Defect Melting Models for Cubic Lattices and Universal Laws for Melting Temperatures

TL;DR

This paper develops simple harmonic lattice models for cubic lattices to derive universal formulas predicting melting temperatures, offering more precise and predictive results than traditional Lindemann's rule.

Contribution

It introduces a new theoretical framework for melting temperatures based on elastic fluctuations and defect excitations in cubic lattices, improving accuracy and systematicity over previous models.

Findings

Universal formulas predict melting temperatures accurately

The new theory is twice as precise as Lindemann's rule

Systematic improvements are possible within the model

Abstract

We set up simple harmonic lattice models for elastic fluctuations in bcc and fcc lattices and the excitation of dislocations and disclinations. From these we derive, in a lowest approximation, universal formulas which predict melting temperatures in good agreement with the experiments. This new theory is more precise than Lindemann's rule by factor 2, and more predictive, since the size of the Lindemann number has to be fixed by experiments. In addition, our theory allows for systematic improvements.