![]() ![]() Identify points where hyperbolas cross by letters (these are low-index planes which are in many zones). Identify as many hyperbolas as possible with dashed lines (some may be straight lines) and Roman Numerals. Identity the hyperbolas on the patterns by tracing the patterns on to tracing paper.Obtain Laue reflection patterns from Si, Ge and Al (or the single crystals which are available).For Polaroid film you must make a note of the arrangement of the face of the film in the camera. It is critical to keep track of the relative arrangement of the sample to the film, if photographic film is used then this is achieved by cutting the corner of the film. (2 s is 2 q for the diffraction peak and tan m is x/y for the Cartesian coordinates of the diffraction peak.) The Greninger Chart gives directly the two angles needed to plot poles on the Wulff net. A new chart must be generated for different sample to detector distances. 475 can be Xeroxed on a transparency and used for a sample to detector distance of 3 cm. (If you were using a 2-d detector the problem of determining g and d could be solved mathematically using the equations which generate the Greninger Chart, pp.Ĥ75.) The Greninger chart shown on p. The Greninger Chart is a simple trigonometric tool to determine g and d for a fixed sample to film distance. The angle of tilt for the zone axis, f, is 90°- g, as shown in figure Of the observed diffraction spot by the trigonometric equations on p. 472 comes through the film and is reflected back and that the wavelength of the radiation is not known so that Bragg's law can not be used.) g and d for the plane normal are related to the angles s and m (Remember that the beam in figure 16.1 p. Geometric construction and is not observed. AB is the projection of the plane normal on the film which is a 476, are determined from a diffraction spot on the hyperbola of reflection following the schematic of figureġ6-4 on p. The angles g and d which are used in the Wulff net to determine the location of a plane normal, figureġ6.4, p. We are only interested in the back reflection method which uses a Greninger chart, pp. 471 describes determination of crystal orientation using Laue patterns. Since Laue patterns involve single crystals, the natural stereographic projection is the Wulff Net as discussed in labģ. The latter two are diamond cubic crystal structures while the first is an FCC structure as discussed in the last lab. This will be done for Al, Ge and Si in this lab. By identification of zone axes it becomes fairly simple to align single crystals for identification of crystal planes using Laue patterns and Wulff nets. (a), and the pages are reflective, light reflecting from the pages will form anĮllipse of reflection spots, one for each page. If the book binding is pointed at the center of the ellipse of figure 3-10 You can think of these planes in analogy with the pages of a splayed book where the book binding is the zone axis. Planes of a zone are planes which have a common direction, the zone axis, lying in all of the planes. The center of these arcs or circles of diffraction spots correspond to the zone axis of a series of planes of a zone. In backscattering only hyperbolas (arcs) are observed as shown in figure 8-1 pp. We will use back scattering in this lab since the samples are metals with low transmission coefficients. The measurement can be conducted in a forward or backward geometry depending on the placement of the film with respect to the samples. The analysis of Laue patterns involves understanding that the diffraction spots are arranged in arcs (hyperbolas) and ellipses in the diffraction pattern. We will produce similar patterns in this lab. 108 shows two Laue patterns in reflection and transmission for a single crystal of aluminum. By using polychromatic radiation most Bragg reflections from a single crystal sample can be accessed just as most reflections are accessed in a powder pattern by variability in orientation of the polycrystalline sample. Laue patterns involve a single crystal sample (single crystals larger than the incident beam), and a polychromatic source which is usually unfiltered radiation from an x-ray tube. If a monochromatic beam hits a single crystal arranged in a particular geometry with the camera it is unlikely that a diffraction peak will be observed. For a Bragg reflection to be observed a single arrangement of geometry, d hkl, q hkl and l must be achieved. 233 (Chapter 8)).īragg's Law provides a strict set of geometric requirements for observation of a diffraction peak. Objective: To become familiar with the back-reflection pattern from single crystal samples using a polychromatic source.īackground: Cullity and Stock: Chapter 16 p. ![]()
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