In XRD analysis of powders, Scherrer's equation can be used to determine the crystalline size of the powders, by measuring the half width of the XRD peaks. And this equation is effective when the crystalline size of the powders is below 100 nm.
However, for nanopowders, the XRD peaks are usually broadened. Then sometimes the peak splitting (if any) becomes less obvious. If this, should we do peak fitting to separate the two peaks before using Scherrer's equation?
A simple illustration is shown in the attachment.
Gilles,
you are right with your evaluation. Unfortunately there are still a few problems related to the question of Shaopeng...
- (this gets me usually quite angry) people should learn how to write that surname.. it is SCHERRER, for ** sake.
* that formula is almost 100 years old and it is quite likely that in those years the community has answered most questions about it. This is the case: Scherrer formula can provide some qualitative estimation of the (coherently scattering) domain size to be employed for comparison. Using it for a quantitative microstructure analysis of a nanosized powder is definitely absurd (and this has been proven several times. Quick check at the hypotheses behind Scherrer equation and this is clear.
So to go back to the question of Shaopeng:
- Scherrer formula is better suited in the form that considers the integral breadth more than the FWHM (following the idea of von Laue)
- you should consider all reflections when doing a microstructure analysis by XRD (a single peak does not provide any useful information). For several reasons it is better if the lattice is known. Therefore you should know where (more or less) to expect the presence of peaks (such as the doublet you show).
- tails of broad peaks are ALWAYS superimposed (even in cases not as extreme as the one you show). If you "fit the peaks" you already force a model to your data (s you extract information from the width of that fitted peak and not from the data itself).
- most people don't even consider the presence of the Ka doublet when doing a Scherrer analysis...
- proper analysis should be done using the whole pattern and using appropriate microstructure models (to take any anisotropy into account). So the suggestion of Gilles to employ the Rietveld method is only partly correct. The Rietveld method is NOT tuned for microstructure analysis, especially for nanosized systems. Peak functions are developed to get the area of the peaks correct for structure refinement. The microstructure broadening models are either obsolete, undocumented or too rough. Thing works well for coarse grains (where you can use those models in an effective way) but can be wrong for domains of a few nm average size.
Moreover the Rietveld method can be in some cases too strict (you have a forcing of a structure model to the data) and in some others not useful (if the structure is not known). You can in any case obtain information on size and strain effects using the Whole Powder Pattern Modelling, currently the state of the art reciprocal space alternative to the Rietveld method for microstructure analysis.. and have most of the problems (microstructure models, peak overlapping, instrumental function, emission profile) taken into account in an appropriate way
Hello!
Yes, of course you have to deconvolute both (or all peaks) before doing your calculation but actually, the best way is doing a complete Rietveld Refinement (be careful, including atomic positions if you know them because in case of strong overlapping, a simple Full Pattern Matching would be dangerous as you don´t force intensities). One issue particularly important to consider is Instrumental Resolution Function, ie the peak profile (including width) due to your difractometer, considering a "perfect" powder (NIST reference material). It can be a long (and expensive for the NIST reference) but this is the only way. Programs to do that: MAUD, Fullprof, JANA and lots of tutorials exist on the web.
Hope it helps
Gilles
Agree with Gilles Gauthier. But I see someone does not deconvolute the broadened peaks in many references... So they are wrong.
I think crystalline has minor difference to grain size. But most people use both as they are the same.
Hi again! yes Shaopeng, they are wrong, moreover if they don´t take into account the instrumental contribution (can be neglect if we are really talking about nanomaterials if think, microstructural effects being predominant). All diffraction techniques allow in theory the determination of crystallite size (indeed coherent scattering domain). Grain size in Materials Science and Engineering is not precise enough and this has always been a source of neverending discussion of it means or how to define it, aggregate, aglomerate, crystallite size... depends the context.
Hope it can help.
Gilles
Yes, interesting discussion, but it doesn´t change the fact that crystallite has a clear definition, for which the size can be calculated or estimated by Diffraction techniques. There is often a confusion between grains and crystallite, as it can be the same thing... or not. In conclusion, the definition and clarity can only comes when you specify the technique that is used to examine the material. But back to the question of Shaopeng, there is indeed no problem. He is asking for crystallite size.
Gilles,
you are right with your evaluation. Unfortunately there are still a few problems related to the question of Shaopeng...
- (this gets me usually quite angry) people should learn how to write that surname.. it is SCHERRER, for ** sake.
* that formula is almost 100 years old and it is quite likely that in those years the community has answered most questions about it. This is the case: Scherrer formula can provide some qualitative estimation of the (coherently scattering) domain size to be employed for comparison. Using it for a quantitative microstructure analysis of a nanosized powder is definitely absurd (and this has been proven several times. Quick check at the hypotheses behind Scherrer equation and this is clear.
So to go back to the question of Shaopeng:
- Scherrer formula is better suited in the form that considers the integral breadth more than the FWHM (following the idea of von Laue)
- you should consider all reflections when doing a microstructure analysis by XRD (a single peak does not provide any useful information). For several reasons it is better if the lattice is known. Therefore you should know where (more or less) to expect the presence of peaks (such as the doublet you show).
- tails of broad peaks are ALWAYS superimposed (even in cases not as extreme as the one you show). If you "fit the peaks" you already force a model to your data (s you extract information from the width of that fitted peak and not from the data itself).
- most people don't even consider the presence of the Ka doublet when doing a Scherrer analysis...
- proper analysis should be done using the whole pattern and using appropriate microstructure models (to take any anisotropy into account). So the suggestion of Gilles to employ the Rietveld method is only partly correct. The Rietveld method is NOT tuned for microstructure analysis, especially for nanosized systems. Peak functions are developed to get the area of the peaks correct for structure refinement. The microstructure broadening models are either obsolete, undocumented or too rough. Thing works well for coarse grains (where you can use those models in an effective way) but can be wrong for domains of a few nm average size.
Moreover the Rietveld method can be in some cases too strict (you have a forcing of a structure model to the data) and in some others not useful (if the structure is not known). You can in any case obtain information on size and strain effects using the Whole Powder Pattern Modelling, currently the state of the art reciprocal space alternative to the Rietveld method for microstructure analysis.. and have most of the problems (microstructure models, peak overlapping, instrumental function, emission profile) taken into account in an appropriate way
Thanks Matteo for the complement, do you have any good reference to quote or program that allow the Whole Powder Pattern Modelling you mention? In which sense is it different from what is called Whole or Full Pattern Matching, implemented in FP, etc...? The name sounds like the same... Don´t you have any structural model restriction in such procedure?
Ciao
Matteo, forget my question. Didn´t know you were at the origin of the alternative WPPM technique ;-) Better have a look at your articles first. Just to know, and answer to Shaopeng, the best program for that: PM2K? Have you ever done any comparison of what can give a program like MAUD and what you obtain with WPPM (same data)? Thanks
This of Gilles and Matteo is a very interesting discussion I have encountered many times when dealing with nanoparticle characterization.
In the majority of cases where a rough estimate of the cohorently scattering domain size is needed (read crystallite size or refer to other threads) a correctly performed characterization with the Scherrer formula will work but as Matteo says, a well-performed analysis is a lot more of taking a peak, making a fit with some pre-established courve (lorentzian in general), calculating FWHM and introducing it in the Scherrer formula with the Scherrer constant value most convenient for the user (only determined for well known particle size distributions not given by the analysis itself).
A meaningful analysis must, at least, consider all contributions to peak shape (instrumental, radiation, etc.) additionally to size, and also use different peaks to determine if there is any component of size anisotropy. And a long etc...
IMHO the use of WPPM is an excess for a rough estimation of crystallite size. WPPM is an excellent method for determining the structural causes of peak broadening, not only caused by size but by other effects too (defects, strains, size, isotropic or anisotropic). Additionally, I may be wrong (Matteo, please correct me if I am) but the implementation of WPPM for any structure is far from simple and the interpretation of the multiple causes of broadening for a triclinic structure is much more complicated than the typical cubic cases that have been thoroughly studied. So it may be true that WPPM is theoretically the best approach (and maybe the only fully correct one) but in practise it seems not very useful for routine work (even less usefull for unexperienced users).
Doing a Rietveld refinement may be the mean path between a rough application of the Scherrer equation and the WPPM method. Since in Rietveld analysis you use all the peaks in the pattern and no good fit will be obtained if there are anisotropic effects not taken into account by the model you will have a better understanding of your nanoparticle size at least. And may additionally determine the presence of strain, etc.. This fit may be phenomenologycal but, in all the cases the use of the Scherrer equation is a reasonable approach, it will be a better approach, and it will also give reasonable results in many cases where the Scherrer equation may be misleading.
Rietveld analysis may not always provide a good result, though, since in many cases the average atomic (crystalline) structure of nanoparticles (specially when the coherently scattering domains are below 10 nm) is different than the average bulk structure that is generally reported in the literature (due to the high surface area/volume ratio in nanoparticles and its physical consequences) and the fit to the observed intensities may be very bad. In such a case the only structural analysis procedure that may include a size component plus defects, etc. may be Pair Distribution Function Analysis (PDF) that is a direct-space aproach that may include all structure-related phenomena in the model.
But again, PDF is another extreme approach not suitable for routine analysis as WPPM. Therefore I would like to stress that Rietveld analysis still is a good aproach for routine work with most nanoparticle systems. Without forgetting that the true physical effects in the sample may well be more complex than the simple answer obtained by the correct use of the method.
Leo,
I understand your doubts... but there is a serious issue here.
If I want to have a rough estimate (i.e. a number), I just take the ruler and get a number using Scherrer formula. Why using the Rietveld method then, that is based on the very same equation?
If I want to have something that at least gives a result that is compatible both with physics and with the experimental data I use the WPPM. At least I have all available physical models for the microstructure and I can at least take the distribution of sizes into account. Right now most models are available for any symmetry.
In most cases what people do with the Rietveld method (the most used black box ever) is to force their data to behave according to their model and not viceversa! If you want to know what happens for people using the Rietveld method on nanoparticles, have a look at :
https://www.researchgate.net/publication/230824264_On_the_modelling_of_the_powder_pattern_from_a_nanocrystalline_material
Cell parameters can be wrong (as you use "apparently" well behaving models) and you start building theories on wrong results! And this should be one of the accurate numbers you obtain from Rietveld analysis....
It is true that people should not use very complex methods without knowing what they do... but hey, this is also valid for the Rietveld method! So welcome the negative thermal parameters or the unphysical bond lengths to get a good fit? sure, as many users don't even check those things...
Article On the modelling of the powder pattern from a nanocrystalline material
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