Difference between revisions of "Friedel pair"
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| − | < | + | <font color="blue">Paire de Friedel</font> (''Fr''). <font color="red">Friedelpaar</font> (''Ge''). <font color="black">Coppia di Friedel</font> (''It''). <font color="purple">フリーデル対</font> (''Ja''). <font color="green">Par de Friedel</font> (''Sp''). |
== Definition == | == Definition == | ||
| + | |||
| + | The couple of reflections ''h'', ''k'', ''l'' and <math>{\bar h}, {\bar k}, {\bar l}</math> is called a Friedel pair, or Bijvoet pair. Their intensities are equal either if the crystal structure is centrosymmetric or if there is no [[Resonant_scattering|resonant scattering]], but differ otherwise. [[Friedel's law]] then does not hold. For crystals with a non-centrosymmetric structure and significant resonant scattering, equivalent reflections generated by the symmetry operations of the point group of the crystal have intensities different from those of equivalent reflections generated by the introduction of an additional inversion centre in normal scattering. Friedel, or Bijvoet, pairs are used in the resolution of the phase problem for the solution of crystal structures and in the determination of absolute structure. | ||
| + | |||
| + | == History == | ||
| + | |||
| + | The use of Friedel's pairs for helping in phase determinations was suggested by Bijvoet, J. M., Peerdeman, A. F. and van Bommel, A. J. (1951), ''Determination of the absolute configuration of optically active compounds by means of X-rays''. ''Nature (London)'', '''168''', 271–272. | ||
== See also == | == See also == | ||
| − | [[Friedel's law]] | + | *[[Friedel's law]] |
| − | + | *Chapter 2.4.3 of ''International Tables for Crystallography, Volume B'' | |
| + | *Chapter 4.2.6 of ''International Tables for Crystallography, Volume C'' | ||
| + | |||
| + | [[Category:X-rays]]<br> | ||
Latest revision as of 13:42, 13 November 2017
Paire de Friedel (Fr). Friedelpaar (Ge). Coppia di Friedel (It). フリーデル対 (Ja). Par de Friedel (Sp).
Definition
The couple of reflections h, k, l and [math]{\bar h}, {\bar k}, {\bar l}[/math] is called a Friedel pair, or Bijvoet pair. Their intensities are equal either if the crystal structure is centrosymmetric or if there is no resonant scattering, but differ otherwise. Friedel's law then does not hold. For crystals with a non-centrosymmetric structure and significant resonant scattering, equivalent reflections generated by the symmetry operations of the point group of the crystal have intensities different from those of equivalent reflections generated by the introduction of an additional inversion centre in normal scattering. Friedel, or Bijvoet, pairs are used in the resolution of the phase problem for the solution of crystal structures and in the determination of absolute structure.
History
The use of Friedel's pairs for helping in phase determinations was suggested by Bijvoet, J. M., Peerdeman, A. F. and van Bommel, A. J. (1951), Determination of the absolute configuration of optically active compounds by means of X-rays. Nature (London), 168, 271–272.
See also
- Friedel's law
- Chapter 2.4.3 of International Tables for Crystallography, Volume B
- Chapter 4.2.6 of International Tables for Crystallography, Volume C