Distortion analysis

rowlesmr

I'm starting up a collaboration with a group at my university who are interested in perovskite materials as components of fuel cells, where I'm going to be doing some structural analysis with both x-ray and neutron data.

Where can I read more on distortion mode analysis?*

More practically, I can follow the John's distortion mode tutorial and go from a parent Pm-3m phase to the Pnma supercell by the transformation matrix [[1 0 1],[0 2 0],[-1 0 1]], with its origin at (0,0,0), but how do I find the transformation matrix?

Thanks

Matthew

*I'm currently reading An Exhaustive Symmetry Approach to Structure Determination: Phase Transitions in Bi2Sn2O7

johnsoevans

Hi Matthew,

Branton's paper on isodistort is a good place to start if you haven't seen it: http://stokes.byu.edu/iso/2006%20Campbell.pdf

In terms of the transformation matrix everything should be available through isodistort. If you look at one of the .inp files from the distortion mode tutorials you'll see that they essentially contains the transformation matrix in terms of the equations which link mode amplitudes (e.g. a1...a20) to the amount atoms move (e.g. W1_dx, W1_dy, W1_dz) to the final coordinates (original + shift; e.g. W1_x = 1/4+ W1_dx;). If you download a .cif from isodistort you'll also see the equivalent information in the file header comments.

Did you find the WO3 structural tutorial, it should be similar to what you need to do: http://community.dur.ac.uk/john.evans/topas_workshop/tutorial_isoriet_wo3_advanced.htm

There's also a tutorial which essentially does much of what's in the Bi2Sn2O7 paper but using WO3 as the example (it's quicker to run):
http://community.dur.ac.uk/john.evans/topas_workshop/tutorial_exhaustive_symmetry.htm

It's a bit involved, but again should be very relevant to your perovskite example. We'll be putting some closely related tutorials on line soon.

Not sure if that answers your question?

John

rowlesmr

Thanks John, I'll have a read.

Disclaimer: I don't know how much of this is due to my not knowing how to use the isodistort website, or my lack of knowledge of space-group theory.

My main question (wrt perovskites) is with regards the transformation matrix. I've indexed a perovskite as Pnma (for argument's sake). How do I know that its transformation matrix is [[1 0 1],[0 2 0],[-1 0 1]], with its origin at (0,0,0)?

I suspect that some of this might come out of the Bi2Sn2O7 paper...

johnsoevans

Matthew,

Two answers: "you don't" and "you do".

In a general case an "isodistort" group-subgroup tree will tell you all the possible children of a parent structure (cells, spacegroups, origins). Only the diffraction data will tell you which is the right choice. The Bi2Sn2O7 paper gives a recipe for checking all of them and choosing the "best" model. "Best" depends on your criteria.

For simple perovskites you know the likely choices already from the literature. For simple tilts it's the Glazer tilt systems (Chris Howard/Harold Stokes did the group-theory approach: http://scripts.iucr.org/cgi-bin/paper?ta0003).
For cation ordering/titles there's the Howard/Kennedy/Woodward paper: https://doi.org/10.1107/S0108768103010073.

John

rowlesmr

I think I'm understanding this a little better now.

Another question:

I've been looking at some ideal Ruddledson-Popper phases (n=3), and if I generate all (~1800 for 2x2x2 P1) children from the I4/mmm parent, I can find an orthorhombic distortion which matches with a published CIF.

In this case, its easy to get a parent phase.

Is there a general method to "make" parent phases? ie given a presumed child structure, how can I find potential parents? I can visualise the distorted phases (in Vesta) and I can sort of see how to make the strs more symmetric, but how to enact that?

johnsoevans

Hi Matthew,

Three possibilities if it's not easy to spot by eye:

1. For most of the "classic" structure types the aristotype is normally well known. If it's less obvious you could look in the icsd and find the highest symmetry report for your structure type. e.g. try the ANX/AB type formula or structure type search.
2. You could try a routine like "findsym" (part of the ISODISTORT suite) or one of the Bilbao routines with a high tolerance. You could try this after making some coordinates closer to special values. e.g. if you had an O at 0.23 you might move it to 0.25.
3. Parents don't always have to be real or even realistic structures. Sometimes it can be convenient to increase symmetry to something that no longer makes chemical sense. I don't think there's a recipe for that other than intuition.

rowlesmr

Thanks John.

I'll expand my methodology with those ideas.

.

Talk about the proverbial rabbit hole!

Looking on the COD for some high symmetry structures lead me to:

Thompson, R. M., and R. T. Downs. 2004. "Model Pyroxenes II: Structural Variation as a Function of Tetrahedral Rotation." American Mineralogist 89 (4): 614-628.

which lead to

Thompson, R. M., and R. T. Downs. 2003. "Model Pyroxenes I: Ideal Pyroxene Topologies." American Mineralogist 88 (4): 653-666.

which lead to

Law, A. D., and E. J. W. Whittaker. 1980. "Rotated and Extended Model Structures in Amphiboles and Pyroxenes." Mineralogical Magazine 43 (329): 565-574.

which lead to

Hawthorne, F. C. 2018. "Bond Topology and Structure-Generating Functions: Graph-Theoretic Prediction of Chemical Composition and St