As mentioned in many discussions here, Scherrers equation is very old-fashioned and not very trustful. Many experienced people already gave up and don't contribute anymore since the same questions are asked again and again and always the same old answers come up. 

I have no idea why people are "wild" to do this and then compare the derived data with grain distributions in SEM and are quite unhappy. It is simply no reliable tool since many terms define the peak width of material which are optimized by advanced techniques in order to get very useful properties. The reason is simply that for such cases the assumptions made do not match anymore your material. It works for simple mixtures of minerals but usually not for technically tortured phases which perhaps do not even earn this term anymore in its classical meaning. 

It is necessary to think before using an equation copied from somewhere. The conditions need to be fulfilled. If this is not given any application is useless. Look for the conditions and you will realize that there are several uncertainties like reflex broadening from your equipment. If you do not know how to correct it leave it. It will generate a meaningless and irritating number only.    

And I totally forgot (see below): Particle is not crystal! Sorry guys, because then the question does not make any sense.

Dear Fouzia

One can obtain the crystallite size using xrd results by employing Scherrer's formula

D=0.9*lambda/(FWHM)*cos(theta).

Best Regards, A. Ahad

As mentioned in many discussions here, Scherrers equation is very old-fashioned and not very trustful. Many experienced people already gave up and don't contribute anymore since the same questions are asked again and again and always the same old answers come up. 

I have no idea why people are "wild" to do this and then compare the derived data with grain distributions in SEM and are quite unhappy. It is simply no reliable tool since many terms define the peak width of material which are optimized by advanced techniques in order to get very useful properties. The reason is simply that for such cases the assumptions made do not match anymore your material. It works for simple mixtures of minerals but usually not for technically tortured phases which perhaps do not even earn this term anymore in its classical meaning. 

It is necessary to think before using an equation copied from somewhere. The conditions need to be fulfilled. If this is not given any application is useless. Look for the conditions and you will realize that there are several uncertainties like reflex broadening from your equipment. If you do not know how to correct it leave it. It will generate a meaningless and irritating number only.    

And I totally forgot (see below): Particle is not crystal! Sorry guys, because then the question does not make any sense.

In most of the cases XRD isn't applicable for particle size measurement. 

In case you take into account the peak broadening you can get Crystalite size, not particle size. However, in some cases these two coincide!

If the particles don't aggregate,I suggest using dynamic light scattering (DLS), otherwise SEM, TEM or any similar microscopic instruments can be better choice.

In many cases, the best method to obtain real size of particles in solid state is using TEM image of the sample. However, in solution, one can use DLS technique. Debye sherrer,s equation can give an estimate of mean crystallite sizes with some assumptions.  

Sorry guys, all of you have provided answers to his question that makes no sense. His question is: "How Can I calculate size of particle by XRD". The answer is simple, you can't because he doesn't define what he means by "particle size". A particle refers to a quantity of matter that has no particular size restriction  Do I assume that you are doing power x-ray diffraction and you want to know average mean size of particle and particle size distribution (PSD) or do I assume you want to look at size of the atom. Obviously I will go with the 1st one. Then I can answer your question.

 You says XRD. Do I presume that you mean Wide angle x-ray diffraction (WAXD) and not SAXS. WAXD provides information on angstrom level such as crystalline structure of a metal or polymer and SAXS will provide information on the long range ordering of crystalline structure or phase structure, such as lamella thickness and phase size in a segregated blend.  There is no way either of the two techniques will provide any info on relatively very very large "particle" structure in question. So, if I m correct in my assumption, there are Varity of instruments available that can give you fast count of PSD. To cite but few examples, Light scattering devises, Microscopy or Fraunhofer diffraction can be used for this purpose. Look into PAMAS particle counter, Particle size analyzer from Beckman or Brookhaven, Accusizer from Malvern etc.

But, if I am wrong in my assumption and your question pertains to size of particles at atomic level then please ignore my answer. Only you can clarify what you mean by "particle size"?

XRD gives an approximate idea about the smallest crystals there are in  a powder  sample which is not same as particle size. One has to use other well known techniques like laser scattering to measure the particle size.

I think this link can help

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

Hi you cant find the particle size directly. If your sample is single crystalline then your crystallite size is your particle size. But your sample is poly grain then you can find only crysttalite size. use n lambada = 2dsin tetha to find the crystalite size.

best