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Nuclear quantum effect with pure anharmonicity and the anomalous thermal expansion of silicon

Kim, D. S. and Hellman, O. and Herriman, J. E. and Smith, H. L. and Lin, J. Y. Y. and Shulumba, N. and Niedziela, J. L. and Li, C. W. and Abernathy, D. L. and Fultz, B. (2018) Nuclear quantum effect with pure anharmonicity and the anomalous thermal expansion of silicon. Proceedings of the National Academy of Sciences of the United States of America, 115 (9). pp. 1992-1997. ISSN 0027-8424. PMCID PMC5834665.

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Despite the widespread use of silicon in modern technology, its peculiar thermal expansion is not well understood. Adapting harmonic phonons to the specific volume at temperature, the quasiharmonic approximation, has become accepted for simulating the thermal expansion, but has given ambiguous interpretations for microscopic mechanisms. To test atomistic mechanisms, we performed inelastic neutron scattering experiments from 100 K to 1,500 K on a single crystal of silicon to measure the changes in phonon frequencies. Our state-of-the-art ab initio calculations, which fully account for phonon anharmonicity and nuclear quantum effects, reproduced the measured shifts of individual phonons with temperature, whereas quasiharmonic shifts were mostly of the wrong sign. Surprisingly, the accepted quasiharmonic model was found to predict the thermal expansion owing to a large cancellation of contributions from individual phonons.

Item Type:Article
Related URLs:
URLURL TypeDescription CentralArticle Information
Kim, D. S.0000-0002-5707-2609
Hellman, O.0000-0002-3453-2975
Lin, J. Y. Y.0000-0001-9233-0100
Shulumba, N.0000-0002-2374-7487
Niedziela, J. L.0000-0002-2990-923X
Li, C. W.0000-0002-0758-5334
Abernathy, D. L.0000-0002-3533-003X
Fultz, B.0000-0002-6364-8782
Additional Information:© 2018 National Academy of Sciences. Published under the PNAS license. Edited by Alexi Maradudin, University of California, Irvine, CA and accepted by Editorial Board Member Zachary Fisk December 26, 2017 (received for review May 18, 2017). Published ahead of print February 13, 2018. The authors thank F. H. Saadi, A. Swaminathan, I. Papusha, and Y. Ding for assisting in sample preparation and discussions. Research at Oak Ridge National Laboratory’s Spallation Neutron Source (SNS) was sponsored by the Scientific User Facilities Division, Basic Energy Sciences (BES), Department of Energy (DOE). This work used resources from National Energy Research Scientific Computing Center (NERSC), a DOE Office of Science User Facility supported by the Office of Science of the US Department of Energy under Contract DE-AC02-05CH11231. Support from the Swedish Research Council Program 637-2013-7296 is also gratefully acknowledged. Supercomputer resources were provided by the Swedish National Infrastructure for Computing. This work was supported by the DOE Office of Science, BES, under Contract DE-FG02-03ER46055. Author contributions: D.S.K., H.L.S., and B.F. designed research; D.S.K., O.H., H.L.S., J.L.N., C.W.L., D.L.A., and B.F. performed research; D.S.K., O.H., J.H., N.S., J.L.N., C.W.L., D.L.A., and B.F. contributed new reagents/analytic tools; D.S.K., O.H., J.H., H.L.S., J.Y.Y.L., N.S., J.L.N., C.W.L., D.L.A., and B.F. analyzed data; and D.S.K., O.H., J.H., H.L.S., J.Y.Y.L., N.S., J.L.N., C.W.L., D.L.A., and B.F. wrote the paper. The authors declare no conflict of interest. This article is a PNAS Direct Submission. A.M. is a guest editor invited by the Editorial Board. This article contains supporting information online at
Funding AgencyGrant Number
Department of Energy (DOE)DE-AC02-05CH11231
Swedish Research Council637-2013-7296
Department of Energy (DOE)DE-FG02-03ER46055
Subject Keywords:thermal expansion; phonon anharmonicity; inelastic neutron scattering; nuclear quantum effects; silicon
Issue or Number:9
PubMed Central ID:PMC5834665
Record Number:CaltechAUTHORS:20180214-150839490
Persistent URL:
Official Citation:Anomalous thermal expansion in silicon revisited. D. S. Kim, O. Hellman, J. Herriman, H. L. Smith, J. Y. Y. Lin, N. Shulumba, J. L. Niedziela, C. W. Li, D. L. Abernathy, B. Fultz. Proceedings of the National Academy of Sciences Feb 2018, 115 (9) 1992-1997; DOI: 10.1073/pnas.1707745115
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:84836
Deposited By: Tony Diaz
Deposited On:15 Feb 2018 00:16
Last Modified:14 Apr 2020 20:12

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