Powder Diffraction at ORNL#

Powder diffraction is a powerful and commonly used technique for characterizing the microscopic structure of materials ranging from battery materials, catalysts, to quantum materials such as superconducting and spintronic materials, and among others. There are two major branches of the powder diffraction technique. The first one (and probably the familiar one) is Bragg diffraction of which the fundamental principle is the Bragg equation infering where the diffraction pattern is supposed to spike as determined by the underlying crystallographic structure. With Bragg diffraction, the only thing of interest is the Bragg peaks and the analysis is centering around the extraction of the intensities and positions of those Bragg peaks. In practice, due to finite instrument resolution, it is unavoidable that the diffraction peaks corresponding to different Miller index will be overlapping which makes it challenging to extract the information associated with each individual composite peak. The breakthrough idea for solving this issue was proposed by Rietveld back in 1969 [Rietveld, 2011]. who realized that a common profile function is shared among the diffraction peaks and such profile funtions are relevant to the characteristics of the beam being used for the diffraction experiment. As such, by constructing the profile function and convolving with the diffraction intensities, the whole diffraction pattern could be established. A nice and succint introduction about the profiling of powder diffraction can be found in Ref. [Cockcroft, 1999].

The Bragg condition is specifically for perfectly periodically repeated arrangement of atoms, and in practice any sort of shift from the ideal position of atoms would diminish the scattering intensity (as indicated by the structure factor). The origin of such shift could be manifold – both static and dynamic. For Bragg diffraction data analysis, since one is only interested in the Bragg peak intensities (along with the positions, for sure), the diminished intensities would be treated as the background and thus subtracted from the diffraction pattern. However, the reduced intensity does not go nowhere, and instead, they become the diffuse scattering signal underneath the Bragg peaks – this is exactly where the name of the renowned book by T. Egami and S. Billinge. [T. Egami, 2012] is coming from. By accumulating statistics and careful treatment of the data (background removal, detector normalization, etc.), the diffuse scattering signal could be brought together with the Bragg peaks to form the so-called total scattering pattern. The diffuse scattering part gives the local structure information which is lost in the Bragg diffraction. Therefore, for systems where the physical properties are strongly correlated with the local variation of the structure but not the average structure, the diffuse scattering signal will be very useful in fetching the information about such local variations to understand and control material properties.

Various types of beam can be utilized to conduct the diffraction measurement, such as X-ray, electron, and neutron. A detailed comparison of various diffraction medium can be found in Ref. [J. Stohr, 2006]. Specifically concerning the total scattering measurement, a large \(Q\)-space coverage is needed to guarantee a high resolution in real-space. With this respect, the neutron source is advantageous since the scattering power of elements upon neutron is nearly a constant across the whole \(Q\)-range, meaning it won’t induce an intrinsic dampening as \(Q\) increases, as is the case for both X-ray and electron. ORNL hosts 12 diffractometers—7 at the Spallation Neutron Source and 5 at the High Flux Isotope Reactor – which are operated and maintained by the Diffraction group. This group contains outstanding neutron scattering scientists with a wide range of scientific interests and expertise. The diffractometers are divided into three suites: powder diffraction instruments, single crystal instruments and advanced diffraction instruments. Current documentation is focusing on the powder diffraction suite and will be covering useful information about both data reduction and data analysis.