OBRABOTKAMETALLOV MATERIAL SCIENCE Vol. 26 No. 3 2024 determined at different periods of time based on the works of K. Röntgen, M. Laue, C. Barclay, D. Thompson, G. Moseley. Fig. 2. The scale of electromagnetic radiation. The area of synchrotron radiation is marked in gray The X-ray region is often divided into ranges of hard (0.1 < λ < 10 Å), soft (10 < λ < 300 Å), and ultrasoft (300 < λ < 1,000 Å) radiation [34]. This division is conventional, but it is important from the point of view of the physics of the monochromator process because these ranges are characterized by different refractive indices, absorption coefficients, and wave polarization features. X-rays are distinguished from visible light by its ability to penetrate deep into substances. The properties of X-ray radiation are straightness of propagation at the speed of light, refraction at interfaces, reflection and scattering at obstacles, interference and diffraction, polarization when scattering or passing through a substance, absorption by substances, and the ability to cause the photoeffect [3, 4]. It has been noted that the principle of operation of monochromators is based on diffraction of X-rays. The first experiments related to this physical phenomenon were performed in 1912 by Max von Laue with his young employees Knipping and Friedrich.Asimple condition allowing to determine the angle corresponding to the diffraction maximum was obtained by the English physicist Bragg [3] and, independently, by the Russian scientist Wolf: 2 sin hkl d n θ = λ. (1) Expression (1), referred to as the Wolf – Bragg condition in the Russian-language literature, shows how the angles θ at which constructive interference of X-ray radiation scattered by a crystal occurs are related to the X-ray wavelength λ and the distance between atomic planes dhkl (Fig. 3). The parameter n in formula (1) represents the order of reflection. The Wolf – Bragg condition serves as a theoretical basis for the design of any monochromator for a synchrotron radiation source. Fig. 3. Schematic of X-ray diffraction on the atomic planes of the crystal and illustration of the angular divergence of the beam Proceeding from the idea that a crystal could be represented as a set of parallel planes with the same dhkl distance between them, Bragg and Wolf believed that X-rays falling on a crystal would diffract only if the grazing angle θ satisfied the condition (1). It means that if a polychromatic (“white”) beam falls on an ideal nonabsorbing crystal of infinite depth, the band of diffracted radiation will be infinitely narrow [3, p. 149]. Such a diffraction mode is ideal, and practically unattainable. In fact, a spectral band of some width Δλ is formed by a monochromator. The causes of broadening are related to thermal deformations of the crystal, rigidity of its mounting, imperfection of the crystal structure, vibrations from the coolant flow, vibrations of the Earth’s crust, and so on. The mentioned circumstances complicate the description of the X-ray diffraction on the crystal. Thus, the ideal variant of fulfillment of the Wolf – Bragg condition is not realized in practice and some scattering of radiation actually occurs (Fig. 3 b).
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