Determination of Ratio of Diamagnetic Anisotropy of a Biaxial Crystal by X-ray Diffraction Measurement

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The ratio of diamagnetic anisotropy of a biaxial crystal (cellobiose: monoclinic, space group P2_{1}) was determined using two X-ray fiber diffraction patterns that were obtained from its microcrystalline powder oriented in static and rotating magnetic fields. We first determined the directions of the magnetic axes with respect to the crystallographic axes. We found that \chi_{3} is parallel to the b^{*}-axis, and the \chi_{1}-axis forms angles of 67.9 and 22.8° with respect to the a^{*}- and c^{*}-axes, respectively. Using the analysis method proposed recently, azimuthal half widths of the X-ray diffraction spots for (hkl) planes of the oriented samples were plotted as a function of \sin^{2}\Phi, where \Phi is an angle that characterizes the direction of the reciprocal vector of the (hkl) plane in the \chi_{1}\chi_{2}\chi_{3} coordinates, with \chi_{1}, \chi_{2}, and \chi_{3} being the principal axes of the magnetic susceptibility tensor. The half width linearly depended on \sin^{2}\Phi as predicted by the proposed method. From the values of the slope and intercept of the plot, the ratio of the diamagnetic anisotropy, r_{\chi}=(\chi_{2}-\chi_{3})/(\chi_{1}-\chi_{2}) was determined, where \chi_{1}>\chi_{2}>\chi_{3}. We estimated that r_{\chi}=1.4{\mbox{--}}1.7.
2012-06-25