Lovesey S W, Scagnoli V, Dobrynin A N, Joly Y, Collins S P
ISIS Facility, STFC, Didcot, Oxfordshire OX11 0QX, UK. Diamond Light Source Ltd, Harwell Science and Innovation Campus, Oxfordshire OX11 0DE, UK.
J Phys Condens Matter. 2014 Mar 26;26(12):125504. doi: 10.1088/0953-8984/26/12/125504. Epub 2014 Mar 6.
Resonant diffraction of x-rays by crystals with anisotropic optical properties is investigated theoretically, to assess how the intensity of a Bragg spot is influenced by effects related to dispersion (birefringence) and absorption (dichroism). Starting from an exact but opaque expression, simple analytic results are found to expose how intensity depends on dispersion and absorption in the primary and secondary beams and, also, the azimuthal angle (rotation of the crystal about the Bragg wavevector). If not the full story for a given application, our results are more than adequate to explore consequences of dispersion and absorption in the intensity of a Bragg spot. Results are evaluated for antiferromagnetic copper oxide, and low quartz. For CuO, one of our results reproduces all salient features of a previously published simulation of the azimuthal-angle dependence of a magnetic Bragg peak. It is transparent in our analytic result that dispersion and absorption effects alone cannot reproduce published experimental data. Available data for the azimuthal-angle dependence of space-group forbidden reflections (0,0, l), with l ≠ 3n, of low quartz depart from symmetry imposed by the triad axis of rotation symmetry. The observed asymmetry can be induced by dispersion and absorption even though absorption coefficients are constant, independent of the azimuthal angle, in this class of reflections.
对具有各向异性光学性质的晶体的X射线共振衍射进行了理论研究，以评估布拉格斑点的强度如何受到与色散（双折射）和吸收（二向色性）相关的效应的影响。从一个精确但不透明的表达式出发，得到了简单的解析结果，以揭示强度如何取决于一次和二次光束中的色散和吸收，以及方位角（晶体绕布拉格波矢的旋转）。对于给定的应用而言，即便我们的结果并非全貌，但也足以探究色散和吸收对布拉格斑点强度的影响。对反铁磁氧化铜和低石英进行了结果评估。对于氧化铜，我们的一个结果再现了先前发表的关于磁性布拉格峰方位角依赖性模拟的所有显著特征。在我们的解析结果中很明显，仅色散和吸收效应无法再现已发表的实验数据。低石英的空间群禁戒反射（0,0, l）（l ≠ 3n）的方位角依赖性的现有数据偏离了由三重旋转对称轴施加的对称性。在这类反射中，即使吸收系数是恒定的，与方位角无关，观察到的不对称性也可能由色散和吸收引起。
