Tutorial ceo2 sizestrain
Size strain – CeO2
Files needed: massonsh.xye, massonbr.xye, ceo2.cif
Learning outcomes: This example shows the use of topas for size/micro strain analysis using the CeO2 round Robin example. Initially we’ll fit a powder pattern of a highly crystalline sample to obtain an instrumental resolution function (IRF) for the old BM16 high resolution diffractometer at the ESRF. We’ll then fit the pattern of a sample which shows significant size/micorstrain broadening using the fixed IRF peak shape and convoluting sample size/micorstrain terms on top.
Background: the theory behind the double Voigt methods used and references are outlined here. Some of the limitations of the approach are discussed in the WPPM tutorial here. The wavelength used was 0.399826 A. sh and br refer to sharp and broad.
1. Save the files above in your working directory.
2. Go through topas-editor or jEdit menus for a Rietveld refinement.
3. Select datafile massonsh.xye.
4. In 2. Instruments and 3. Corrections select Synchrotron and enter wavelength of 0.399826 A. Select to refine zero point. Note that the emission profile width is set to 0.00001 meaning it is delta-function like.
5. Read in cif file CeO2.cif.
6. Type “beq @ 1” at the end of each site line to refine atomic displacement parameters.
7. Send the INP to TOPAS then refine. You may find that it takes several cycles to converge as default scale factor is not very sensible.
8. You might find the following peak shape values and scale useful if things diverge:
scale scal_CeO2 0.0000006239`TCHZ_Peak_Type(pku, 0.00040989078`,pkv,-0.000149722649`,pkw, 2.95690228e-05`,!pkz, 0,pkx, 0.00515690164`,pky, 0.00281320157`)9. You should be able to get Rwp of ~ 7.1% or lower.
10. Now save the input file as massonbr_riet_01.inp. Change the datafilename to massonbr.xye. Fix all the peak shape parameters. i.e. peak shape should look something like:
CHZ_Peak_Type(!ku, 0.000583803234,!pkv,-0.000181698976,!pkw, 3.08947187e-05,!pkz, 0, !pkx, 0.00297938029, !pky, 0.00311873483)
Simple_Axial_Model(!axial, 1.13206498)11. Click on “Send to TOPAS”. Clear all data in TOPAS then refine. You should get Rwp around 76%. The calculated peak shape is far sharper than the experimental. This is due to the sample contribution to the peak shape.
12. Introduce the following macro to describe sample broadening due to size and strain. The various terms are defined here.
LVol_FWHM_CS_G_L(1, 4489.51014, 0.89, 5424.90744, !csgc, 10000, !cslc, 10000)
e0_from_Strain( 0.00004, !sgc, 0.0001, !slc, 0.0001)13. Refine again. You should still get Rwp ~75%. The csgc and cslc are the crystallite size gaussian and lorentzian broadening contributions in nm. 10000 nm corresponds to an essentially infinite crystal size which will lead to no broadening. Similarly, the Gaussina (sgc) and Lorentzian (slc) microstrain contributions are infinitely small.
14. Set the size and strain components to refine. i.e. remove all the “!” values in the above macro. On refining you should get Rwp ~ 3.74%. The first number in the LVol macro should be around 22.5 nm. This is the volume weighted mean column height referred to as DV in the paper by Balzar.