Extinction, polarization and crystal monochromators

Abstract

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.

Polarization of synchrotron radiation

“…The difficulty of predicting the effect of one such reflection is well documented (e.g. Jennings, 1981). The effect of two reflections is further complicated by the common practice of slight misalignment to suppress harmonic wavelengths (Bonse, Materlik & Schr6der, 1976;Materlik & Kostroun, 1980); such an adjustment may change the polarization because the two polarization components have different rocking-curve widths (Zachariasen, 1945).…”

General calculation of the polarization factor for multiple coherent scattering of unpolarized and plane-polarized X-rays

“…Determining the correct polarization ratio K from experiment can be complicated and subject to several errors, some of which can be rather subtle (Mathieson, 1982;Jennings, 1981;LePage, Gabe & Calvert, 1979;Evans, Hine, Richards & Tichy, 1980;Vincent & Flack, 1980). If the K cannot be determined with confidence, then either no monochromator should be used or a special geometry should be used that eliminates the polarization effect for the monochromator, such as the method of Mathieson (1978).…”

“…When strongly diffracting crystals are used as monochromators, as often is the case in single-crystal structure studies, dynamical rather than kinematical theory applies and the degree of perfection can influence the polarization factor greatly (Jennings, 1981;Mathieson, 1982). This requires a modification in McMaster's matrix treatment.…”

“…Although X-ray tubes produce unpolarized characteristic radiation, completely polarized radiation is allowed because synchrotron radiation that is nearly completely polarized now is used for some studies (Vincent, 1982). Circular polarization is not allowed, although it is possible to include it, because the resulting equations would be much more complicated and because highintensity X-ray sources with circular polarization are not yet available.When strongly diffracting crystals are used as monochromators, as often is the case in single-crystal structure studies, dynamical rather than kinematical theory applies and the degree of perfection can influence the polarization factor greatly (Jennings, 1981;Mathieson, 1982). This requires a modification in McMaster's matrix treatment.…”

Intensity of secondary scattering of X-rays by non-crystalline materials. Transmission gemoetry with an incident-beam monochromator

“…I of perfect-crystal dynamical theory. Thus, when K,,, is required, it must be measured experimentally, or a method that causes K,,, to cancel must be found (Jennings, 1981;Mathieson, 1982;Dwiggins, 1983).…”