Hi everyone.
I have seen in several papers that Scherrer´s equation is widely used for estimating the crystallite size (from XRD peak broadening) without taking care of its theoretical-experimental coherence. I see that the theoretical hypothesis of this equation is generally not considered and incorrectly extended to any case, blearing the real validity of this approach for estimating crystallite size.
For example, this model completely neglects the influence of lattice strains (or dislocations) on the XRD peaks broadening, which is considered in other models like that proposed by Williamson-Hall. It is known that lattice strains can introduce significant peak broadening, especially for high diffraction angles (θ). Moreover, I have not found any exact and rigorous criterion to consider under what conditions the peaks broadening is mainly due to crystallite size concerning lattice strains.
Regarding this point, let me doubt of the validity of Scherrer´s equation for estimating crystallite sizes in any context, as commonly done.
What do you think about this issue?. Are you agree or disagree?. Share your opinion!
Although there are some limitations, this equation is widely used to estimate the crystallite size of materials.
You are completely right Simon Roa ,
if one has the chance to apply Williamsen-Hall approach (e.g. in the case multiple significant peaks belonging to one phase) one should use the W-H equation. The latter reduces to the Scherrer equation, when the strain is set to zero.
Bearing in mind the range of the shape factor, which enters both equations, one should regard the Scherrer as well as W-H equation as a rough estimate of the crystallite size. Moreover this value is only a single number, which does not describe a size distribution, which in reality is always present. Thus the crystallite size here is only an estimate of some kind of a mean value.
So please take this number is as rough estimate, not more.... and be careful with the number of digits when presenting such a number.
With respect to the kind of mean number please see page 17 (How is Crystallite Size Defined) of the following link below (from Scott A. Speakman):
(but sorry, I do not know the original reference)
"Scherrer method (using FWHM) gives the ratio of the root-mean-fourth-
power to the root-mean-square value of the thickness"
http://prism.mit.edu/xray/oldsite/CrystalSizeAnalysis.pdf
Last but not least; for quite narrow peaks: do not forget to correct the peak widths for the instrumental broadening using appropriate reference materials.
Dear Simon Roa
The Scherer formula is not valid when XRD peaks are broaden .....or high value of FWHM..
thank you
Dear Simon Roa ,
these papers might be of interest for the applicability of the Scherrer equation:
Article The Scherrer equation and the dynamical theory of X-ray diffraction
Article The limit of application of the Scherrer equation
Article Scherrer formula: estimation of error in determining small n...
Article Modified Scherrer Equation to Estimate More Accurately Nano-...
Dear S. K. Parida ,
are there any numerical limits with respect to the peak width known?
Or any thumb rule(s)?
Any references are welcome...
Thanks in advance
G.M.
- Badges
- Science method
- Similar topics
- Methodology
- Crystallography
- X-ray Diffraction