Crystal imperfection broadening and peak shape in the Rietveld method

Abstract The Rietveld method requires a two-part starting model (see Chapter 1 and elsewhere), a structural model based on approximate atomic positions and a non-structural model which takes into account the contributions of individual line profiles in terms of analytical or other differentiable functions. Both must be considered in order to achieve an optimum representation of the observed pattern. The total intensity of Bragg reflections and, to a first approximation, their positions, are determined by the structural model, but the non-structural model, and hence the representation of diffraction lines, depends on the instrument used and on the microstructural and other properties of the sample. As is also explicitly noted in Chapters 7 and 9, structural imperfections should therefore be taken into account when considering the physical origin of line shapes. These imperfections can be diverse and include: the dimensions and morphology of coherently diffracting domains (crystallite-size effects), variation in interatomic distances due to internal stresses or non-stoichiometry, micro-twinning, stacking faults, dislocations, and other forms of atomic disorder. Microstructural features directly influence the shape of line profiles. The influence depends on the direction and magnitude of the diffraction vector.