1.
About crystallite size estimation. XRD peak broadening is produced by both size and strain. The XRD peak full-width-at-half-maximum (FWHM) cannot be used for crystallite size estimation directly. Diffraction peaks have different shapes, e.g. Lorentzian or Gaussian, depending on size and microstrain contribution. Therefore, in order to estimate crystallite size, peak shapes have to be deconvoluted into Lorentzian and Gaussian components and only one of them is related to crystallite size.
Let me know that which components to be used in Crystalline Size and Strain estimation?
2.
Is deconvolution required for major peaks or for all the peaks in XRD?
no no no no guys... you are missing a very important point!!! microstrain (as people call the root mean strain) is ALWAYS anisotropic!!! we have elastic anisotropy and this is reflected in the breadth as well (see e.g. the works of Popa, in J. Appl. Cryst. rediscovered also by Stephens in the same journal). The HUGE problem in line profile analysis is that peaks are neither Gaussian nor Lorentzian. Actually, besides the emission profile (sum of Lorentzians in energy), the peaks cannot be Voigtian as the Voigtian cannot represent a size distribution!
Moreover Scherrer formula assumes that the breadth and "large part" of the peak can be approximated by a Gaussian, quite an unlikely case (and already physically wrong for the reason expressed above)..
We have published this stuff several times and proposed also alternatives that takes physics correctly into account (people tend to forget it). This said, it is not possible (if you want to do things accurately) to do the separation into Lorentzian and Gaussian parts, but you can separate things into instrument, size and strain provided you make sufficient assumptions and you have a sufficiently large number of independent reflections. Deconvolution is always needed and should be done simultaneously for all peaks (if you select the information you are never sure you get it right). A good trick to do this deconvolution without actually doing it, is to use a convolutive approach: you synthesise the profiles ab initio and you fit the model to the data. That's the basis of the WPPM approach, and you avoid the ill posedness of the deconvolution.
To be honest the size strain round robin paper is good but I would not classify it as outstanding, sorry. We have proven that the round robin "result" can be improved substantially by doing the analysis in a more accurate way. It is however a good starting point.
peter, I hope you will not kick my butt is I would say that your book is good but not focused on this topic. So for microstructure analysis by diffraction there are two major reference books: the one edited by Snyder, Fiala, Bunge (Defect and Microstructure Analysis by Diffraction) and by the one edited by Mittemeijer and Scardi (Diffraction Analysis of the Microstructure of Materials). They are already obsolete in some parts, but they can give you some idea of the progress in the field, with a higher degree of specialization.
An please read the literature, the hypotheses and use Scherrer equation in a qualitative or relative way. Otherwise there is the risk is that you will publish "my crystallites have the size of *** nm" and the only thing you can seriously do with that number is to play bingo.
It's an interesting point. I have always just used the FWHM of the raw data without any fitting for the crystallite size, under the assumption of course that strain is negligible. Are there any references for the statement that only 1 of Lorentzian or Gaussian is related to crystal size?
The size and strain terms have different angular dependence (1/cos(theta) as compared to tan(theta)), and so can be separated if enough peaks are collected over a sufficient 2theta range. If there is shape anisotropy then this becomes more complicated, as there will be an additional hkl dependence on the size parameter.
FYI - "strain" or "microstrain" is a term frequently (at least in this context) used to accommodate all the contributions to peak broadening not due to crystallite size (after correcting for instrumental broadening of course). So in this context strain includes chemical inhomogeneities, vacancies and defects, stacking faults, etc. Assumption that strain is negligible is likely to cause you to derive a smaller crystallite size than is real because you are attributing all the broadening to size via the Scherrer equation, which may not be (and probably is not) correct.
There are many excellent papers to refer to - one might start by looking at the Accuracy in Powder Diffraction conference proceedings, or some of the papers by Tomas Ungar and his colleagues.
Here is an outstanding round robin study on size-sttrain broadening analysis:
"Size–strain line-broadening analysis of the ceria round-robin sample"
D. Balzar, N. Audebrand, M. R. Daymond, A. Fitch, A. Hewat, J. I. Langford, A. Le Bail, D. Louer, O. Masson, C. N. McCowan, N. C. Popa, P. W. Stephens and B. H. Toby
J. Appl. Cryst. (2004). 37, 911–924
You might also refer to section 2.9.1: Peak Shape Functions in the book "Fundamentals of Powder Diffraction and Structure Characterization of Materials" by Pecharsky and Zavalij for useful information on profile fitting.
no no no no guys... you are missing a very important point!!! microstrain (as people call the root mean strain) is ALWAYS anisotropic!!! we have elastic anisotropy and this is reflected in the breadth as well (see e.g. the works of Popa, in J. Appl. Cryst. rediscovered also by Stephens in the same journal). The HUGE problem in line profile analysis is that peaks are neither Gaussian nor Lorentzian. Actually, besides the emission profile (sum of Lorentzians in energy), the peaks cannot be Voigtian as the Voigtian cannot represent a size distribution!
Moreover Scherrer formula assumes that the breadth and "large part" of the peak can be approximated by a Gaussian, quite an unlikely case (and already physically wrong for the reason expressed above)..
We have published this stuff several times and proposed also alternatives that takes physics correctly into account (people tend to forget it). This said, it is not possible (if you want to do things accurately) to do the separation into Lorentzian and Gaussian parts, but you can separate things into instrument, size and strain provided you make sufficient assumptions and you have a sufficiently large number of independent reflections. Deconvolution is always needed and should be done simultaneously for all peaks (if you select the information you are never sure you get it right). A good trick to do this deconvolution without actually doing it, is to use a convolutive approach: you synthesise the profiles ab initio and you fit the model to the data. That's the basis of the WPPM approach, and you avoid the ill posedness of the deconvolution.
To be honest the size strain round robin paper is good but I would not classify it as outstanding, sorry. We have proven that the round robin "result" can be improved substantially by doing the analysis in a more accurate way. It is however a good starting point.
peter, I hope you will not kick my butt is I would say that your book is good but not focused on this topic. So for microstructure analysis by diffraction there are two major reference books: the one edited by Snyder, Fiala, Bunge (Defect and Microstructure Analysis by Diffraction) and by the one edited by Mittemeijer and Scardi (Diffraction Analysis of the Microstructure of Materials). They are already obsolete in some parts, but they can give you some idea of the progress in the field, with a higher degree of specialization.
An please read the literature, the hypotheses and use Scherrer equation in a qualitative or relative way. Otherwise there is the risk is that you will publish "my crystallites have the size of *** nm" and the only thing you can seriously do with that number is to play bingo.
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