Primary extinction

Corrections for primary extinction in the two-beam approximation (the Blackman correction) uses the following relation between the observed and calculated (kinematical) reflection intensity [2] ... 

Although measurements with diffractometer interfaced with EDC cameras have been performed at 80-100 kv, however, this old-type system has a lot of limitations linked to the extremely long time (several hours) to scan ED patterns and the beam size (from microns to mm) of the electron diffraction cameras. Again, the problem of correcting intensities from dynamical contribution has not been addressed satisfactory, as primary extinction (dynamical) corrections have been proposed for known stmctures using the Blackman formula . ... 

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,... 

In most structure determinations small crystals 0-1-0 5 mm across are now used. Primary extinction is rare and not likely to be en-... 

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... 

Fresnel-Kirchhoff theory of diffraction discussed in Section 1.3, the diffracted wave is x/2 out of phase with the incident wave. Thus, the twice-diffracted wave 2 is x out of phase with T, and the two waves interfere destructively. Consequently, in a perfect crystal we should expect the intensities of both the transmitted and the diffracted waves to decrease very rapidly as they penetrate the crystal. This phenomenon is observed and is known as primary extinction. The degree of primary extinction is clearly related to the thickness of the crystal and to the crystal perfection. 

In x-ray diffraction, primary extinction is rarely encountered with powder specimens because the individual crystals are very small. However, primary extinction can become pronounced for single crystals of the order of 1 mm thick. For such crystals, the diffracted intensity is critically dependent on the crystal perfection. In a distorted crystal, the singly diffracted wave Si may not be at the exact Bragg angle at A. This wave may, therefore, pass through the crystal without having its intensity significantly reduced by interference with a transmitted wave T. 

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. 

Extinction effects, which are dynamical in nature, may be noticeable in diffraction from nearly perfect and/or large mosaic crystals. Two types of extinction are generally recognized primary, which occurs within the same crystallite, and secondary, which originates from multiple crystallites. Primary extinction is caused by back-reflection of the scattered wave into the crystal and it decreases the measured scattered intensity Figure 2.51, left). Furthermore, the re-reflected wave is usually out of phase with the incident wave and thus, the intensity of the latter is lowered due to destructive interference. Therefore, primary extinction lowers the observed intensity of very strong reflections from perfect crystals. Especially in powder diffraction, primary extinction effects are often smaller than experimental errors however, when necessary they may be included in Eq. 2.65 as ... 

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. 

Other advantages for diffraction at synchrotron sources include the minimization of systematic errors, which limit the accuracy with which crystallographic models can be refined. Both extinction and absorption are strongly dependent on crystal size and wavelength with the primary extinction characterized by an extinction length ... 

Inside the totally reflecting range, is real and the wave is strongly attenuated. In X-ray diffraction theory, this phenomenon is referred to as primary extinction. The extinction length, defined as the distance over which the amplitude of the incident wave decreases to /e of its value, is P/Q at the centre of the reflexion band. 

L is the average size of the mosaic blocks ]/ 2n(p is the average angle of disorientation of the blocks Q <=/Q is the reflectivity of the crystal when account is taken of primary extinction. 

The maximum reflection intensity for a given focus width will be higher, the greater the reflectivity of the crystal. This means that Q should be equal to Q, the reflectivity of an ideally mosaic crystal. Consequently, to obtain the greatest intensity Im, crystals must be selected which have no appreciable primary extinction, i.e., the size of the mosaic blocks should not exceed 10" cm. Crystals with relatively high dislocation densities satisfy this condition. 

Numerous authors have emphasized the effects of crystallite size on diffraction data and these effects include primary extinction for well-crystallized phases such as quartz and calcite, particle statistics, microabsorption, and preferred orientation. 

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. 

An encouraging result from our recent study of the N3 dye molecule bound to a Ti02-coated oxidized silver sphere is that an IPCE enhancement factor of 9.9 was obtained for a Ti02 thickness of 2.0 nm, in excellent agreement with the experimental value of 6.0. Furthermore, the observed red shift of the primary extinction peaks of the PDSSC relative to the plasmon maximum was also found in our simulations. By comparing the location of the experimental extinction peaks, we are able to estimate theoretically the thickness of an intermediate Ag20 layer that is not experimentally measurable yet and is found to be essential in limiting the photovoltaic efficiency of the PDSSC. 

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