Symmetry-Mode (ISODISTORT) Rietveld Refinement - WO3

Cif files needed: wo3_pm3m.cif, wo3_p21n_80056.cif

Data files needed: HRP37287_bs.xye, d8_03901_030c.xy, d8_03901_850c.xy

Cheat files (not) needed: d8_03901_030c_01.inp, d8_03901_850c_04.inp, hrp37287_bs_iso_03.inp, wo3_p21n_ISODISTORT.str, wo3_p4_ncc_ISODISTORT.str

Learning Outcomes: This tutorial applies ideas developed in the simple Distortion-mode Rietveld tutorial. We'll work through a slightly more complex example using x-ray and/or neutron data. We'll also investigate how you can determine the space group of a material using ISODISTORT.

We'll use the example of WO3 which undergoes a number of phase transitions on cooling from high temperature. At high temperature one might expect the material to have the simple cubic structure of ReO3 (Pm-3m, infinite network of corner shared WO6 octahedra), though this has never been observed. However the 7 lower symmetry structures can all be described as distortions of this structure. At room temperature WO3 is monoclinic P21/n with a 2ax2ax2a cell, where a is the cell parameter of the ReO3 form. At low temperature it is monoclinic Pc with a 2^0.5x2^0.5x2 cell. From ~800-900 C it is tetragonal P4/ncc with a 2^0.5x2^0.5x2 cell.

In the first part of the tutorial we'll use ISODISTORT to generate a description of the P21/n structure.

We'll then use this description to fit time of flight neutron data to determine which symmetry modes are important (this section could be skipped).

Finally we'll fit 30 C and 850 C X-ray data. The room temperature data can be well described with just 5 symmetry modes. With a few assumptions, we will deduce the symmetry at 850 C directly from symmetry mode amplitudes.

There's lots more description of the WO3 system and the ideas in this tutorial in the IUCr Computing newsletter artice "Rietveld refinement of structural distortion mode amplitudes" by Branton J. Campbell, John S.O. Evans, Francesca Perselli and Harold T Stokes (linked here). N.B.some of the specific labelling may have changed relative to that paper.

Authors: John and Branton

Note: depending on when you installed jedit menus "distortion mode" may be used instead of "symmetry mode" and ISODISPLACE for ISODISTORT.

Create a P21/n Description of WO3 in ISODISTORT

The procedure for this is very similar to the one you used for the LaMnO3 example. The file you should create is linked here in case you have problems.

1. Upload wo3_pm3m.cif to the ISODISTORT website.

2. Select monoclinic cell choice 2 to end up in P21/n.

3. Choose Method 3 and enter the primitive real-space superlattice matrix {(2 0 0),(0 2 0),(0 0 2)}.

4. Selected point group Monoclinic: 2/m C2h.

5. There are several options in the pull down list for this point group, and several with different origin choices for P21/n. In general you'd have to try all origin choices. However, lets jump to the answer we want and select the option "P2_1/n, basis = {(0,0,-2),(-2,0,0),(0,2,0)}, origin = (0,1/2,1/2). This is currently 6th in the list for P2_1/n.

6. Select the bullet to output topas.str and save to your directory as wo3_p21n_ISODISTORT.str.

7. At this point you might like to select the bullet for "view distortion". See what effect e.g. the O R4+ (rotates octahedra) or W M3- (moves W's off centre) modes have on the structure.

8. You might also like to select the bullet for "view diffraction" and then select the "powder" option. See what effect changing different mode amplitudes has on intensities. Investigate peak splitting using the strain mode sliders.

Distortion-Mode Fit Time of Flight Neutron Data (optional)

We'll now fit tof neutron data using symmetry modes. Skip this if you just want to move to the X-ray example.

1. You might first want to perform a normal refinement of the tof data which were recorded on the hrpd back scattering bank. You can do this by working through the "Simple tof Rietveld" menus.

2. Use file wo3_p21n_80056.cif and HRP37287_bs.xye. For this data collection t0=0.80, difc=48199.28 difa=-5.54. Refine 30000-120000 microsecs. With 6 background terms, 24 xyz's, 8 isotropic temperature factors and a single sample peakshape term you should get Rwp = 7.23%. N.B. these were the first data collected with the new hrpd beam guide so they're not "perfect".

3. Switch to a symmetry mode model. The easiest way to do this is to open wo3_p21n_ISODISTORT.str and paste its contents over the str section of the input file created in 2 (make sure you keep the peak shape section).

4. You may need to manually change some symmetry mode amplitudes from 0.0 to start things off. If you refine all amplitudes you should get exactly the same R-factor as in 2. If you get stuck, try simulated annealing of mode amplitudes. Alternatively put all amplitudes to 0 and manually start a2, a7, a8 and a19 at 1.0.

5. You should find that there are only 9 symmetry modes with amplitude of > 0.1 Angstrom (this is the sum of rms displacements in the supercell). If you fix all but these modes at 0.0 you should get Rwp = 7.40%.

Conclude: you can get a comparable fit with 9 distortion-mode amplitudes as 24 xyz parameters.

Distortion-Mode Fit of X-ray Data

In this section we'll do a distortion-mode refinement of room temperature X-ray data. We'll learn a "trick" for working out cell parameters after phase transitions. We'll try and "guess" the space group of WO3 at 850 C.

1. Set up an input file for symmetry mode refinement of d8_03901_030c.xy using wo3_p21n_ISODISTORT.str created above by working through the "Symmetry Mode Rietveld Refinement" menus. For the instrument select "Durham d9" (sorry, confusing!). Initially refine just to 50 degrees 2-theta by adding "finish_X 50" to the input file.

2. Because the cell parameters are pseudo-cubic you will get a very bad fit to the data - e.g. only a single peak will be calculated for the 200, 020 and 002 reflections.

3. One way of determining cells of distorted systems like this is simulated annealing. Put the command "continue_after_convergence" at the top of the file. Then change the cell parameter lines to read:

a @ 7.52 val_on_continue = Rand(7.3,7.8);
b @ 7.52 val_on_continue = Rand(7.3,7.8);
c @ 7.52 val_on_continue = Rand(7.3,7.8);
al @ 90.00000 val_on_continue = Rand(88,92);
be @ 90.00000 val_on_continue = Rand(88,92);
ga @ 90.00000 val_on_continue = Rand(88,92);

after a few cycles of simulated annealing you should get sensible cell parameters, with one angle (beta) non-90. Fix alpha and gamma to be exactly 90. To match other parts of the tutorial if your beta is 89.2 change it to 90.8.

4. Once the cell is reasonable refine out to 90 degrees 2-theta. Put a single temperature factor on all atoms. Try refining just the modes with amplitudes >0.25 A from neutron data. Those are a2 (X5-), a4 (M3-), a7 (R4+), a8 (R4+) and a19 (M3+). You may need to displace values slightly from zero. You should get Rwp = 9.3%. Save this file so you have it later.

5. Try refining all 24 ampliutdes (use a different .inp filename). You should get Rwp = 9.02 % - only a marginal improvement for a fit with 24 structural parameters over 5.

6. Using the file with just 5 modes refining change the name of the data set to d8_03901_850c and try refining the high temperature data. You should see that these data are considerably less complex than at 30 C showing that at least one phase transition has occured.

7. After refinement you should find that a~b~7.468, c~7.85 Angstroms and all angles are ~90 degrees suggesting the material is tetragonal. Force the cell to be metrically tetragonal and you should get Rwp = 13.1%.

8. Next look at which of the mode amplitudes are really significant - i.e. which ones are really needed to fit the data. Remember that with X-ray data on WO3 O displacements are going to be very hard to pin down. Try setting a2 and a19 to zero - the fit doesn't get significantly worse. Try setting R4+ modes (a7 and a8) to zero. Now wRp rises from ~13.1% to 13.7% suggesting these modes are important. Conclude that the important modes are a4 (M3-) and R4+ (a7, a8). You might also note that forcing a7 and a8 to have the same magnitude has little effect on Rwp (it only increases to ~13.2%)

9. With these modes identified it's possible to use ISODISTORT to determine what the space group is. Upload wo3_pm3m.cif to ISODISTORT and select method 2. Specify 2 coupled IR's. Choose M and R then specifically select M3- and R4+. You might need to click on "generate isotropy subgroups" if offered. The highest symmetry tetragonal choice is 130 P4/ncc. Select this and save the topas.str file as wo3_p4_ncc_ISODISTORT.str. Note the full description given is:

P1(1)P1(1)(a,0,0;b,0,0) 130 P4/ncc basis {(1,1,0),(-1,1,0),(0,0,2)} origin (0,-1/2,-1/2)

this implies a cell of 2^0.5x2^0.5x2 relative to the original cubic cell (smaller than the P21/n cell we are using). The (a,0,0) is consistent with the Eu(a) and Eu(b) R4+ modes having identical magnitude in step 8.

10. Try doing a default symmetry mode refinement based on wo3_p4_ncc_ISODISTORT.str. You should get Rwp = 13.457 % for 19 parameters. This spacegroup choice is therefore completely compatible with the experimental data. Warning: there may currently be a small bug in ISODISTORT output. The line describing the O_1_y coordinate should read "O_1_y = 1/2 - O_1_dx". It's corrected in wo3_p4_ncc_ISODISTORT.str. Alternatively you can select origin choice 1 when you first read the structure in.

Other Work

1. You might like to try playing with the "View Diffraction" feature of ISODISTORT. In the diffraction window select "powder" pattern. You can then e.g. vary the strain modes and see the effect on peak splitting patterns. This can be done after point 6 of the first exercise.

2. You might like to try fitting neutron diffraction data on the low temperature Pc form of WO3 which are linked here. Data are noisy as only collected for 60 seconds. Important modes in the Pc structure are M3-, R4+, G4-. The cell is 2^0.5x2^0.5x2 relative to the Pm-3m cell. Cheat files wo3_p3_ISODISTORT.str and HRP37378_bs_iso_01.inp. I got Rwp = 19.995%.


[Modified 31-Jul-2017 by John S.O. Evans. Pages checked for Google Chrome.]