Lab 7: Rietveld Refinement

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Materials Science 142
Applications of Diffraction Techniques

Laboratory Exercises 7: Reitveld Refinement
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Assigned: 5/24/06
Due:6/01/06, 5pm

Goal: Extract crystallographic data from X-ray powder diffraction data.

You are provided with diffraction data for a sample that contains a mixture of SrPrO3 and SrPr2O4, SrPr03_riet.xy. Data were collected using the Siemens D-500, Cu Ka radiation, in 0.01° steps, with a dwell time of 15 s/step. You are to perform refinement of the preliminary structural data to obtain relevant crystallographic data (e.g. lattice parameters, atomic coordinates, atomic displacement factors, and phase fractions). If you have a material relevant to your own research, you are highly encouraged to collect diffraction data from that material instead.

For performing the refinement, you can chose to use the XPert Pro software, or a freeware program entitled Rietica and available from ANSTO (Australian Nuclear Science and Technology Organization). Detailed instructions for using Rietica are provided below. For instructions on using XPert Pro for Rietveld refinement see your TA, Mikhail Kislitsyn.

Starting atomic coordinates for SrPrO3 are given in the cif file, SrPrO3.cif. Starting atomic coordinates for SrPr2O4 are given in a paper by Fiscus and zur Loye. The 'cif' file is an ascii file with crystallographic data compiled in a standard format that many programs can import.

If using your own sample, collect diffraction data over an appropriate 2 range. Record the instrument settings.

Input the data for analysis into the program you are using (again, see below for detailed instructions for Rietica) and also enter the crystallographic data for the two phases using the information provided. The cif file can be imported to provide the crystallographic data for SrPrO3, whereas the data for SrPr2O4 will have to be entered manually.

Sequentially turn on parameters for refinement. Do not use the automatic sequence option offered by XPert Pro.

In general, you will have to your judgment as to whether to keep a parameter turned on for refinement as you proceed to turn on the following parameters, or to turn it off to prevent the refinement from 'blowing up.' Simultaneous refinement of highly correlated parameters causes this problem and must be avoided. For example, occupancies and displacements parameters should not be simultaneously refined. Similarly, the overall scale factor should not be refined at the same time as the occupancy factors of all of the atoms. One amongst these parameters must be fixed. Also, it is important to refine the parameters most uncorrelated with other parameters first. The refinement strategy suggested in Young's "Rietveld Method" (p. 35) is

1. Scale factor - stable
2. Specimen displacement - stable
3. Flat background - stable
4. Lattice parameters - stable
5. More background - stable
6. W, in the Caglioti function for peak widths-poorly stable
7. x, y, z (atomic coordinates) - fairly stable
8. Occupancies and isotropic (thermal) displacement parameters - not generally stable
9. U, V, (in the Caglioti function) and other profile parameters - not generally stable
10. Aniostropic (thermal) displacement parameters - not generally stable
11. Zero point - stable

In most cases it is not very meaningful to refine anisotropic displacement parameters using conventional X-ray diffraction data. If you must limit the refinement to isotropic parameters in order to prevent the displacements of the atoms from becoming 'non-positive definite' then do so.

As you proceed with the refinement, you must periodically examine the difference plot (plot of Icalc - Iobs). This will provide you with insight as to what parameters might be misbehaving and whether you have selected the appropriate peak profile function. If appropriate, you may chose to change the values of parameters such as the scale factor and flat background to more closely match the data and get the refinement 'jump-started.'

Report:

Derived Bragg R-factor, goodness-of-fit (GOF), Rp, and Rwp

Plot of calculated and measured I(2Q), as well as difference plot

Molar and weight percentages of phases with standard deviations

Space group and cell parameters of both phases with standard deviations

Indexed 2Q, Icalc, Iobs (integrated intensities)

Wycoff positions, site multipicities, atomic coordinates and displacement parameters for atoms in SrPrO3 with standard deviations. For coordinates fixed by the Wycoff position, standard deviations are meaningless and not reported.

Bond distances and angles in SrPrO3 with standard deviations

Total number of refined parameters and their roles (e.g. 4 background parameters, 6 profile parameters, etc.)

Statement as to which profile function was selected

For the write-up, use the abbreviated lab report format described for lab 5. In this case, however, references are required.

Instructions for Rietica.