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Quantitative crystal structure descriptors from multiplicative congruential generators

Hornfeck, Wolfgang (2012) Quantitative crystal structure descriptors from multiplicative congruential generators. Acta Crystallographica Section A, A68 (2), pp. 167-180. DOI: 10.1107/S0108767311049853. ISSN 0108-7673.

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Official URL: http://journals.iucr.org/a/issues/2012/02/00/issconts.html

Abstract

Special types of number-theoretic relations, termed multiplicative congruential generators (MCGs), exhibit an intrinsic sublattice structure. This has considerable implications within the crystallographic realm, namely for the coordinate description of crystal structures for which MCGs allow for a concise way of encoding the numerical structural information. Thus, a conceptual framework is established, with some focus on layered superstructures, which proposes the use of MCGs as a tool for the quantitative description of crystal structures. The multiplicative congruential method eventually affords an algorithmic generation of three-dimensional crystal structures with a near-uniform distribution of atoms, whereas a linearization procedure facilitates their combinatorial enumeration and classification. The outlook for homometric structures and dual-space crystallography is given. Some generalizations and extensions are formulated in addition, revealing the connections of MCGs with geometric algebra, discrete dynamical systems (iterative maps), as well as certain quasicrystal approximants.

Document Type:Article
Title:Quantitative crystal structure descriptors from multiplicative congruential generators
Authors:
AuthorsInstitution or Email of Authors
Hornfeck, Wolfgangwolfgang.hornfeck@dlr.de
Date:12 January 2012
Journal or Publication Title:Acta Crystallographica Section A
Refereed publication:Yes
In SCOPUS:Yes
In ISI Web of Science:Yes
Volume:A68
DOI:10.1107/S0108767311049853
Page Range:pp. 167-180
ISSN:0108-7673
Status:Published
Keywords:Kristallstrukturen, Zahlentheorie, Strukturchemie
HGF - Research field:Aeronautics, Space and Transport (old)
HGF - Program:Space (old)
HGF - Program Themes:W FR - Forschung unter Weltraumbedingungen (old)
DLR - Research area:Space
DLR - Program:W FR - Forschung unter Weltraumbedingungen
DLR - Research theme (Project):W - Vorhaben Materialwissenschaftliche Forschung (old)
Location: Köln-Porz
Institutes and Institutions:Institute of Materials Physics in Space
Deposited By: Dr. Wolfgang Hornfeck
Deposited On:23 Feb 2012 13:05
Last Modified:07 Feb 2013 19:39

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