Crystal Structure Determination: The Role of the Cosine Seminvariants

by Herbert A. Hauptman

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The central theme of this monograph is that the cosine seminvariants are the key to crystal structures. The cosine seminvariants are the cosines of those linear combinations of the phases (the so-called structure seminvariants) whose values, for a given functional form for the geometric structure factor, are uniquely determined by the crystal structure alone and are there- fore independent of the choice of permissible origin. It follows that the cosine seminvariants themselves are uniquely determined, in general, by the observed magnitudes of the normalized structure factors. The values of the cosine seminvariants in turn lead unambiguously to the values of the individual phases and thus to the crystal structure by means of the E-map (Fourier synthesis). It is this property of the cosine seminvariants, that they serve to link the observed magnitudes with the desired phases of the normalized structure factors, which accounts for their importance and explains the emphasis which is here placed on their role.
  • ISBN10 0306307030
  • ISBN13 9780306307034
  • Publish Date 8 September 1972
  • Publish Status Active
  • Out of Print 17 October 2003
  • Publish Country US
  • Publisher Springer Science+Business Media
  • Imprint Kluwer Academic/Plenum Publishers
  • Edition 1972 ed.
  • Format Hardcover
  • Pages 419
  • Language English