I need to know whether the modified Scherrer equation is useful in calculating the accurate size of the nanoparticle comparing Williamson-Hall equation.
As for as I know, Sherrer formula can be used to determine the absolute values of some nanoparticle. I used it myself and gives quite accurate value when you compare it with other size determining techniques.
In case of William Hall equation it is more useful when you are using them in relative sense for the calculation the particle size of the same type of material made by different processes and want to compare them.
For more detail you can look the following links in research gate.
https://www.researchgate.net/post/How_to_calculate_crystallite_size_from_modified_Williamson-Hall_Method
https://www.researchgate.net/publication/235445862_X-ray_analysis_of_ZnO_nanoparticles_by_WilliamsonHall_and_sizestrain_plot_methods
Data X-ray analysis of ZnO nanoparticles by Williamson–Hall and s...
X-ray broadening arises mainly due to three reasons. instrumental broadening, particle size effect and strain. To get rid of the instrumental broadening, you should record the XRD pattern of a Si single crystal and subtract the FWHM of the reference from that of your sample. Now, the corrected FWHM of your sample may be used to determine particle size and strain if you use William Hall plot. But for that you need to have at least three different peaks whose FWHM and peak positions may be recorded correctly. Scherrer equation on a single peak will give similar value as WH plot if the strain component in your sample is insignificant. Otherwise, it will always underestimate the size of the particle. In this context, I want to mention that the equation is valid only for small particles and never for large particles beyond 100nm. Moreover, the particle should be spherical. Otherwise, you need to change the geometric factor accordingly. Coming to the comparison with other techniques, TEM will give similar size if the extent of agglomeration is less, otherwise it will always overestimate the size of the particle.
Dear Mohammad,
we can calculate crystallite size (Grain size) from the PXRD data by applying Sheerer formula rather than definite particle size. I hope you know that their is difference between the particle size which you can accurately determine by the TEM and crystallite size which is obtained from the XRD data.
If you compare crystallite size and particle size obtained by above mentioned methods, they will be never exactly same.
Kind regards
Gowhar
I think this link can help
http://www.instanano.com/characterization/theoretical/xrd-size-calculation/
Dear Admin, My question is that if i have a alloy that composed up of two or three materials than which peak i select to calculate the crystal size for example if i have Copper alloy in which iorn as well as silver also present than for (1) which element peak we choose and (2) which specific peak we choose for crystal size calculation because there are many peaks for single element.
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