Size Strain – CeO2
Learning outcomes: This example shows the use of topas for size/strain analysis using the CeO2 round Robin example. Initially we’ll fit a powder pattern of a highly crystalline sample to obtain an instrumental peak shape function. We’ll then fit the pattern of a sample which shows significant size/strain broadening using an instrumental peak shape and convoluting sample size/strain terms on top.
Background: the theory behind this is and references are outlined 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 the menu for a Simple Rietveld refinement.
3. Select datafile massonsh.xye.
4. In Instruments/Corrections select Synchrotron and enter wavelength of 0.399826 A. Select to refine zero point.
5. Read in cif file CeO2.cif.
6. Type “beq @ 1” at the end of each site line to refine atomic displacement parameters.
7. Use “Save/send to topas” button and refine in topas. 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,0.000477324636,pkv,-0.000133003347,pkw, 2.32467957e-05,!pkz, 0.00,pkx, 0.00339`,pky, 0.00309`)
9. You should be able to get Rwp of ~ 6.97% 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:
TCHZ_Peak_Type(!pku, 0.000477324636,!pkv,-0.000133003347,!pkw, 2.32467957e-05,!pkz, 0.00,!pkx, 0.00339197454,!pky, 0.00308823283) Simple_Axial_Model(!axial, 1.20686`)
11. Click on the “Save/Send to topas”. Clear all data in topas then refine. You should get Rwp around 75%. The calculated peak shape is far sharper than the experimental.
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 ~74%. The csgc and cslc are the crystallite size gaussian and lorentzian broadening components in nm. 10000 nm corresponds to an essentially infinite crystal size which will lead to no broadening.
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 nm. This is the volume weighted mean column height referred to as DV in the paper by Balzar.