As I understand you have used a Gaussian or a Lorentzian lineshape to fit the Bragg peaks? I would recommend the pseudo-Voigt function, which is a linear combination from Gaussian and Lorentzian.Maybe that helps?

Dear Bendoumia, can you post the original xrdml file.

Hard to say without more information, but if you have not enabled the FJC correction for axial divergence, I would strongly recommend you do so.

Good day. I would like to receive the original xrdml file.

Dear bendoumia;

if you calculate the crystallite size and microstrain, it would be interesting to choose the pseudo-voigt function for represent the line profil of Silicon SRM 640-c as standard reference material or better, with the LaB6 who gives many peaks than the SRM 640-c.

Also, should be preferable to use the intergated width (Aire/Imax : °2Theta) instead of the FWHM (°2Theta). You can consult my doctoral thesis at the library of USTHB (SARI Ali ).

For a more thourough discussion we would need details about the standard, sample preparation and the instrument parameters used, and pattern simulation should be done with one of the more widely accepted Rietveld programs (e.g. GSAS or Fullprof, which are free for academic use).

One experimental detail which is evident from your 28.4º peak is the step size: I would try to use ~0.05 instead of ~0.1º, this increases the number of points per peak and improves the possibility to discriminate between the Gaussian and Lorentzian terms. And if you can, extend your scan until 140º, this adds 2 more peaks and makes refinement of the angle dependent terms in the peak width more stable.

In my experience with proper Si standards, peaks are well simulated with the only use of three Gaussian (U, V, W) and 2 Lorentzian (X, Y) terms, plus a small correction (Finger-Cox-Jephcoat mentioned by Edward) for axial divergence causing the asymmetry towards low angles (nicely visible in the red trace of your Fig. 2). And, of course, peak position usually needs a correction for pattern origin and, sometimes, transparency or sample displacement (this needs a wide scanning interval). As for the unit cell, I usually refine it even if it should comply with the specifications of the standard, but if you want, you may follow earlier discussions about this issue.

your Silicon "Powder" standard must be certified for Line Position and Line Profils. See (below) an XRD pattern spectra of SRM 640c recorded with a step size 0.05 °2Theta using an X'Pert Pro MPD diffractometer. Finally, coeficients of Cagliottit were deduced from the following instrumentals curves.

Thank you for all to be interested by my question

For the function that describe the profile I have choosed the pseudo voigt, but to get the Gauss Coefficients and Lorentz Coefficients which define the instrument coefficients, I must select in the additional Graphics pane: Show Graphics > Half width Plot > Broadening (Gaus+Lorentz) which give us the Gaussian and Lorentzian components of the peak profiles plotted individually, and both must follow a caglioti equation to be sure that my coefficients are correct.

For the step size use it is 0.01

M Ali Sari your first Fig is The FWHM Statistics plot which I can obtain it by selecting in the additional graphics: Show Graphics > Halfwidth Plot > FWHM Statistics

But I try to follow all the instruction of HPS tutorial to be sure of my results, for that I verified: the agreement indices, the difference plot, the FWHM plot and for the plot of Gaus and Lorentz I have got this problem

For the original xdm it is attached

my first figure shows (FWHM)2 and not FWHM.

I think it would be better to review optics of incident beam, the incident slit 1/32 that has used as anti-scatter slit in your experiment is generally used for alligner the goniometer (horizontal position "Zero" the faisseau RX). It's good to work with a slot divegence 1/16 with the mask 10 mm. It should be noted that the monochromator reduces the X-Ray beaum (45 to 50% Imax). Thus, It would be better to keep it if you do not have a programmable beam attenuator.

Uses the help from HighScorePlus, you can found an example of structural refinement of standards material using Rietveld method for establish the pseudo-Voigt profil function.

Dear Bendoumia, comments from the Ali Sari are really good. You have some problem with geometry of your setup. I saw some irregular displacement cca. 0,005 degree, after correction of this replacement Rietveld Refinement is pass.