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A classification of the symmetries of uniform discrete defective crystals

Nicks, Rachel

Authors

Rachel Nicks rachel.nicks@nottingham.ac.uk



Abstract

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.

Journal Article Type Article
Journal Journal of Elasticity
Print ISSN 0374-3535
Electronic ISSN 1573-2681
Publisher Humana Press
Peer Reviewed Peer Reviewed
Volume 117
Issue 2
Institution Citation Nicks, R. (in press). A classification of the symmetries of uniform discrete defective crystals. Journal of Elasticity, 117(2), doi:10.1007/s10659-014-9470-9
DOI https://doi.org/10.1007/s10659-014-9470-9
Keywords Crystals, Defects, Lie groups
Publisher URL http://link.springer.com/article/10.1007/s10659-014-9470-9
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf
Additional Information The final publication is available at Springer via http://dx.doi.org/10.1007/s10659-014-9470-9

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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