Spectral Measurements with Aligned and Misaligned Two-Crystal Spectrometers. I. Theory of the Geometrical Window

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Abstract
It is shown in this paper that (1) the geometrical window of the instrument is a function of the alignment of the crystals, the beam, and the rotation axes as well as the vertical divergence, (2) even for the case of perfect spectrometer alignment, errors are introduced into the measurement of the spectral parameters because of the presence of a finite vertical divergence in the x‐ray beam, and (3) improper beam and crystal alignment cause inaccuracies in the measurement of spectral parameters, e.g., wavelength position, linewidth, line shape, and asymmetry. Calculations which predict the effects of vertical divergence and of beam and crystal misalignment on the geometrical window and also on the wavelength position, line shape, linewidth, and line asymmetry of the (1,+1) and (1,−1) curves are made for the case of CuKα radiation reflected from calcite crystals. In particular, it is shown that the error in the measurement of the Bragg angle, i.e., wavelength, is 61/2 times more sensitive to misalignment of the central ray of the x‐ray beam than it is to total vertical divergence.