"Tilting" in perovskites is all about the subtle arrangements of atoms in materials, which is inherently related to the properties of materials, such as capacitors and piezoelectrics. Tilt is also something we can control, by doping a material with another type of atom. By controlling tilt, we can design novel materials.
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| http://www.nature.com/nphoton/journal/v8/n7/full/nphoton.2014.134.html |
I am not a materials scientist by training, but a computational chemist with a background in simulations of water, peptides, and using machine learning. So I don't think of atomic structures are rigid arrangements of atoms, but being dynamic. So I see perovskites not as neat octahedral units of B site atoms surrounded by oxygen atoms (or whatever the X site atom happens to be). In reality these octahedral units are irregular, and fluctuating, especially at ambient conditions and when heated. But if you only consider X-ray diffraction determined crystal structures, you may be led into thinking the opposite.
So what do we mean by "tilt"?
Tilt means that the octahedral units that we have defined, are aligned in a manner that means the octahedral units either do, or do not, superimpose upon their neighbours. This tilt is classically defined by Glazer (using a frustrating description of rotation if you prefer Euler angles!), and from which we get different crystal structure classifications that differ by the manner the octahedral units tilt and overlap.
In the material calcium titanate, all the A site atoms are barium, the B site titanium, and X sites are oxygen. At high temperatures calcium titanate exhibits no tilt. It's cubic. But when we start to dope the material on the A site, with larger or smaller ions, such as barium, we begin to distort the structure. Or if we cool the material down, tilting emerges.
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| AA′3B4X12 perovskite structure showing the octahedral environment of the B cation http://pubs.rsc.org/en/Content/ArticleHtml/2010/JM/b926757c |
Distorting the material has a knock on effect on the ions in the material. The titanium now no longer sits in an isotropic (so a fully symmetric and even) electrostatic field created by the oxygen atoms about it. This means the titanium atoms get shifted. The same happens with the calcium ions too.
It's this combination of distortion that generates a dipole moment - a displacement of electrostatic charge in a particular direction within the crystal structure.
So what is the challenge in materials science?
Exploring how we can dope materials, and manipulate this tilting, in a targeted manner, relies on experiment and theory working in tandem. X-ray diffraction defined structures do not show the oscillations but use structure factors to account for thermal scattering that induces oscillations of the atomic positions. From Transmission Electron Microscopy (TEM) we can generate diffraction patterns which can show this oscillation of structure. And from theory, via simulations of atoms via Molecular Dynamics, we can assess the degree of tilting (not defined by Glazer), and begin to predict TEM diffraction patterns.
The hope then is that a combination of techniques, both experimental and theoretical, can reveal further insight into the complex relationship of atomic structure and materials properties.
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| Atomic resolution image of 2D halide perovskite CsPbBr 3 . (a) Structure model of cubic CsPbBr 3 perovskite unit cell. Cs (green) occupies the corner A-site while Pb (gray) occupies the body-center Bsite , and Br (brown) occupies the face-center. Pb−Br 6 octahedron is formed within the Cs cube framework. (b) Structure model of single layer 2D CsPbBr 3 NS. (c) Atomically resolved phase image of a 2D CsPbBr 3 NS obtained by reconstructing 80 low dose-rate AC-HRTEM images via exit-wave reconstruction. The [001] structure projection of a unit cell is overlaid on the image. http://pubs.acs.org/doi/abs/10.1021/acs.nanolett.6b03331 |
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