Automatic numerical evaluation of vacancy-mediated transport for arbitrary crystals: Onsager coefficients in the dilute limit using a Green function approach |
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Authors: | Dallas R. Trinkle |
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Affiliation: | 1. Department of Materials Science and Engineering, University of Illinois, Urbana-Champaign, IL, USA.dtrinkle@illinois.edu |
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Abstract: | AbstractA general solution for vacancy-mediated diffusion in the dilute-vacancy/dilute-solute limit for arbitrary crystal structures is derived from the master equation. A general numerical approach to the vacancy lattice Green function reduces to the sum of a few analytic functions and numerical integration of a smooth function over the Brillouin zone for arbitrary crystals. The Dyson equation solves for the Green function in the presence of a solute with arbitrary but finite interaction range to compute the transport coefficients accurately, efficiently and automatically, including cases with very large differences in solute-vacancy exchange rates. The methodology takes advantage of the space group symmetry of a crystal to reduce the complexity of the matrix inversion in the Dyson equation. An open-source implementation of the algorithm is available, and numerical results are presented for the convergence of the integration error of the bare vacancy Green function, and tracer correlation factors for a variety of crystals including wurtzite (hexagonal diamond) and garnet. |
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Keywords: | Diffusion lattice Green function Onsager coefficients mass transport |
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