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Phonon-Phonon Interactions in Strongly Bonded Solids: Selection Rules and Higher-Order Processes

Navaneetha K. Ravichandran and David Broido
Phys. Rev. X 10, 021063 – Published 18 June 2020
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Abstract

We show that the commonly used lowest-order theory of phonon-phonon interactions frequently fails to accurately describe the anharmonic phonon decay rates and thermal conductivity (κ), even among strongly bonded crystals. Applying a first-principles theory that includes both the lowest-order three-phonon and the higher-order four-phonon processes to 17 zinc blende semiconductors, we find that the lowest-order theory drastically overestimates the measured κ for many of these materials, while inclusion of four-phonon scattering gives significantly improved agreement with measurements. We identify new selection rules on three-phonon processes that help explain many of these failures in terms of anomalously weak anharmonic phonon decay rates predicted by the lowest-order theory competing with four-phonon processes. We also show that zinc blende compounds containing boron (B), carbon (C), or nitrogen (N) atoms have exceptionally weak four-phonon scattering, much weaker than in compounds that do not contain B, C, or N atoms. This new understanding helps explain the ultrahigh κ in several technologically important materials like cubic boron arsenide, boron phosphide, and silicon carbide. At the same time, it not only makes the possibility of achieving high κ in materials without B, C, or N atoms unlikely, but it also suggests that it may be necessary to include four-phonon processes in many future studies. Our work gives new insights into the nature of anharmonic processes in solids and demonstrates the broad importance of higher-order phonon-phonon interactions in assessing the thermal properties of materials.

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  • Received 9 November 2019
  • Revised 5 March 2020
  • Accepted 28 April 2020

DOI:https://doi.org/10.1103/PhysRevX.10.021063

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Navaneetha K. Ravichandran*

  • Department of Mechanical Engineering, Indian Institute of Science, Bangalore 560012, India

David Broido

  • Department of Physics, Boston College, Chestnut Hill, Massachusetts 02467, USA

  • *navaneeth@iisc.ac.in

Popular Summary

The frequencies of collisions between phonons—the elementary quanta of atomic vibrations—dictate phonon lifetimes as well as the intrinsic resistance to heat conduction in insulating crystals. For almost 100 years, approximations in which only three phonons collide have been assumed to be adequate, particularly for strongly bonded solids. Here, we show that the three-phonon collision approximation catastrophically fails to accurately describe the intrinsic phonon lifetimes and heat transport in many common strongly bonded zinc blende crystals. Instead, corrections involving collisions between four phonons are required to accurately match measured thermal conductivity data.

We show several ways in which hypothetical phonon frequency spectra can be engineered to make some three-phonon collisions vanish. Unusually small three-phonon collision rates found in some of the studied materials are explained by the proximity of their phonon frequency spectra to these hypothetical ones. In contrast, no such trends are found for four-phonon collisions, which instead show relatively uniform collision rates with the remarkable caveat that compounds containing boron, carbon, and nitrogen have much weaker four-phonon collision rates compared to the materials not containing these atomic species.

This work shows that failures of the three-phonon collision approximation are ubiquitous among the studied compounds. At the same time, the remarkably weak four-phonon collisions in compounds containing boron, carbon, and nitrogen help those materials retain high thermal conductivities. These insights into the interplay between three-phonon and four-phonon collisions give a fundamental understanding of phonon decay rates and thermal conduction in solids, and they inform computational schemes designed to interrogate these fundamental material properties.

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Vol. 10, Iss. 2 — April - June 2020

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