Octahedral tilting in the tungsten bronzes. Addendum.

Abstract

The studies of octahedral tilting in the tungsten bronzes [Whittle et al. (2015). Acta Cryst. B71, [342][343][344][345][346][347][348] were continued in the context of a more general approach to cooperative rotations of interconnected rigid units [Campbell et al. (2018). Acta Cryst. A74, 408-424]. That more general approach has detailed possible structures not identified in our 2015 paper. A brief comment on the implications of finite tilts for octahedral distortion is included.In a recent paper on the tungsten bronzes (Whittle et al., 2015) we attempted to enumerate the possibilities for tilting of the WO 6 octahedra in the hexagonal and tetragonal tungsten bronzes. There is no reason to doubt the structures we presented there. It soon became apparent, however, that at least in the case of tetragonal tungsten bronze (TTB) we had missed a number of acceptable tilt structures. Recall that TTB has a starting structure in space group P4/mbm, and that from searches at all the special points of the Brillouin zone we reported finding only one acceptable tilt system, at the A-point (k = 1 2 ; 1 2 ; 1 2 ). Through a subsequent analysis of TTB using the computer program CRUSH (Giddy et al., 1993), and from a paper (Smirnov & Saint-Gré goire, 2014) of which regrettably we were unaware until our work was in print, we realized that we should have found tilt systems at the Z-and R-points (k = 0; 0; 1 2 and k = 0; 1 2 ; 1 2 ) as well. Many of the arguments presented in our previous paper were sound. For example we argued that tilting around the unique (z) axis was not possible for three octahedra cornerlinked around a triangular channel. It followed that the only possible tilting would be around axes in the horizontal (x-y) planes. Any tilting around axes in a horizontal layer implied tilting in the reverse sense around layers above and below. This meant there must be a doubling of the c parameter and so we needed to consider only those (special) points of the Brillouin zone with k z = 1 2 . For HTB, with parent symmetry P6/ mmm, these are the A-, H-and L-points (k = 0; 0; 1 2 , k = 1 3 ; 1 3 ; 1 2 and k = 1 2 ; 0; 1 2 ) while for TTB they are the Z-, A-and R-points already mentioned. The ISOTROPY computer program (Stokes et al., 2014) was used to list the irreducible representations (irreps 1 ) at each of those points leading to tilting of the octahedra centred on the W atoms, these atoms being on Wyckoff 3f in HTB or on 2d and 8i in TTB. Irreps implying tilting of the octahedra around the z axis were immediately eliminated, which in the case of TTB for example left for consideration only Z þ 5 , A À 5 and R 1 . But the examination of

Octahedral tilting in the polar hexagonal tungsten bronzes RbNbW2O9 and KNbW2O9

“…S2 of the supporting information. This proposed structure remains consistent with the Cmcm model suggested by Whittle et al (2018) but includes an additional displacive À 2 À mode. Rietveld refinement was carried for both compositions in each Cmc2 1 model.…”

“…A subsequent study by Campbell et al (2018) acknowledged an additional tilting mode (A 6 + ) leading to a Cmcm model in which some octahedra remain untilted. In an addendum to their initial work, Whittle et al (2018) also proposed that the most likely HTB structures would have octahedral tilts of equal magnitude. The work presented by Whittle and Campbell however, does not consider the combination of tilting modes together with atomic displacements related to off-centering of B-site cations (i.e.…”

Structures and phase transitions in barium sodium niobate tungsten bronze (BNN)

“…The tilt systems in Ima2 and Cmc2 1 can be inspected in Campbell et al (2018) [supporting information under the labels A 5 À P3(a,a) and Z 5 + P1(a,0), respectively]. Both are seen to feature combinations of tilted with untilted octahedra, combinations which Whittle et al (2018b) considered unlikely to occur. In addition, a ferroelastic transition to either of these space groups might be continuous, whereas on our reading of the lattice parameter data in Aamlid et al (2020), it is definitely not.…”

Multi-analyser detector (MAD) for high-resolution and high-energy powder X-ray diffraction

“…structure of the main phase (Estevez-Rams et al, 2003). Octahedra in subsequent layers of this structure along the c axis are constraint to tilt in the opposite sense reducing the likelihood of stacking faults (Whittle et al, 2015(Whittle et al, , 2018Campbell et al, 2018). These might, however, originate at possible cation defect sites.…”