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The linear relations of the neutron and X-ray optics in crystal powder diffractometers are extended with second-order terms. An expression for the angular deviation from the Bragg-peak position is derived which reduces to that of Wilson [Mathematical Theory of X-ray Powder Diffractometers (1963). Amsterdam: Philips Technical Library] for the case of characteristic X-rays in parafocusing geometry. A technique of computing second-order aberration effects is described. Line-shift formulae are given for conventional and curved-crystal diffractometers.
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