12/6/2023 0 Comments Xray diffraction equationsAlthough wavelengths change while traveling from one medium to another, colors do not, since colors are associated with frequency. It follows that the wavelength of light is smaller in any medium than it is in vacuum. Where λ λ is the wavelength in vacuum and n is the medium’s index of refraction. As it is characteristic of wave behavior, interference is observed for water waves, sound waves, and light waves. Here we see the beam spreading out horizontally into a pattern of bright and dark regions that are caused by systematic constructive and destructive interference. Passing a pure, one-wavelength beam through vertical slits with a width close to the wavelength of the beam reveals the wave character of light. The laser beam emitted by the observatory represents ray behavior, as it travels in a straight line. In Figure 17.2, both the ray and wave characteristics of light can be seen. Interference is the identifying behavior of a wave. However, when it interacts with smaller objects, it displays its wave characteristics prominently. As is true for all waves, light travels in straight lines and acts like a ray when it interacts with objects several times as large as its wavelength. The range of visible wavelengths is approximately 380 to 750 nm. Although such plane-wave moiré images are not widely observed in a nearly pure form, knowledge of their properties is essential for the understanding of diffraction moiré fringes in general.Where c = 3.00 × 10 8 c = 3.00 × 10 8 m/s is the speed of light in vacuum, f is the frequency of the electromagnetic wave in Hz (or s –1), and λ λ is its wavelength in m. Then, the properties of moiré fringes derived from the above theory are explained for the case of a plane-wave diffraction image, where the significant effect of Pendellösung intensity oscillation on the moiré pattern when the crystal is strained is described in detail with theoretically simulated moiré images. Firstly, prior to discussing the main subject of the paper, a previous article on the two-dimensionality of diffraction moiré patterns is more » restated on a thorough calculation of the moiré interference phase. A detailed and comprehensive theoretical description of X-ray diffraction moiré fringes for a bicrystal specimen is given on the basis of a calculation by plane-wave dynamical diffraction theory. « lessĪ detailed and comprehensive theoretical description of X-ray diffraction moiré fringes for a bicrystal specimen is given on the basis of a calculation by plane-wave dynamical diffraction theory, where the effect of the Pendellösung intensity oscillation on the moiré pattern is explained in detail. Finally, the results are found to be in agreement with dynamical X-ray diffraction calculations made with the Takagi–Taupin equations specialized to a surface having convex or concave features, as reported in the accompanying paper. Topographic images were obtained as a function of rocking angle, and in the case of 8.200 keV the surface morphology is evident. The results at 8.100 keV allow an alternative explanation based on strain near the surface to be more » ruled out. Features arising from surface undulations were not observed at 8.100 keV, but were observed at 8.200 keV. The grazing angles of incidence were near 1.08 and 0.33° for these two energies, respectively. A crystal with an asymmetry angle of 46 ± 0.1° between the surface and the (111) planes was studied. The results are reported of an X-ray diffraction study of an Si crystal designed and fabricated for very asymmetric diffraction from the 333 reflection for X-ray energies of 8.100 and 8.200 keV.
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