An Elementary Introduction to Direct Methods

  • H. Schenk
Part of the NATO ASI Series book series (NSSB, volume 274)


In a diffraction experiment intensities Ihkl are measured whereas Fhkl = |Fhkl|exp(i φhkl) are necessary to image the electron density. Now |Fhkl| can be calculated straightforward from Ihkl but the relative phases φhkl are lost in the experiment and cause the so called phase problem. Direct methods try to evaluate phases φhkl “directly” from the measured diffraction intensities Ihkl by using relationships among the phases, relationships, whose values are based on the intensities only. Roughly it can be stated that, since the crystal structure can be described by a limited number of parameters (the positions of the atoms) and since many more intensities can be measured, relationships among the structure factors Fhkl, and thus among the phases φhkl, must exist. Direct Methods identify and use these phase relationships to solve the phase problem.


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  1. Schenk, H. (1979). J. Chem. Ed. 56, 383.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • H. Schenk
    • 1
  1. 1.Laboratory for CrystallographyUniversity of AmsterdamAmsterdamThe Netherlands

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