Crystallographic topology and its applications

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Geometric topology and structural crystallography concepts are combined to define a new area we call Structural Crystallographic Topology, which may be of interest to both crystallographers and mathematicians. In this paper, we represent crystallographic symmetry groups by orbifolds and crystal structures by Morse - functions. The Morse function uses mildly overlapping Gaussian thermal-motion probability density functions centered on atomic sites to form a critical net with peak, pass, pale, and pit critical points joined into a graph by density gradient-flow separatrices. Critical net crystal structure drawings can be made with the ORTEP-III graphics pro- An orbifold consists of an underlying ... continued below

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25 p.

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Johnson, C.K.; Burnett, M.N. & Dunbar, W.D. October 1, 1996.

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Description

Geometric topology and structural crystallography concepts are combined to define a new area we call Structural Crystallographic Topology, which may be of interest to both crystallographers and mathematicians. In this paper, we represent crystallographic symmetry groups by orbifolds and crystal structures by Morse - functions. The Morse function uses mildly overlapping Gaussian thermal-motion probability density functions centered on atomic sites to form a critical net with peak, pass, pale, and pit critical points joined into a graph by density gradient-flow separatrices. Critical net crystal structure drawings can be made with the ORTEP-III graphics pro- An orbifold consists of an underlying topological space with an embedded singular set that represents the Wyckoff sites of the crystallographic group. An orbifold for a point group, plane group, or space group is derived by gluing together equivalent edges or faces of a crystallographic asymmetric unit. The critical-net-on-orbifold model incorporates the classical invariant lattice complexes of crystallography and allows concise quotient-space topological illustrations to be drawn without the repetition that is characteristic of normal crystal structure drawings.

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25 p.

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OSTI as DE96014610

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  • 17. congress and general assembly of the International Union of Crystallography (IUCr), Seattle, WA (United States), 8-17 Aug 1996

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  • Other: DE96014610
  • Report No.: CONF-960883--1
  • Grant Number: AC05-96OR22464
  • Office of Scientific & Technical Information Report Number: 392732
  • Archival Resource Key: ark:/67531/metadc675925

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  • October 1, 1996

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  • July 25, 2015, 2:20 a.m.

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  • Jan. 25, 2016, 12:09 p.m.

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Johnson, C.K.; Burnett, M.N. & Dunbar, W.D. Crystallographic topology and its applications, article, October 1, 1996; Tennessee. (digital.library.unt.edu/ark:/67531/metadc675925/: accessed September 25, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.