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Acta Cryst. (2014). A70, C391
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We have used resonant multi-beam diffraction with the primary reflections G=(h/2 h/2 0) and G=(h/4 h/4 0) (h is an odd number) to investigate the charge ordering and Jahn-Teller distortion, respectively, in La0.5Sr1.5MnO4 low temperature phase. While the Renninger scans with G=(h/2 h/2 0) shows several Aulfhellung-type four-beam diffraction, most of the multi-beam diffraction with G=(h/4 h/4 0) has an Umweganregung-type nature. A detailed study of multi-beam diffraction anomalous fine structure (M-DAFS) of (0 0 0)/(3/2 3/2 0)/(1 -1 0)/(5/2 1/2 0) OUT diffraction is carried out. Its triplet invariant phase approach 1800 when the x-ray energy is tuned away from manganese K-edge, and approach 900 when the x-ray energy is tuned on manganese K-edge. In other words, its multi-beam diffraction profile shows strong asymmetry when (3/2 3/2 0) diffraction intensity is dominated by Jahn-Teller distortion, and becomes more symmetric when charge ordering dominated. This characteristic can be successfully simulated by tensor form dynamical x-ray diffraction theory accompanied with FDMNES software [1] calculations.

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An algorithm for calculating the 2θ diffraction profiles is developed based on the dynamical theory of X-ray diffraction for multi-beam cases. The connection between the 2θ-scanned profiles and the excitation of modes is revealed.
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