Octahedral tilting in the tungsten bronzes

Whittle, Thomas A.; Schmid, Siegbert; Howard, Christopher

doi:10.1107/s2052520615008252

Cited by 25 publications

(36 citation statements)

References 37 publications

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“…Octahedral tilting in TTBs is otherwise restricted by the connectivity in the xy plane, which prevents tilting around the z axis. Tilts around axes in the xy plane are however possible, and often lead to a √ 2 × √ 2 × 2 supercell relative to the aristotype [10,38], in line with a recent group-theoretical analysis [39]. A √ 2 × √ 2 × 2 supercell was also reported for pure SN with TTB structure [40], although for intermediate SBN compositions, doubling of the c parameter has to our knowledge not been reported.…”

supporting

confidence: 80%

Origin of ferroelectric polarization in tetragonal tungsten-bronze-type oxides

et al. 2016

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The origin of ferroelectric polarization in the tetragonal tungsten-bronze-type oxide strontium barium niobate (SBN) is investigated using first-principles density functional calculations. We study in particular the relationship between the polarization and the cation and vacancy ordering on the alkali earth lattice sites. Lattice dynamical calculations for paraelectric structures demonstrate that all cation configurations that can be accommodated in a 1 × 1 × 2 supercell result in a single unstable polar phonon, composed primarily of relative Nb-O displacements along the polar axis, as their dominant instability. The majority of the configurations also have a second octahedral tilt-mode instability which couples weakly to the polar mode. The existence of the tilt mode is strongly dependent on the local cation ordering, consistent with the fact that it is not found experimentally. Our results suggest that ferroelectricity in the SBN system is driven by a conventional second-order Jahn-Teller mechanism caused by the d 0 Nb 5+ cations, and demonstrate the strong influence of the size of Sr and Ba on the lattice distortions associated with polarization and octahedral tilting. Finally, we suggest a mechanism for the relaxor behavior in Sr-rich SBN based on Sr displacement inside pentagonal channels in the TTB structure. PACS numbers: 71.15.Mb, 77.80.Jk, 77.80.bg Ferroelectric oxides with tetragonal tungsten-bronze (TTB) structure have been known since 1953 [3], and their polar properties are both widely studied and used in applications. One of the simplest TTB compounds, lead metaniobate (Pb 5 Nb 10 O 30 or PN), is commercially available and attractive for hightemperature piezoelectric sensor applications. In spite of their popularity, however, a fundamental explanation of the mechanism leading to spontaneous polarization in TTBs has to our knowledge not been reported. One possible origin is Nb 5+ , which is a ferroelectrically active cation in perovskites owing to a second-order Jahn-Teller mechanism enabled by its d 0 electron configuration [4,5]. Fundamental studies on TTBs are challenging, partly due to multiple competing phases: PN, for example, is at ambient temperature metastable in the TTB structure with respect to a rhombohedral polymorph [6][7][8]. Most other tungsten-bronze oxides are solid solutions with structural and chemical disorder, consistent with many of them being relaxor-type ferroelectrics [9][10][11].The aristotype unit cell with the general formula (A1) 2 (A2) 4 C 4 (B1) 2 (B2) 8 O 30 has six sites available for A-type cations and ten for B-type. The structure is highly anisotropic, with the A1 and A2 sites forming channels along the c direction. The A1 sites are formally 12-coordinated and similar to the A sites in perovskites, while the A2 sites are pentagonal and formally 15-coordinated. The B1 and B2 sites are octahedrally coordinated, with corner-sharing BO 6 octahedra forming the structural framework. Many niobates and tantalates crystallize as TTBs where Nb or Ta resides on the octa...

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confidence: 80%

Origin of ferroelectric polarization in tetragonal tungsten-bronze-type oxides

et al. 2016

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“…1, 2 and 3, and supporting information in Campbell et al (2018). There were tilting patterns, particularly those associated with irrep A þ 6 , that were missed in our earlier work (Whittle et al, 2015). For TTB we found structures associated with all of the irreps Z þ 5 , A À 5 and R 1 -see Tables 4 and 5 As explained by Campbell et al (2018), and emphasized by Phillips (2018), our new analysis rests on a linearization of equations, valid for infinitesimal angles of tilt.…”

mentioning

confidence: 57%

“…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.…”

mentioning

confidence: 99%

Octahedral tilting in the tungsten bronzes. Addendum.

Whittle

Schmid

Howard

2018

Acta Crystallogr B Struct Sci Cryst Eng Mater

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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

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“…Careful Rietveld analysis is required to ascertain the exact nature of this structural distortion. Possible octahedral tilt modes in HTBs were first predicted by Whittle et al (2015) with regards to the aristotype structure, space group P6/mmm, a 0 ' 7, c 0 ' 4 Å . Their work suggested that to maintain the corner-linked network of BO 6 octahedra, tilting could only be introduced via the irreducible representations A 3 + and L 2 À , resulting in models with P6 3 /mmc and P6/mmm symmetry and unit cells of a 0 Â 2c 0 and 2a 0 Â 2c 0 , respectively.…”

Section: Structure Determination From Pndmentioning

confidence: 99%

Octahedral tilting in the polar hexagonal tungsten bronzes RbNbW₂O₉ and KNbW₂O₉

McNulty

Gibbs

Lightfoot

et al. 2019

Acta Crystallogr Sect B

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The ambient‐temperature structures (orthorhombic, space group Cmc21) of the polar hexagonal tungsten bronzes RbNbW2O9 and KNbW2O9 have been determined by high‐resolution powder neutron diffraction. Displacement of the A‐site cation along the polar c axis with concomitant octahedral tilting occurs to optimize the A cation bonding environment, hence reducing the coordination from 18 to 16. This effect is more evident in KNbW2O9 due to decreased A cation size. The octahedral tilting in both compositions results in a doubling of the c axis that has not previously been reported, highlighting the importance of neutron diffraction as a complementary technique for structural determination of such systems.

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Octahedral tilting in the tungsten bronzes

Cited by 25 publications

References 37 publications

Origin of ferroelectric polarization in tetragonal tungsten-bronze-type oxides

Origin of ferroelectric polarization in tetragonal tungsten-bronze-type oxides

Octahedral tilting in the tungsten bronzes. Addendum.

Octahedral tilting in the polar hexagonal tungsten bronzes RbNbW₂O₉ and KNbW₂O₉

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Octahedral tilting in the tungsten bronzes

Cited by 25 publications

References 37 publications

Origin of ferroelectric polarization in tetragonal tungsten-bronze-type oxides

Origin of ferroelectric polarization in tetragonal tungsten-bronze-type oxides

Octahedral tilting in the tungsten bronzes. Addendum.

Octahedral tilting in the polar hexagonal tungsten bronzes RbNbW2O9 and KNbW2O9

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Octahedral tilting in the polar hexagonal tungsten bronzes RbNbW₂O₉ and KNbW₂O₉