Friedel- and Bijvoet-pair techniques

Creagh, D. C.

doi:10.1107/97809553602060000592

International
Tables for
Crystallography
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

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International Tables for Crystallography (2006). Vol. C. ch. 4.2, p. 251

Section 4.2.6.3.2.2. Friedel- and Bijvoet-pair techniques

D. C. Creagh^b

4.2.6.3.2.2. Friedel- and Bijvoet-pair techniques

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The Bijvoet-pair technique (Bijvoet et al., 1951) is used extensively by crystallographers to assist in the resolution of the phase problem in the solution of crystal structures. Measurements of as many as several hundred values for the diffracted intensities $[I_{hkl}]$ for a crystal may be made. When these are analysed, the Cole & Stemple (1962) observation that the ratio of the intensities scattered in the Bijvoet or Friedel pair is independent of the state of the crystal is assumed to hold. This is a necessary assumption since in a large number of structure analyses radiation damage occurs during the course of an experiment.

For simple crystal structures, Hosoya (1975) has outlined a number of ways in which values of $[f'(\omega,{\bf g}_{hkl})]$ and $[f''(\omega,{\bf g}_{hkl})]$ may be extracted from the Friedel-pair ratios. Measurements of these corrections for atoms such as gallium, indium, arsenic and selenium have been made.

In more complicated crystal structures for which the positional parameters are known, attempts have been made to determine the anomalous-scattering corrections by least-squares-refinement techniques. Measurements of these corrections for a number of atoms have been made, inter alia, by Engel & Sturm (1975), Templeton & Templeton (1978), Philips, Templeton, Templeton & Hodgson (1978), Templeton, Templeton, Philips & Hodgson (1980), Philips & Hodgson (1985), and Chapuis, Templeton & Templeton (1985). There are a number of problems with this approach, not the least of which are the requirement to measure intensities accurately for a large period of time and the assumption that specimen perfection does not affect the intensity ratio. Also, factors such as crystal shape and primary and secondary extinction may adversely affect the ability to measure intensity ratios correctly. One problem that has to be addressed in this type of determination is the fact that $[f'(\omega,0)]$ and $[f''(\omega,0)]$ are related to one another, and cannot be refined separately.

References

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Cole, H. & Stemple, N. R. (1962). Effect of crystal perfection and polarity on absorption edges seen in Bragg diffraction. J. Appl. Phys. 33, 2227–2233.Google Scholar

Engel, D. H. & Sturm, M. (1975). Experimental determination of f′′ for heavy atoms. Anomalous scattering, edited by S. Ramaseshan & S. C. Abrahams, pp. 93–100. Copenhagen: Munksgaard.Google Scholar

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Philips, J. C., Templeton, D. H., Templeton, L. K. & Hodgson, K. O. (1978). L-III edge anomalous X-ray scattering by cesium measured with synchrotron radiation. Science, 201, 257–259.Google Scholar

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International Tables for Crystallography (2006). Vol. C. ch. 4.2, p. 251