I. INTRODUCTION
Compounds that form with tungsten bronze-type structures have been investigated extensively because of their technologically important properties. They have been shown to display non-linear optical behaviour as well as ferroelectric, pyroelectric, and piezoelectric properties (Yuan et al., Reference Yuan, Chen and Wu2005; Massarotti et al., Reference Massarotti, Capsoni, Bini, Azzoni, Mozzati, Galinetto and Chiodelli2006; Ko and Kojima, Reference Ko and Kojima2010; Jennene Boukharrata and Laval, Reference Jennene Boukharrata and Laval2011; Nair et al., Reference Nair, Subramanian and Santhosh2011). These properties allow tungsten bronze-type compounds to be used in, for example, memory storage, oscillator devices, phase-conjugated mirrors, as well as in infrared-radiation detectors.
Tungsten bronze-type compounds have the general formula, A 3B 5C 2O15. This structure type is defined by a network of corner sharing BO6 octahedra. The octahedra define three distinct cavity sites (A1, A2, and C) forming tunnels running along the c-direction. These cavity sites can be occupied by a variety of metal cations.
There are five separate metal sites in the tungsten bronze-type structure that are made distinct by their size and their local environment. The A1 site is 12-coordinate, similar to a perovskite A site. The A2 site is a larger 15-coordinate site, whereas the C site is a small nine-coordinate cavity, which is generally unoccupied. The two B sites are six-coordinate octahedral sites with different surroundings. When all sites are listed separately the general formula becomes A1A2 2B1B2 4C 2O15.
The large A sites of the tungsten bronze allow for a variety of alkaline, alkaline earth, and Pb2+ cations to occupy the cavities. The smaller B sites are generally occupied by transition-metal cations such as Ti4+, Zr4+, Nb5+, and Ta5+. Li+ and small rare-earth cations, e.g. Er3+ and Lu3+, have been shown to occupy the small C site, but for this work the C site remains vacant.
The work in this paper focuses on compounds formed in the BaxSr3−xTiNb4O15 (0 ≤ x ≤ 3) system, with the stepwise substitution of barium for strontium from Sr3TiNb4O15 to Ba3TiNb4O15. The strontium-rich end of this series has been reported previously by several groups; however, a discrepancy over the symmetry, crystal system, and space group, as well as the cell parameters, remains (Ainger et al., Reference Ainger, Brickley and Smith1970; Neurgaonkar et al., Reference Neurgaonkar, Nelson and Oliver1992; Rao et al., Reference Rao, Subrahmanyam and Rao1997; Chi et al., Reference Chi, Gandini, Ok, Zhang and Halasyamani2004; Yuan et al., Reference Yuan, Chen and Wu2005), which we have partially addressed previously (Whittle et al., Reference Whittle, Brant, Schmid, Schmid, Withers and Lifshitz2013). The barium-rich end of the series is well known, with the structure being determined from both powder and single-crystal X-ray diffraction (Stephenson, Reference Stephenson1965; Ainger et al., Reference Ainger, Brickley and Smith1970; Neurgaonkar et al., Reference Neurgaonkar, Nelson and Oliver1992; Chi et al., Reference Chi, Gandini, Ok, Zhang and Halasyamani2004; Yuan et al., Reference Yuan, Chen and Wu2005; Massarotti et al., Reference Massarotti, Capsoni, Bini, Azzoni, Mozzati, Galinetto and Chiodelli2006). There has been only one report of the series of compounds between the two end members, but no details were given apart from point-group symmetries (Neurgaonkar et al., Reference Neurgaonkar, Nelson and Oliver1992). In this paper, we report the structural investigation of the BaxSr3−xTiNb4O15 (0 ≤ x ≤ 3) system using synchrotron X-ray powder-diffraction data.
II. EXPERIMENTAL
A. Sample preparation
Polycrystalline samples were prepared using standard solid-state synthesis techniques. Reagent oxides and carbonates were weighed out in stoichiometric ratios with x = 0.0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 1.2, 1.8, 2.0, 2.4, and 3.0. Samples were ground by hand using an agate mortar and pestle. These samples were then pressed into dense pellets using a pellet press at 8 tonnes. Reagents used include: BaCO3 (Aithaca 99.997%), SrCO3 (Sigma Aldrich, 99.9%), TiO2 (Aithaca, 99.999%), and Nb2O5 (Aithaca, 99.999%). The samples were calcined at 950 °C for 36 h and then sintered with intermittent grinding at 1300 °C for periods of 24–72 h.
B. Data collection
Synchrotron X-ray powder-diffraction data were collected at the powder-diffraction beamline, 10-BM, at the Australian Synchrotron using the MYTHEN microstrip detector and an Si(111) monochromator. Data were collected during two synchrotron experiments using wavelengths of λ = 1.158 704(1) and 0.825 21(1) Å, accurately determined by refinement against an LaB6 standard.
III. RESULTS AND DISCUSSION
A. Crystal-structure refinements
The discrepancy in the literature concerning Sr3TiNb4O15 arises from the proposal of three distinct models for its structure. The first model is a tetragonal P4bm structure common to many tungsten bronzes (Ainger et al., Reference Ainger, Brickley and Smith1970). Later work by Neurgaonkar et al. (Reference Neurgaonkar, Nelson and Oliver1992) suggested that Sr3TiNb4O15 had mm2 symmetry. They determined that the structure was C-centred, requiring a rotation and a doubling of the unit cell in the ab-plane. This resulted in the structure being modelled with Cmm2 symmetry. More recent studies of Sr3TiNb4O15 (Chi et al., Reference Chi, Gandini, Ok, Zhang and Halasyamani2004) found no evidence for the C-centring and reverted back to a primitive structure while maintaining the mm2 point-group symmetry. This study determined that Sr3TiNb4O15 formed with Pba2 space-group symmetry. Our work on Sr3TiNb4O15 (Whittle et al., Reference Whittle, Brant, Schmid, Schmid, Withers and Lifshitz2013) showed that none of these models correctly described the structure. We found evidence in the form of superlattice reflections for a doubling of the unit cell along the c-direction. Furthermore, the model that best fit the data had Pna21 symmetry.
Considering the orthorhombic symmetry of Sr3TiNb4O15 and the tetragonal symmetry of Ba3TiNb4O15, a phase transition must exist somewhere in the composition range between them. The change of symmetry from orthorhombic to tetragonal was reported to occur when the ratio of strontium-to-barium was approximately 2.2:0.8 (Neurgaonkar et al., Reference Neurgaonkar, Nelson and Oliver1992). Synchrotron X-ray diffraction patterns were collected across BaxSr3−xTiNb4O15 for x = 0–3. Analysis of these patterns revealed that the phase transition occurred much closer to the strontium end than previously reported. Figure 1 illustrates the 140 and 410 reflections for high strontium-content members of the BaxSr3−xTiNb4O15 series. The splitting of these reflections is indicative of the lower-symmetry orthorhombic structure. If the reflections are not split, then it is indicative of the higher-symmetry tetragonal structure. It was determined from analysis of the diffraction data that the x = 0.1 compound formed with the orthorhombic symmetry, whereas the x = 0.3 compound formed with tetragonal symmetry. Ba0.2Sr2.8TiNb4O15, i.e. x = 0.2, can be seen to form right on the boundary between the two phases, with the pattern more similar to that of a tetragonal phase while some orthorhombic character remains.
(Color online) Synchrotron X-ray diffraction patterns for members of the BaxSr3−xTiNb4O15 series from x = 0.0–0.5 collected at λ = 0.825 21 Å.
Refinements were performed against synchrotron X-ray diffraction data for all compositions synthesised. A summary of the refinement results are given in Table I. The cell volumes of these compounds (in the tetragonal setting) expand linearly with increasing barium content as expected. A representative refinement profile is shown in Figure 2.
(Color online) Plot of observed X-ray powder diffraction data for Ba2SrTiNb4O15 (red). Calculated data from the Rietveld refinement are in blue. The positions of the allowed reflections for the P4bm space group are marked with vertical black lines. The bottom black line shows the difference between the observed and the calculated data.
Cell parameters, volume, space group, and R-factors for structural refinement against synchrotron X-ray diffraction data.
Anisotropic displacement parameters were refined for the metal atoms. Similar displacement parameters were observed for all tetragonal compositions in the series. The displacement parameters show that the cation in the large 15-coordinate site is displaced predominately within the ab-plane. This is in contrast to the smaller A site and the B site. The anisotropic displacement parameters in these sites are predominately elongated in the c-direction and less in the ab-plane. See Table II and Figure 3 for displacement parameters of Ba3TiNb4O15.
(Color online) Structure of Ba3TiNb4O15 showing isotropic displacement of metal cations. The displacement of barium ions is shown in blue, titanium/niobium in grey, and oxygen in red. The figure on the left side is looking down the c-direction showing the ab-plane and B–O bonds are indicated. The right side figure is looking down the a-direction and the bonds are not indicated to highlight the displacement of titanium/niobium atoms.
Anisotropic displacement parameters for Ba3TiNb4O15.
B. A-site cation ordering
The two distinct A sites in the tungsten bronze-type structure are of considerably different size and as such it is expected that barium and strontium ions might order into those sites. To test the A-site ordering two models were constructed for each compound. The first model was disordered with barium and strontium randomly distributed across both sites. The second model, the ordered model, was constructed such that barium was placed preferentially on the large 15-coordinate site and strontium preferentially on the 12-coordinate site. In this ordered model, barium was only placed on the smaller site (or strontium on the larger site), when the composition did not allow the preferred site only to be occupied. The special case Ba2SrTiNb4O15 was chosen, such that the ions could perfectly order on the two sites. The quality of refinement was significantly improved in this case by ordering the A-site cations. With no other additional refinable parameters, R obs was seen to reduce from 6.89 to 3.35 and R p improved from 6.29 to 4.74. The ordered model showed a better overall fit to the data and particular reflections showed a dramatic improvement in matching the intensity of the observed data. Figure 4 illustrates the 220 reflection in both the ordered and disordered model. In the disordered model, the reflection is overcalculated, while in the ordered model the calculated pattern shows a very good fit to the data.
(Color online) Refinement profiles for Ba2SrTiNb4O15, left-disordered, right-ordered. Observed data are shown in red, the calculated pattern in blue, and the difference in black. Illustrated is the 220 reflection.
Additionally, bond valence sum calculations (Table III) for both refined models show that barium is over bonded in the smaller 12-coordinate site, whereas strontium is under bonded in the larger 15-coordinate site. This provides additional evidence that it is unfavourable for barium to occupy the smaller site, or for strontium to occupy the larger site.
Bond–valence sum calculations for Ba2SrTiNb4O15. Calculations for both the ordered and disordered models are shown.
IV. CONCLUSION
A series of compounds in the BaxSr3−xTiNb4O15 system were synthesised and their structures were refined using the Rietveld method against synchrotron X-ray diffraction data. The composition at which a phase transition occurs between the tetragonal and orthorhombic symmetries was determined. It was found to be different from that published in the literature, occurring closer to the strontium end. Anisotropic displacement parameters were determined for the metal cations and for all tetragonal members similar displacement parameters were observed. These show larger displacements in the 15-coordinate A site and smaller displacements for the 12-coordinate A and the B sites. Finally, strong evidence was found for the preferential ordering of barium and strontium cations into the two different A sites.
ACKNOWLEDGEMENTS
The authors thank the Australian Synchrotron, as part of the research presented here was undertaken at the powder diffraction beamline. The help of Dr. Qinfen Gu during the data collections is gratefully acknowledged.
