# Please tell me how to calculate Crystal Size using XRD Data?

I have the following data from XRD of my nanoparticles. kindly tell me how to calculate size/dia of these particles:

No. Pos. [°2Th.] FWHM [°2Th.] d-spacing [Å]

1. 6.0974, 0.3149, 14.49535,

2. 40.9764, 0.576, 2.20077,

No. Pos. [°2Th.] FWHM [°2Th.] d-spacing [Å]

1. 6.0974, 0.3149, 14.49535,

2. 40.9764, 0.576, 2.20077,

## Popular Answers

Mathias Strauss· University of CampinasAnother point is that Scherrer not always gives you a real crystallite size value, this because the FWHM is affected not only by the particle size as by the structural strain. It must be pointed out also that the shape constant (k = 0.89 ~0.9) is used for spherical particles, so that you need to be sure that your crystallits are spherical.

Edward Andrew Payzant· Oak Ridge National Laboratory1) lambda is the wavelength of the radiation used to collect the data. For example 1.54Å for Cu K-alpha or 1.79Å for Co K-alpha. So it is independent of the sample chemistry.

2a) the answer might be: "both" - the so-called Scherrer constant is a function of the crystallite geometry so 0.94 and 0.89 are both potentially "correct" values of this constant. You can look this up in a variety of references.

2b) the useful answer might also be: "it probably doesn't matter" - because except in unusual circumstances the error in the derived crystallite size is likely much larger than the ~4% difference between the two constants.

## All Answers (75)

Edward Andrew Payzant· Oak Ridge National LaboratorySujoy Bepari· IIT KharagpurRavi Ananth· OnSight Technology USALarry made this point earlier, "In truth, depending on your material, there can be many other factors that affect peak shape and width (distribution in stoichiometry, disorder caused by point defects, line defects, planar defects(for example stacking faults))."

The Scherrer approach neglects the change in FWHM from anything other than "size". The "particle" shape must also be assumed. As Edward Andrew, has pointed out, the instrumental broadening is certainly nowhere to be found in this publication. Need some explanation, don't you think? The paper you have presented (shared) must have been reviewed and approved by the Mullocracy or something. It is fundamentally flawed like the hypothesis of "Genesis" and a single "Adam & Eve". Now I see the point made by folks like Matteo Leoni and others about researchers publishing "trash" and other gullible ones swallowing the pabulum. I'm the only one among all of you fellows that can claim to be in the "trash" business (NJ Medical Waste) :-)

Have you critically reviewed this article yet? Here is another glaring & blatant error, "Scherrer Equation was developed in 1918, to calculate the nano crystallite size by XRD radiation of wavelength λ (nm) from measuring full width at half maximum of peaks (β) in radian located at any 2θ in the pattern." The Scherrer equation uses the integral half width (β) not the FWHM (H) of the experimental Bragg profile. I see no attempt to detect the Bragg profile shape in this paper. "XRD radiation", what's that? Who edited this "junk"?

"A Philips XRD instrument with Cukα radiation using 40 KV and 30 mA, step size of 0.05° (2θ) and scan rate of 1°/min were employed." No mention of the beam conditioning apparatus used. Was the Rachinger correction applied for K Alpha 1 & 2 presence? You know that would affect the measured Bragg FWHM dramatically. Shoddy work!

BTW for a Gaussian Bragg peak shape the, integral breadth, β, is related to the FWHM peak width, H, by β = 0.5 H (π / log e 2)^1/2. You can choose to neglect or ignore this and pontificate all day long in futility :-)

I had no clue about this until recently myself! Guilty! :-(

Ravi Ananth· OnSight Technology USAEdward Andrew Payzant· Oak Ridge National LaboratoryThank you for your kind offer though.

Edward Andrew Payzant· Oak Ridge National LaboratoryEdward Andrew Payzant· Oak Ridge National LaboratoryI note that the journal publisher has been flagged on this site: in a list of "Potential, possible, or probable predatory scholarly open-access publishers". You make judge for yourself what that means.

Ravi Ananth· OnSight Technology USAIn my opinion, the root cause of such errors is the "spatial blindness" of the conventional XRD powder methods and the desire (convenience) to use "formulae" blindly. Scherrer himself must have used tremendous intuition and copious experimental observations with 2D film to come up with this elegant empirical approach that we in modern times are yet unable to apply properly with all our fancy quantitative tools in XRD.

BTW thanks for being the "hawk eye" in the discussion and keeping us all in line! It is an invaluable contribution. I'd have no idea about the credibility of such publications without your scrutiny and diligence. As I've already admitted regarding the Scherrer approach, "I had no clue about this until recently myself! Guilty!". Thanks to you fellows on RG.

Now, let us see if we can exclude "wanton and unabashed plagiarism", (regurgitation) without credit to original authors by some of us illustrious RG members, with the same zeal. I wonder about the contents of such RG member’s publications who can’t even come up with their own words. Glad that Sujoy is not guilty of this at least :-)

http://en.wikipedia.org/wiki/Paul_Scherrer

Ravi Ananth· OnSight Technology USAToo bad the authors (including the editors & referees) of the referenced paper aren't available to defend their position.

Ravi Ananth· OnSight Technology USAEdward Andrew Payzant· Oak Ridge National LaboratoryIt is pretty clear in the referenced paper that the calculations of crystallite size are grossly wrong. The final pattern with sharp peaks cannot possibly be from a 35nm powder sample, as they have calculated.

It is good they are not trying to defend the paper. The only defense is simple: "we made an invalid assumption, and the conclusions are bunk". What is really too bad is that the referees and editor are not available to defend their acceptance of this shoddy work.

Andrew

Lawrence Margulies· University of GuelphAjay Kumar· Central University of Punjabout of different diffracted peaks, which peak we have to select for particle size calculation using Sherrer formula.

Ravi Ananth· OnSight Technology USAThe calculation using Scherrer formula assumes a certain shape factor and generally isotropic. In real life crystals neither of those assumptions are true but far from it.

"usually an average of all peaks" will only smudge the data and give you an average "isotropic" reciprocal space parameter and hence a "smudged" interpretation. The use of "(h00), (0k0) and (00l) peaks" will give a better estimate of the an-isotropic character of the real life sample.

José M. Amigó· University of ValenciaThe broadening of X-ray diffractions reflections can be investigated using different methods: (1) the Scherrer method, (2) the Warren-Averbach approach, (3) the Langford method, (4) several whole pattern analysis approaches (Kojdecki method, Leoni method,...), (5) and others.

Bakhtyar K. Aziz· University of SulaimaniThe parameter B ( full width at half maximum) should be converted to radians instead of degrees , so the

Bmust be multiplied by 3.14 and divided by 180Another point is that , cos Theta is cos ( angle /2) because the reading is 2 theta

good luck

Ghassa Jasim· University of Babylonyou can use the equation of Debye-Scherrer methods Dv = Kλ/βcosθ

Where Dv, presents average nanoparticle size; K, depicts

Scherrer constant (i.e. 0.9); λ, means radiation wavelength;

β, implies full width at half maximum; and θ, infers diffraction

pattern angle.

Ghassa Jasim· University of BabylonHow to measure the yield percentage of CNTs produced from alcohols as carbon source with using catalyst Fe/MgO and without using catalyst by CVD method?José M. Amigó· University of ValenciaThere are several mathematical models to study the microstructural parameters of crystalline materials (Scherrer, Williamson-Hall, Langford, Leoni, Kojdecki and others).

Vitaliy Dereviankin· Portland State UniversityBEST ANSWER AMONG ALL OTHERS (spamy) ones....

!!!!!!!!!!!!!!!!!!!!!!!!!! How to use Scherrer equation correctly!!!!!

Bakhtyar K. Aziz · 5.58 · 3.62 · University of Sulaimani

The parameter B ( full width at half maximum) should be converted to radians instead of degrees , so the B must be multiplied by 3.14 and divided by 180

Another point is that , cos Theta is cos ( angle /2) because the reading is 2 theta

good luck

Abubaker Elshiekh Abdelrahman· King Khalid UniversityRoughly you can use Deby-Sherrier equation but you need to know the stack length Lc due to (002), (004) Bragg plane and stack diameter La due to (110), (220), (111), (131) (131) Bragg plane

Also you can use the X-ray analysis Traces program from Diffraction Technology PTG LTD, Australia to assess the accuracy of the values.

Abubaker Elshiekh Abdelrahman· King Khalid UniversityI agree with prof Mathias Strauss. Then diffraction intensity profiles first correct to background line intensity and instrumental broadening and then fitted into a symmetrical Gaussian distribution. The crystallite parameters of your sample such as d002 spacing stack diameter (La) and stack height, (Lc) can be calculated from the full width at half maximum (FWHM) of the diffraction peaks using Bragg’s equation and Deby-Sherrier equation

Can you help by adding an answer?