A classification of the symmetries of uniform discrete defective crystals

Crystals which have a uniform distribution of defects are endowed with a Lie group description which allows one to construct an associated discrete structure. These structures are in fact the discrete subgroups of the ambient Lie group. The geometrical symmetries of these structures can be computed...

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Main Author:	Nicks, Rachel
Format:	Article
Language:	English
Published:	Springer 2014
Online Access:	http://eprints.nottingham.ac.uk/36153/ http://eprints.nottingham.ac.uk/36153/ http://eprints.nottingham.ac.uk/36153/ http://eprints.nottingham.ac.uk/36153/1/1310.0324v1.pdf

id	nottingham-36153
recordtype	eprints
spelling	nottingham-361532017-10-14T16:43:17Z http://eprints.nottingham.ac.uk/36153/ A classification of the symmetries of uniform discrete defective crystals Nicks, Rachel Crystals which have a uniform distribution of defects are endowed with a Lie group description which allows one to construct an associated discrete structure. These structures are in fact the discrete subgroups of the ambient Lie group. The geometrical symmetries of these structures can be computed in terms of the changes of generators of the discrete subgroup which preserve the discrete set of points. Here a classification of the symmetries for the discrete subgroups of a particular class of three-dimensional solvable Lie group is presented. It is a fact that there are only three mathematically distinct types of Lie groups which model uniform defective crystals, and the calculations given here complete the discussion of the symmetries of the corresponding discrete structures. We show that those symmetries corresponding to automorphisms of the discrete subgroups extend uniquely to symmetries of the ambient Lie group and we regard these symmetries as (restrictions of) elastic deformations of the continuous defective crystal. Other symmetries of the discrete structures are classified as ‘inelastic’ symmetries. Springer 2014-02-18 Article PeerReviewed application/pdf en http://eprints.nottingham.ac.uk/36153/1/1310.0324v1.pdf Nicks, Rachel (2014) A classification of the symmetries of uniform discrete defective crystals. Journal of Elasticity, 117 (2). pp. 189-211. ISSN 1573-2681 http://link.springer.com/article/10.1007/s10659-014-9470-9 doi:10.1007/s10659-014-9470-9 doi:10.1007/s10659-014-9470-9
repository_type	Digital Repository
institution_category	Local University
institution	University of Nottingham Malaysia Campus
building	Nottingham Research Data Repository
collection	Online Access
language	English
description	Crystals which have a uniform distribution of defects are endowed with a Lie group description which allows one to construct an associated discrete structure. These structures are in fact the discrete subgroups of the ambient Lie group. The geometrical symmetries of these structures can be computed in terms of the changes of generators of the discrete subgroup which preserve the discrete set of points. Here a classification of the symmetries for the discrete subgroups of a particular class of three-dimensional solvable Lie group is presented. It is a fact that there are only three mathematically distinct types of Lie groups which model uniform defective crystals, and the calculations given here complete the discussion of the symmetries of the corresponding discrete structures. We show that those symmetries corresponding to automorphisms of the discrete subgroups extend uniquely to symmetries of the ambient Lie group and we regard these symmetries as (restrictions of) elastic deformations of the continuous defective crystal. Other symmetries of the discrete structures are classified as ‘inelastic’ symmetries.
format	Article
author	Nicks, Rachel
spellingShingle	Nicks, Rachel A classification of the symmetries of uniform discrete defective crystals
author_facet	Nicks, Rachel
author_sort	Nicks, Rachel
title	A classification of the symmetries of uniform discrete defective crystals
title_short	A classification of the symmetries of uniform discrete defective crystals
title_full	A classification of the symmetries of uniform discrete defective crystals
title_fullStr	A classification of the symmetries of uniform discrete defective crystals
title_full_unstemmed	A classification of the symmetries of uniform discrete defective crystals
title_sort	classification of the symmetries of uniform discrete defective crystals
publisher	Springer
publishDate	2014
url	http://eprints.nottingham.ac.uk/36153/ http://eprints.nottingham.ac.uk/36153/ http://eprints.nottingham.ac.uk/36153/ http://eprints.nottingham.ac.uk/36153/1/1310.0324v1.pdf
first_indexed	2018-09-06T12:40:23Z
last_indexed	2018-09-06T12:40:23Z
_version_	1610861902823424000

A classification of the symmetries of uniform discrete defective crystals

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