Transmission Laue method

There are two variations of the Laue method, depending on the relative positions of source, crystal, and film (Fig. 3-5). In each, the film is flat and placed perpendicular to the incident beam. The film in the transmission Laue method (the original Laue method) is placed behind the crystal so as to record the beams diffracted in the forward direction. This method is so called because the diffracted beams are partially transmitted through the crystal. In the back-reflection Laue method the film is placed between the crystal and the x-ray source, the incident beam passing through a hole in the film, and the beams diffracted in a backward direction are recorded. 

The positions of the spots on the film, for both the transmission and the back-reflection method, depend on the orientation of the crystal relative to the incident beam, and the spots themselves become distorted and smeared out if the crystal has been bent or twisted in any way. These facts account for the two main uses of the Laue methods the determination of crystal orientation and the assessment of crystal quality. 

Fig. 5-10 Focusing of diffracted beam in the transmission Laue method. 5 = source, C = crystal, F = focal point.

In either Laue method, the diffraction spots on the film, due to the planes of a single zone in the crystal, always lie on a curve which is some kind of conic section. When the film is in the transmission position, this curve is a complete ellipse for sufficiently small values of 0, the angle between the zone axis and the transmitted beam (Fig. 8-12). For somewhat larger values of 0, the ellipse is incomplete because of the finite size of the film. When 0 = 45°, the curve becomes a parabola when 0 exceeds 45°, a hyperbola and when 0 = 90°, a straight line. In all cases, the curve passes through the central spot formed by the transmitted beam. 

The angular relationships involved in the transmission Laue method are illustrated in Fig. 8-13. Here a reference sphere is described about the crystal at C, the incident beam entering the sphere at / and the transmitted beam leaving at O. The film is placed tangent to the sphere at O, and its upper right-hand corner, viewed from the crystal, is cut off for identification of its position during the x-ray exposure. The beam reflected by the lattice plane shown strikes the film at R, and the normal to this plane intersects the sphere at P. 

Fig. 8-13 Relation between plane normal orientation and diffraction spot position in the transmission Laue method.

Fig. 8-18 Use of a stereographic ruler to plot the pole of a reflecting plane on a stereographic projection in the transmission Laue method. Pole 1 is the pole of the plane causing diffraction spot 1.

This method [8.10, 8.11] is a variant of the transmission Laue method and exploits the focusing effect shown in Fig. 5-10. A large increase in sensitivity is obtained by increasing the source-to-crystal and crystal-to-film distances to the order of 50 cm. One therefore has a rather long optical lever that can disclose slight disorientations of the crystal. 

In this section we will discuss perturbation methods suitable for high-energy electron diffraction. For simplicity, in this section we will be concerned with only periodic structures and a transmission diffraction geometry. In the context of electron diffraction theory, the perturbation method has been extensively used and developed. Applications have been made to take into account the effects of weak beams [44, 45] inelastic scattering [46] higher-order Laue zone diffraction [47] crystal structure determination [48] and crystal structure factors refinement [38, 49]. A formal mathematical expression for the first order partial derivatives of the scattering matrix has been derived by Speer et al. [50], and a formal second order perturbation theory has been developed by Peng [22,34],... 

Fig. 3-7 Location of Laue spots (a) on ellipses in transmission method and (b) on hyperbolas in back-reflection method. (C = crystal, F = film, Z.A. = zone axis.)...

When monochromatic radiation is used to examine a powder specimen in a Laue (flat-film) camera, the result is often called, for no particularly good reason, a pinhole photograph. (There is no general agreement on the name of this method. Klug and Alexander [G.39], for example, call it the monochromatic-pinhole technique. ) Either a transmission or a back-reflection camera may be used. A typical transmission photograph, made of fine-grained aluminum sheet, is shown in Fig. 6-11. 

Described below are the-three main methods of determining orientation back-reflection Laue, transmission Laue, and diffractometer. Nor should the old etch-pit method be overlooked. This is an optical method, involving the reflection of visible light from the flat sides, of known Miller indices, of etch pits in crystal surfaces. Although not universally applicable, this method is fast and requires only simple apparatus [G.25]. 

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... 

The Laue s method supports two versions in transmission and in back-reflection. Figure 5.15, depending on place where the film relative to the X-ray source and crystal is placed. For transmission Laue diffraction the film is placed behind the crystal and the spots will be recorded as the bases of ellipses shape of some imaginary cones of scattering beams. Figure 5.15-left-up. Instead, for the back-reflection Laue s diffraction, the... 

In 1914, Professor Max Von Laue was awarded the Nobel Prize in Physics for his discovery that x-rays could be diffracted by crystals. Von Laue used a simple transmission x-ray experiment and a copper sulfate crystal to collect the diffraction pattern on a photographic plate. Von Laue formulated a simple theoretical description for the resulting diffraction patterns formed on the plate and showed not only that x-rays can be used for diffraction but also that the crystal lattices postulated in the previous century by Bravais could be observed by this method. ... 

Fig. 8. Three X-ray topographic methods (a) back-reflection Berg-Barrett, (b) transmission Berg-Barrett, (c) Borrmann anomalous transmission. In the Laue case X-ray interferometer (d) two coherent beams are produced by the beam splitter the transmission mirror recombines the beams to form one interference pattern at the analyzer.

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