Tables for
Volume H
Powder diffraction
Edited by C. J. Gilmore, J. A. Kaduk and H. Schenk

International Tables for Crystallography (2018). Vol. H, ch. 1.1, p. 15

Section Information content in the background

R. E. Dinnebiera* and S. J. L. Billingeb,c

aMax-Planck-Institute for Solid State Research, Heisenbergstrasse 1, D-70569 Stuttgart, Germany,bDepartment of Applied Physics and Applied Mathematics, Columbia University, 500 West 120th Street, Room 200 Mudd, MC 4701, New York, NY 10027, USA, and cCondensed Matter Physics and Materials Science Department, Brookhaven National Laboratory, PO Box 5000, Upton, NY 11973–5000, USA
Correspondence e-mail: Information content in the background

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As discussed above, the elastic scattering from a crystalline powder consists of sharp rings, or peaks, of scattering at the 2θ angles where the Bragg or von Laue laws are satisfied. In general these sharp peaks sit on top of a `background' which is broad and somewhat featureless. There are two components to this background, illustrated in Fig. 1.1.1[link]: extraneous counts in the detector from things other than the sample, and non-Bragg scattering from the sample itself. The former are rarely of interest scientifically and the objective of a good experimental design is to minimize them as far as possible, or explicitly measure and subtract them, and then account well in any model or data interpretation for the part that cannot be eliminated from the measurement. Historically, the diffuse-scattering signals from the sample itself were also considered to be an inconvenience to be minimized and removed, and indeed in many cases this is still the best course of action (for example, sample fluorescence can be eliminated by choosing to work at an X-ray energy that lies below the absorption edge of a constituent atom). However, the diffuse `background' from the sample can contain crucial information about defects, disorder and nanoscale order in the sample, and increasingly we are interested in studying it in order to understand the properties of the material that is under investigation. In some cases, such as glasses, liquids and samples of small nanoparticles, there is no Bragg scattering at all and only a diffuse scattering signal (see Chapter 5.6[link] ).

All the intensity scattered by the sample can be categorized as either coherent or incoherent and as elastic or inelastic, which are defined as follows. The coherency of the signal derives from whether or not the scattered waves interfere with each other constructively, and the resulting intensities are different in each case. For coherent scattering, the waves contributing to the signal are all summed first, before the wave amplitude is squared, to find the intensity distribution, which is the modulus squared of the resulting wave. For incoherent waves, one simply squares the amplitude of each wave to get its intensity and sums these together to get the total intensity. Switching to a consideration of the elasticity of the scattering, we define the scattering as elastic if the incident and scattered waves have the same energy, in which case no energy was exchanged during the scattering process between the incident wave and the sample, and inelastic scattering as the opposite. Inelastic scattering may result in a gain or a loss of energy of the scattered particle depending on the nature of the scattering, which results in a change in the wavelength of the scattered particle. There are also some non-scattering processes that can take place, such as absorption and fluorescence, but emissions resulting from these processes can also be categorized by whether or not they are coherent and elastic. It should be noted that the total energy of the system must be conserved during the scattering process, and so when a scattered wave gains or loses energy it exchanges it with the sample. This is used as a way of probing excitations in a material. Table 1.1.1[link] summarizes many of the types of diffuse scattering coming from a sample and categorizes them by their coherency and elasticity.

Table 1.1.1| top | pdf |
Types of scattering from a sample

Type of scatteringCoherentIncoherent
Elastic Bragg scattering Laue monotonic diffuse scattering
  Magnetic Bragg scattering Neutron incoherent scattering
  Bragg scattering from ferroelectric/magnetic order Multiple scattering (incoherent)
  Diffuse scattering from static defects  
  Diffuse signal from small nanoparticles (<10 nm)  
  Scattering from amorphous material (except excitations)  
  Multiple scattering (coherent)  
Inelastic Thermal diffuse scattering Compton scattering
  Spin-wave scattering Fluorescence
  Paraelectric/paramagnetic scattering Incoherent scattering from hydrogen
  Scattering from liquids  

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