期刊
PHILOSOPHICAL MAGAZINE
卷 97, 期 28, 页码 2514-2563出版社
TAYLOR & FRANCIS LTD
DOI: 10.1080/14786435.2017.1340685
关键词
Diffusion; lattice Green function; Onsager coefficients; mass transport
类别
资金
- U.S. Department of Energy, Office of Basic Energy Sciences, Division of Materials Sciences and Engineering through Frederick Seitz Materials Research Laboratory [DE-FG02-05ER46217]
- Office of Naval Research [N000141210752]
- National Science Foundation [1411106]
- National Science Foundation (NSF)
- Direct For Mathematical & Physical Scien
- Division Of Materials Research [1411106] Funding Source: National Science Foundation
A general solution for vacancy-mediated diffusion in the dilutevacancy/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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