Many resaerchers  evaluated the odered crystallite graphitic structures in terms of various parameters including interlayer spacing (d), crystallite height (Lc) along c-axis, crystallite width (La) along a-axis.

The Scherrer formula is used to obtain the crystallite height (Lc)  and the crystallite width (La) : 

Lc = (K*λ)/(B002*cosθ002),  La = (K*λ)/(B10*cosθ10), 

where λ is the wavelength

B002 , B10 - FWHM,  

K = 0.91 for Lc   and K=1.84 for La

Not crystallite height, it may  crystallite size,,,,,,,,,,,,,,,,,

Use Scherrer equation or.................

Peakfit software,

interlayer spacing (d) can be calculated from Bragg's law and the crystallite size from Scherrer equation. Not the crystallite height.

Your crystallite size of 13-14 A is very small (crystals formed by a few atoms). I am not sure that a few atoms can give a diffraction.

Thank you all.

I am not sure that "Crystallite Height" can be calculated from XRD data. Or you may think Height = Size in your case. I support ans by Atli and Mahato.

Thank you Dr. Meetei. I've been thinking to consider that but I can't do that without being certain. For this, I need to know the crystallite height/size of Natural Graphite (angstrom). Can you help me with that? 

Dear Salehin, you can use your XRD data to Scherrer formula for calculating the size. And if you like to know dimension (length, height, width or size) you can observe your sample under HRTEM. 

Hi, 

With XRD, you can calculate the crystallite size which in a way also means crystalliete diameter. XRD will not give you crystallite hight and I do not know what is this crystallite height? as we do not encounter this in XRD. 

You can use schrrer formula to estimate the crystallite size. its not accurate but it will give you an estimate. The general rule of the thumb is, if the peaks are broad, you have small crystallite size. 

for your comparison. the d spacing would be best. forget about the crystallite size, it may or may not be accurate. As I said, its an estimate. 

Hope it helps

Excellent!! Thank you for your answer Jibran Khaliq, and I am going to proceed as you said. By the way, I am attaching a paper where you'll find this crystallite height and other information which made me curious to present my data in that way. I emailed the author last day, no reply though!!!

In (hkl) dependent XRD measurements one measures the "column height/length" along the specific direction normal to the (hkl). Correlation distances!

"crystallite diameter" will work if the diffracting domains are spherical. This is seldom the case in practice.

"You can use schrrer formula to estimate the crystallite size". Appreciate the use of the key-word "estimate" :-)

"IF" one is able to swim past the challenge due to preferred orientation, the effect on sampling size of incidence/diffraction angles, 2Theta depended absorption effects, 2Theta dependent Compton scattering differences (plus others) and assume a diffracting domain shape somehow, then you may apply the Scherrer approach empirically, perhaps? But the Scherrer approach has been and can be continued to use effectively for relative qualitative analyses with reasonable precision. TEM or other corroboration would be quintessential.

There are many other expert discussion regarding the details of the Scherrer approach and cautions on RG.

Thank you very much Mr. Ravi Ananth. It's a wonderful explanation with resource. 

Dear Mr. Jibran Khaliq, I'm sorry for not uploading that paper as I said. I did not find the soft copy of that. Anyway, please have a look on these attached photos of the relevant sections of the paper which compelled me to ask this question. I thank you all for helping me to learn whole lot new stuffs. 

Salehin.

which is the relation between the Young modulus and the rate of crystallinity in natural fibres

which is the situations to say the Young modulus increases with the increase in rate of crystallinity

which is the situations to say the Young modulus reduced with the increase in rate of crystallinity

compare your 2theta value with your standard material JCPDS card no, in that you will get the H,K.L value from that you can calculate all you need.

Many resaerchers  evaluated the odered crystallite graphitic structures in terms of various parameters including interlayer spacing (d), crystallite height (Lc) along c-axis, crystallite width (La) along a-axis.

The Scherrer formula is used to obtain the crystallite height (Lc)  and the crystallite width (La) : 

Lc = (K*λ)/(B002*cosθ002),  La = (K*λ)/(B10*cosθ10), 

where λ is the wavelength

B002 , B10 - FWHM,  

K = 0.91 for Lc   and K=1.84 for La

Anna! "K = 0.91 for Lc   and K=1.84 for La". How does one arrive at these numbers?

I really appreciate the answer of Anna papova. she explained regarding calculation of crystallite size and height using scherrers equation. This is the first time I am hearing about crystallite height calculation from XRD. If she could have provided some references, it would be better.

To Mr.Manjunath K.

1) Saikia BK, Boruah RK, Gogoi PK

A X-ray diffraction analysis on graphene layers of Assam coal.

J Chem Sci, 2009 - 121(1):103-106.. 

2) Lota K, Sierczynska A, and Lota G

Supercapacitors based on nickel oxide/carbon materials composites. International Journal of Electrochemistry.

Article ID: 321473, doi:10.4061/2011/321473.

To Mr. Ravi Ananth 

I recomend you to see the following paper:

Saikia BK, et al. A X-ray diffraction analysis on graphene layers of Assam coal. J Chem Sci, 2009 - 121(1):103-106.

And one more note.

It is considered that if you have natural graphite structure so you you should take K=0.91 (or K=1), as we can obtain 2 defenite peaks of (100) and (101) planes

Anna! Are these arbitrary factors (" K=0.91 (or K=1)") or is there a rationale for arriving at these numbers? Thanks!

Hi!

I will try to make it easier.

Each diffraction/scattering peak has a position and a shape profile. From the position (peak maximum) one obtains the average distance between objects, and from the shape (FWHM) the correlation length - or average size of the cluster or domain.

Said this, the first peak at ca 25 deg (q = 1.76 A-1, d = 3.56 A) corresponds to the average distance between graphene sheets, and the FWHM is giving you the distance along the d-spacing which accounts for the number of sheets in the domain (distance between the first and the last sheet in the cluster; sorry, I cannot evaluated since I have not the data…).

At ca 44 deg (q = 3.05 A-1, d = 2.06 A) a visible peak is present which corresponds to the in-plane distance between rings. Assuming that this distance is the same along the two in-plane directions of a sheet, the peak maxima will give you the average distance and the FWHM the distance which accounts for the total number of rings in a sheet (diameter of the sheet if circular).

Fine. What to do, then? First plot intensity versus wavevector (q) - avoid 2theta!

q = 4*pi*sin(theta)/lambda

Fit each single peak, and obtain the maxima (qmax) and the FWHM.

The distance related to each peak is d = 2*pi/qmax (your interlayer spacing), and the correlation length (your crystallite height (Lc)  and the crystallite width (La)) is x = 2*pi/FWHM. That simple!!! and avoid difficult approximations and formulae.

If you have any further question, please contact me.

SALUT!

Tony

I think we've come quite a bit ahead of the mundane application of the century aged, highly intuitive Scherrer equation. I continue to learn it better each time.

Questions still needing clarification:

1. How is the "K" factor in the Scherrer equation determined? (in practice)

2. "First plot intensity versus wave vector (q) - avoid 2theta! q = 4*pi*sin(theta)/lambda". Other than in the case of the synchrotron where the "Lambda" can be nearly a "delta function" (single value), how does one account for a range of wavelengths usually present in XRD observations? Let's say powder diffractograms with conventional  desk-top sealed tube generators. I think, this would have to be done using known calibration "standards".

3. Can the shape of the Bragg profile be used to derive the distribution and other characteristics of the correlation lengths along the "q" vector ? Such as the presence of stacking faults, for instance. In other words, could we deconvolute the  distribution of the diffracting domain sizes through the observed Bragg profile? Knowing the theoretical profile and/or that from a known standard characterizing "instrumental profile".

4. Can a similar approach be used to interpret Bragg profiles from single crystals where there is no more the issue of  "particle size" being convoluted on the FWHM any longer? Now we can quantify the diffracting domain size distribution within the mono crystal by studying the Bragg profile shape w.r.t. theory or "known standard", yes?

Literature references, as presented by many contributors to this important discussion, would be deeply appreciated.

I will do my best...

1. Rule of thumb...

2. No, you use a monochromator to select one single wavelength... in my two SAXS machines we use 1.5418 A wavelength.

3. Yes, that's the magic.

4. Well, for highly crystalline materials you might underestimate the domain size, but you will get an approximation.

Check, papers from Wim de Jeu and others... check also my papers.

SALUT!

Tony 

http://www.instanano.com/characterization/d-value-calculation/xrd-d-value-calculation/

1. "Rule of thumb..." immediately suspect without a "calibration" chart. I guess it depends on the "thumb" size eh :-) Are there many assumptions in the rule? Like for example, the shape of the CDD (coherent diffracting domain). 

2. "No, you use a monochromator to select one single wavelength... in my two SAXS machines we use 1.5418 A wavelength". So, then, tell us how you make this "near-delta function" at 1.5418 A  for your wavelength without a synchrotron? Most of the HRXRD units with fancy beam conditioners themselves have "instrument profiles" which is euphemism for  "wavelength dispersion" and "monochromator Nanostructure", isn't it? :-)

3. "Yes, that's the magic." I'm keenly interested in being able to deconvolute and image the various defect types from observed Bragg profiles topographically in both poly crystalline and mono crystalline materials. I'll look through the literature references as recommended and post comments later.

4. Share your expertise in the attached RG questions when convenient.

P.S. The Scherrer formula uses β, the integrated breadth of the Bragg profile in Radians. Not the FWHM :-) It may be possible to compute β from FWHM once you assume a "shape" for the Bragg profile.

https://www.researchgate.net/profile/Ravi_Ananth/questions

https://www.researchgate.net/post/What_is_the_likely_Nanostructural_origin_for_observations_of_the_LiF_113-XRD_reflection_rocking_curve_integrated_breadth_squared_b2_map