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The accuracy of the determination of the structure factors from a powder diffraction measurement is studied in light of a representative example: nickel with Cu Kct radiation. Various sources of error in the absolute measurement and methods of sample characterization are discussed. The contributions of various extraneous scattering mechanisms are assessed. From these considerations it is possible to separate the Bragg scattering, providing measurements are made through virtually the entire angular range. Results are given in detail for a standard sample, a duplicate of which can be made available to interested workers. The relationship of these results to the structure factors of the sample is discussed in terms of a model calculation, in terms of line shape analysis, and in terms of some comparative measurements on various samples of Ni and MgO. All these analyses indicate the impossibility of preparing a single sample which is ideally mosaic. Thus it is incorrect to relate the measured integrated reflection to the structure factor with the customary simple formula when high accuracy is required.

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The thermal diffuse scattering (TDS) contribution to X-ray Bragg peaks is discussed in terms of its two experimental components, the included and the background parts. The discussion is primarily directed towald situations where detailed elastic constant information and a large computer are not available. Graphs are displayed which, in the spherical average approximation, allow an accurate assessment of the influence of all the experimental variables on the TDS contribution. It is shown that, even in the general case where spherical averaging is a poor approximation, the included TDS varies linearly with length of scan for small scans. A technique for determining the constant of proportionality is suggested. Thus the included TDS may be evaluated even though the elastic constants are not known.

A number of theories are examined for their predictions of extinction coefficients at large values of extinction, especially as applied to polarization ratios. Although several theories give the behavior expected on the basis of physical reasoning (a polarization ratio approaching unity), the popular theories of Zachariasen [Acta Cryst. (1967), 23, 558-564] and Becker & Coppens [Acta Cryst. (1964), A30, 129-147, 148-153] do not show the correct asymptotic behavior. Although this shortcoming may be of no consequence in ordinary crystallographic applications, it is misleading in predicting the correct polarization factor to be used in connection with a crystal-monochromated apparatus, where the monochromator is usually adjusted to maximize its extinction. The importance of measuring, rather than estimating, the polarization ratio of a crystal monochromator is therefore re-emphasized.