Multiphase Rietveld refinement

Fundamental Parameters Peak Shape Fitting

Learning Outcomes: This example introduces the concepts of fundamental parameters peak fitting whereby the instrument and sample contributions to the peak shape are explicitly calculated as opposed to fitted using e.g. an empirical pseudo-voigt function.

Topas advantages: complex peak shapes can be simulated using a small number of physically sensible parameters.

1. Save the datafile in your working directory.

2. Work through the simple Pawley refinement menus.

3. Click on “Select Data File” and navigate to find the file d9_00260.raw.

4. In Instrument/Corrections select “Durham_d9” – the diffractometer used to collect the data.

5. Click on “Refine zero point” to flag that zero should be refined.

6. The samples was an a highly crystalline sample of CeO2. Use spacegroup Fm3m and cell parameter of 5.41 Angstroms.

7. Try running the refinement using the TCHz peak shape. You should get Rwp~18.6% refining the default parameters. A slightly lower R-factor (17.4%) can be achieved if you also refine pkx and pkz.

8. Comment out the TCHz peak shape line and the simple axial line and introduce the following lines at the end of the input file:

Radius(250)
Slit_Width( !det_slit , 0.20)
Full_Axial_Model(12, 15, 12, 4, 4)
LVol_FWHM_CS_G_L(1, 4489.51014, 0.89, 5424.90744, !csgc, 10000, !cslc, 10000)

‘e0_from_Strain( 0.00004`, sgc, 0.00010`_LIMIT_MIN_0.0001, slc, 0.00010`_LIMIT_MIN_0.0001)

These lines describe the instrumental geometry and detector slit used. See the topas manual for full details. The Full_Axial_Model macro describes:

Full_Axial_Model(filament_cv, sample_cv, detector_cv, psol_cv, ssol_cv)
[filament_cv]: Tube filament length in [mm].
[sample_cv]: Sample length in axial direction in [mm].
[detector_cv]: Length of the detector (= receiving) slit in [mm].
[psol_cv, ssol_cv]: Aperture of the primary and secondary Soller slit in [°].

10. The refinement should converge rapidly to give Rwp around 25%. N.B. there are no refined peak shape parameters here.

11. Try refining parameter cslc, which introduces a lorentzian size contribution to the peak shape. Rwp should refine to 18.1% – lower than the pseudo-voigt modelabove. Try refining some of the instrumental parameters to see their influence. Letting the divergence slit refine to 0.3 mm gives Rwp~17.8%. Adding either strain terms or a gaussian size broadening leads to no further improvement in Rwp.

12. Try putting !csgc back to 10000 (infinite size) and changing e.g. the parameter det_slit to e.g. 0.05 mm. This gives an indication of the peak width you could get with this set up using a smaller slit. In this way you can rapidly assess what experimental configuration of Sollers/detector slit/etc are suitable to obtain the highest quality information on a given sample.