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Zeitschrift für Kristallographie - Crystalline Materials

Editor-in-Chief: Pöttgen, Rainer

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


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Volume 230, Issue 12

Issues

Coincidence indices of sublattices and coincidences of colorings

Manuel Joseph C. Loquias
  • Institute of Mathematics, University of the Philippines Diliman, C.P. Garcia Avenue, University of the Philippines Campus, Diliman, Quezon City, 1101, Philippines
  • Lehrstuhl für Mathematik und Statistik, Montanuniversität Leoben, Franz-Josef-Straße 18, A-8700 Leoben, Austria
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ Peter Zeiner
Published Online: 2015-12-01 | DOI: https://doi.org/10.1515/zkri-2015-1864

Abstract

Even though a lattice and its sublattices have the same group of coincidence isometries, the coincidence index of a coincidence isometry with respect to a lattice Λ1 and to a sublattice Λ2 may differ. Here, we examine the coloring of Λ1 induced by Λ2 to identify how the coincidence indices with respect to Λ1 and to Λ2 are related. This leads to a generalization of the notion of color symmetries of lattices to what we call color coincidences of lattices. Examples involving the cubic and hypercubic lattices are given to illustrate these ideas.

Keywords: coincidence index; coincidence site lattice; color coincidences; color symmetry

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About the article

Corresponding author: Peter Zeiner, Fakultät für Mathematik, Universität Bielefeld, Universitätsstraße 25, 33501, Germany, Tel.: +49-521-1064791, Fax: +49-521-1066481, E-mail:


Received: 2015-05-29

Accepted: 2015-11-12

Published Online: 2015-12-01

Published in Print: 2015-11-01


Citation Information: Zeitschrift für Kristallographie - Crystalline Materials, Volume 230, Issue 12, Pages 749–759, ISSN (Online) 2196-7105, ISSN (Print) 2194-4946, DOI: https://doi.org/10.1515/zkri-2015-1864.

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