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

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

doi:10.1073/pnas.1707745115

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

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

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74 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	1992-1997
Number of pages	6
Journal	Proceedings of the National Academy of Sciences of the United States of America
Volume	115
Issue number	9
DOIs	https://doi.org/10.1073/pnas.1707745115
State	Published - Feb 27 2018

Funding

ACKNOWLEDGMENTS. 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. 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.

Keywords

Inelastic neutron scattering
Nuclear quantum effects
Phonon anharmonicity
Silicon
Thermal expansion

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Kim, D. S., Hellman, O., Herriman, J., Smith, H. L., Lin, J. Y. Y., Shulumba, N., Niedziela, J. L., Li, C. W., Abernathy, D. L., & 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), 1992-1997. https://doi.org/10.1073/pnas.1707745115

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Kim, DS, Hellman, O, Herriman, J, Smith, HL, Lin, JYY, Shulumba, N, Niedziela, JL, Li, CW, Abernathy, DL & 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, vol. 115, no. 9, pp. 1992-1997. https://doi.org/10.1073/pnas.1707745115

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AU - Kim, D. S.

AU - Hellman, O.

AU - Herriman, J.

AU - Smith, H. L.

AU - Lin, J. Y.Y.

AU - Shulumba, N.

AU - Niedziela, J. L.

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AU - Fultz, B.

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AB - 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.

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KW - Nuclear quantum effects

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

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