Crystallite size measurement using XRAY diffraction

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Crystallite size can also cause peak broadening. The well known Scherrer equation explains peak broadening in terms of incident beam divergence which makes it possible to satisfy the Bragg condition for non-adjacent diffraction planes. Once instrument effects have been excluded, the
crystallite size is easily calculated as a function of peak width (specified as the full width at half maximu[...]
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Crystallite size can also cause peak broadening. The well known Scherrer equation explains peak broadening in terms of incident beam divergence which makes it possible to satisfy the Bragg condition for non-adjacent diffraction planes. Once instrument effects have been excluded, the
crystallite size is easily calculated as a function of peak width (specified as the full width at half maximum peak intensity (FWHM)), peak position and wavelength. Warren and Averbach's method takes not only the peak width into account but also the shape of the peak.

This method is based on a Fourier deconvolution of the measured peaks and the instrument broadening to obtain the true diffraction profile. This method is capable of yielding both the crystallite size distribution and lattice microstrain.The Scherrer and the Warren-Averbach methods do not give the same value for the crystallite size.

That is because they each yield different characteristic averages from the crystallite size distribution.But by combining the results of the Scherrer and the Warren-Averbach methods and making reasonable assumptions regarding crystallite shape and size distribution it is possible to arrive at a single size distribution.

In this experiment both the Scherrer and the Warren-Averbach methods are used to measure the crystallite size in several fine, even nano-crystalline, powders. Coarser powders, larger than 1
micron, may be analyzed to illustrate the limitations of these techniques.
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