As we know scherrer equation is limited to nano-scale crystallites, what are the other methods to calculate crystallite size if the size ranges above 100nm? Our obtained crystallites are above 100 nm. I have a pdf of XRD data of my sample, in which the sizes have been automatically measured. I want to know on basis of which method the XRD instrument calculated the size.
Any kind of help is highly appreciated.
Dear Munmun Basak ,
I'll give some thoughts on the question only, however the restrictions imposed by the 100 nm must be carefully checked on each method, in particular to the anisotropic size broadening effect.
A few points are necessary to mention before: to define peak width to be used in the calculations, the Full Width at Half Maximum (FWHM) and Integral Breadth are two usual and easy methods.
Langford and Wilson suggest that even when using the integral breadth, somehow a step forward to the FWHM, there is a Scherrer constant K that varies with the shape of the crystallites.
Crystallite size is defined as the cube root of the volume of a crystallite, assuming that all crystallites have the same size and shape (unusual in natural and synthetic samples).
Therefore, the Scherrer method, uses FWHM, gives the ratio of the root-mean-fourth-power to the root-mean-square value of the thickness.
Stokes and Wilson's method, which uses the integral breadth, determines the volume average of the thickness of the crystallites measured perpendicular to the reflecting plane.
The Warren-Averbach method uses the variance methods giving the ratio of the total volume of the crystallites to the total area of their projection on a plane parallel to the reflecting planes. The mathematical treatment here requires no neighbouring peak overlap et al., all over the diffraction peaks taking into account.
Even to the methods described above, the anisotropic size broadening will be a concern.
Depending on the profile fit function, the peaks may be deconvoluted. Therefore, the crystallite size is calculated from one of the above-cited methods. Not all peak profile functions allow the deconvolution, so it is a previous decision if a calculation or comparison is necessary or desirable.
My intention was to give some topics to consider.
Best regards,
WNM
Dear Munmun Basak,
You can consider Williamson-Hall Method for your estimation.
You may also find the following RG thread useful:
https://www.researchgate.net/post/How-to-calculate-crystallite-size-from-modified-Williamson-Hall-Method
Also go through the following texts:
1) Article Williamson-Hall analysis in estimation of lattice strain in ...
2) http://prism.mit.edu/xray/newsite/oldsite/5a%20Estimating%20Crystallite%20Size%20Using%20XRD.pdf
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