Distortion-Mode (ISODISPLACE) Rietveld Refinement - LaMnO3
Files needed: lamno3.xy; lamno3_pm3m.cif
Learning Outcomes: This example shows how to perform a "distortion-mode" Rietveld analysis that refines symmetry-motivated distortion-mode amplitudes rather than atomic xyz coordinates. These group-theoretically derived distortion 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 distortion modes. The distortion-mode details are calculated using the ISODISPLACE software of Harold Stokes and Branton Campbell. For it to work, you'll need the "Distortion 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 Pbnm , a non-standard setting of Pnma (#62). Its supercell is related to the cubic Pm-3m parent cell by the transformation matrix {(-1,0,1),(1,0,1),(0,2,0)}. You will generate the superstructure in terms of symmetry-motivated distortion modes using ISODISPLACE, save the results to a .str file, and use this file to set up a Rietveld analysis with jedit.
1. Save the lamno3.xy datafile and lamno3_pm3m.cif file above in your working directory.
2. Go to the ISODISPLACE 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 as {-1 0 1 1 0 1 0 2 0} in the bij boxes then click the adjacent "OK" button.
4. On the next page select the point group which is orthorhombic: mmm D2h for Pnma. Then look through the drop-down menu of distortion symmetries compatible with these constraints, 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, select the "TOPAS.STR" bullet and click "OK" to save the superstructure to your working directory on your local computer, using "lamno3_distorted.str" in your working directory on your local computer.
6. On the "distortion" page, if you are interested in visualizing the distortion modes, select the "View distortion" bullet and click "OK". This will open up an interactive Java applet in which each slider bar represents one structural degree of freedom. These distortion-mode amplitudes will be the degrees of freedom in the subsequent refinement.
7. To perform a Rietveld analysis that refines symmetry-motivated distortion-mode amplitudes rather than the atomic xyz coordinates, work through the "Distortion Mode Rietveld Refinement" menus in jedit. If you just want to use the ISODISPLACE coordinates to perform a normal refinement go to instruction 12.
8. Browse to locate the data file (lamno3.xy) and select the diffractometer type (Durham_d5000_solx). Click on "Read ISODISPLACE str" and browse to locate the superstructure (lamno3_distortion.str).
9. Change the space group to the "short" symbol "Pnma" from the long symbol "P 21/n 21/m 21/a". 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 input file to topas and run a refinement. You should get wRp around 29.634%. The distortion mode amplitudes can then be refined by allowing parameters a1-a7 to refine (b1-b5 describe occupancies). It may be necessary to do a few cycles of simulated annealing for the refinement to converge. At the top of the file remove the comment marker from "randomize_on_errors" and "continue_after_convergence". You should rapidly get an wRp of ~8.728%.
11. In this refinement atomic coordinates are controlled by the 7 refinable distortion-mode amplitudes a1-a7. You should be able to get a very good refinement using just modes a3, a7 and a2. Use view_structure to look at how each mode distorts the structure. If you reset all amplitudes to 0 you'll be back to an undistorted perovksite structure. The values of a1-a7 are the summed rms displacements of atoms in the supercell. Their magnitude gives an indication of the significance of that distortion-mode.
12. Alternatively, you can use the same ISODISPLACE-generated superstructure to perform a standard xyz-coordinate refinement that yields exactly the same R-factor. From the "distortion" page in ISODISPLACE, choose the "CIF" bullet and click "OK", which generates a distortion-mode CIF that also contains the standard xyz-coordinate description of the distorted structure. Then 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. A model input file is linked here.
Modified 18-Jun-2009 by John S.O. Evans.
