Quantity of FWHM(Full Width at Half Maximum) is a commonly used crystallographic parameter, mainly due to clear definition and ease of determination. In case of crystalline powders containing grains of same size (mono-dispersive), there exists a simple relation between FWHMand the grain size, called Scherrer equation. In a more realistic case of polidisperse powders, single parameter FWHM is not sufficient to determine both properties of Grain Size Distribution: it's average <R> and dispersion . In order to derive two unknowns, two equations are needed - that's why determination of full Grain Size Distribution requires two line widths to be used: and - measured at and of line maximum, respectively.
Detailed derivation of method is skipped here and can be found in .
We assume gamma Grain Size Distribution of crystallites:
We present expressions that can be readily used in order to
obtain average size1 of the grain in a powder and dispersion of the GSD as
a function of measured values of
Another example of usage of the is given on Fig.3. It shows standard GSD evaluation for BN nanocrystals from profile of (111), (220) and (311) diffraction lines. Standard deviations do not exceed 1% for average sizes determined and 4% for dispersions. Such a small deviations are due to good quality of diffraction data (smooth experimental curves).
In next section a practical supplement to the method is presented. It allows for direct application of parameters obtained during fitting Pearson7 curve to the experimental peak profile. Curve Pearson7 is commonly used in popular crystallographic software.