Polarization of crystal monochromated X-rays

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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.

Section: Polarization Ratiomentioning

confidence: 99%

International Union of Crystallography Commission on Crystallographic Apparatus. Accuracy of structure factors from X-ray powder intensity measurements

Suortti¹,

Jennings²

1977

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“…If the scattering in the monochromator obeys the kinematic theory, the polarization ratio will simply be cos220a, where 0 a is the Bragg angle; if the monochromator is perfect, the polarization ratio will be cos 20 a. However, as has been pointed out by Jennings (1968Jennings ( , 1981, when severe extinction occurs in a mosaic crystal, much of the incident energy of each polarization will be diffracted and the polarization ratio could approach unity. Le Page, Gabe & Calvert (1979) have described a method of experimentally determining polarization ratios and obtained values greater than cos 20 a for Cu Ka and Mo Ka radiations.…”

Section: Introductionmentioning

confidence: 99%

The reflectivity of a pyrolytic graphite monochromator

Lawrence¹

1982

It is shown that a pyrolytic graphite monochromator crystal scatters X-rays as a mosaic crystal in accordance with the Darwin formulism, both for reflecting power and integrated intensity, over a range in wavelength from 0.5 to 1.54 A. The scattering cannot be considered kinematic and, from estimates of the reflectivities parallel and perpendicular to the diffraction plane, polarization ratios are calculated which are in accord with published values. A simple description of the scattering process is given. The variation of polarization ratio with mosaic spread is discussed.

“…The left-hand horizontal hatched region shows that the assumption of a Lorentzian mosaic distribution does not qualitatively change the behavior, though it does increase the fraction of the reflection curve for which extinction effects are not severe. The results also do not depend strongly on m for m > ½ (Jennings, 1968). The upper curve is Ka vs (Q'/Q) (o(Q'/21arl) for the dislocation model in symmetrical reflection.…”

Section: Experimental Situationmentioning

confidence: 91%

“…The polarization ratio is thus approximately unity. This result has been known for some time (Jennings, 1968). It is, however, often overlooked in crystallographic applications.…”

Section: Introductionmentioning

confidence: 91%

Extinction, polarization and crystal monochromators

Jennings¹

1981

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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.