PolyDis: simple quantification tool for distortion of polyhedra in crystalline solids

Abstract

A new simple approach to quantitative measures of coordination polyhedra distortions from ideal symmetry is provided with PolyDis. Within the mathematical basis, it minimizes the normalized displacements of given polyhedra to the ideal shape. Applications are discussed, where PolyDis was used to analyze the temperature dependent distortion of LaAlO3, rare earth metal radius dependent distortion of RMnO3 and the increasing structural distortion of (A3N)As with varying alkaline earth metal, all being perovskites. Additionally, the more complex structures of SrCuRSe3 and CsCu3R2Se5 comprising trigonal prisms, octahedra and tetrahedra are treated with PolyDis.

Heteroatom Manipulation of Zeolite Crystallization: Stabilizing Zn-FAU against Interzeolite Transformation

“…This configuration breaks the symmetry of the regular tetrahedron (SiO 4 ) and distorts the local geometry ( Figure S19 ). The average distortion of the tetrahedral (TO 4 ) bond upon Al or Zn substitution ( Table S3 ) is quantified based on the deviation of positions of oxygen atoms from the four vertices of a corresponding regular tetrahedron 43 (see the Methods section). The original site (SiO 4 ) is very close to a regular tetrahedron with a consistent Si–O length of 1.6 Å.…”

Metal‐Rich Ternary Perovskite Nitrides

“…For the series ( A 3 N)As with A = Mg, Ca, Sr, Ba the distortion was recently analyzed to monotonically increase with rising ionic radius of the alkaline‐earth metal ion, due to the increasing size of the cuboctahedral void upon unit cell enlargement and despite the growing spatial requirement of the A 2+ ions (see Figure ). A quantification of the distortion based on a simple analysis of the local coordination polyhedra revealed the deviation from ideal cubic structure to be nearly exclusively due to distortion of the cuboctahedral surrounding of As 3– , demonstrating the rigidity of the A 6 N ‐octahedra , . An analogous situation in terms of composition, electrical properties and structural relationships is realized for the group 14 element oxides ( A 3 O) E (14) [ A = Ca, Sr, Ba, Eu, Yb; E (14) = Si, Ge, Sn, Pb] …”

“…A quantification of the distortion based on a simple analysis of the local coordination polyhedra revealed the deviation from ideal cubic structure to be nearly exclusively due to distortion of the cuboctahedral surrounding of As 3-, demonstrating the rigidity of the A 6 N-octahedra. [10,19] An analogous situation in terms of composition, electrical properties and structural relationships is realized for the group 14 element oxides (A 3 O)E (14) [A = Ca, Sr, Ba, Eu, Yb; E(14) = Si, Ge, Sn, Pb]. [20][21][22][23][24][25] The compounds (Ba 3 N)E with the larger E = Sb, Bi crystallize in the hexagonal 2H-perovskite variant (BaNiO 3 structure type, see Figure 3), although the Goldschmidt tolerance factor should even decrease compared to the respective cubic strontium or calcium compounds.…”

Polynator: a tool to identify and quantitatively evaluate polyhedra and other shapes in crystal structures

“…In a different vein, a symmetry-independent method that quantifies the distortion according to the sphericity of an ellipsoid fitted to the coordination environment was proposed by Cumby & Attfield (2017). Yet another approach was taken with the PolyDis software, which allows the user to fit models of the most frequently encountered polyhedra to their data based on minimal average distances (Stoiber & Niewa, 2019).…”