A classification of the symmetries of uniform discrete defective crystals

Nicks, Rachel

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.

Citation

Nicks, R. (in press). A classification of the symmetries of uniform discrete defective crystals. Journal of Elasticity, 117(2), https://doi.org/10.1007/s10659-014-9470-9

• Journal Article Type: Article
• Acceptance Date: Jan 26, 2014
• Online Publication Date: Feb 18, 2014
• Deposit Date: Sep 1, 2016
• Publicly Available Date: Sep 1, 2016
• Journal: Journal of Elasticity
• Print ISSN: 0374-3535
• Electronic ISSN: 1573-2681
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 117
• Issue: 2
• DOI: https://doi.org/10.1007/s10659-014-9470-9
• Keywords: Crystals, Defects, Lie groups
• Public URL: https://nottingham-repository.worktribe.com/output/723091
• Publisher URL: http://link.springer.com/article/10.1007/s10659-014-9470-9
• Additional Information: The final publication is available at Springer via http://dx.doi.org/10.1007/s10659-014-9470-9