Background modelling in Rietveld analysis

Abstract The Rietveld Method was devised as a complete powder-diffraction-pattern fitting technique, which necessitates modelling the total scattering from crystalline samples. Typical scattering patterns from purely crystalline materials without defects can be reliably modelled simply by convoluting the calculated Bragg intensities with the resolution function of the diffraction instrumentation and adding a background contribution accounting for incoherent scattering, air scattering, and Thermal Diffuse Scattering. (See Chapters 7 and 8 for accounts of crystalline size and microstrain effects on the observed reflection profiles.) Many diffraction experiments, however, involve the analysis of scattering patterns containing additional non-crystalline scattering components which are not accounted for by conventional background functions. These com-ponents are observed in Rietveld analyses as broad oscillations superimposed on the sharp Bragg pattern. One example of this is thermal diffuse scattering (TDS) for which the corrections are well known (Chapter 9; Cooper and Rouse 1968; Windsor 1981 ). Other examples include scattering from: ( 1) amorphous containers, (2) incompletely crystallized samples, and (3) separate amorphous phases. These scattering phenomena can be characterized as interference functions developed from short-range interactions between atoms in the sample. Successful refinement of the crystalline structure requires precise modelling of these additional non-crystalline contributions. This can be accomplished through the use of empirical functions such as higher-order polynomials.