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

Alessio Zaccone, Konrad Samwer

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.

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

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 , 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 from viscosity data. The same framework also rationalizes the empirical rule relating the glass-transition and melting temperatures.
Paper Structure (6 sections, 49 equations, 3 figures)

This paper contains 6 sections, 49 equations, 3 figures.

Table of Contents

  1. End Matter
  2. Dislocation energetics
  3. Configurational entropy derivation
  4. Relation between fragility, Poisson’s ratio, and KSZ parameter
  5. Relation between the KSZ parameter $\lambda$ and Poisson’s ratio
  6. Physical interpretation

Figures (3)

  • Figure 1: Construction of the idealized, cooperativity-free melting point and the corresponding universal relaxation time. (a) Schematic Arrhenius plot of the relaxation time $\tau(T)$. The solid line represents the experimentally observed non-Arrhenius (VFT) behavior including cooperativity, while the dashed line shows the extrapolated Arrhenius behavior expected in the absence of cooperativity. (b) Same construction applied to poly(ethylene oxide) ($m=139$). Reproduced with permission from Ref. Lunkenheimer2025. Copyright (2025) by the American Physical Society.
  • Figure 2: Mechanism of dislocation-loop--mediated melting in three-dimensional crystals.
  • Figure 3: Fragility index as a function of Poisson ratio according to the empirical equation of Sokolov and Novikov SokolovNovikov2004, calibrated over very many different substances.