![]() ![]() 38-16b shows, in x-ray diffraction there is nearly complete cancellation in all but certain very specific directions in which constructive interference occurs and forms bright spots. In fact, the reflections from various planes are closely analogous to interference effects in thin films (Section 37 -5)As Fig. While we are using the term reflection, remember that we are dealing with an interference effect.(38-16) is called the Bragg condition, in honor of Sir William Bragg and his son Laurence Bragg, two pioneers in x-ray analysis. CAUTION This phenomenon is called Bragg reflection, and Eq. Because there are many different sets of parallel planes, there are also many values of d and many sets of angles that give constructive interference for the whole crystal lattice. (38-16) is satisfied, where d is now the distance between adjacent planes. There is also constructive interference between planes when Eq. Waves from all the scatters in a given plane interfere constructively if the angles of incidence and scattering are equal. Figure 38-19 shows two different sets of parallel planes that pass through all the scatters. We can extend this discussion to a three-dimensional array by considering planes of scatters instead of rows. In the case of electromagnetic waves, the wave induces an oscillating. The situation might be a ripple tank with an array of small posts. waves striking an array of small conducting spheres, or x rays incident on an array of atoms. 38-18a, in which a plane wave is incident on a rectangular array of scattering centers. Since that time, -ray diffraction has proved to be an invaluable research tool, both for measuring x-ray wavelengths and for the study of crystal structure. To introduce the basic ideas, we consider first a two-dimensional scattering situation, as shown in Fig. These experiments verified that x rays are waves, or at least have wavelike properties, and also that the atoms in a crystal are arranged in a regular pattern (Fig. ![]() Figure 38-16b is a photograph of such a pattern. The scattered x rays did form an interference pattern, which they recorded on photographic film. The first x-ray diffraction experiments were performed in 1912 by Friederich, Knipping, and von Laue, using the experimental setup sketched in Fig. That is, a beam of x rays might be scattered (that is, absorbed and re-emitted) by the individual atoms in a crystal, and the scattered waves might interfere just like waves from a diffraction grating. Putting these two ideas together, Max von Laue (1879-1960) proposed in 1912 that a crystal might serve as a kind of three-dimensional diffraction grating for x rays. At about the same time, the idea began to emerge that in a crystalline solid the atoms are arranged in a regular repeating pattern, with spacing between adjacent atoms also of the order of 10-10 m. The micrograph shows a field of crystalline particles outlined by a large selection aperture (6 µm at the specimen).X rays were discovered by Rontgen (1845-1923) in 1895, and early experiments suggested that they were electromagnetic waves with wavelengths of the order of 10-10 m. The figure above is electron diffraction patterns from selected small areas. Metals tend to give very strong electron diffraction patterns, whereas biological specimens generally diffract quite weakly. \), whereĮlectron diffraction provides a basis for studying the structure of crystals and of identifying materials. ![]()
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