Free energies of interfaces from quasi-harmonic theory: A critical appraisal |
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Authors: | A Hairie F Hairie B Lebouvier G Nouet E Paumier N Ralantoson A P Sutton |
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Institution: | (1) LERMAT, URA CNRS 1317, ISMRA, 6 Bd du Marechal Juin, 14050 Caen Cedex, France;(2) Department of Materials, Oxford University, OX1 3PH, England |
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Abstract: | A critical assessment is given of the quasi-harmonic approximation, and various approximations to the quasi-harmonic approximation, with regard to predicting the free energy and atomic structure of grain boundaries in silicon at elevated temperatures. The quasi-harmonic results are compared with those obtained by molecular dynamics and thermodynamic integration. It is found that the quasi-harmonic approximation yields accurate excess free energies and atomic structures of grain boundaries at 1,000 K. The anharmonic contribution to the free energy that is absent in the quasi-harmonic contribution is virtually the same at a grain boundary in Si and in the perfect crystal. The second-moment and Einstein approximations to the full quasi-harmonic theory yield unreliable free energies, but reasonably accurate atomic structures. However, excess free energies are quite well described by the Einstein model. It is concluded that the quasi-harmonic approximation works remarkably well in silicon. The simplest approximations to the phonon density of states lead to unreliable results for the free energy, but cancellation of errors occurs to a large extent when excess free energies are computed. |
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Keywords: | Free energy grain boundaries in silicon thermodynamic properties computer simulation quasi-harmonic approximation anharmonicity |
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