Borrmann effect

This method also involves reflection of Ka radiation in transmission, but there are two additional restrictions the crystal must be nearly perfect and fairly thick, such that fit has a value of the order of 10. We would then expect the transmission factor IJIo to be = 5 x 10 , so that the transmitted and diffracted beams would be too weak to detect. Very surprisingly, Borrmann [8.24] found that both beams were fairly strong, if the crystal were set at the exact Bragg angle 6g. The Borrmann effect is also called anomalous transmission. 

Fig. 8-36 Anomalous transmission or Borrmann effect, (a) Experimental arrangement, (b) intensities of diffracted and transmitted beams as a function of angular position 6 of crystal C, which is 0.75 mm thick. Cu Ka. radiation. Campbell [8.25].

Fig. 8-37 Borrmann effect, (a) Formation of topographic images, (b) Topograph of a crystal of Fe + 3 percent Si, 0.36 mm thick, showing magnetic domains (black and white stripes) and dislocations (white lines). 020 reflection, Co Ka radiation. (Courtesy of Carl Cm. Wu [8.26].)...

The Borrmann effect is completely inexplicable by elementary theory, and an understanding of it can be gained only by a study of the complex theory of diffraction by a perfect crystal [G.30, 8.27, 8.28]. 

Absorbing systems the Borrmann effect The Borrmann effect is the anomalous increase in the transmitted X-ray intensity when a crystal is set for Bragg reflexion. An analogous optical effect in absorbing cholesteric media in the vicinity of the reflexion band has been predicted and confirmed experimentally. The origin of the effect can be readily understood by extending the dynamical theory to include absorption. However, in contrast to the X-ray case, the polarization of the wave field and the linear dichroism play an essential part. 

Nityananda and Kini have applied the theory to obtain exact solutions for reflexion and transmission by a plane parallel film bounded on either side by an isotropic medium. The treatment allows for the contribution due to reflexion at the cholesteric-isotropic interface. In general, for each circular polarization at normal incidence the reflected and transmitted waves consist of both circular polarizations. Four coefficients, two for reflexion and two for transmission, are required to describe the problem fully and the solution consists of matching the incoming and reflected waves on one side of the slab with four waves within the slab (two in the forward direction and two in the backward direction) and the transmitted wave on the other side. An extension of the treatment to absorbing media yields the theory of the Borrmann effect. ... 

For certain applications the polarization of the x radiation is important. As follows from theory, synchrotron radiation is perfectly linearly polarized in the plane of the electron orbit and elliptically polarized outside the plane (Figure 4). However, in practice one has to take into account the finite size and position stability of the radiation source as well as the polarizationchanging properties of monochromators. Therefore it is desirable to determine the actual polarization experimentally. The linear polarization can be measured by diffraction methods, such as, e.g., by Bragg reflection at 2d = 90° or by observing the high Laue transmission for the polarization component with electric vector parallel to the crystal lattice (Borrmann effect). By employing multiple reflection arrangements polarization ratios can be determined even at the level of A simple and fast method... 

Such decomposition, which has as subsidiary the decomposition of the absorption in a normal component, away from the Bragg angle, and one anomalous, associated to each branch of DS, is directly transposed in the Borrmann phenomenology. But the anomalous effect of absorption, i.e., the Borrmann effect, appears only under the condition of the thick crystal, or more accurate for the jj.t 1 case (Bormann, 1940, 1950, 1954, 1955, 1959). 

From now on the necessity of the quantum approach of the d5mamical effects in the crystal fields propagation is required, within the approximation of the two transmitted-dififiacted waves, through which, the Borrmann effect should appear naturally integrated and correlated with the anomalous energetic propagation for the DS. 

In terms of phase s continuity at propagation, both between the DS branches but also between the transmitted-dififiacted directions, the quantum fiormalism ofi the Borrmann effect will be developed for a deeper understanding of the phase transfer, as coming from the photons transfer phenomenology the present discussion follows (Biagini, 1990 Birau Putz, 2000). 

Therefore, the classical treatment of the Borrmann effect has the quality of the immediate interpretation of the recorded fluorescence spectra (see Putz, 2014) but does not fully respond to what is happening with this energy, intimate-dynamically manifested in the anomalous absorption. Here s why, the quantum view can causally present the dififaction phenomenology in d5mamic evolution, where the asymmetrical propagation naturally derives fi om the quantum definition itself of diflBaction the coherent (dynamic) photonic transfer derivedfrom the dynamic localization, (5.312) and (5.313). 

As long as the quantum transfer takes place reciprocally (d5mamic, self-consistently), i.e., between the two fields associated to the two branches of DS, the Borrmann effect appears only as an effect of the photonic statistic as5mimetry caused by diffraction, while canceling the phasic dispersion effect. 

Therefore, these results are confirmed here, i.e. by the Borrmann effect based on the previous discussions, and, consecutively, the appearance of the dynamic standing waves, as a directly correlated effect with the thick crystal condition, here at 1. 

Worth specifying that after the presented detailed study centered on the matter of the propagation with the formation of Standing Waves -SW, we have reached the conclusion that the Borrmann effect is not a random phenomenon, but it is always the companion of the propagation in the crystal that suffered a dynamic scattering with X-ray on the thick crystal... 

Moreover, the quantum modeling of the Borrmann effect gives a general view of the self-consistency, seen as the mutual (dynamic) free photonic transfer under the conditions of the dynamic localization. 

The generalized quantum transfer is a good win in the understanding of the X-ray propagation in crystal, being present both between the directions (in the table being simply called quantum jump), but also between the fields associated to the DS branches when become the full (direct and inverse) Borrmann effect, both being correlated by the asymmetric form of the photonic distribution. 

Borrmann was already quite familiar with the Dahlem research institutes. He worked under Laue at the KWI for Physics in 1935 while a student of Walther Kos-sel, and he moved to Hechingen in 1943 along with the rest of the institute. There he remained true to the line of research he had begun under Kossel in Danzig, the most important result of which was the identification of the Borrmann effect demonstrated in 1941. The Bormann effect refers to the anomalously low absorption of X-rays by ideal crystals when the X-rays strike the ciystals at angles that... 

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