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Open AccessArticle

Non-Crystallographic Layer Lattice Restrictions in Order-Disorder (OD) Structures

Institute of Chemical Technologies and Analytics, Vienna University of Technology, Getreidemarkt 9/194-SC, Vienna 1060, Austria
Symmetry 2014, 6(3), 589-621; https://doi.org/10.3390/sym6030589
Received: 11 March 2014 / Revised: 27 June 2014 / Accepted: 3 July 2014 / Published: 21 July 2014
(This article belongs to the Special Issue Crystal Symmetry and Structure)
Symmetry operations of layers periodic in two dimensions restrict the geometry the lattice according to the five two-dimensional Bravais types of lattices. In order-disorder (OD) structures, the operations relating equivalent layers generally leave invariant only a sublattice of the layers. The thus resulting restrictions can be expressed in terms of linear relations of the a2, b2 and a · b scalar products of the lattice basis vectors with rational coefficients. To characterize OD families and to check their validity, these lattice restrictions are expressed in the bases of different layers and combined. For a more familiar notation, they can be expressed in terms of the lattice parameters a, b and . Alternatively, the description of the lattice restrictions may be simplified by using centered lattices. The representation of the lattice restrictions in terms of scalar products is dependent on the chosen basis. A basis-independent classification of the lattice restrictions is outlined. View Full-Text
Keywords: order-disorder theory; local symmetry; lattice order-disorder theory; local symmetry; lattice
MDPI and ACS Style

Stöger, B. Non-Crystallographic Layer Lattice Restrictions in Order-Disorder (OD) Structures. Symmetry 2014, 6, 589-621.

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