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

Symmetry

关键词: order-disorder theory;    local symmetry;    lattice;   

DOI  :  10.3390/sym6030589

来源: mdpi

【 摘 要 】

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 γ. 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.

【 授权许可】

CC BY   
© 2014 by the authors; licensee MDPI, Basel, Switzerland