Dear brother, you have to calculated the crystalline size for each peak in the XRD after that take the average of this results.   

Dear brother, you have to calculated the crystalline size for each peak in the XRD after that take the average of this results.   

Dear Arwind,

I fear that there is no real alternative other than Scherrer equation or the Williamsen-Hall approach.

However please have a look at an interesting diccussion on crystallite size determination,  model aspects and history here on RG  from about two weeks ago. 

https://www.researchgate.net/post/What_is_the_difference_between_Scherrer_and_Williamson-Hall_equation?_tpcectx=qa_overview_following&_trid=1QI4yM6xbxmWrTuVECWHnPT0_

Apply Scherrer  formula to calculate the crystalline size.

Dear Arvind,

There are indeed methods better suited than the Scherrer approach, but it might be a good idea to first re-assess what the crystallite size/shape really mean.

The crystallite size/shape is not the size/shape of particles as measured by a particle size analyser - except in the rare instance that each powder particle behaves as a single diffracting unit. It is also definitely not the grain/subgrain size/shape in case of bulk material.

The crystallite size/shape from XRD is just a mathematical model which tries to link the diffraction pattern to a' virtual' diffracting unit, i.e. the crystallite. 'Virtual' in this sense  does not mean imaginary, but rather that this unit cannot be physically isolated and observed in the 'real' sense. A real diffracting unit could change its size/shape during processing, resulting in changes to the corresponding diffraction pattern. The crystallite size/shape that is modelled from XRD tries to map these changes from the diffraction pattern and give us a physical sense of what is happening. This information can be very useful if this link between processing and change in pattern can be explained, but by itself the crystallite shape may not have much physical significance.

With that rather long preamble out of the way, I'd like to point out that XRD analysis has seen big developments, and the Scherrer formula is one of the oldest, most basic approaches towards studying crystallites. With the correct assumptions and limitations considered, it is still valid, but in a very narrow range of physical situations. A better, more recent (though still decades old; not cutting-edge) way to study non-spherical crystallites is via Rietveld refinement, where the whole pattern is used, not just the peaks. The Popa model (reference below) specifically models the shape of non-spherical crystallites using spherical harmonic functions, and is the most suitable method that I am aware of. I have found this to be very useful while studying bulk deformation, because the results from the model can be correlated quite well to physical behaviour.

However, please keep searching, because the field is continuously growing and there may well be better, more recent ways that specialists in the field can point out.

Ref: https://www.researchgate.net/publication/244634656_The_hkl_Dependence_of_Diffraction-Line_Broadening_Caused_by_Strain_and_Size_for_all_Laue_Groups_in_Rietveld_Refinement

Article The (hkl) Dependence of Diffraction-Line Broadening Caused b...

Well articulated Aashranth!

The key challenge with using the Scherrer approach is the inability to differentiate between size broadening and strain broadening. Besides, the effect of preferred orientation is completely ignored in the Scherrer methodology, isn't it?

It would be very helpful to know more about the material system that you are referring to. Please provide more details and post your XRD data whenever possible for the best feedback from the RG membership.

If the particles are non-spherical, then the process (what method?) of creating a thin film by allowing these particles (what material?) to settle on the substrate (what material?) would introduce anisotropy, wouldn't it?

"you have to calculated the crystalline size for each peak in the XRD after that take the average of this results" - provided the Bragg profile's "integrated breadth" is unaffected by strain, preferred orientation and shape. Unlikely! :-)

Despite all these limitations, one may still use the Scherrer approach to get a pretty good idea of the diffracting domain size for relative evaluation and estimation purposes. The answer will seldom match the results from SEM, TEM etc.

Aashranth and Ravi,

thanks for your valuable comments.

Dear colleague Arvind Kumar

Have a nice time and good day.

To calculate the crystallite size you two ways:

1- Scherrer Equation

2- TEM

You calculate crystallite size using Scherrer equation as you mentioned and you can calculate from TEM as well. If the crystallite size is spherical as you mentioned you can calculate the diameter with any software; TEM is supported by such this software for crystallite size calculation or if you already finished your TEM analysis without crystallite size calculation then you can use ImageJ softwareto calculate your crystallite size or crystallite diameter, ImageJ has free downloaded. For non spherical shapes always the average of the dimensions be mentioned. To make a practice issue you can follow many papers concerning that issue

I wish this is useful and help you.

Yours

A. EL-Denglawey

Dear Admin, My question is that if i have a alloy that composed up of two or three materials than which peak i select to calculate the crystal size for example if i have Copper alloy in which iorn as well as silver also present than for (1) which element peak we choose and (2) which specific peak we choose for crystal size calculation because there are many peaks for single element.

For any shape of the material we use scherrer formula.. In scherrer formula

D=k lamda/beta cos theta.

From the equation " k " is nothing but shape constant.. If your particle is in spherical shape use 0.9, otherwise use 0.8....

Best wishes