I am dealing with the in-situ XRD tensile test, after the correction of instrumental broadening, then I want to use Scherrer Formula to calculate the crystalline size by integrated breadth from Lorentz part. this experiment used Synchrotron x-rays at APS, argonne national lab.
D=k*lambda/beta/cos(theta)
The result is that when I try to use 4 different diffraction planes (they are 200, 310, 321 and 330), they end up giving me different crystalline size. (shown in the below figure, the x-axis is the engineering strain in the tensile test)?
Is there anything wrong with my calculation or if there is some other explanation or other method to use other diffraction planes to calculate the crystalline size?
Thanks.
If your particles have a "shape" and are small enough, it is totally normal to obtain a (hkl)-dependent peak broadening. The best solution for you would be to make a refinement of your diffraction pattern (instead of using Scherrer formula) with a package that enables to refine the grains microstructure and includes anisotropic broadening. It is the case for Fullprof, but it's probably also possible with other packages.
If your particles have a "shape" and are small enough, it is totally normal to obtain a (hkl)-dependent peak broadening. The best solution for you would be to make a refinement of your diffraction pattern (instead of using Scherrer formula) with a package that enables to refine the grains microstructure and includes anisotropic broadening. It is the case for Fullprof, but it's probably also possible with other packages.
I agree with the suggested solution: it is better to use Rietveld refinement of the entire diffraction pattern. The are many free software that you can use (CCP14 website)
First of all, if you use the integral breadth of a peak to evaluate the crystallite size (the Stokes-Wilson approach), the formula is D = lambda/[beta.cos(theta)], with no k constant.
Secondly, the crystallite size calculated from the breadth of a given (hkl) reflection is a measure of the structural coherence length along the direction, i.e., in the direction of the reciprocal lattice vector K = hb1 + kb2 + lb3, where bi are the primitive reciprocal lattice vectors. Now if the crystallites are not close to spherical in shape, it is normal to find different crystallite dimension when using the bradths of different reflections. The crystallite dimensions in your figure demonstrate that the crystallites in your sample are elongated along the (200) direction.
In general you can have many other contrubutions to peak broadening besides particle size. Since you are doing a tensile test, for sure you will get some (maybe very large) contribution from microstrain. The particle size and microstrain contributions can be separated by a Williamson-Hall analysis (Google "Williamson Hall XRD") because they have different angular dependencies. As previously mentioned a full profile analysis will enable determination of particle size and microstrain contributions.
I agree with Boyer's statement. You can use W-H analysis or modified W-H analysis for calculating particle size and microstrain.
There was a lot of discussions here in Researchgate about this matter. You probably would want to check them first. A general advice is not to use Scherrer equation or Williamson-Hall plot if you really want obtaining reliable physical results.
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