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Zeitschrift für Kristallographie - Crystalline Materials

Editor-in-Chief: Pöttgen, Rainer

Hrsg. v. Antipov, Evgeny / Boldyreva, Elena V. / Friese, Karen / Huppertz, Hubert / Jahn, Sandro / Tiekink, E. R. T.

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Band 234, Heft 5


Coordination sequences and layer-by-layer growth of periodic structures

Anton Shutov / Andrey Maleev
Online erschienen: 20.12.2018 | DOI: https://doi.org/10.1515/zkri-2018-2144


A new approach to the problem of coordination sequences of periodic structures is proposed. It is based on the concept of layer-by-layer growth and on the study of geodesics in periodic graphs. We represent coordination numbers as sums of so called sector coordination numbers arising from the growth polygon of the graph. In each sector we obtain a canonical form of the geodesic chains and reduce the calculation of the sector coordination numbers to solution of the linear Diophantine equations. The approach is illustrated by the example of the 2-homogeneous kra graph. We obtain three alternative descriptions of the coordination sequences: explicit formulas, generating functions and recurrent relations.

Keywords: coordination sequences; 2-homogeneous graphs; layer-by-layer growth; periodic structures


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Erhalten: 31.10.2018

Angenommen: 23.11.2018

Online erschienen: 20.12.2018

Erschienen im Druck: 27.05.2019

Quellenangabe: Zeitschrift für Kristallographie - Crystalline Materials, Band 234, Heft 5, Seiten 291–299, ISSN (Online) 2196-7105, ISSN (Print) 2194-4946, DOI: https://doi.org/10.1515/zkri-2018-2144.

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