"My question is, if we use Rietveld refinement to get particle size, is the size measured a volume weighted size distribution or weighted by a different factor? Whatever the answer is, please point to a paper or provide a derivation to support the answer."
Your expert input on this subject would be deeply appreciated. This question was posed in the following LinkedIn discussion by Richard Riman, Distinguished Professor at Rutgers, The State University of New Jersey:
https://www.linkedin.com/groupItem?view=&gid=2683600&item=5930174769977638912&type=member&commentID=5931825362622259200&trk=hb_ntf_LIKED_GROUP_DISCUSSION_COMMENT_YOU_CREATED#commentID_5931825362622259200
Thanks Roberto!
Would anyone please help identify some sort of a publication substantiating the above?
I will only answer for the Bruker TOPAS code. Clearly there are different Rietveld packages which function in slightly different ways. Within Topas using inbuilt macros you are calculating the volume weighted mean column height. (see Bruker TOPAS V4.2 Technical Reference Manual Page 31 (2009)) Essentially this line broadening analysis gives you a single point on the (volume weighted) size distribution curve. Use of double-Voigt during Rietveld, Le Bail or Pawley fitting theoretically allows a size distribution to be derived for an assumed distribution function (usually log-normal). Nowadays, it is widely accepted that this double- Voigt approach, i.e., a Voigt-function approximation for both size-broadened and strain-broadened profiles is a better model than the simplified integral-breadth methods. (Balzar et al, J. Appl. Cryst., 37, 2004, 911)
From the paper ‘Domain size analysis in the Rietveld method’ by W.I.F. David, M. Leoni, and P. Scardi (Materials Science Forum Vol. 651 (2010) 187) the authors advance the Rietveld method to produce physically sound models to account for domain-size effects. The TOPAS macro language allows fast and effective models to be implemented for the analysis of both mono-dispersed and poly-dispersed systems, providing results that in the most simple cases are compatible with the more advanced Whole Powder Pattern Modelling techniques of microstructure analysis. Hence limited size distribution analysis can be derived from Rietveld analysis which I believe is behind the original question posed.
Article PM2K: A flexible program implementing Whole Powder Pattern Modelling
Article Domain Size Analysis in the Rietveld Method
Scherrer equation gives a fairly correct qualitative information crystallite size. A qualitative line-broadening analysis of X-ray diffraction patterns of the samples was performed using simplified methods (Langford, 1978, 1999; Williamson & Hall, 1953). In order to extract the line-profile parameters of each simple (position, FWHM, integral breadth and line shape) the PROFILE fitting program from Socabim, available in the software package DIFFRACT-AT supplied by Bruker AXS, can be used (now, the program TOPAS Bruker gives similar results). The observed XRD lines were approximated using the pseudo-Voigt or Pearson VII functions.
The sizes of the crystallites are characterized by the volume-weighted crystallite size distribution, which may be interpreted as the density of probability of finding a crystallite of an assumed shape and size, taken with a weight proportional to its volume, in an analysed sample. The size of a crystallite is any of its linear dimensions, while the shape is described by the ratio of its characteristic dimensions (like edge lengths of a prism); either the size or the shape are treated as model parameters.
Jose - Current versions of TOPAS with fundamental parameters based approach have moved on considerably from the old Socabim PROFILE programs. Please if possible use TOPAS for best results!
Thanks Tim! Remember to post this on the LinkedIn discussion as well.
https://www.linkedin.com/groupItem?...EATED#commentID_5931825362622259200
The actual answer is no. It is not a direct measurement of the volume weighted average. The only way to get a direct measurement of the true grain volume average and distribution (as in a pure measured histogram which is not fit to any function) is to use the total crystallography or 3DXRD technique (that is unless you want to destroy your sample by serial sectioning).
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