Toward the theoretically observable limit of electron density distribution by single-crystal synchrotron X-ray diffraction: The case of orbitally ordered Ti-3d1 in YTiO3
Abstract
The theoretically observable limit of electron density distribution by single-crystal X-ray diffraction is discussed. When Forb and δF are defined as, respectively, the partial structure factor for an orbital and the deviation of the observed F from the true F, the accuracy of electron density attributable to Forb is chiefly determined by the number of reflections satisfying the condition Forb/F > δF/F. Since Forb/F, which is generally small for crystals with large F(0,0,0), is constant under a given set of experimental conditions, δF/F must be reduced to increase the number of reflections satisfying Forb/F > δF/F. The present paper demonstrates how to reduce δF mathematically and experimentally, and the following topics are covered: the Poisson statistics, accumulation of errors in the data collection and reduction procedure, multiple diffraction, conversion error from F2 to F in refinement programs, which is unavoidable when the input quantities have different dimension from F, weighting of reflections, and tips. For demonstration, observation of the electron density of the Ti-3d1 orbital in YTiO3 by synchrotron single-crystal X-ray diffraction is presented.
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