Electronic properties of crystalline materials observed in X-ray diffraction

The few electrons in valence states of a material participate in many of its physical properties, including both structural and transport properties. In the diffraction of X-rays, or neutrons, valence electrons can lead to weak Bragg reflections that are extremely sensitive signatures of their charge and magnetic degrees of freedom. In this regard, diffraction instruments supplied with X-rays from a synchrotron source are particularly useful because the brightness, tuneability and polarization of the X-rays are all helpful in making valuable observations. The data obtained from Bragg diffraction can be analyzed on the basis of an atomic model, which has the virtue that it can be used as a common platform for the analysis of X-ray and neutron diffraction and, in addition, the analysis of observations made with X-ray absorption, NMR, EPR, muon and Mössbauer spectroscopies. We present the salient features for the calculation of structure factors based on an atomic model and applied to the analysis of Bragg diffraction by non-magnetic and magnetic materials, with an emphasis on resonant X-ray Bragg diffraction. The presentation contains a new treatment of parity-odd events found in the mixed electric dipole–electric quadrupole channel of scattering. In addition we discuss the complementary observation of dichroic signals, including natural circular and magnetochiral dichroism. rvey of available analytical tools is complemented by a series of worked examples demonstrating the application of the formalism to different materials with different crystal structures and resonant ions: dysprosium borocarbide ( DyB 2 C 2 ), vanadium sesquioxide ( V 2 O 3 ) , gadolinium tetraboride ( GdB 4 ), chromium sesquioxide ( Cr 2 O 3 ), haematite and perovskite-type manganites.