OBRABOTKAMETALLOV MATERIAL SCIENCE Vol. 26 No. 3 2024 , hkl d hkl d d d = + δ (6) where θd and dd are the diffraction angle and the interplanar spacing for the case corresponding to the ideal fulfillment of the Wolf – Bragg condition; δθ and δdhkl are the possible errors of the corresponding quantities. Deviations from the ideal operation mode of the monochromator, caused by the expansion of the crystal during its heating, as well as by vibration due to the turbulent flow of the cooling liquid, or transmitted from the foundation, are the reasons for the device to transmit diffracted waves corresponding to a certain range of energy. This means that the radiation passed through the monochromator is a beam characterized by a range of wavelengths Δλ. The reasons mentioned above affect the grazing angle θd and the interplanar spacing dd, the values of which are related by condition (1) to a specific wavelength corresponding to a specific radiation energy. Thermal heating and vibrations of various nature are negative factors that are manifested directly during operation of the monochromator. At the same time, there are additional factors that decrease the degree of monochromaticity of radiation caused by imperfections in crystal structure (non-planarity of the outer surface, mosaicity of the material). Mosaicity is one of the possible defects of crystal structure. Amonocrystal installed in a monochromator consists of many “blocks” disoriented relative to each other at small angles (Fig. 6). The mosaicity of the crystal, as one of the factors determining the degree of monochromaticity of radiation, was analyzed by Darwin as early as 1922 [6]. Nonplanarity is understood as the distance between the real and ideal surface of a crystal plate. Roughness (depressions and protrusions) that has appeared at the last stage of surface processing also has a negative effect on the monochromaticity of radiation. Fig. 6. Demonstration of crystal mosaicity on the example of five blocks disoriented relative to each other at small angles When solving a certain class of problems, it is sufficient (and sometimes necessary) to provide a degree of monochromaticity corresponding to the so-called “pink” beam (Fig. 4 b) [7]. The spectral width of the “pink” radiation is 1÷3 orders of magnitude greater than that of monochromatic radiation. To form a Fig. 5. Demonstration of the effect of thermal expansion of the local crystal zone (highlighted with a circle), caused by the thermal effect of synchrotron radiation, on the diffraction of X-rays. According to [5]
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