Automatic numerical evaluation of vacancy-mediated transport for arbitrary crystals: Onsager coefficients in the dilute limit using a Green function approach

摘要

A general solution for vacancy-mediated diffusion in thedilute-vacancy/dilute-solute limit for arbitrary crystal structures is derivedfrom the master equation. A general numerical approach to the vacancy latticeGreen function reduces to the sum of a few analytic functions and numericalintegration of a smooth function over the Brillouin zone for arbitrarycrystals. The Dyson equation solves for the Green function in the presence of asolute with arbitrary but finite interaction range to compute the transportcoefficients accurately, efficiently and automatically, including cases withvery large differences in solute-vacancy exchange rates. The methodology takesadvantage of the space group symmetry of a crystal to reduce the complexity ofthe matrix inversion in the Dyson equation. An open-source implementation ofthe algorithm is available, and numerical results are presented for theconvergence of the integration error of the bare vacancy Green function, andtracer correlation factors for a variety of crystals including wurtzite(hexagonal diamond) and garnet.