-Clapeyron (CC) relation often employ the constant latent heat approximation to maintain analytical functions of the sublimation and boiling curves. To address the complex thermodynamics of the solid-liquid transition, we develop a two-phase analytical model by modifying the CC equation to account for a variable enthalpy of fusion along the melting line (ML). Our methodology utilizes recent theoretical and experimental progress demonstrating that the isobaric heat capacity of crystalline solids near the melting point features a dominant anharmonic, volume-dependent component. Consequently, the latent heat is correlated to the specific volumes of the coexisting phases. Differentiation of this modified CC relation yields a second-order differential equation governing ML. By imposing appropriate e boundary conditions, physically acceptable approximate parabolic solutions are derived. The parameters of these analytic functions are defined exclusively by fundamental thermophysical properties, including the bulk moduli, thermal expansion coefficients, and specific volumes of the coexisting phases, as well as the isobaric heat capacity of the solid. Our derivation, rooted in solid-state anharmonicity, yields approximate parabolic scaling laws that corroborate with a recent universal model derived from the Phonon Theory of Liquids [K. Trachenko, Phys. Rev. E 109, 034122 (2024)], supporting the universal parabolic nature of melting curves from a completely distinct theoretical foundation.