Thie difference in grain size measured by AFM, TEM and XRD was discussed in RG. Please do a search in RG.

In AFM and XRD, you don't measure the same things. In XRD you "estimate" the mean crystallite size. 

My Dear Atilla Atli,

           Thank you very much.Can you give me more details or references. 

Hi Ghaleb AL-Dahash, these are some of the discussions about your question, 

https://www.researchgate.net/post/Why_is_there_a_difference_in_the_crystalline_size_of_the_nanoparticle_as_measured_from_TEM_image_and_XRD_analysis_of_the_same_sample

https://www.researchgate.net/post/Particle_size_or_crystallite_size_estimation_from_powder_XRD_and_AFM

Thank you very much for all.

Zongying Han: More specifically, XRD estimates the crystallite size using peak broadening. The Scherrer equation was simply the earliest attempt to quantify the size broadening, and there are many other more advanced XRD-based methods to be found in the literature, such as Williamson-Hall, various full pattern fitting routines, etc. You should look to papers (or postings on RG) by Matteo Leoni for guidance on this.

Thank you very much

Can any one give me the XRD-data or pattern of Pt and Au-Ag alloy .

or ASTM card

Dear colleague Dahash,

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:

a single gold crystal,

many grains with a grain size

Dear Ahmed I. Osman,

Thank you very much.

Regards

Ghaleb

Dear Ghaleb AL-Dahash,

You are very welcome

have a very good day

Ahmed

I think this link can help

http://www.instanano.com/characterization/theoretical/xrd-size-calculation/

Dear Dheeraj Kumar

Thank you so much.

Regards

Ghaleb