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The mathematical functions necessary for Rietveld refinement of time-of-flight neutron powder diffraction patterns from spallation sources are developed and a computer program for least-squares analysis is described. The results of Rietveld refinements of nickel and a low-carbon steel are described and discussed. The method fully exploits the high resolution (Δd/d ~ 0.3 ~ 0.5%) available with powder diffractometers currently in operation on these sources and examples are given of precise determination of atom coordinates, thermal parameters, lattice parameters and the detection of small strains.
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