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Thermodynamic Limit of Crystal Defects with Finite Temperature Tight Binding

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Abstract

We consider a tight binding model for localised crystalline defects with electrons in the canonical ensemble (finite Fermi temperature) and nuclei positions relaxed according to the Born–Oppenheimer approximation. We prove that the limit model as the computational domain size grows to infinity is formulated in the grand-canonical ensemble for the electrons. The Fermi-level for the limit model is fixed at a homogeneous crystal level, independent of the defect or electron number in the sequence of finite-domain approximations. We quantify the rates of convergence for the nuclei configuration and for the Fermi-level.

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Authors and Affiliations

  1. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China

    Huajie Chen

  2. Departments of Mathematics, Physics and Chemistry, Duke University, Box 90320, Durham, NC, 27708, USA

    Jianfeng Lu

  3. Mathematics Institute, University of Warwick, Coventry, CV47AL, UK

    Christoph Ortner

Authors
  1. Huajie Chen
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  2. Jianfeng Lu
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  3. Christoph Ortner
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Corresponding author

Correspondence to Huajie Chen.

Additional information

Communicated by G. Friesecke

Huajie Chen’s work was partially supported by the Fundamental Research Funds for the Central Universities, China under Grant 2017EYT22. Jianfeng Lu’s work was supported in part by the National Science Foundation under Grants DMS-1312659 and DMS-1454939. Christoph Ortner’s work was supported by ERC Starting Grant 335120.

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Chen, H., Lu, J. & Ortner, C. Thermodynamic Limit of Crystal Defects with Finite Temperature Tight Binding. Arch Rational Mech Anal 230, 701–733 (2018). https://doi.org/10.1007/s00205-018-1256-y

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  • DOI: https://doi.org/10.1007/s00205-018-1256-y

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