Using integral breadth or FWHM based conventional size-strain analysis method like W-H plot on XRD data, one can get estimation of apparent crystallite size and microstrain present in the sample. While in case of whole powder pattern fitting approach using the Rietveld/Lebail fitting of XRD pattern, one can tell whether size and strain have Gaussian or Lorentzian character along with estimation of apparent crystallite size and microstrain.
My question is what is the physical meaning/origin of Gaussian size broadening, Lorentzian size broadening, Gaussian strain broadening and Lorentzian strain broadening in diffraction pattern ?
or
Under what condition the size and/or strain behaviour of material will leads to the Lorentzian/Gaussian character of XRD peak profile ?
The FWHM or integral breadth gives always only an average (not THE average but a specific average) of the underlying crystallite size distribution/column-length distribution. That average may be a quite special an unfavourable average. The actual shape of the broadening contains the info about the character of the distrubutions.
A.L.
Dear Dr. Andreas Leineweber,
Could you please refer some review article or literature where Lorentzian/Gaussian character of XRD peak profile is discussed for size/strain distribution.
Thank you
The profile shape functions can be constructed with any shape dependence on angle and hkl direction, based on a functions representing both instrument and specimen contributions. A smaller number of refineable profile parameters is required to reduces parameter correlations and the most common approaches are based on the Gaussian and Lorentzian components. But there is no physical law imposing Gaussian- or Lorentzian-type diffraction line profile broadening related to microstructural effects.
A higher sophisticated approaches avoid physical constraints inherent to arbitrarily selected line profile functions. Instead physically models are used to describe microstructural broadening, by characterizing the effects of crystallites size, shape, lattice defect, density etc from first principles. This so-called Whole Powder Pattern Modeling (WPPM) approach currently represents the state of the art for quantitative microstructural analysis of nanocrystalline materials (Scardi & Leoni, 2001, 2004; Scardi et al. 2010).
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