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Solve - An old midterm question 3.67 - Determine the expected diffraction angle for the first-order reflection from the (310) set of planes for BCC chromium (Cr) when monochron latic radiation of wavelength 0.0711 nm is used. (Hint: Bragg's law)
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To determine the expected diffraction angle for the first-order reflection from the (310) set of planes for BCC chromium (Cr) when monochromatic radiation of wavelength 0.0711 nm is used, we can use Bragg's law.Bragg's law states that the condition for constructive interference (diffraction) of X-rays by a crystal lattice is given by:nλ = 2d sin θwhere n is the order of diffraction, λ is the wavelength of the incident radiation, d is the interplanar spacing of the crystal lattice, and θ is the diffraction angle.For the first-order reflection, n = 1. The interplanar spacing d for the (310) set of planes can be calculated using the lattice constants a of the BCC crystal structure. For BCC chromium, a = 0.287 nm. The interplanar spacing d for the (310) set of planes is given by:d = a / sqrt(310^2 + 310^2 + 310^2)Substituting the values, we get:d = 0.287 / sqrt(310^2 + 310^2 + 310^2) nmNow, we can use Bragg's law to calculate the diffraction angle θ:1λ = 2d sin θSubstituting the values, we get:1/0.0711 = 2(0.287 / sqrt(310^2 + 310^2 + 310^2)) sin θSolving for θ, we get:θ = arcsin((2 * 0.287) / (sqrt(310^2 + 310^2 + 310^2) * 0.0711)) nmθ ≈ 28.8 degreesTherefore, the expected diffraction angle for the first-order reflection from the (310) set of planes for BCC chromium (Cr) when monochromatic radiation of wavelength 0.0711 nm is used is approximately 28.8 degrees.