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The temperature factor of an atom in a molecular crystal has been derived in terms of the rigid-body parameters (u2) and (ω2), where (u2) is the mean-square amplitude of translational displacement of the molecule in any direction and (ω2) is the mean-square amplitude of angular (librational) displacement about any axis through the centre of inertia of the molecule. The analysis, which is appropriate to a cubic crystal containing rigid molecules undergoing isotropic thermal motion, is correct to the second power of (ω2); the second-order treatment is necessary for interpreting accurate Bragg intensity data such as those discussed in a subsequent paper. Substitution of the temperature factor into the structure-factor equation yields an expression containing terms which can be identified with the first, second and third cumulants of the `cumulant expansion' model of thermal motion.

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