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Multiscale modeling for epitaxial growth. (English) Zbl 1105.82029

Sanz-Solé, Marta (ed.) et al., Proceedings of the international congress of mathematicians (ICM), Madrid, Spain, August 22–30, 2006. Volume III: Invited lectures. Zürich: European Mathematical Society (EMS) (ISBN 978-3-03719-022-7/hbk). 1419-1432 (2006).
Summary: Epitaxy is the growth of a thin film on a substrate in which the crystal properties of the film are inherited from those of the substrate. Because of the wide range of relevant length and time scales, multiscale mathematical models have been developed to describe epitaxial growth. This presentation describes atomistic, island dynamics and continuum models. Island dynamics models are multiscale models that use continuum coarse-graining in the lateral direction, but retain atomistic discreteness in the growth direction. Establishing connections between the various length and time scales in these models is a principal goal of mathematical materials science. Progress towards this goal is described here, including the derivation of surface diffusion, line tension and continuum equations from atomistic, kinetic models.
For the entire collection see [Zbl 1095.00006].

MSC:

82D25 Statistical mechanics of crystals
82C24 Interface problems; diffusion-limited aggregation in time-dependent statistical mechanics
82C28 Dynamic renormalization group methods applied to problems in time-dependent statistical mechanics
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