Happy new year!
I want to know how to calculate crystallite size using XRD data.
(I got the information from TOPAS, my powder have larger than 200nm)
I can calculate using scherrer equation, but some people say it is incorrect method for over 200nm size crystallite.
So I want to ask you, Is there nice method or references for calculating large crystallite size?
Thank you.
Dear Suncheol Kim!!
As we know that the calculation of crystallite size using Scherrer formula has limitations when crystallite size is more than 100 nm. Normally the Scherrer equation is applicable to determine the crystallite sizes in the submicron ranges but its accuracy level decreases for crystallite sizes more than 100 nm. This is due to the fact that, crystallite size broadening becomes comparable or close to the instrumental broadening for larger crystallite sizes. You can used modified Scherrer formula with Williamson-Hall (W-H) plot method for better accuracy. This method can be applied for the systems having crystallite size larger than 100 nm.
The limit is due to instrumental broadening, always present when a powder pattern is collected, that could be of the same order of the sample broadening. This is particularly true for laboratory diffractometer. If you collect the pattern at the synchrotron facility you can reduce the instrumental contribution, and try to determine a more correct size value for your sample
Respected Sir,
You can use:
1. Williamson-Hall Equation
2. Nelson-Relay plot to calculate the crystallite size using XRD data.
3. Can also use XPert HighScore Plus software.
For more details refer the attachments.
http://dx.doi.org/10.22036/pcr.2019.205211.1688
Hope this information is useful.
Sadhana Yadav
Marcella Bini
Rayappa Shrinivas Mahale
Thank you very much!!
I will try to understand what you suggest me.
I wish your healthy life!
Good luck!
The upper limit for determining crystallite size (i.e., primary particles / crystalline domain) is instrument dependent and is not something you can change by plotting the data in different ways. Other size-strain analysis approaches such as Williamson-Hall and Warren-Averbach are limited by the data (i.e., sample profile resolution) in the same ways as Scherrer. If you dig into the TOPAS macros for size-strain analysis, you will see these isotropic size-strain macros are using the Double-Voigt approach which is an integral breadth method (see papers by Balzar). While this may sound different than the Scherrer formula, the same instrument-based limitations are true even if other methods have better accuracy for profile modeling and microstructure determination.
You can determine the upper size limit by plotting the FWHM from your instrument profile function vs. 2theta assuming you have a standard reference material (e.g., NIST Si, LaB6, CeO2) that is "free" of size and strain broadening. A high-resolution instrument like 11-BM at the Advanced Photon Source has a minimal instrument contribution so you can resolve sample-based broadening for SRMs that cannot be seen on a typical instrument.
Here's an example: https://11bm.xray.aps.anl.gov/images/LaB6FWHMvs2Theta_large.jpg
While synchrotron X-rays have higher flux and often higher energy than laboratory X-ray sources, the peak shape resolution is not necessarily better. Again, this can be determined by measuring a standard material using the same experiment geometry as your sample. Many diffraction beamlines use 2D area detectors which improve your counting statistics immensely and enable rapid measurements with excellent signal to noise, but the upper limit for sample broadening is typically similar to a conventional lab diffractometer (e.g., 100 - 200 nm) since you are limited by the pixel size on the detector and sample-to-detector distance.
You can use the fundamental parameters approach (implemented in TOPAS) to simulate peak broadening for different size crystallites and you will see that the peak shape change is not resolvable above 100 - 200 nm. For example, you should expect that the broadening from 200 and 250 nm crystallites will be approximately indistinguishable if you are modeling your instrument profile properly.
If you are trying to look at particle sizes in the sub-micron to micron range, diffraction is not the correct tool for the job. Small-angle scattering techniques can often resolve large features like this depending on the Q-range accessible on the instrument and the expected feature size from your sample - this comes with a ton of caveats of course since you are looking at differences in density, but it may be more tractable to your problem.
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