Hidden universality in dislocation-loops mediated three-dimensional crystal melting

TL;DR

This paper reveals a universal energy ratio for dislocation loops at melting, explaining empirical observations and connecting melting behavior to microscopic dislocation properties across different materials.

Contribution

It demonstrates a universal ratio between dislocation loop energy and thermal energy at melting, independent of material-specific details, within dislocation-mediated melting theory.

Findings

Universal energy ratio $oxed{ ext{E}_* ext{ } ext{approx.} ext{ } 25.1}$ for dislocation loops at melting.

Microscopic explanation for empirical viscosity-based energy scale $oxed{ ext{approx.} 24.6}$.

Rationalization of the empirical $2/3$ rule relating glass transition and melting temperatures.

Abstract

Understanding why and how crystalline solids melt remains a central problem in condensed-matter physics. Dislocation loops are fundamental topological excitations that control the thermodynamic stability of crystals, yet their role in setting universal aspects of melting has remained unclear. Here we show, within dislocation-mediated melting theory, that the free-energy condition for loop proliferation leads to a universal ratio between the energy of a minimal dislocation loop and the thermal energy at melting. For minimal dislocation loops that begin to proliferate at the onset of melting, this ratio takes the purely geometric value $\mathcal{E}_* = E_{\rm loop}/(k_B T_m) \approx 25.1$, independent of elastic moduli and chemistry-dependent details. This result provides a microscopic explanation for recent empirical findings by Lunkenheimer \emph{et al.}, who identified a closely related universal energy scale $\approx 24.6$ from viscosity data. The same framework also rationalizes the empirical $2/3$ rule relating the glass-transition and melting temperatures.