Tutorial isoriet

Symmetry-Mode (ISODISTORT) Rietveld Refinement – LaMnO₃

Files needed: lamno3.xy; lamno3_pm3m.cif

Learning Outcomes: This example shows how to perform a “symmetry-mode” Rietveld analysis that refines symmetry-motivated symmetry-mode amplitudes rather than atomic xyz coordinates. These group-theoretically derived symmetry modes tend to produce intuitive geometric motions like polyhedral rotations, shears, etc., and are related to the traditional basis of atomic xyz coordinates by a simple linear transformation (i.e. a square matrix). You can also refine site occupancies based on symmetry modes. The symmetry-mode details are calculated using the ISODISTORT software of Harold Stokes and Branton Campbell. For it to work, you’ll need the “Symmetry Mode Refinement” menus installed. These are installed automatically when you install jedit menus.

The example used here is a well-known distortion of LaMnO3 [Rodriguez-Carvajal et al., PRB 57 R3189 (1998)] with space group #62. In the standard Pnma setting, its supercell is related to the cubic Pm-3m parent cell by the transformation matrix {(1 0 1),(0 2 0),(-1 0 1)}. You will generate the superstructure in terms of symmetry modes using ISODISTORT, save the results to a TOPAS .str file, and use this file to set up a symmetry-mode Rietveld analysis with jedit.

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.

1. Download the files listed above to the working directory on your local computer.

2. Go to the ISODISTORT website and follow the “upload parent structure from a CIF file” link. Browse to find the “lamno3_pm3m.cif” file in your working directory, click the “Upload” button, and then click “OK” on the next page to finish importing the undistorted parent structure.

3. Under the “Method 3” heading, which allows you to “search over arbitrary k points for specified space group and basis”, select point group mmm and select the “conventional or primitive real-space supercell shape” bullet. Then enter the supercell basis (i.e. size and shape) as {(1 0 1),(0 2 0),(-1 0 1)}. Click the adjacent “OK” button to proceed.

4. This new page contains a list of all possible distortions consistent with your constrains (supercell size/shape, point symmetry). Only one of these distortions is realized in low-temperature LaMnO₃. Select the one with space-group #62 and origin = (0,0,0), and click “OK”. This will open the “distortion” page in a new window.

5. On the “distortion” page, the “View distortion” option (selected by default) will allow you to visualize the distortion within an interactive Java applet in which each slider bar represents a unique symmetry mode. Just click “OK” to open the applet window. These symmetry-mode amplitudes will be the structural degrees of freedom that we refine in the steps below. Note that each mode amplitude is defined as the square root of the sum of the squares of all atomic displacements that it generates within the supercell (i.e. root-summed-squared displacement). The larger the amplitude, the greater the structural impact. Close the applet window when finished.

6. Back on the “distortion” page, select the “TOPAS.STR” bullet and click “OK” to save this superstructure to a file called “lamno3_distorted.str” in the working directory on your local computer.

7. You now have a decision to make. If you want to perform a normal Rietveld refinement of the atomic xyz coordinates of this superstructure, skip staight to step 12 below. If you instead want to directly refine the symmetry-mode amplitudes, complete steps 8 through 11.

8. Work through the “Symmetry Mode Rietveld Refinement” menu in jedit. Begin by browsing to locate the data file (lamno3.xy). Select the diffractometer type (Durham_d5000_solx). Then click on “Read ISODISTORT.str” and browse to locate the superstructure (lamno3_distortion.str).

9. It might be necessary to distort the metrically cubic cell before refining. Try changing the cell parameters to:

a @ 5.74
b @ 7.69
c @ 5.54

10. Save this input file as “lamno3_distorted.inp”, send it from jedit to TOPAS, and run a single-convergence refinement — all displacive mode amplitudes (a1-a7) are fixed at zero by default. You should get wRp around 29.634%. Now turn the profile parameters and lattice parameters off, add the view_structure keyword to visualize the progress of the refinement, and enable simulated annealing mode by removing the comment marker from “randomize_on_errors” and “continue_after_convergence”. Running several convergence cycles should rapidly achieve an wRp of ~8.728%.

11. Reset all mode amplitudes back to 0 in order to return to the undistorted perovksite structure, and perform additional symmetry-mode refinements using only modes a2, a3, and a7. The fit with these three modes alone should still be quite good.

12. Continuing from step 7, the superstructure that we generated in ISODISTORT can alternatively be used to perform a standard xyz-coordinate refinement that yields exactly the same R-factor. From the “distortion” page in ISODISTORT, choose the “CIF file” option and click “OK” to generate a symmetry-mode CIF file. Among other things, this file contains the standard xyz-coordinate description of the distorted structure. Work through “Durham Menus: Simple Rietveld Refinement” in Jedit to read in the distorted structure. The 7 refinable coordinates are La(x,z), O1(x,y,z) and O2(x,z).

13. To bypass the workshop exercise and go straight to the result, download this input file: lamno3_symmodes.inp.