X-Ray Diffraction for Materials Research: From Fundamentals to Applications
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This informative new book describes the principles of X-ray diffraction and its applications to materials characterization. It consists of three parts. The first deals with elementary crystallography and optics, which is essential for understanding the theory of X-ray diffraction discussed in the second section of the book. Part 2 describes how the X-ray diffraction can be applied for characterizing such various forms of materials as thin films, single crystals, and powders. The third section of the book covers applications of X-ray diffraction.
conventional unit cell. Thus, for compounds of the type MX, only half of the tetrahedral sites should be filled. The resulting structure is the sphalerite structure in which four atoms of one kind are at the unit cell corners and face centers and four atoms of a different kind occupy every other tetrahedral site (Figure 2.47(a)). The sphalerite structure is sometimes called the zinc blende structure. The Bravais lattice is also FCC with two different atoms associated with one lattice point. The
of c = 2.998 × 108 m/s in vacuum, the wavelength is inversely proportional to the frequency, and vice versa. The electromagnetic radiation is classified by its wavelength or frequency into radio wave, microwave, infrared (IR) light, visible light, ultraviolet (UV) light, X-rays, and γ-rays. However, there are no sharp boundaries between the regions. Figure 1.4 shows the whole spectrum of the electromagnetic radiation. Our naked eyes can sense a relatively small range of wavelengths (400–700 nm)
+ AD equals the wavelength λ. Consider a configuration shown in Figure 4.7(b). Even when the scattering angle θ2 is different from the incident angle θ1, the path length difference between the rays 1S’ and 2S’, i.e., the length C’A + AD’, may be equal to one wavelength. In this case, however, diffraction does not take place in the θ2 direction. Explain why? (a) 1S’ (b) 1S Plane wave 2S’ 2S θ C B θ θ1 θ D d B θ2 D’ C’ d A A FIGURE 4.7 (a) Symmetric and (b) nonsymmetric
where k = 4π sin q / l . This atomic scattering factor plays a significant role in X-ray diffraction. Atomic scattering factors are used to calculate the structure factor for a given Bragg peak. For any atom, it is a function of sinθ/λ, where θ is half the scattering angle and λ, the X-ray wavelength. When the scattering occurs in the forward direction, i.e., the scattering angle 2q = 0, the above Eq. (5.8) reduces to ∞ f = 4π ∫ρ(r )r 2 dr = Z (5.9) 0 It is evident from Eq. (5.8) that f
distances (e.g., interference and diffraction). On the contrary, particle characteristics will be more obvious in the case of absorption because it occurs quite fast in specific positions. The radiation intensity (I) means the energy transferred across unit cross-section per unit time and has units of j/m2·s. FIGURE 1.5 Wave-particle duality. When the wavelength and frequency are fixed, the intensity of the electromagnetic wave is proportional to the square of its amplitude. Thus, if the