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arXiv · 2401.00412

Toward the theoretically observable limit of electron density distribution by single-crystal synchrotron X-ray diffraction: The case of orbitally ordered Ti-3d^1 in YTiO_3

Terutoshi Sakakura·Yoshihisa Ishikawa·Shunji Kishimoto·Yasuyuki Takenaka·Kiyoaki Tanaka·Shigeki Miyasaka·Yoshinori Tokura·Yukio Noda·Nobuo Ishizawa·Hajime Sagayama·Hajime Yamamoto·Hiroyuki Kimura
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Abstract

The theoretically observable limit of electron density distribution by single-crystal X-ray diffraction is discussed. When F_{orb} and {\delta}F 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 F_{orb} is chiefly determined by the number of reflections satisfying the condition F_{orb}/F > {\delta}F/F. Since F_{orb}/F, which is generally small for crystals with large F(0,0,0), is constant under a given set of experimental conditions, {\delta}F/F must be reduced to increase the number of reflections satisfying F_{orb}/F > {\delta}F/F. The present paper demonstrates how to reduce {\delta}F 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 F^2 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-3d^1 orbital in YTiO_3 by synchrotron single-crystal X-ray diffraction is presented.

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Terutoshi Sakakura, Yoshihisa Ishikawa, Shunji Kishimoto, Yasuyuki Takenaka, Kiyoaki Tanaka, Shigeki Miyasaka, Yoshinori Tokura, Yukio Noda, Nobuo Ishizawa, Hajime Sagayama, Hajime Yamamoto, Hiroyuki Kimura. 2023-12-31. Toward the theoretically observable limit of electron density distribution by single-crystal synchrotron X-ray diffraction: The case of orbitally ordered Ti-3d^1 in YTiO_3. https://arxiv.org/abs/2401.00412

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