Secondary extinction

Becker, P.J. and Coppens, P. (1974) Extinction within the limit of validity of the Darwin transfer equations. I. General formalisms for primary and secondary extinction and their application to spherical crystals, Acta Crystallogr., A, 30, 129-147. 

HO. Bacon, G. E., and R. D. Lowde Secondary Extinction and Neutron Crystallography. Acta crystallogr. (London) I, 303 (1948). 

The other possible sources of error are primary and secondary extinction effects, inadequate sample thickness, and finally, instrument-related errors. These issues are addressed in the literature [1]. 

The intensities of crystal reflections are in some circumstances reduced by effects known as primary and secondary extinction. If the crystal is not ideally imperfect but consists of rather large lattice blocks, the intensities of the reflections are proportional to a power of F between 1 and 2 this is primary extinction . Secondary extinction affects only the strongest reflections and is due to the fact that the top layer of a crystal (the part nearest the primary beam) reflects away an appreciable proportion of the primary beam, thus in effect partially shielding the lower layers of the crystal the strongest reflections are therefore experimentally less strong than they should be in comparison with the weaker reflections. The relation between the actual intensity p and the intensity p which would be obtained if there were no secondary extinction is, for reflection at a large face,... 

Both primary and secondary extinction effects may usually be avoided by powrdering a crystal. For this and other reasons the intensities of the arcs on powder photographs are likely to be more reliable than those of other types of photograph but in practice, in structure determination it is only possible to use powder intensities alone for very simple structures for complex crystals reflections from different planes overlap seriously. 

There are, of course, many difficulties, the most severe being that of obtaining a reasonably monochromatic beam of sufficient strength. Even under the best conditions such a beam is usually less effective by a factor of about 105 than an X-ray beam. Because of this, very large crystal specimens are necessary. The absorption is small, but secondary extinction presents another difficulty for which it is not easy to make corrections. 

Extinction (see Section 2.2.2) is the phenomenon that reduces the observed intensity of the incident or diffracted beams by internal scattering and backscattering parallel to the incident beam direction. Primary extinction is assumed to take place when the different crystal blocks (domains) are sufficiently mutually misoriented that the reduction in intensity takes place oifly within each block. In secondary extinction, the size of the blocks is assumed to be so small that loss of intensity within each block is negligible. Instead, the reduction takes place by adjacent blocks scattering and rescattering the... 

Structure Solution and Refinement. The structure was solved by direct methods. Infonnadon on the collection of data and the refinement are given in Table SV. All atoms refined anisotro-pically. A correction for secondary extinction was applied (coefficient... 

Inspection of the residuals ordered in ranges of (sin )/X, Fob and parity and values of (he individual indexes showed no unusual features or trends, other than those caused by (he strong pseudotranslation of V2C in (he structure. There was no indication of secondary extinction in the high-intensity low-angle data. 

Extinction An effect of dynamical diffraction whereby the incident beam is weakened as it passes through the crystal. If the crystal is perfect there may be multiple reflection of the incident beam, which then is out of phase with the main beam and therefore reduces its intensity (primary extinction). If the crystal is mosaic, one block may diffract the beam, and is not then available to a second block similarly aligned (secondary extinction). Both effects result in a diminution of the intensities so that the most intense Bragg reflections are systematically smaller than those calculated from the crystal structure. The effect can be reduced by dipping the crystal in liquid nitrogen, thereby increaising its mosaicity. 

Zacharicisen, W. H. The secondary extinction effect. Acta Cryst. 16, 1139-1144... 

Secondary extinction Figure 2.51, right) occurs in a mosaic crystal when the beam, reflected from a crystallite, is re-reflected by a different block of the mosaic, which happens to be in the diffracting position with respect to the scattered beam. This dynamical effect is observed in relatively large, nearly perfect mosaic crystals it reduces measured intensities of strong Bragg reflections, similar to the primary extinction. It is not detected in diffraction from polycrystalline materials and therefore, is always neglected. 

R. J. Nelmes, (1980). Acta Cryst., A36,641-653. Anisotropy in thermal motion and in secondary extinction. 

From the model for takii account of the secondary extinction of mosaic crystals [7], it can be established that the reflection intensity from a crystal exhibiting both primary and secondary extinctions is determined by the following relationship ... 

E is the extinction coefficient. It depends on the mosaic structure of the crystal and has two components. The secondary extinction (the most important) takes into account that a fraction of the incident beam is reflected by the planes. The primary extinction takes into account the loss of intensity due to multiple reflections from different lattice planes. 

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