Reconstituting the Glazer tilt notation for Perovskites from sampling molecular dynamics.
These codes are written in the Julia Language [ http://julialang.org ].
[ http://www.unf.edu/~michael.lufaso/spuds/potato.html ]
Potato generates representative tilted perovskite structures, when you specify the Glazer tiling notation & tilt variables.
Smash was essentially envisaged as providing the reverse process (hence being reconstituted potato!), going from molecular dynamics of pervoskites (particularly, the very soft lead-halide and friends) to reconstructing glazer-tilting angles, and other quantitative figures. A key problem with interpreting such MD is the lack of a reference, as the structure is so soft that it is difficult to define whether the motion of the octahedra is rotation or distortion.
In many ways, they are the succesors to MAPI-MD [ https://github.com/jarvist/MAPI-MD-analysis ] , which wholly concentrated on the molecules present in hybrid perovskites, providing symmetry-reduced orientation and auto-correlation functions of molecules.
Currently implemented are methods to analysis the internal field generated by perovskite distortions.
- XDATCAR / VASP MD reader
- XYZ / Empirical (LAMMPS) MD reader
- Calculation of Octahedra Ellipsoid (a la Cumby's PIEFACE [ https://doi.org/10.1038/ncomms14235 ].
- Average location of Iodine octahedra; generating a local dipole with the Pb site
- Glazer tilting + Pb-I-Pb bond distortions in a Kinematic approach
- Molecular (+ other bonds) symmetry-reduced alignment, as [ https://github.com/jarvist/MAPI-MD-analysis ]
- Autocorrelation functions, as [ https://github.com/jarvist/MAPI-MD-analysis ]
A WORK IN PROGRESS!!! HERE BE DRAGONS
Glazer, A. M. “The Classification of Tilted Octahedra in Perovskites.” Acta Crystallographica Section B Structural Crystallography and Crystal Chemistry 28, no. 11 (November 15, 1972): 3384–92. [ http://dx.doi.org/10.1107/S0567740872007976 ] Introduces the a(+)b(+)c(-) perovskite tilt classifcation, identifies 23 different possibilities to produce 'intermeshing gears' with a repeat of 2
Glazer, A. M. “Simple Ways of Determining Perovskite Structures.” Acta Crystallographica Section A 31, no. 6 (November 1, 1975): 756–62. [ http://dx.doi.org/10.1107/S0567739475001635 ] Simple geometric method described by Glazer to define the tilt class
Woodward, P. M. “Octahedral Tilting in Perovskites. I. Geometrical Considerations.” Acta Crystallographica Section B Structural Science 53, no. 1 (February 1, 1997): 32–43. [ http://dx.doi.org/10.1107/S0108768196010713 ] Uses POTATO to investigate the different tilt possibilities, finding that some of the Glazer tilt classes are impossible without Octahedra distortion
Beanland, Richard. “Structure of Planar Defects in Tilted Perovskites.” Acta Crystallographica Section A Foundations of Crystallography 67, no. 3 (May 1, 2011): 191–99. [ http://dx.doi.org/10.1107/S0108767311002042 ] Constructs a similar system to Glazer, where the distortion is treated as a second-rank deformation tensor, which is easier to directly deal with mathematically
Shapere, Alfred, and Frank Wilczek. “Gauge Kinematics of Deformable Bodies.” American Journal of Physics 57, no. 6 (June 1, 1989): 514–18. [ http://dx.doi.org/10.1119/1.15986 ] Paper showing the deep connection with rotation of a deformable body and the geometric phase; example limited to co-incident rotating spheres
Littlejohn, Robert G., and Matthias Reinsch. “Gauge Fields in the Separation of Rotations and Internal Motions in the N-Body Problem.” Reviews of Modern Physics 69, no. 1 (January 1, 1997): 213–76. [ http://dx.doi.org/10.1103/RevModPhys.69.213 ] Long review covering Gauge Fields as applied to N-body problems