Octahedral tilting in the tungsten bronzes

The effect of cation size on structure and properties of Ba-based tetragonal tungsten bronzes Ba4M2Nb10O30 (M = Na, K or Rb) and Ba4M2Nb8Ti2O30 (M = Ca or Sr)

The second largest family of oxide ferroelectrics, after perovskites, are the tetragonal tungsten bronzes (TTB) with the general formula A24A12C4B12B28O30. Cation disorder in TTBs is known to occur if the size difference between cations is small, but the impact of cation disorder on structure and properties has not yet been extensively addressed. In this study we investigate the effect of the size of the M cation, including cation disorder, on the crystal structure and dielectric properties in the two series Ba4M2Nb10O30 (BMN, A = Na, K and Rb) and Ba4M2Nb8Ti2O30 (BMNT, M = Ca, Sr). Dense and phase pure ceramics in the two series were prepared by a two-step solid state synthesis route. The crystal structures of the materials were characterized by powder X-ray diffraction combined with Rietveld refinement. A close to linear relation between the in-plane lattice parameter (a) and the size of the M-cation were observed. Ba4M2Nb8Ti2O30 was shown to possess cation disorder on the A-sites in line with previous work on Ba4M2Nb10O30. Thermodynamic calculations from density functional theory also indicated a drive for cation disorder in the three BMN compositions. Non-ambient temperature X-ray diffraction revealed contraction of the in-plane (a) and expansion of the out-of-plane (c) lattice parameters at the ferroelectric phase transition for Ba4M2Nb10O30. The ferroelectric transition temperature acquired by dielectric spectroscopy showed a systematically increasing TC with decreasing size of the M-cation within both compositional series studied. The compositional dependence of TC is discussed with respect to the size of the M-cation, cation disorder and the tetragonality, as well as the Ti-content. The relaxor to ferroelectric properties observed by polarization-electric field hysteresis loops are discussed in relation to the relative size of cations on the on A1 and A2 sites and the Ti-content.

Revisiting the structures and phase transitions of Ba2NaNb5O15

The room-temperature and low-temperature structure(s) of Ba2NaNb5O15 (BNN) have been debated since the structure was proposed in the 1960s. This work revisits the structures and phase transitions of BNN, combining high-resolution X-ray and neutron powder diffraction with density functional theory calculations. Temperature-dependent high-resolution X-ray powder diffraction patterns are collected from 4 to 918 K, and sequential batch Rietveld refinement using a symmetry mode approach to describe the structure is used to extract the main structural changes as a function of temperature. The data show that the average structure of BNN is best described by the Ama2 space group, and no other structural phase transitions were observed below the ferroelastic transition. The symmetry mode analysis, combining results from diffraction and density functional theory, shows significant octahedral tilting and corrugations of both the A1 and A2 sites along the c direction. A strong correlation between the spontaneous strain and the octahedral tilting was observed, and a potential connection with emerging microstructure at low temperatures is proposed, all enabled by the symmetry mode approach used in this work.

The ISOTILT software for discovering cooperative rigid-unit rotations in networks of interconnected rigid units

A user-friendly web-based software tool called 'ISOTILT' is introduced for detecting cooperative rigid-unit modes (RUMs) in networks of interconnected rigid units (e.g. molecules, clusters or polyhedral units). This tool implements a recently described algorithm in which symmetry-mode patterns of pivot-atom rotation and displacement vectors are used to construct a linear system of equations whose null space consists entirely of RUMs. The symmetry modes are first separated into independent symmetry-mode blocks and the set of equations for each block is solved separately by singular value decomposition. ISOTILT is the newest member of the ISOTROPY Software Suite. Here, it is shown how to prepare structural and symmetry-mode information for use in ISOTILT, how to use each of ISOTILT's input fields and options, and how to use and interpret ISOTILT output.

Theoretical and computational improvements to the algebraic method for discovering cooperative rigid-unit modes

A linear-algebraic algorithm for identifying rigid-unit modes in networks of interconnected rigid units has recently been demonstrated. This article presents a series of enhancements to the original algorithm, which greatly improve its conceptual simplicity, numerical robustness, computational efficiency and interpretability. The improvements include the efficient isolation of constraints, the observation of variable-block separability, the use of singular value decomposition and a quantitative measure of solution inexactness.

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

For high-resolution powder diffraction in material science, high photon energies are necessary, especially for in situ and in operando experiments. For this purpose, a multi-analyser detector (MAD) was developed for the high-energy beamline P02.1 at PETRA III of the Deutsches Elektronen-Synchrotron (DESY). In order to be able to adjust the detector for the high photon energies of 60 keV, an individually adjustable analyser-crystal setup was designed. The adjustment is performed via piezo stepper motors for each of the ten channels. The detector shows a low and flat background as well as a high signal-to-noise ratio. A range of standard materials were measured for characterizing the performance. Two exemplary experiments were performed to demonstrate the potential for sophisticated structural analysis with the MAD: (i) the structure of a complex material based on strontium niobate titanate and strontium niobate zirconate was determined and (ii) an in situ stroboscopy experiment with an applied electric field on a highly absorbing piezoceramic was performed. These experiments demonstrate the capabilities of the new MAD, which advances the frontiers of the structural characterization of materials.

Structural Evolution of Ferroelectric and Ferroelastic Barium Sodium Niobate Tungsten Bronze

The crystal structure of the ferroelastic and ferroelectric tungsten bronze Ba₂NaNb₅O₁₅ (BNN) has been debated. Here, we re-examine the crystal structure of BNN by ambient powder X-ray diffraction combined with density functional theory calculations. We demonstrate that the room temperature space group is Cmm2 with significant cation disorder on the Ba and Na cation sublattices. Density functional theory calculations reveal a relatively flat energy landscape between structures of different symmetries, including the energetics of cation disorder. We also study the structural evolution and the ferroelectric and ferroelastic phase transitions by high-temperature X-ray diffraction and dilatometry. The ferroelectric phase transition at 570 °C is of first order and cause the cell to expand in the c direction, while the ferroelastic distortion starting at 270 °C takes place in the ab plane and does not affect the polarization. The phase transitions are not coupled, which means that BNN is a ferroic material with two primary and uncoupled order parameters.

The space group of the tetragonal tungsten bronze Ba₂NaNb₅O₁₅ was confirmed experimentally to be Cmm2 with partly Na and Ba cation disorder, while the most energetically favorable ordered structure was identified as Bbm2 by first-principles calculations. The thermal evolution of the crystal structure was determined, including a ferroelectric phase transition with contraction in the c direction at 570 °C and a ferroelastic transition at 270 °C, which is decoupled from the polarization and takes place in the ab plane.

Hester J, Gu Q, Liu Y, Schmid S. Synthesis, structure and dielectric properties of the Sr3Ti1−xZrxNb4O15, (0 ≤ x ≤ 1), series of tungsten bronze type compounds

High temperature phase transitions from Pna2₁ to P4/mbm are observed for all compositions, and transition temperatures increase with Zr content.

Octahedral tilting in the polar hexagonal tungsten bronzes RbNbW2O9 and KNbW2O9

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.

An Electronically Driven Improper Ferroelectric: Tungsten Bronzes as Microstructural Analogs for the Hexagonal Manganites

Since the observation that the properties of ferroic domain walls (DWs) can differ significantly from the bulk materials in which they are formed, it has been realized that domain wall engineering offers exciting new opportunities for nanoelectronics and nanodevice architectures. Here, a novel improper ferroelectric, CsNbW₂ O₉ , with the hexagonal tungsten bronze structure, is reported. Powder neutron diffraction and symmetry mode analysis indicate that the improper transition (T_C = 1100 K) involves unit cell tripling, reminiscent of the hexagonal rare earth manganites. However, in contrast to the manganites, the symmetry breaking in CsNbW₂ O₉ is electronically driven (i.e., purely displacive) via the second-order Jahn-Teller effect in contrast to the geometrically driven tilt mechanism of the manganites. Nevertheless CsNbW₂ O₉ displays the same kinds of domain microstructure as those found in the manganites, such as the characteristic six-domain "cloverleaf" vertices and DW sections with polar discontinuities. The discovery of a completely new material system, with domain patterns already known to generate interesting functionality in the manganites, is important for the emerging field of DW nanoelectronics.

An algebraic approach to cooperative rotations in networks of interconnected rigid units

Crystalline solids consisting of three-dimensional networks of interconnected rigid units are ubiquitous amongst functional materials. In many cases, application-critical properties are sensitive to rigid-unit rotations at low temperature, high pressure or specific stoichiometry. The shared atoms that connect rigid units impose severe constraints on any rotational degrees of freedom, which must then be cooperative throughout the entire network. Successful efforts to identify cooperative-rotational rigid-unit modes (RUMs) in crystals have employed split-atom harmonic potentials, exhaustive testing of the rotational symmetry modes allowed by group representation theory, and even simple geometric considerations. This article presents a purely algebraic approach to RUM identification wherein the conditions of connectedness are used to construct a linear system of equations in the rotational symmetry-mode amplitudes.