I want to Identify the crystallite size distribution from XRD data, preferably without the use of software. Please suggest me any method. If the software is necessary I'm a user of X'Pert Highscore Plus.
Thank you in advance
There are excellent YT videos out there, which explain the necessary steps, e.g.:
https://www.youtube.com/watch?v=lZ1VESKBxKY
The FWHM of the peaks you can extract from your Software (https://www.youtube.com/watch?v=MroBkmoZ6aI).
Ah yes sorry, I only know about variance methods like the Warren-Averbach approach. But I never used it on my own, maybe it helps.
One of the first four hits searching
xrd size distribution is: Article Determination of size distributions in nanosized powders by ...
See equations 8 and 11 there.
Note, they incorrectly call diffractograms "spectra" - when plotting d or q on the x-axis, the data may be from a spectrum, although constant energy and wavelength data is far more common. When plotting 2theta on the x-axis, constant wavelength data is implied, so the data is not a spectrum; it is a diffractogram.
Note, very good quality data with very well-defined peak shapes are required for the calculations to have any validity.
XRD peak shapes can be use for estimating crystallite size distribution. Traditional methods (Scherrer eqn & Williamson-Hall plot) uses only width part of XRD peaks and peak shapes are ignored, so these methods gives only mean sizes. If peak shape parameters (eta of phi) are known than use table 1 or Fig 5 of below reference:
Article Significance of diffraction peak shapes in determining cryst...
In this article lognormal size distribution is considered.
If peak broadening is much larger than instrumental effect and purely due to size effect (i.e. instrumental & microstrain are ignorable) then peak shape could be directly used.
In other cases (size, strain, instrumental all effect are present) either Rietveld/ LeBail fitting (X'Pert Highscore Plus/GSAS/FullProf) or Williamson-Hall approach could be used to deconvolve peak shape due to size part as per methodology of this article.
Hopefully, it may be useful.
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