Influence of Chemical Heterogeneities on Line Profiles

Influence of Chemical Heterogeneities on Line Profiles

Copyright: © 2014 |Pages: 29
DOI: 10.4018/978-1-4666-5852-3.ch005
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Abstract

The chemical composition fluctuation in a material may cause line broadening due to the variation of the lattice parameter, which yields a distribution of the profile centers scattered from different volumes of the material. The nature of line broadening induced by chemical heterogeneities is similar to a microstrain-like broadening in the sense that the peak width increases with the magnitude of the diffraction vector. However, the dependence of compositional broadening on the orientation of diffraction vector (i.e. the anisotropic nature of this effect) differs very much from other types of strain broadening (e.g. from that caused by dislocations). The anisotropic line broadening caused by composition fluctuation is parameterized for different crystal systems and incorporated into the evaluation procedures of peak profiles. This chapter shows that the composition probability distribution function can be determined from the moments of the experimental line profiles using the Edgeworth series. The concentration fluctuations in decomposed solid solutions can also be determined from the intensity distribution in the splitted diffraction peaks.
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The Concept Of Compositional Microstrain

Let us assume that the chemical composition in a polycrystalline material varies from crystallite to crystallite. The various composition in the different crystallites yields different lattice parameters and therefore shifts of the centers of peak components scattered from different crystallites as illustrated schematically in Figure 1 (Leineweber & Mittemeijer, 2006). Therefore, an individual crystallite with a given composition contributes to a certain reflection hkl of the powder diffraction pattern with a profile having Dirac-delta shape and located at the scattering angle which corresponds to the chemical composition of the crystallite. In the case of reflection hkl the distribution of the interplanar spacing of lattice planes (hkl) in the different crystallites is the reason of peak broadening. The deviation of the interplanar spacing (dhkl) from the ideal value (d0,hkl) due to alloying or impurity elements can be regarded as a lattice strain (εhkl) using the following formula (Leineweber, 2009):

. (5.1)

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