There is a discussiion soomewhere in RG about grain size and crystallite size. XRD is for crystallite size, there is, the size of monocrystslline domains withhin grains. Incidentally grain and crystallite size can be the same, usually there are not. 

What do you mean by "accurate grain size"? If you use the Scherrer equation to calculate grain size the accuracy dependes on uncertainties of peak position, its FWHM value and applied Scherrer constant. So if you would like to improve your accuracy in this way I suppose you have to improve the quality of the peak profile fit, which could be done by improving measurement quality (for example by increasing counting time and/or decreasing step size). And of course you'll have to choose an appropriate value of the Scherrer constant, which is not so easy trick, since it dependes on grain shape and XRD is sensitive to coherence lenght/grain size in the direction of scattering vector only.

Moreover, the accuracy could be improved by careful subtraction of the instrumental boardening, which could be done using reference materials like LaB6 or W (from NIST for example). If you use Cu X-ray tube careful subtraction of the K_alpha_2 line from a pattern could be also helpful (using Rachinger algorithm for example).

Cheers!

Its accuracy depends on plenty factor such as calculating FWHM, background, residual stress and etc. For example, if you use mechanical milling to synthesize a powder or decrease the mean particle/crystallite size of your sample, the residual stress will decrease the accuracy Scherrer equation. However, if you have annealed sample or any other sample that has not residual stress, the errors of the Scherrer equation are restricted in calculating FWHM which means how accurate you can fit a curve similar to your XRD peaks, although you might use any software to do it.

You might know that transmission electron microscopy (TEM) shows accurate mean crystallite size. You can use it for your case to find out the accuracy of crystallite size in your samples.

Unless you check the grain size with TEM, it can be completely off. A good practice is to compare your values with TEM results, and if they agree then you can use XRD grain size. I have seen 50% difference between XRD and TEM myself, and that is why you need to be careful.

FWHM works only is the grain size does not exceed 120-150 nm and it doesn't take polystallinity into account. Then it's always better to compare XRD-FWHM results with TEM or SEM images.

Measurements of grain size in XRD is not an accurate for determination of particle size because the formula used is assumed there is no strain at all (Schrer fromula). For accurate particle size measurement you can use TEM.

The accuracy of grain size from XRD depends on the material kind, as different approach should be adopted in case of organics, inorganics hybrids etc.

The main problem is related to the combination of strain effects (or for organic short range order) with grain size ads contribution to peak enlargement. In spite of these drawbacks reliable measurements come from XRD line profile analysis.

TEM in this respect is valuable even though not of general use, i.e. right magnification level attained.

When you fit your peak profile with pseudo-Voigt function you should obtain two FWHM values. One is connected to coherence lenght/grain size (the FWHM of Cauchy/Lorentz component) and the other is related to microstrains (and that is FWHM of Gauss component). Using this approach you should be able to distinguish between broadenings connected with coherence lenght and related to microstrains.

Take a look at the round robin results in this excelente paper of Mr. Balzar

http://mysite.du.edu/~balzar/SSRR.pdf 

There is a discussiion soomewhere in RG about grain size and crystallite size. XRD is for crystallite size, there is, the size of monocrystslline domains withhin grains. Incidentally grain and crystallite size can be the same, usually there are not. 

There is a LOT of discussion in RG on this topic already. Simply do a search on "Scherrer" or "crystallite size".

Note that with TEM: (1) you are assuming that the sample preparation will not alter the microstructure, (2) you are assuming that the very small sampling volume is fully representative of the bulk, (3) you are assuming that a 2-D slice of this small volume allows you to determine the size of 3-D grains. If all three assumptions are met, then you get an accurate answer.

With XRD: you are assuming that from fitting the full pattern or individual peak profile you can unambiguously refine a "crystallite size" parameter. If you have (1) a fairly uniform and narrow crystallite size distribution and (2) accurately modeled shape anisotropy, microstrain, and instrumental broadening, then you can get a reasonably accurate answer.

What I see in the literature (and on postings in RG) is that the assumptions (both for TEM and XRD) are more frequently NOT met than one might expect. And often the results are given to much higher precision/accuracy than is supported by the data.

Sir,

Please read the article, "The uncertainty in the grain size calculation from X-ray diffraction data" Author: Pawel E. Tomaszewski, published in Phase Transitions, 2013, Vol. 86, Nos. 2–3, 260–266, http://dx.doi.org/10.1080/01411594.2012.715301

I have attached the paper.

Hope this paper can answer your question.

XRD isn't accurate for the measurement of grain size. It gives you the crystallite size via Scherrer equation. The small crystallites combine/agglomerate together to form the particles and small particles combine/agglomerate to form the grain. The size of the particle/grains can better and more efficiently be calculated via SEM and TEM rather than XRD. I hope I made myself clear.

Good luck!

First of all, this is not grain size, but coherently diffracting domain size which is also termed as crystallite size. Secondly, which method are you using to estimate the crystallite size?

Response to Suchitra Sen's question:

I am using integral broadening method to measure grain size.

Indeed, as Edward pointed out above, there is quite a lot of discussion about this on RG. Below are some of the topics you might find related to your question (and give some part of the answer as well) if you do a search. Hopefully you will find very interesting information, but you will also see sometimes the rather 'divergent' opinions of the different contributors :). Have a look and try to make your own opinion

Regards

      cristian

https://www.researchgate.net/post/What_are_the_standard_methods_for_determining_powder_particle_size?_tpcectx=home_feed

https://www.researchgate.net/post/How_can_I_find_out_whether_a_synthesised_material_is_nano_or_not?_tpcectx=home_feed

https://www.researchgate.net/post/Why_is_the_MOF_particle_size_usually_not_calculated_through_the_Scherrer_equation?_tpcectx=home_feed 

https://www.researchgate.net/post/If_you_scatter_X-rays_from_a_bulk_polycrystalline_material_how_do_you_determine_the_mean_crystallite_size?_tpcectx=home_feed

XRD will give crystallite size. For particle size, please use TEM analysis. For calculate crystallinity index: divide the size from TEM with Size from XRD.

For more details: https://www.researchgate.net/publication/236589274_Electrolytic_Synthesis_and_Characterization_of_Silver_Nanopowder?ev=prf_pub

Particle size, also called grain size, refers to the diameter of individual grains of sediment. The term may also be applied to other granular materials. This is different from the crystallite size, which is the size of a single crystal inside the particles or grains. A single grain can be composed of several crystals (Source: Wikipedia).

Article Electrolytic Synthesis and Characterization of Silver Nanopowder

The most precise way to measure particle size (and particle size distribution as well as 3D shape) is by small angle x-ray diffraction (SAXS), but that isn't what you asked so I'm not sure why so many people are addressing a question you didn't answer (and incorrectly at that). You can also get the crystallite or grain size and grain size distributions by XRD as well by measuring at higher angles (as long as you are not using any kind of line broadening method which is as bad as trying to measure 3D grain or particle size using SEM or TEM, so don't even bother). If you contact me I can give you references on using x-ray diffraction to determine grain volume distributions from the nm to mm length scale. For larger grains you can also  get the three dimensional shape with an error of a micron or so for bulk polycrystalline samples. If it's a single crystal you can get the full 3D shape with sub nano-meter resolution.

So to finally be the first person to actually answer your question:

It is extremely accurate and precise. For polycrystalline materials there is no other existing method which can measure 3D grain distribution (or if for those of you who like to play semantics, 3D orientation distributions which covers any of the various words you'd like to argue about the definition of) as well as x-ray diffraction methods.

What you determine with Scherrer  formula in XRD is Crystallite Size. A grain may composed of so many crystallites. So XRD will never give you exact grain size. Therefore, for measuring grain or particle size, TEM is the best technique.

Shiv,

Did you read the entire discussion? Is there something you disagree with in my comments above? If so please be specific. There are many other X-ray methods besides line broadening analysis to determine crystallite or particle size and shape, so I have to disagree with your statement: . "So XRD will never give you exact grain size." 

The "crystallite size" depends on so many factors, that its value is only approximative. You ca read my paper published in "Phase transitions"!

There are so many ways to measure all of these: particle size, grain size, and crystallite size using x-ray methods. SAXS, tomography (phase contrast), Holography, Coherent Diffraction Imaging, Topo-Tomography, Diffraction Contrast Tomography, 3DXRD microscopy. None of these have anything to do with line-broadening (which is why they actually give accurate results).

There are many WAYs (experimental methods as you listed, Lawrence) - Ok, but there are many ways to calculate the grain/crystallite size using diffraction data! Unfortunately!

You will find two my papers on this subject. The second is in Polish, but you could see the figures!

Best regards to all :-)

It is sad that the methods you covered in your papers are still used today. Small angle x-ray scattering (SAXS) for example will give very accurate results on the size distributions (not just an average) and shape for nano-crystalline materials. Have you tried comparing results from SAXS measurements?

Unfortunately, I have no access to SAXS. But you are right - this will be very interesting to compare both experiments.

However, the majority of people who need the data on crystallite size have the powder diffractometer, only. That is why I compared the different calculations based on the same diffraction pattern to show how great error can be made.

Dear Lawrence,

I have not quoted that I disagree with your comment.  However, I always believe that XRD will not give you exact grain size whenever you talks about diffraction of X-ray from crystal planes. Moreover, it can provide some close value.

Yes, you are right and I agree with your comment  "There are many other X-ray methods besides line broadening analysis to determine crystallite or particle size and shape". One example is SAXS as you have quoted above.

the main problem of crystallite size in materials resides in the range. From 3 to 70 nm the methods based on Hosemann or Warren-Averback approches are quite reliable for organics or inorganics respectively, provided that accurate measurements are performed. The problems arise when the upper limit is exceeded in this case are HRTEM, AFM/STM or SEM are clearly preferable.

I need to measure domain size of some synthesize graphite oxide in different conditions. What are the limitations of the scherrer equation should I care with?

Hi

Scherrer’s equation:

Particle Size = (0.9 x λ)/ (d cosθ)

λ = 1.54060 Å (in the case of CuKa1) so, 0.9 x λ = 1.38654

Θ = 2θ/2 (in the example = 20/2)

d = the full width at half maximum intensity of the peak (in Rad) – you can calculate it using Origin software.

To convert from angle to rad

Rad = (22 x angle) / (7 x 180) = angle x 0.01746

Example: if d = 0.5 angle (θ)

= (22 x 0.5)/ (7x 180) = 0.00873 rad

Have a very good day and best of luck

First of all I recommend the paper "The uncertainty in the grain size

calculation from X-ray diffraction data" published in the joural "Phase Transitions" Fortunately the text is available on my page. There are olasi other appaers, but this one clearly indicate that the Scherrer formula is... wrong or could not be used!  There are to many errors souces which could not be even estimated. Thus this formula give the approximation, only. The only possible use is for the study of relative changes of this parameter (for example with temperatrure etc.). Never use it to see how big/small the greains (crystallites!) are! The better approximation (only the approxination!) can be obtained by Williamson-Hall method.

I think this link can answer you well sir,

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

Using Scherrer's equation can estimate the crystalline size < ~180nm with reasonable accuracy. However, for the extremly thin or small particles, the diffraction signal can be very broad and hard to be extracted from the background. Thus, using Scherrer's equation on such particles/materials can biased to thicker/bigger result.

I am dealing with graphene, which is usually too thin for measuring the thickness from Scherrer's equation.