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Duality in simple single atomic type crystal structures
Author(s) -
Ruhnow M.
Publication year - 2012
Publication title -
crystal research and technology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.377
H-Index - 64
eISSN - 1521-4079
pISSN - 0232-1300
DOI - 10.1002/crat.201100627
Subject(s) - delocalized electron , duality (order theory) , polyhedron , crystal (programming language) , connection (principal bundle) , simple (philosophy) , type (biology) , crystal structure , physics , basis (linear algebra) , dual (grammatical number) , chemistry , theoretical physics , crystallography , quantum mechanics , geometry , mathematics , combinatorics , computer science , art , ecology , philosophy , literature , epistemology , biology , programming language
Crystal structures can be interpreted as a systematic arrangement of atoms and interstices. Their spatial arrangement follows the duality principle. By using mathematical polyhedra it is possible to show an overall scheme in the simple crystal structures that is possibly hidden from view by the utilization of the hard‐sphere‐model or charge density distributions. In addition there is a dual connection between the shape of the atoms and the arrangement of these atoms (i.e. the crystal structure). Therefore, the shape is expected to control the arrangement, with some possible feedback from the arrangement on the shape. On the basis of the dual principle a connection can be recognized between some crystal structures. Allotrope transitions can also be explained by using this principle. Moreover, physical parameters which are connected to the crystal structure like atomic arrangement and E( k ) of delocalized electrons also follow the duality principle. Consequently, it is possible to conclude that duality represents a basic principle of the simple single atomic type crystal structures. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)