Direct Correlation Function of a Crystalline Solid

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2021
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Lin, Shang-Chun
Oettel, Martin
Kahl, Gerhard
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Physical Review Letters. American Physical Society (APS). 2021, 127(8), 085501. ISSN 0031-9007. eISSN 1079-7114. Available under: doi: 10.1103/PhysRevLett.127.085501
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Direct correlation functions (DCFs), linked to the second functional derivative of the free energy with respect to the one-particle density, play a fundamental role in a statistical mechanics description of matter. This holds, in particular, for the ordered phases: DCFs contain information about the local structure including defects and encode the thermodynamic properties of crystalline solids; they open a route to the elastic constants beyond low temperature expansions. Via a demanding numerical approach, we have explicitly calculated for the first time the DCF of a solid: based on the fundamental measure concept, we provide results for the DCF of a hard sphere crystal. We demonstrate that this function differs at coexistence significantly from its liquid counterpart—both in shape as well as in its order of magnitude—because it is dominated by vacancies. We provide evidence that the traditional use of liquid DCFs in functional Taylor expansions of the free energy is conceptually wrong and show that the emergent elastic constants are in good agreement with simulation-based results.

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ISO 690LIN, Shang-Chun, Martin OETTEL, Johannes M. HÄRING, Rudolf HAUSSMANN, Matthias FUCHS, Gerhard KAHL, 2021. Direct Correlation Function of a Crystalline Solid. In: Physical Review Letters. American Physical Society (APS). 2021, 127(8), 085501. ISSN 0031-9007. eISSN 1079-7114. Available under: doi: 10.1103/PhysRevLett.127.085501
BibTex
@article{Lin2021Direc-54811,
  year={2021},
  doi={10.1103/PhysRevLett.127.085501},
  title={Direct Correlation Function of a Crystalline Solid},
  number={8},
  volume={127},
  issn={0031-9007},
  journal={Physical Review Letters},
  author={Lin, Shang-Chun and Oettel, Martin and Häring, Johannes M. and Haussmann, Rudolf and Fuchs, Matthias and Kahl, Gerhard},
  note={Article Number: 085501}
}
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