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Symmetry Description of OD Crystal Structures in Group Theoretical Terms

OD structures of layers are the geometric models of a certain class of crystal structures – so-called polytypes – with local order and generally global disorder. The set of all partial and total symmetry operations of an OD structure does not form a space group, but a groupoid. Here a group-theoreti... Full description

Journal Title: Acta Applicandae Mathematica 1998, Vol.52(1), pp.261-269
Main Author: Grell, Juliana
Format: Electronic Article Electronic Article
Language: English
Subjects:
Quelle: Springer Science & Business Media B.V.
ID: ISSN: 0167-8019 ; E-ISSN: 1572-9036 ; DOI: 10.1023/A:1005939931744
Link: http://dx.doi.org/10.1023/A:1005939931744
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recordid: springer_jour1005939931744
title: Symmetry Description of OD Crystal Structures in Group Theoretical Terms
format: Article
creator:
  • Grell, Juliana
subjects:
  • symmetry groups and groupoids
  • double cosets
  • aperiodic crystal structures
  • OD structures
  • polytypes
ispartof: Acta Applicandae Mathematica, 1998, Vol.52(1), pp.261-269
description: OD structures of layers are the geometric models of a certain class of crystal structures – so-called polytypes – with local order and generally global disorder. The set of all partial and total symmetry operations of an OD structure does not form a space group, but a groupoid. Here a group-theoretical ansatz is made for an OD symmetry description showing the relation between the set of symmetry operations of an OD structure and some symmetry groups which is based on considerations of cosets and double cosets with respect to the symmetry groups of certain periodic parts of the structure.
language: eng
source: Springer Science & Business Media B.V.
identifier: ISSN: 0167-8019 ; E-ISSN: 1572-9036 ; DOI: 10.1023/A:1005939931744
fulltext: fulltext
issn:
  • 1572-9036
  • 15729036
  • 0167-8019
  • 01678019
url: Link


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subjectsymmetry groups and groupoids ; double cosets ; aperiodic crystal structures ; OD structures ; polytypes
descriptionOD structures of layers are the geometric models of a certain class of crystal structures – so-called polytypes – with local order and generally global disorder. The set of all partial and total symmetry operations of an OD structure does not form a space group, but a groupoid. Here a group-theoretical ansatz is made for an OD symmetry description showing the relation between the set of symmetry operations of an OD structure and some symmetry groups which is based on considerations of cosets and double cosets with respect to the symmetry groups of certain periodic parts of the structure.
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titleSymmetry Description of OD Crystal Structures in Group Theoretical Terms
descriptionOD structures of layers are the geometric models of a certain class of crystal structures – so-called polytypes – with local order and generally global disorder. The set of all partial and total symmetry operations of an OD structure does not form a space group, but a groupoid. Here a group-theoretical ansatz is made for an OD symmetry description showing the relation between the set of symmetry operations of an OD structure and some symmetry groups which is based on considerations of cosets and double cosets with respect to the symmetry groups of certain periodic parts of the structure.
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abstractOD structures of layers are the geometric models of a certain class of crystal structures – so-called polytypes – with local order and generally global disorder. The set of all partial and total symmetry operations of an OD structure does not form a space group, but a groupoid. Here a group-theoretical ansatz is made for an OD symmetry description showing the relation between the set of symmetry operations of an OD structure and some symmetry groups which is based on considerations of cosets and double cosets with respect to the symmetry groups of certain periodic parts of the structure.
copDordrecht
pubKluwer Academic Publishers
doi10.1023/A:1005939931744
pages261-269
date1998-07