Analysis of Disordered Materials Using Total Scattering and the Atomic Pair Distribution Function

Abstract

Without a doubt, our ability to determine the atomic structure of complex materials has revolutionized our understanding of these materials over the last decades. Neutron scattering with its unique abilities has contributed greatly to this success. The range of applications of neutron scattering in geosciences are apparent when reading through this volume of Reviews in Mineralogy & Geochemistry. Usual structure determination, the realm of crystallography, is based on the analysis of Bragg intensities. In this article we want to look beyond or underneath the Bragg peaks and discuss the atomic pair distribution function (PDF) method as an approach to more fully understand the atomic structure of complex materials, from the local to the medium range all the way to the long range structure of the material. As mentioned above, structure determination is commonly based on the analysis of Bragg peaks either using single crystal diffraction (Ross and Hoffman 2006, this volume) or powder diffraction (Harrison 2006, this volume). However, one needs to keep in mind, that the structure resulting from Bragg scattering is only the long range average structure of the material. Many materials owe their interesting properties to defects within the material and obviously a complete structural picture and understanding of the properties will require knowledge of the “true” atomic structure. Geological samples are no exception and in fact are among the most complex systems known. Deviations from the average structure, e.g., in form of defects, manifest themselves as diffuse scattering. This is illustrated in an example shown in Figure 1⇓. Two 2D structures have been simulated; both have the same lattice parameters, contain one atomic site in the unit cell as well as contain a total of 30% vacant sites. The difference is the vacancy ordering. Figure 1a⇓ shows the structure with a …