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On new settings in some centrosymmetric space groups: an apparently paradoxical situation

Published/Copyright: July 28, 2010
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Zeitschrift für Kristallographie - Crystalline Materials
From the journal Zeitschrift für Kristallographie - Crystalline Materials Volume 212 Issue 5

Abstract

In the crystal systems where two crystallographic axes are related by symmetry, there are certain centrosymmetric space groups which do not include a two-fold rotation that interchanges the two said axes and inverts the third, or, in rhombohedral cases, interchanges two and inverts all the three axes. When the set of atomic coordinates describing a structure with any one of such space groups is transformed by such a two-fold rotation, not present in the space group, a different set of coordinates, equally valid but unrelated to the first set by any operation of the space group, is obtained. Thus one is confronted with the apparently paradoxical situation that depending on the choice of the positive direction of a crystallographic axis, two different descriptions (four in certain cubic cases) may exist even for a centrosymmetric structure. Since such a situation is particularly confusing when isostructurality of crystals is investigated, it has been considered worthwhile to compile a list of all the centrosymmetric space groups where this complication may arise.

Published Online: 2010-7-28
Published in Print: 1997-5-1

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Articles in the same Issue

  1. Surface X-ray diffraction on clean and Cs-covered Ag(001)
  2. On the structure of mathematical expressions and crystals
  3. On new settings in some centrosymmetric space groups: an apparently paradoxical situation
  4. Towards the structure determination of proteins from the near edge anomalous dispersion of sulphur: a comparison of first results from trypsin with the known structure
  5. The crystal structures of the cryptates Ag(C222)X, X = ClO4−, NO3−, ClO3−, BrO3−, IO4−, ReO4−, BF4−, PF6−, AsF6−, and Na(C222)X, X = ClO4−, IO4−, ReO4−
  6. Crystal structure of three diaza-crowns-18
  7. The crystal structure and disorder in tetrapropylammonium tetrafluoroborate, (n-C3H7)4NBF4
  8. Crystal and molecular structure of unsubstituted and p-methoxy-substituted acetylbenzoylmethanatoboron difluoride
  9. Structure of 2,10 dichloro 6-(2,3 dimethylphenoxy) dibenzo [d,g] [1,3,6,2]dioxathiaphosphocin 6-sulphide
  10. Crystal structure of bis(triisopropylphosphin)dibromonickel(II), [Ni(Pi-(C3H7)3)2Br2]
  11. Crystal structure of bromo(tricarbonyl)(cyclopentadienyl) molybdenum(II), (C5H5)Mo(CO)3Br
  12. Crystal structure of metaclopromide tetrathiocyanatocobaltate, C28H44O4N6Cl2 · [Co(NCS)4]
  13. Crystal structure of 4-cyanophenyl 4-heptylbenzoate, H3C(CH2)6(C6H4)O(CO)(C6H4)CN
  14. Crystal structure of N-p-methoxybenzylidene p-phenylazoaniline, HCO(C6H4)CN(C6H4)NN(C6H5)
  15. Crystal structure of 2-chlorophenol morpholino complex, (C6H4OCl)2(C4H10ON)
  16. Crystal structure of lignocaine tetrabromozincate, (C14H22ON2)4(ZnBr4)2
  17. Crystal structure of 1:2;7:8-dibenzo-3,6,15,18-tetraaza-tricyclo[13.3.0.02,6] octadeca-1(18),2,4,10,16-pentaene-8,12-diyne, C22H14N4
  18. Crystal structure of 11:12-benzo-13:14-naphtho-1,10-diazabicyclo[8.2.2] tetradeca-5,11,13-triene-3,7-diyne dichloromethane solvate, C22H14N4 · CH2Cl2
  19. Crystal structure of 5-(3,5-di-tert-butyl-4-hydroxybenzyl)-1,3,5-tri-tert-butyl-2-oxo-bicyclo[4.1.0]hept-3-ene, C34H54O2
  20. Biokompatible Werkstoffe und Bauweisen. Implantate für Medizin und Umwelt
  21. Grundlagen der Festkörperphysik
  22. Crystallography
  23. Quasicrystals and Geometry
  24. Tables of Physical and Chemical Constants
  25. Praktische Physik
https://doi.org/10.1524/zkri.1997.212.5.347

Articles in the same Issue

  1. Surface X-ray diffraction on clean and Cs-covered Ag(001)
  2. On the structure of mathematical expressions and crystals
  3. On new settings in some centrosymmetric space groups: an apparently paradoxical situation
  4. Towards the structure determination of proteins from the near edge anomalous dispersion of sulphur: a comparison of first results from trypsin with the known structure
  5. The crystal structures of the cryptates Ag(C222)X, X = ClO4−, NO3−, ClO3−, BrO3−, IO4−, ReO4−, BF4−, PF6−, AsF6−, and Na(C222)X, X = ClO4−, IO4−, ReO4−
  6. Crystal structure of three diaza-crowns-18
  7. The crystal structure and disorder in tetrapropylammonium tetrafluoroborate, (n-C3H7)4NBF4
  8. Crystal and molecular structure of unsubstituted and p-methoxy-substituted acetylbenzoylmethanatoboron difluoride
  9. Structure of 2,10 dichloro 6-(2,3 dimethylphenoxy) dibenzo [d,g] [1,3,6,2]dioxathiaphosphocin 6-sulphide
  10. Crystal structure of bis(triisopropylphosphin)dibromonickel(II), [Ni(Pi-(C3H7)3)2Br2]
  11. Crystal structure of bromo(tricarbonyl)(cyclopentadienyl) molybdenum(II), (C5H5)Mo(CO)3Br
  12. Crystal structure of metaclopromide tetrathiocyanatocobaltate, C28H44O4N6Cl2 · [Co(NCS)4]
  13. Crystal structure of 4-cyanophenyl 4-heptylbenzoate, H3C(CH2)6(C6H4)O(CO)(C6H4)CN
  14. Crystal structure of N-p-methoxybenzylidene p-phenylazoaniline, HCO(C6H4)CN(C6H4)NN(C6H5)
  15. Crystal structure of 2-chlorophenol morpholino complex, (C6H4OCl)2(C4H10ON)
  16. Crystal structure of lignocaine tetrabromozincate, (C14H22ON2)4(ZnBr4)2
  17. Crystal structure of 1:2;7:8-dibenzo-3,6,15,18-tetraaza-tricyclo[13.3.0.02,6] octadeca-1(18),2,4,10,16-pentaene-8,12-diyne, C22H14N4
  18. Crystal structure of 11:12-benzo-13:14-naphtho-1,10-diazabicyclo[8.2.2] tetradeca-5,11,13-triene-3,7-diyne dichloromethane solvate, C22H14N4 · CH2Cl2
  19. Crystal structure of 5-(3,5-di-tert-butyl-4-hydroxybenzyl)-1,3,5-tri-tert-butyl-2-oxo-bicyclo[4.1.0]hept-3-ene, C34H54O2
  20. Biokompatible Werkstoffe und Bauweisen. Implantate für Medizin und Umwelt
  21. Grundlagen der Festkörperphysik
  22. Crystallography
  23. Quasicrystals and Geometry
  24. Tables of Physical and Chemical Constants
  25. Praktische Physik
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