Melting Temperature of Metals Based on the Nearly Free Electron Model

TL;DR

This paper introduces a formula for metal melting temperatures based on the nearly free electron model, linking electronic properties to melting behavior and aligning well with experimental data.

Contribution

It derives a new melting temperature formula from phonon instability analysis within the nearly free electron model, incorporating vibrational effects.

Findings

Predicted melting temperatures closely match experimental data within 10%.

The theory confirms the validity of the Lindemann criterion.

Provides a unified electronic-based approach to metal melting points.

Abstract

We propose a general formula for the melting temperature of metals in terms of electronic mass, electronic number, and nearest-neighbor lattice distance. We derive it from the instability of the transverse phonon in the solid phase, using the nearly free electron model. Including higher order terms of vibrations enhanced near the melting temperature, the electronic restoring force is reduced and the ionic one is negligible. This fact greatly brings down the melting temperature, bringing it close to experimental data in the range of 10 % for Cs, Cu, Au, and Ba. Also, this theory confirms the Lindemann criterion.