Laue method back-reflection

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. 

Fig. 8-11 Use of a stereographic ruler to plot the pole of a reflecting plane on a stereo-graphic projection in the back-reflection Laue method. Pole 1 is the pole of the plane causing diffraction spot 1.

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]. 

This procedure may be illustrated by determining the orientation of the aluminum crystal whose back-reflection Laue pattern is shown in Fig. 3-6(b). Fig. 8-5 is a tracing of this photograph, showing the more important spots numbered for reference. The poles of the planes causing these numbered spots are plotted stereographically in Fig. 8-6 by the method of Fig. 8-4 and are shown as solid circles. 

The back-reflection Laue pattern of an aluminum crystal rotated into the orientation described above is shown in Fig. 8-22. Note that the arrangement of spots has 2-fold rotational symmetry about the primary beam, corresponding to the 2-fold rotational symmetry of cubic crystals about their <110> axes. (Conversely, the observed symmetry of the Laue pattern of a crystal of unknown structure is an indication of the kind of symmetry possessed by that crystal. Thus the Laue method can be used as an aid in the determination of crystal structure.)... 

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... 

The obtained low index surfaces were examined by Laue back reflection X-ray diffraction photograph method. Figures 2—10 show the obtained photographs. They represent a typical diffraction pattern for each surface and show that the quality of the each surface is high. The areas of the low index surfaces are 0.028, 0.024 and 0.025 cm for Ptdll), (110) and (100), respectively. 

Figure 4.9 The Laue back-reflection method. The direction of the incident beam and the reciprocal lattice are fixed in space, and wavelengths are selected out of the beam. The Ewald sphere may be any diameter between the short and long wavelength cutoffs. The larger circle shows an intermediate wavelength and the diffracted beams that result at this wavelength...

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.)...

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. 

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. 

Specialized books on the Laue methods are those of Amoros et al. [G.40] and Preuss et al. [G.45]. The latter contains a catalog of back-reflection patterns, many generated by a computer. 

The surface orientation of the boule is determined by an X-ray method (typically Laue back-reflection). The boule is mounted in such a way that when it is cut the slices have the desired surface orientation. 

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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