Coordination sequences and coordination waves in matter

A possible way of partitioning a space into polycubes (n-dimensional modifications of Golomb polyominoes, which are generally nonconvex) is used as a basic model of ordered matter structure. It is suggested that layer-by-layer growth of a structure, occurring along the geodetics of the digraph of a...

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Bibliographic Details
Published in:Crystallography reports 2006-01, Vol.51 (1), p.2-10
Main Authors: Rau, V. G., Pugaev, A. A., Rau, T. F.
Format: Article
Language:English
Subjects:
CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY
CRYSTAL GROWTH
CRYSTAL MODELS
CRYSTAL STRUCTURE
LAYERS
MATTER
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Summary:A possible way of partitioning a space into polycubes (n-dimensional modifications of Golomb polyominoes, which are generally nonconvex) is used as a basic model of ordered matter structure. It is suggested that layer-by-layer growth of a structure, occurring along the geodetics of the digraph of a net defined by the local rules of bonding of polycubes, justifies the phenomenological laws of shaping (self-similarity during the growth, independence of the polyhedron shape on the 'seed,' the symmetry of the growth polyhedron, etc.). Specific results of the analysis of number sequences of the increase in coordination circles for planar periodic partitions of model and real crystal structures, as well as the preliminary results of investigation of standing coordination topological waves, revealed for the first time in computer experiments, are reported.
ISSN:1063-7745
1562-689X
DOI:10.1134/S1063774506010020