Could you please specify the source of your question? Is there any observation behind it or you are just curious?

By fact, the size may be a non isotropic quantity. Thus if you have ZnO (or CuO) whiskers grown along particular direction (001) and you estimate their crystallite size from the broadening of 001 reflection you will get the length of the whiskers. In turn if you will measure the size of the same particles by chemical absorption method (BET for example) you will get the diameter of a shere with equivalent surface, which will be obviously smaller than the length of the whisker.

Was this the case? :)

No

No, in fact commonly you could observe that crystallite size observed by DRX for example is lesser than the particles observed by TEM/SEM.

It would make no sense. In polycrystalline materials crystallites are the portion of volume of crystal diffracting coherently, that is, as a single crystal. Grain boundaries are one of the limits of these crystallites (among other crystal defects). As any kind of limit would confine the domain of coheret diffraction, the crystallites can not be extended over the size of particles. They can, as much, be of the same size, but I can not think of a case where particles were smaller than crystallites.

YES, but only in the case when the grain/partile in noncrystalline ie. is amorphous. In the case of crystalline matter,the correct answer is NO :-)

Technically there aren`t crystallites in an amorphous material, so you can't tell if they are bigger or smaller than the particles... that would be an indetermination :)

Could you please specify the source of your question? Is there any observation behind it or you are just curious?

By fact, the size may be a non isotropic quantity. Thus if you have ZnO (or CuO) whiskers grown along particular direction (001) and you estimate their crystallite size from the broadening of 001 reflection you will get the length of the whiskers. In turn if you will measure the size of the same particles by chemical absorption method (BET for example) you will get the diameter of a shere with equivalent surface, which will be obviously smaller than the length of the whisker.

Was this the case? :)

Dear Pablo,

There is possible to have in the same powder two different grains/particles: crystallines and amorphous. In such a case crystallites can be (not necessarily!) greater than amorphous particles. Why such partices are amorphous? They are to small to be of crystalline phase and can be treates sd clusters, only.

On general, the particles are greater than crystallites as they contain several crystallites or amorphous shell.

Pawel (=Pablo in Polish)

Does this help?

http://www.researchgate.net/post/What_is_the_difference_between_crystallite_size_grain_size_and_particle_size

Dear Andrey Sir,

I have calculated the crystallite size based on scherrer equation and particle size based on BET analysis. In this case the particle size is coming considerably lower than the crystallite size!!! :( .. How is it possible? anything wrong in BET analysis? Could you please clarify sir

How did you measure the crystallite size? Did you have a look on your particles in electron microscope? May you give an example values you have got?

I measured the crystallite size based on PXRD using scherrer equation considering the major peaks...

For eg Average crystallite size of a sample (ZnO) based on scherrer equation (PXRD) is 14 nm but its surface area is 95 m2/g sir !!

And what size did you calculate from 95m2/g? :)

Yes sir it is giving 11.2 nm [based on, Particle size = 6000/(surface area x density)]

Well, than I would check the formula :)

It will take you 2 min to derive it and then you see where your mistake comes from.

The right answer is 1.1 micron

Wait, you may be right....

Yes sir kindly clarify...

Yes, you are correct - 11nm - long time since I made my physical practical courses :)

Than the only explanations I see is that your particles are elongated.

I would give it a go in an electron microscope - you see it immediately.

Electron microscope ??

I have its SEM image .... Sir you are telling me to go for TEM? :)

Daer Prashanth Gopala Krishna

i was reading that equation that you asking, i suggest to use the TEM to avoid any problem in future because the TEM more accurate than other method which it confirm the XRD results if you have lower agglomeration of particles. other wise you can use the zeta sizer to measure particle size distribution.

good luck

Muneer

Thank you sir.. You mean to say to go for Particle size by DLS using Zeta sizer... ?Please clarify sir

I suppose that you all should read my paper on the errors in use of Scherrer equation! This equatin give a very big errors without any possibility to establish the value of this error.

Best regards :-)

Dear Pawel, could you please tell me the title of tour paper.. ?

Prashanth! Please post all your available data to get the best answeres from the expert RG membership. XRD is probably the only NDE in situ tool available to quantify & image Nano structure. However, you need to clarify the semantics of particle size and crystallite size. If you mean "diffracting domain size" then that could be smaller than the "particle size" and potentially the "crystallite size" as well. Depends on how you define crystallite size. The term diffracting domain size is more relevant to conventional XRD measurements (including sub-grain structure), in my opinion. There are other discussions in RG that delve into this issue of definition in much greater depth. Already posted earlier.

http://www.flickr.com/photos/85210325@N04/10221065324/

Scherrer equation should be used prudently. The "shape factor" of the diffracting domains is critical in such analyses. I once again suggest a thorough review of the basics of XRD using this phenomenal book by andre Guinier.

http://www.flickr.com/photos/85210325@N04/10515372183/

Pablo! There are materials that have crystalline and amorphous phases mixed. Some block co-polymers are examples.

Andrey! You make an excellent point regarding the potential effects of "preferred oriention" on the Sherrer formula and the accompanying analyses. Real time 2D diffractograms are a possible solution. Never-the-less, the use of the Scherrer approach is questionable. For conventional liniear diffractograms acquired with 0D point counters the whole pattern fitting approch of Matteo Leoni (RG member) would work better. I'll post a link if you folks are interested.

Dear Ravi Sir, I am repeating the BET analysis.. Very soon I will come out with my data.. Kindly could you explain what diffracting domain size is and how it is measured or determined?

and sir Please post the link that you were telling ..

Prashantha! I'm interested in your query due to its "fundamental" nature. "Sir", you must reserve for folks with stature such as Sir C. V. Raman. I'd encourage you to just use my 1st name "Ravi". That's fine! I do appreciate your gesture. Thanks! :-)

BTW What does BET stand for?

I suggest you follow Matteo Leoni and look at some of his publications and comments on RG. You'll find all the details. The discussion I was referring to, was posted earlier by Ahmad Amer of Ain Shams University in Egypt: http://www.researchgate.net/post/What_is_the_difference_between_crystallite_size_grain_size_and_particle_size

I'd suggest a thorough review of Andre Guinier's book for a full understanding of the term "diffraction domain". http://en.wikipedia.org/wiki/Coherent_diffraction_imaging. This in my opinion would be the smallest coherently diffracting region of the sample and may be different in various (hkl) directions. SAXS measurements would yield the "size" you may be interested in. I'm sure others will come up with even better and more appropriate definitions. If I were you I'd forward a link to folks like Matteo Leoni, Edward Andrew Payzant and other stalwarts in XRD that are RG members as well to join and share their knowledge. Below is an extreme example of preferred orientation and a corresponding 2D X-ray diffractogram. You'll realize how distorted the corresponding linear conventional diffractogram (also shown on the image) could be in the presence of "preferred orientation".

Note: The use and interpretation of the Scherrer approach may require a lot of caution and forethought.

http://www.flickr.com/photos/85210325@N04/7944785794/in/set-72157632728981912

Thanks Ravi :).. Brunauer-Emmett-Teller (BET) Surface Area Analysis gives precise specific surface area evaluation of materials by nitrogen multi layer adsorption measured as a function of relative pressure using a fully automated analyser. The technique encompasses external area and pore area evaluations to determine the total specific surface area in m2/g yielding important information in studying the effects of surface porosity and particle size in many applications. The particle size of nanoparticles can be calculated using the following equation for either spherical- or cubic-shaped nanoparticles.

Average Particle Size = ( 6000 / BET surface area X Density)

Average Particle Size = in nm

Surface area = (sq. m/g)

Density = (g/cc) .

There may be certain limitations, which I am not aware...

Ya sure Ravi,. thanks for your suggestion.. I will send the link to them too and request for their opinion :)

BET will not yield the "diffracting domain size" derived through XRD. The XRD measurement will always be smaller than your estimates through BET. Similar argument for TEM & SEM measurements from a statistical perspective. My opinion.

Ya exactly that is what I am expecting... Should see what BET results give.

The title of my paper is "The uncertainty in the grain size calculation from X-ray diffraction data:; it was published in 2012. I could send you a copy by e-mail. Please ask in: [email protected]

Best regards!

Pawel! Please forward to [email protected]. Thanks!

Dear namesake Pawel, :)

I completely agree with your description of a material composed of different grains, with big crystallites and smaller amorphous particles. I'm not aware of techniques able to distinguish crystalline particles from amorphous when measuring their size, but if we are considering the same composition I guess the size difference (enough to prevent crystallization) would be big enough to get bimodal particle size distributions in DLS or even laser diffractometry measurements.

It is of great interest the different values for particle size that can be obtained with the different techniques (BET, DLS, TEM, ...). Results need to be understood under the physics of the determinations and compared in consequence. But in the case of this question I think most of us agree that when comparing XRD crystallite size determinations through Scherrer equation with BET measurements the higher uncertain probably came from Scherrer equation. (Once aggregation, porosity and other effects affecting BET are considered).

In my previous answer I was considering the general situation you also describe, "On general, the particles are greater than crystallites as they contain several crystallites or amorphous shell." . I did not consider the situation you describe first or the block co-polymers also commented by Ravi. Thanks both for your input!

Small Angle XRD (SAXS) would yield similar values as "DLS or even laser diffractometry measurements" and may not be sensitive to the crystalline/amorphous "particle size". However, WAXS or (hkl) profile analyses (such as Scherrer equation or WPPM) would be sensitive only to the crystalline components. However, if the "amorphous hallo" extends to the (hkl) region then it must be correctly deconvoluted numerically to isolate the crystalline component contribution even in WAXS data.

Below is an example of the sensitivity of 2D WAXS method to all the constituents in any composite including their constituent "diffracting domain size".

http://www.flickr.com/photos/85210325@N04/7920887956/in/set-72157632728981912

It depends on the atomic radius.

The measured crystallite size in a given direction can never be larger than the particle size in that direction since that would imply structural coherence length beyond the boundaries of the sample which does not make sense. If the particle is a single crystallite then the physical particle size and crystallite size should in principle be the same. However, the Sherrer equation for determining the crystallite size involves uncertainties due to approximations made in deriving the formula, which would lead to small non-physical variations in the results obtained by applying the Sherrer equation. In addition, the argument of Andrey Chuvilin applies very well to the evaluation of the crystallite size

Sami! It depends on the material system (crystalline, amorphous, composite?) and the definitions of phases and domains in question. In the classical sense they will only be the same if the "coherently diffracting domain size" matches with the crystallite size. This is seldom so due to the presence of subgrain structure and other lattice defects. Andrey Chuvilin's remarks are valid for the paradigm proposed. In my opinion.

Sami, you first sentence is wrong. The oposite statement may be correct :-)

According to the definition: particle can be formed by several crystallites, thus the linear dimension of crystallite should be the same or SMALLER that the dimension of particle.

Sami, as Mr pawel told a particle is formed by many crystallites... so how the particle size cannot be greater than the crystallite size?

or you mean to say it is only due to the limitations of scherer equation?

I'd suggest all interested to review this RG discussion noted by Ahmad Amer:http://www.researchgate.net/post/What_is_the_difference_between_crystallite_size_grain_size_and_particle_size

The subject of present interest is discussed in great depth by some of the leading experts in RG, in my humble opinion. A lot of "brain hours" to absorb and ponder in this discussion. Share your thoughts.

Honoring the two Braggs a century later for the first X-ray crystal structure and the first X-ray spectrometer: http://www.tandfonline.com/doi/pdf/10.1080/0889311X.2013.797410

Note the word "spectrometer" and its use for quantifying XRD spectra! My observation is that no matter how much one monochromates the incident beam, there is always a spectrum of wavelengths or the "instrumental profile" in any XRD system. Therefore, it should not be such a "huge" infraction to use such terminology in connection with X-ray diffractograms.

http://www.flickr.com/photos/85210325@N04/11604959265/

Ravi: I agree.

Pawel and Prashanth: I agree completely with your argument. It is the other way around. I just switched the argument by mistake. I have just edited the answer. Thanks for the comments

It's cool Sami. Do take advantage of the "Edit" button to amend, as I do often.