Scherrer formula provides relatively a smaller value for the particle size as the width of the diffraction peak is caused by, apart from the particle size, a variety of other factors including inhomogeneous strain and instrumental effects. However, if you make study for a series of samples to understand the influence of chemical modifications or processing conditions, the relative contributions by the inhomogeneous strain and the instrumental effects to the peak broadening are assumed to be very small and can be neglected for the simple reason that the same same error, if any is common to all the samples in the series.
In that given scenario, what is of utmost importance is the accuracy in the estimates of peak broadening (FWHM). We usually do best fits to all the major peaks ((for Voigt/Gaussian/Loreantzian shapes depending up on the data) using ORIGIN and averaging them to get the accurate values of FWHM and 2theta.
If we further do Rietveld structural refinement, we get a new set of the same parameters out of simulations for comparison.
Any way, if you still need any help from us in estimating FWHM or crystallite size values for your XRD data, please feel free to send me a message at ([email protected]).
Attached please find the file of a paper in regard to calculating errors of nano-crystallite size using Scherre Equation. I hope it will be helpful for you.
Please find herewith another paper. The authors corrected the peak broadening and hence calculated the crystallite size using Scherrer equation. Best of luck.