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

International Tables for Crystallography (2006). Vol. C, ch. 7.5, p. 666

Section 7.5.1. Distributions of intensities of diffraction

A. J. C. Wilsona

aSt John's College, Cambridge CB2 1TP, England

7.5.1. Distributions of intensities of diffraction

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Intensities of diffraction have two distinct probability distributions: (1) the a priori probability that an arbitrarily chosen reflection of a particular substance will have a particular `true' intensity (R in the notation used below), and (2) the probability that a `true' R will have an observed value [R_{o}]. The distributions of the first type depend on the symmetry and composition of the material, and are treated in Chapter 2.1[link] of Volume B of International Tables for Crystallography (Shmueli, 2001[link]). The distributions of fluctuations of the second type, variations of the values [R_{o}] observed for a particular reflection, are treated here.

The crude counts or counting rates are rarely used directly in crystallographic calculations; they are subjected to some form of data processing to provide `intensities of reflection' [I_{o}] in a form suitable for the determination of crystal structures, electron densities, line profiles for the study of defects, etc. The resulting intensity for the jth reflection, [I_{o,\,j}], will be directly proportional to the corresponding [R_{o,\,j}]; when no confusion can arise, one of the subscripts will be omitted. The value of the proportionality factor [c_{j}] in [ I_{o,\,j} = c_{j}R_{o,\,j}\eqno (7.5.1.1)]will be different for different reflections, since they will occur at different Bragg angles, have different absorption corrections, etc.

References

Shmueli, U. (2001). Editor. International tables for crystallography. Vol. B. Reciprocal space, 2nd ed. Dordrecht: Kluwer Academic Publishers.








































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