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dc.contributor.advisor Kuhs, Werner F. Prof. Dr.
dc.contributor.author Beukemann, Alexander
dc.date.accessioned 2015-03-06T13:03:34Z
dc.date.available 2015-03-06T13:03:34Z
dc.date.issued 2015-03-06
dc.identifier.uri http://hdl.handle.net/11858/00-1735-0000-0022-5DE7-F
dc.language.iso deu de
dc.rights.uri http://creativecommons.org/licenses/by-nc-nd/3.0/
dc.subject.ddc 910 de
dc.subject.ddc 550 de
dc.title Analyse der vierperiodischen Minimalnetze de
dc.type doctoralThesis de
dc.title.translated Analysis of 4-periodic minimal nets de
dc.contributor.referee Scheitler, Gerhard Prof. Dr.
dc.date.examination 2015-02-11
dc.description.abstracteng Periodic structures – e. g. crystal structures – are analyzed by means of group theory. The concept of a crystal structure is extendable to the n-dimensional space and the 4-dimensional space groups are known [Brown, Bülow, Neubüser, Wondratscheck, Zassenhaus, 1978]. As quasi-periodic and incommensurate structures can be the result of a projection of a higher - periodic structure, it is also worth to enhance the knowledge about higher-periodic structures by graph theoretical means. Thereby the atoms of a crystal can be assigned to the vertices, and the chemical bonds to the edges of a graph being a periodic net. Minimal nets [Beukemann, Klee, 1992] are nets, where the deletion of any edge together with and its translational equivalent edges results in a structure that is no longer connected. It’s special about a minimal net to have a 1:1 relation to its quotient graph [Chung, Hahn, Klee, 1984] that represents the topology of the net by a finite graph, presenting the adjacency relations between the classes of translational equivalent vertices and edges of the periodic net. 3-periodic minimal nets are analyzed by several authors such as Bonneau, Delgado-Friedrichs, O’Keeffe, Yaghi, Eon. Now the complete class of 4-periodic minimal nets (111 nets) is analyzed by comparing their substructures such as trees, chains, cycles and sub-networks. Net to subnet relations are identified and methods for net conversions are proposed. Different principles for the construction of those structures are applied. The embedding of two nets is discussed in detail. Single cycles of the minimal net 6(3)1 – number 1 of minimal nets with 6 classes of vertices and vertex degree 3 (quotient graph K3,3) – where mapped to polygons of a Penrose pattern. The minimal net 3(4)1 could be embedded into the 4-dimensional space by a “symmetric labelling” of the edges of its quotient graph. A reference work with graphics and cycle class sequences of all 2-, 3- and 4-periodic minimal nets is attached. de
dc.contributor.coReferee Sowa, Heidrun Prof. Dr.
dc.subject.ger Periodische Strukturen de
dc.subject.ger Quotientengraph de
dc.subject.ger Minimalnetz de
dc.subject.ger Kreisklassen de
dc.subject.ger Periodische Netze de
dc.subject.ger Referenz de
dc.subject.ger 2-periodische Minimalnetze de
dc.subject.ger 3-periodische Minimalnetze de
dc.subject.ger 4-periodische Minimalnetze de
dc.subject.eng Periodic structures de
dc.subject.eng quotient graph de
dc.subject.eng minimal nets de
dc.subject.eng cycle classes de
dc.subject.eng periodic nets de
dc.subject.eng reference de
dc.subject.eng 2-periodic minimal nets de
dc.subject.eng 3-periodic minimal nets de
dc.subject.eng 4-periodic minimal nets de
dc.identifier.urn urn:nbn:de:gbv:7-11858/00-1735-0000-0022-5DE7-F-9
dc.affiliation.institute Fakultät für Geowissenschaften und Geographie de
dc.subject.gokfull Geologische Wissenschaften (PPN62504584X) de
dc.identifier.ppn 819684147

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