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• W3099813842 abstract "We study the continuum limit in 2+1 dimensions of nanoscale anisotropic diffusion processes on crystal surfaces relaxing to become flat below roughening. Our main result is a continuum law for the surface flux in terms of a new continuum-scale tensor mobility. The starting point is the Burton, Cabrera and Frank (BCF) theory, which offers a discrete scheme for atomic steps whose motion drives surface evolution. Our derivation is based on the separation of local space variables into fast and slow. The model includes: (i) anisotropic diffusion of adsorbed atoms (adatoms) on terraces separating steps; (ii) diffusion of atoms along step edges; and (iii) attachment–detachment of atoms at step edges. We derive a parabolic fourth-order nonlinear partial differential equation (PDE) for the continuum surface height profile. An ingredient of this PDE is the surface mobility for the adatom flux, which is a nontrivial extension of the tensor mobility for isotropic terrace diffusion derived previously by Margetis and Kohn (2006 Multisci. Model. Simul. 5 729–58). Approximate, separable solutions of the PDE are discussed." @default.
• W3099813842 created "2020-11-23" @default.
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• W3099813842 date "2008-05-20" @default.
• W3099813842 modified "2023-09-26" @default.
• W3099813842 title "Anisotropic diffusion in continuum relaxation of stepped crystal surfaces" @default.
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• W3099813842 doi "https://doi.org/10.1088/1751-8113/41/23/235004" @default.
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