which is the best method to determine crystalline size from SEM or AFM or XRD ? should the values identical in all techniques?
You should distinguish between the terms "crystallite" and "grain".
While XRD gives you information about the crystallite dimensions, or in other words, coherently scattering domains, SEM and AFM rather provide information about the grain dimensions. Meanwhile grains are composed of crystallites.
Full width at half maximum (FWHM) of X-ray diffraction peaks reciprocally depends on the crystallite dimensions. Thats why XRD peaks of single crystals are very sharp and intense, because single crystal can be considered as one large crystallite. The XRD peaks of nanocrystalline materials are in turn broad and hardly differ from amorphous-like diffractograms.
Like Hoda Mohseni told, for determination of crystallite dimensions you could simply use Scherrer equation. But then be aware of the instrumental broadening to the peaks, which may be eliminated once you determine / calibrate it for your apparatus using a standard sample of e.g. NBS-Silicon or LaB6. Scherrer equation is also involved in some more sophisticated methods like Rietveld refinement, Williamson-Hall plot method, Warren-Averbach, etc. These are implemented in various freely and commercially available software for XRD analysis and provide extensive information about the material, including e.g. crystallite dimensions and internal strain (accounting also for instrumental broadening). Noteworthy, I guess for single crystalline sample the term "crystallite dimension" would make no sense, and software-realized Scherrer equation, being limited to 100 nm, would always yield values of 100nm for single crystals or large crystallites, independently on what their actual sizes are. And from my particular experience, any values below 10-12 nm would rather be doubtful as well.
Finally, comparing to XRD, I guess SEM and AFM are simply not able to see the crystallites due to technical reasons, e.g. limited resolution. Therefore, values obtained by XRD, SEM and AFM, should or even would not necessarily be identical. It may be so in case of truly nanocrystalline material, where grain and crystallite are same entities. Perhaps TEM would be helpful.
Here is some interesting discussion concerning crystallites, grains and particles.
https://www.researchgate.net/post/Can_anyone_clarify_the_difference_between_Grain_size_particle_size_and_crystallite_size
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