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Updated: May 16, 2026
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Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
Published on: June 7, 2018
Quantifying Gibbs measures of disordered crystals up to the solid-liquid phase transition
Vladislav Efremkin1, Julian Heske2, Thomas D Kühne1,2,3
1Center for Advanced Systems Understanding, Helmholtz Zentrum Dresden-Rossendorf, Görlitz D-02826, Germany.
PNAS Nexus
|May 15, 2026
Summary
Reconstructing condensed matter lattices from atomic Voronoi cells solves a long-standing problem. Specific Voronoi facets uniquely identify crystalline structures, enabling quantification of the Gibbs measure for disordered systems.
Area of Science:
- Condensed matter physics
- Materials science
- Statistical mechanics
Background:
- Quantifying configuration space and Gibbs measure in disordered systems is challenging.
- The Gibbs paradox prohibits atom ordering or labeling.
- Existing methods struggle with thermal disorder in condensed matter.
Purpose of the Study:
- To develop a method for reconstructing condensed matter lattices from atomic Voronoi cells.
- To overcome the Gibbs paradox in analyzing disordered systems.
- To identify fundamental signatures of crystalline phases.
Main Methods:
- Utilizing Voronoi cells of atoms to reconstruct the system's lattice.
- Analyzing the statistics of Voronoi cell facets.
- Investigating the crystalline phase of silicon as a model system.
Main Results:
- The lattice of disordered systems can be reconstructed solely from Voronoi cells.
- Four specific large Voronoi facets were identified in crystalline silicon, present with probability one up to the melting point.
- These facets enable lattice reconstruction and optimal configuration representation.
Conclusions:
- Voronoi cell facets provide a robust method for lattice reconstruction, irrespective of thermal disorder.
- The identified stable Voronoi facets are a fundamental signature of the crystalline solid phase.
- This approach offers a pathway to quantifying the Gibbs measure across the solid phase.
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