text: Before exploring Rietveld refinement, it is necessary to establish a greater understanding of powder diffraction data and what information is encoded therein in order to establish a notion of how to create a model of a diffraction pattern, which is of course necessary in Rietveld refinement. A typical diffraction pattern can be described by the positions, shapes, and intensities of multiple Bragg reflections. Each of the three mentioned properties encodes some information relating to the crystal structure, the properties of the sample, and the properties of the instrumentation. Some of these contributions are shown in Table 1, below.
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  The structure of a powder pattern is essentially defined by instrumental parameters and two crystallographic parameters: unit cell dimensions, and atomic content and coordination. So, a powder pattern model can be constructed as follows:
  # Establish peak positions: Bragg peak positions are established from Bragg's law using the wavelength and d-spacing for a given unit cell. 
  # Determine peak intensity: Intensity depends on the structure factor, and can be calculated from the structural model for individual peaks. This requires knowledge of the specific atomic coordination in the unit cell and geometrical parameters.
  # Peak shape for individual Bragg peaks: Represented by functions of the FWHM (which vary with Bragg angle) called the peak shape functions. Realistically ab initio modelling is difficult, and so empirically selected peak shape functions and parameters are used for modelling. 
  # Sum: The individual peak shape functions are summed and added to a background function, leaving behind the resultant powder pattern.
  It is easy to model a powder pattern given the crystal structure of a material. The opposite, determining the crystal structure from a powder pattern, is much more complicated. A brief explanation of the process follows, though it is not the focus of this article.
  To determine structure from a powder diffraction pattern the following steps should be taken. First, Bragg peak positions and intensities should be found by fitting to a peak shape function including background. Next, peak positions should be indexed and used to determine unit cell parameters, symmetry, and content. Third, peak intensities determine space group symmetry and atomic coordination. Finally, the model is used to refine all crystallographic and peak shape function parameters. To do this successfully, there is a requirement for excellent data which means good resolution, low background, and a large angular range.