DOI: 10.5176/2251-1911_CMCGS15.42
Authors: Mikhail M. Bouniaev and Nikolai P. Dolbilin
Abstract: The main goal of the local theory for crystals developed in the last quarter of the 20th century by Delone (Delaunay) and a group of researchers associated with him is to develop a methodology to determine a crystalline structure from the pair-wise identity of local arrangements around each atom. In this presentation we review some history and development of the local theory. This review was sparked by a recent interest in the local theory from crystallographers in the context of non-classical approach to crystallization as an attachment of primary clusters or nanoparticles, and modeling the process by finite automata.
Keywords: Crystalline Structures; Delone Set; Regular Point Set; Crystal; Local Theory
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