Octahedral tilting in the tungsten bronzes
Thomas A Whittle1, Siegbert Schmid1, Christopher J Howard2
1School of Chemistry, The University of Sydney, Sydney, NSW 2006, Australia.
Summary
Group theory analysis reveals new octahedral tilting patterns in hexagonal and tetragonal tungsten bronzes (HTB and TTB). This work clarifies structural complexities and identifies potential new crystal structures for these materials.
Area of Science:
- Solid State Chemistry
- Crystallography
- Materials Science
Background:
- Hexagonal and tetragonal tungsten bronzes (HTB and TTB) exhibit complex crystal structures.
- Understanding octahedral tilting is crucial for characterizing these materials.
Purpose of the Study:
- To investigate possible octahedral tilting patterns in HTB and TTB using group theory.
- To determine the correct space groups and identify potential new structural configurations.
Main Methods:
- Application of group theory principles.
- Utilized the ISOTROPY computer program for structural analysis.
- Systematic search of symmetry-related points in Brillouin zones.
Main Results:
- Identified a new space group (P6₃22) for HTB structures, correcting previous interpretations based solely on W cation displacement.
- Discovered a second, unreported tilting pattern for HTB in space group P6/mmm with a larger unit cell.
- Found a specific octahedral tilting pattern for TTB in space group I4/m.
- Identified acceptable tilt patterns for TTB in Bbmm and a non-centrosymmetric variant in Bbm2 for larger unit cells.
Conclusions:
- The study clarifies the crystallographic descriptions of HTB and TTB by incorporating octahedral tilting.
- New structural possibilities and correct space groups have been identified, advancing the understanding of tungsten bronze materials.
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