Separation After Peak Shape Modeling

Why and How to Use a Model If the graphical method of Warren-Aver-BACH does not work because of weak reflections, overlapping reflections, or problems with the subtraction of background scattering one may resort to modeling the peak shape in Eq. (8.13). Suitable shapes have been resulting from direct peak-shape visualization based on Eq. (8.16) from p. 107. Eor proper data recording and preparation refer to Sect. 8.2.5.1. 

After each peak has been described by the parameters of a model function, the convolution in Eq. (8.13) can be carried out analytically. As a result, equations are obtained that describe the effects of crystal size, lattice distortion, and instrumental broadening on the breadth of the observed peak. Impossible is in this case the separation of different kinds of lattice distortions. 

Polydispersity Different Crystal Size Averages. The crystal sizes in the polycrystalline samples are not identical. So it is important to know, what kind of average (cf. Sect. 1.2) is returned by the method. 

The indirect method described here returns the weight-average crystal size [121], irrespective of the model shape chosen. On the other hand, the direct Fourier inversion according to Warren-Averbach returns the number average of the crystal size distribution. 

Model Gaussian Peaks. If all the terms on the right-hand side of Eq. (8.13) can be modeled by Gaussians, the square of the integral breadth of the observed peak 

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