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The use of periodic graphs for representing and analysing crystal structures

  • Hans-Joachim Klein
Published/Copyright: July 16, 2012
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Zeitschrift für Kristallographie - Crystalline Materials
From the journal Zeitschrift für Kristallographie - Crystalline Materials Volume 227 Issue 8

Abstract

Several graph forms are discussed which are suited for modelling crystal structures at different levels of detail. Graphs with nodes representing atoms or special views of coordination polyhedra and edges representing bonds or different forms of connections between polyhedra are considered. Space-group symmetries are used to fold infinite graphs to finite representations which allow to develop algorithms for computing properties of structures effectively. Some applications are presented which demonstrate the usage of the graph forms.

Keywords: Periodic graphs; Minimal representation; Polyhedra graphs; Substructure search
* Correspondence address: Universität Kiel, Institut für Informatik, Hermann-Rodewald-Straße 3, 24118 Kiel, Deutschland,
Published Online: 2012-07-16
Published in Print: 2012-08

© by Oldenbourg Wissenschaftsverlag, München, Germany

Articles in the same Issue

  1. Elastic stiffness coefficients of thenardite and their pressure and temperature dependence
  2. Compressibility of microporous materials with CHA topology: 2. ALPO-34
  3. A Detailed Study of the Dehydration Process in Synthetic Strelkinite, Na[(UO2)(VO4)] · nH2O (n = 0, 1, 2)
  4. Mixed-ligand coordination of the (UO2)2+ cation and apophyllite topology of uranyl chlorochromate layer in the structure of ((CH3)2CHNH3)[(UO2)(CrO4)Cl(H2O)]
  5. Synthesis, crystal structure and optical properties of the catena-metaphosphates Ce(PO3)4 and U(PO3)4
  6. The Solid Solution CeAgxZn11–x (x ≤ 2.5)
  7. Ruthenate-ferrites AMRu5O11 (A = Sr, Ba; M = Ni, Zn): Distortion of kagome nets via metal–metal bonding
  8. A Mixed Valent Thioantimonate(III,V): [SbS3]3– and [SbS4]3– as bidentate ligands: Solvothermal synthesis and crystal structure of {Mn(dien)2}2[MnSb2S7]
  9. Hydrates of the Alkali Trioxidomonosulfidomolybdates and -tungstates: K2[(Mo/W)O3S] · 1.5H2O and (Rb/Cs)2[(Mo/W)O3S] · H2O
  10. Crystal structure of 1,4-diazoniabicyclo[2.2.2]octane diiodide monohydrate
  11. Derivation of bond-valence parameters for some cation-oxygen pairs on the basis of empirical relationships between ro and b
  12. The role of the Pb2+ lone electron pair for bond valence sum analysis in mullite-type PbMBO4 (M = Al, Mn and Fe) compounds
  13. The role of lone pairs in the ferroelastic phase transition in the palmierite-type lead phosphate-arsenate solid solution
  14. The role of H2O in controlling bond topology:I. The [6]Mg(SO4)(H2O)n (n = 0–11) structures
  15. Towards systematics of calcite biocrystals: insight from the inside
  16. The use of periodic graphs for representing and analysing crystal structures
  17. Book Review
https://doi.org/10.1524/zkri.2012.1494
Keywords for this article
Periodic graphs; Minimal representation; Polyhedra graphs; Substructure search

Articles in the same Issue

  1. Elastic stiffness coefficients of thenardite and their pressure and temperature dependence
  2. Compressibility of microporous materials with CHA topology: 2. ALPO-34
  3. A Detailed Study of the Dehydration Process in Synthetic Strelkinite, Na[(UO2)(VO4)] · nH2O (n = 0, 1, 2)
  4. Mixed-ligand coordination of the (UO2)2+ cation and apophyllite topology of uranyl chlorochromate layer in the structure of ((CH3)2CHNH3)[(UO2)(CrO4)Cl(H2O)]
  5. Synthesis, crystal structure and optical properties of the catena-metaphosphates Ce(PO3)4 and U(PO3)4
  6. The Solid Solution CeAgxZn11–x (x ≤ 2.5)
  7. Ruthenate-ferrites AMRu5O11 (A = Sr, Ba; M = Ni, Zn): Distortion of kagome nets via metal–metal bonding
  8. A Mixed Valent Thioantimonate(III,V): [SbS3]3– and [SbS4]3– as bidentate ligands: Solvothermal synthesis and crystal structure of {Mn(dien)2}2[MnSb2S7]
  9. Hydrates of the Alkali Trioxidomonosulfidomolybdates and -tungstates: K2[(Mo/W)O3S] · 1.5H2O and (Rb/Cs)2[(Mo/W)O3S] · H2O
  10. Crystal structure of 1,4-diazoniabicyclo[2.2.2]octane diiodide monohydrate
  11. Derivation of bond-valence parameters for some cation-oxygen pairs on the basis of empirical relationships between ro and b
  12. The role of the Pb2+ lone electron pair for bond valence sum analysis in mullite-type PbMBO4 (M = Al, Mn and Fe) compounds
  13. The role of lone pairs in the ferroelastic phase transition in the palmierite-type lead phosphate-arsenate solid solution
  14. The role of H2O in controlling bond topology:I. The [6]Mg(SO4)(H2O)n (n = 0–11) structures
  15. Towards systematics of calcite biocrystals: insight from the inside
  16. The use of periodic graphs for representing and analysing crystal structures
  17. Book Review
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