Effects of dispersion and absorption in resonant Bragg diffraction of x-rays.

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.

[1]  S. A. Aseyev,et al.  Ultrafast electron diffraction and electron microscopy: present status and future prospects , 2014 .

[2]  D. Khalyavin,et al.  X-ray diffraction by magnetic charges (monopoles) , 2013, 1307.5164.

[3]  U. Staub,et al.  Chiral properties of hematiteα-Fe2O3inferred from resonant Bragg diffraction using circularly polarized x rays , 2013, 1306.4923.

[4]  S. Collins,et al.  X-ray Birefringence in highly Anisotropic Materials , 2013 .

[5]  W. Stephen,et al.  A Guide to Electronic Multipoles in Photon Scattering and Absorption , 2013 .

[6]  H. Nakao,et al.  Resonant X-ray Scattering Experiments on the Ordering of Electronic Degrees of Freedom , 2013 .

[7]  H. Tolentino,et al.  Birefringence and polarization rotation in resonant x-ray diffraction , 2012 .

[8]  Yoshikazu Tanaka,et al.  Determination of absolute chirality using resonant X-ray diffraction , 2012 .

[9]  A T Boothroyd,et al.  Observation of Orbital Currents in CuO , 2011, Science.

[10]  U. Staub,et al.  Parity- and time-odd atomic multipoles in magnetoelectric GaFeO 3 as seen via soft x-ray Bragg diffraction , 2009 .

[11]  V. Scagnoli,et al.  Analysis of azimuthal-angle scans in resonant x-ray Bragg diffraction and parity even and odd atomic multipoles in the multiferroic modification of the terbium manganate TbMnO 3 , 2009 .

[12]  H. Ohashi,et al.  Right handed or left handed? Forbidden x-ray diffraction reveals chirality. , 2008, Physical review letters.

[13]  A. Kirfel,et al.  Polarization anisotropy of X-ray atomic factors and 'forbidden' resonant reflections. , 2005, Acta crystallographica. Section A, Foundations of crystallography.

[14]  K. Knight,et al.  Electronic properties of crystalline materials observed in X-ray diffraction , 2005 .

[15]  C. Brouder.  Angular dependence of X-ray absorption spectra , 1990 .