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Unified theory of thermal transport in crystals and glasses

Abstract

Crystals and glasses exhibit fundamentally different heat conduction mechanisms: the periodicity of crystals allows for the excitation of propagating vibrational waves that carry heat, as first discussed by Peierls, while in glasses the lack of periodicity breaks Peierls’s picture and heat is mainly carried by the coupling of vibrational modes, often described by a harmonic theory introduced by Allen and Feldman. Anharmonicity or disorder are thus the limiting factors for thermal conductivity in crystals or glasses. Hitherto, no transport equation has been able to account for both. Here, we derive such an equation, resulting in a thermal conductivity that reduces to the Peierls and Allen–Feldman limits, respectively, in anharmonic crystals or harmonic glasses, while also covering the intermediate regimes where both effects are relevant. This approach also solves the long-standing problem of accurately predicting the thermal properties of crystals with ultralow or glass-like thermal conductivity, as we show with an application to a thermoelectric material representative of this class.

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Fig. 1: Bulk thermal conductivity of CsPbBr3 as a function of temperature.
Fig. 2: Vibrational properties and heat conduction mechanisms in CsPbBr3.

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Data availability

Raw data were generated using the SCITAS High Performance Computing facility at the École Polytechnique Fédérale de Lausanne. Derived data supporting the findings of this study are available at https://doi.org/10.24435/materialscloud:2019.0001/v2.

Code availability

Quantum ESPRESSO is available at www.quantum-espresso.org; the scripts related to the computation of the third-order force constants using the finite-difference method are available at bitbucket.org/sousaw/thirdorder; the D3Q package for Quantum ESPRESSO is available at sourceforge.net/projects/d3q/. The custom code developed in this work will be made available in a next release of the D3Q package.

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Acknowledgements

This research was partially supported by the NCCR MARVEL, funded by the Swiss National Science Foundation.

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The project was conceived by all authors. M.S. performed the numerical calculations and prepared the figures with inputs from N.M. and F.M. All authors contributed to the editing of the manuscript.

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Correspondence to Francesco Mauri.

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Simoncelli, M., Marzari, N. & Mauri, F. Unified theory of thermal transport in crystals and glasses. Nat. Phys. 15, 809–813 (2019). https://doi.org/10.1038/s41567-019-0520-x

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