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  • Featured in Physics
  • Open Access

Bond-Network Entropy Governs Heat Transport in Coordination-Disordered Solids

Kamil Iwanowski1,2, Gábor Csányi3, and Michele Simoncelli1,2,*

  • 1Department of Applied Physics and Applied Mathematics, Columbia University, New York, New York, USA
  • 2Theory of Condensed Matter Group, Cavendish Laboratory, University of Cambridge, Cambridge, United Kingdom
  • 3Applied Mechanics Group, Mechanics, Materials and Design, Department of Engineering, University of Cambridge, Cambridge, United Kingdom

  • *Contact author: michele.simoncelli@columbia.edu
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Phys. Rev. X 15, 041041 – Published 4 December, 2025

DOI: https://doi.org/10.1103/w4p6-b9mp

Abstract

Understanding how the vibrational and thermal properties of solids are influenced by atomistic structural disorder is of fundamental scientific interest and paramount to designing materials for next-generation energy technologies. While several studies indicate that structural disorder strongly influences the thermal conductivity, the fundamental physics governing the disorder-conductivity relation remains elusive. Here we show that order-of-magnitude, disorder-induced variations of conductivity in network solids can be predicted from a “bond-network” entropy, an atomistic structural descriptor that quantifies heterogeneity in the topology of the atomic-bond network. We employ the Wigner formulation of thermal transport to demonstrate the existence of a relation between the bond-network entropy and observables such as smoothness of the vibrational density of states and macroscopic conductivity. We also show that the smoothing of the vibrational density of states encodes information about the thermal resistance induced by disorder and can be directly related to phenomenological models for phonon-disorder scattering based on the semiclassical Peierls-Boltzmann equation. Our findings rationalize the conductivity variations of disordered carbon polymorphs ranging from nanoporous electrodes to defective graphite used as a moderator in nuclear reactors.

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Research News

How Disorder Regulates Heat Flow

Published 22 January, 2026

A new theory linking atomic disorder to heat flow offers a strong foundation for predicting thermal conductivity in materials ranging from crystals to amorphous carbon.

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Popular Summary

Atomic structural disorder—such as defects, dislocations, and grain boundaries—strongly affects how heat flows through network solids used in energy technologies, including nanoporous carbon electrodes and graphite moderators. Yet, existing models of heat transport in disordered materials cannot fully explain how atomic structure relates to macroscopic conductivity in materials that are neither fully crystalline nor glassy. We address this long-standing challenge by developing a framework that directly links the degree of atomic disorder to the thermal conductivity of complex network solids.

To quantify disorder, we introduce a measure called bond-network entropy, which counts the number of distinct local atomic arrangements within a material’s bonding network. Using this descriptor together with the Wigner heat-transport equation, we establish clear connections between atomic-level disorder, patterns of atomic vibration, and the distances over which these vibrations relax. This combined approach allows us to extend the classic “phonon liquid” concept, originally proposed by Kittel, to describe how increasing disorder modifies the behavior of atomic vibrations and thereby the material’s ability to conduct heat.

Our results provide a unified understanding of how structural disorder governs thermal transport in systems that blend crystalline and glassy characteristics. This perspective offers practical guidance for designing materials with tailored heat conduction—such as advanced carbon electrodes, thermal insulators, and plasma-facing components in fusion reactors—by precisely tuning their internal atomic structures.

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Phys. Rev. X 15, 041041– Published 4 December, 2025
  • Received 27 December 2024
  • Accepted 22 October 2025
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