OBRABOTKAMETALLOV MATERIAL SCIENCE Vol. 26 No. 3 2024 Degree of monochromaticity of radiation “White” radiation entering the monochromator includes a wide range of wavelengths, which is determined by the radiation source (for example, a bending magnet or wiggler). Amonochromator, as noted earlier, should select a narrow band of wavelengths from this range (Fig. 4). a b Fig. 4. Dependence of SR photon flux density on radiation energy (E): a – monochromatic radiation (degree of monochromaticity ΔЕ/Е = Δλ/λ = 10-4–10-3); b – “pink” radiation (ΔЕ/Е = Δλ/λ = 10-2–10-1) The ratio of the select band width Δλ to the peak value of the transmitted radiation wavelength λ determines the degree of monochromaticity. By differentiating the Wolf – Bragg dependence, we obtain: 2 cos . hkl d d d ⋅ θ ⋅ θ = λ (2) Substituting 2dhkl with λ/sinθ, we have: ctg , ∆λ = θ ⋅ ∆θ λ (3) where θ is the slip angle; Δθ is the deviation of the slip angle caused by thermal deformation and vibration of the crystal. In some cases, it is convenient for the specialists dealing with the diffraction of X-rays to operate not only with the value of the radiation wavelength λ, but also with the value of the photon energy E corresponding to a certain wavelength. It is not difficult to show that: ctg . E E ∆ ∆λ = = θ ⋅ ∆θ λ (4) Thus, the degree of monochromaticity is determined by the grazing angle θ and the value of the deviation Δθ [4]. In an ideal case, the value of the diffraction angle θ on the crystal does not change during the experiment. However, in fact, as we have noted, this assumption is not fulfilled. One of the most important reasons for the deviations observed in the experiment is related to the influence of heat flow, which results in heating of some local zone of the crystal (Fig. 5, highlighted by a circle). The result of such an effect, accompanied by thermal expansion of the material, is a distortion of its crystal structure [5]. The thermal effect leads to deformation, first of all, of the first crystal of the monochromator, thus causing a deviation from the Wolf – Bragg condition. The result of heating is a local distortion of the crystal lattice of the material (increase in the interplanar distance dhkl). The heat accumulated in the crystal is the cause of material expansion, formation of a convex zone and scattering of radiation at different angles. It should be noted, however, that the change in the dhkl parameter can be associated with the quality of manufacturing the crystal, and the presence of defects of various nature in it. Thus: ; d θ = θ + δθ (5)
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