You find the size of the coherent scattering domains. As far as I know the only strict relation this size has to crystalline or particles size is that the latter ones are an upper limit. In papers I always use the term "apparent domain size", to avoid any confusion with sizes determined by other techniques and to prevent overinterpretation of the data.
Yes there is change is between crystallite size and particle size. as is i am rite, particle is made up of several crystallite. and scherrer equation gives the crystallite size. particle size can be calculated fron SEm or TEM
The answer is hidden in your question only. A particles can be made of several crystals. So they are diffrent and crystallite size are generally less or equal to particle size. From XRD you can only get crystallite size.
Also note that you may have different crystallite sizes depending on which reflection that you choose, in the case of so-called anisotropic line broadening. Dislocations on distinct slip systems or defects such as anti-phase boundaries can lead to different sizes of the scattering domains in different directions e.g. , or .
Note that in some of these cases, even with these defects you would not really call the particle a polycrystal, but you could still have a smaller coherent scattering domain than the primary crystal size (e.g by TEM).
Crystallite Size is Different than Particle Size. A particle may be made up of several different crystallites or just one crystallite so in this case (particle size = crystallite size)
Crystallite size often matches grain size, but there are exceptions
Crystallites are coherent diffraction domains in X-ray diffraction.
Particles are chunks/pieces (usually very small, below 1 mm) of solid matter, ensembles of atoms. Particles can be as small as two atoms (the nitrogen particle for example, N2)
Grains are volumes, inside crystalline materials, with a specific orientation.
Particles can be polycrystalline, single crystal or amorphous. A 100 nanometer particle of gold, for instance, can be made of: