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 often 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 and magentic moments based on symmetry modes. The symmetry-mode details are calculated using the ISODISTORT software of Harold Stokes and Branton Campbell. For the tutorial you can either use the standard Rietveld/Pawley menus in topas-editor or the “Symmetry Mode Refinement” menus of jEdit.

To view the disortion modes you currently (spring 2025) might need to install the standalone isoviz viewer. There are instructructions here.

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 or VS Code topas-editor.

Authors: John and Branton

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

2. Go to the ISODISTORT website and follow the “Import parent structure from a CIF structure file” instruction. Click on “Choose file” then browse to find the “lamno3_pm3m.cif” file in your working directory, click the “OK” button to upload. You’ll be taken to the “search” page.

3. On the search page you can choose to consider just displacive distortions that move atoms (the default and what we’ll do here) or also consier occupational and magnetic distortions. Go to the “Method 3” heading, which allows you to “search over arbitrary k points for specified space group and lattice”, select point group mmm and select the “Specify a real-space sublattice of the parent lattice” 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 in the top of this page section to proceed.

4. This new page that opens contains a list of all possible distortions consistent with your choices (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) (it should be about halfway down), and click “OK” at the bottom of the list. This will open the “distortion” page in a new tab.

5. On the “distortion” page you can click on “interactive viewer” to visualise the distortions a slider bar for each unique symmetry mode. This viewer is in development, so you could instead click “OK” to “Save interactive distotion” then use isoviz to view the modes (see link above for how to install isoviz). 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. Try playing with the various slider bars and see what structural distortions they create. You should notice that one mode amplitude (a single parameter) can move several atoms in the structure. Oxygen R4+ and M3- modes lead to coupled tilting of octahedra; M2+ leads to MnO₆ bond lengths either expanding or contracting.

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.

8a. If you’re using VS Code topas-editor follow the TOPAS_Durham menus for a standard Rietveld/Pawley fit and read your structure in from the str file.Begin by browsing to locate the data file (lamno3.xy). Select the diffractometer type (BB_CuKa2_PSD Durham d7/d9). Then click on “Read ISODISTORT.str” and browse to locate the superstructure (lamno3_distortion.str). When the INP file is ready click ctrl-k0; this will fold away the ISODISTORT equations making the file easier to read.

8b. If you’re using jEdit, work through the “Symmetry Mode Rietveld Refinement” menus.

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. Send the INP 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 29.9%. 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 making sure the lines “randomize_on_errors” and “continue_after_convergence” are present at the top of your INP file. Set the mode amplitudes a1 to a7 to refine by removing exclamation marks in front of them. Running several convergence cycles should rapidly achieve an Rwp of ~9.73%. Try turning the cell parameters back on if you don’t get quite as low an Rwp. [Note you get a lower Rwp in this case if you switch to the Cu_Ka2() emission profile – around 8.7%]

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 (Rwp ~10.3%)

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. Set up to do a Rietveld in the standard way and read in a CIF file. In topas-editor you will see that the space_group name is highlighted in pink and underlined as it is in non-TOPAS syntax. Change it to Pnma. 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.