Glazer notation for Octahedral Tilting in Perovskites
This tutorial explains how Glazer notation is used to identify Perovskites of different symmetries based on their atomic positioning.
What are Perovskites?Permalink
Perovskites are structures that take the form ABX
Image source: Yi et al.1
Octahedral tiltingPermalink
Goldschmidt’s Tolerance Factor given from the following equation predicts the stability of perovskites.
where, r
The following figure displays octahedral tilting and its effects2.
NotationPermalink
- The sequence of the symbols corresponds to the crystallographic axes i.e. first symbol = tilt along a [100] etc.
- Identical characters indicate the same amplitude of tilt.
- The superscript indicates zero-tilt (0), in-phase-tilt (+) or anti-phase-tilt (-) of subsequent layers of octahedra.
- There exists 15 tilt systems for perovskites. The following is an example.
Structure | Glazer notation |
---|---|
a | a |
b | a |
c | a |
d | a |
e | a |
Table 1: The Glazer notations for the halide perovskite structures in the previous figure.
The following table summarizes the different types of tilting possible for different space groups3.
ReferencesPermalink
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Yi, Z., Ladi, N., Shai, X., Li, H., Shen, Y., & Wang, M. (2019). Will organic–inorganic hybrid halide lead perovskites be eliminated from optoelectronic applications?Nanoscale Adv., 1, 1276-1289. ↩
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Butler, K. (2018). The chemical forces underlying octahedral tilting in halide perovskitesJ. Mater. Chem. C, 6, 12045-12051. ↩
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Shojaei, F. & Yin, W.-J. Stability trend of tilted perovskites. arXiv:1803.05604 [cond-mat] (2018). ↩
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