Ferroelectric Tungsten Bronzes

Abstract

Ferroelectric materials are everywhere in the modern society, from consumer electronics to car engines. Applications cover a whole range of devices such as sensors, actuators and transducers due to their dielectric or piezoelectric properties. Almost all technologically important ferroelectrics have the perovskite crystal structure, and the dominating material is lead zirconate titanate (PZT). In recent years, there has been an increasing desire to develop lead-free alternatives to PZT, although no definite replacement has yet emerged. Exploration of materials with other crystal structures is an attractive route towards finding lead-free alternatives. Ferroelectrics with tetragonal tungsten bronze (TTB) structure have been known for more than 60 years, including lead metaniobate, which is commercially available for high temperature piezoelectric sensor applications. In this work, ferroelectric tungsten bronzes were investigated by combining experiments with first-principles density functional theory (DFT) calculations. The principal goal was to obtain a fundamental understanding of the origin of polarization in this class of materials, which is expected to receive more attention in the years to come. A major part of the thesis is focused on the materials strontium barium niobate (SBN) and lead metaniobate (PN). While they both have the TTB structure, they are different in terms of space group symmetry and orientation of polarization with respect to the structural framework. Moreover, the dielectric behaviour of SBN changes with the Sr/Ba ratio, with Ba-rich compositions being classical ferroelectrics and Sr-rich compositions relaxors. Despite the fact that this has been known for decades, the origin of this fundamental difference has so far not been investigated in depth. Both SBN and PN are “unfilled” TTBs, meaning that the structure contains a mixed occupancy of cations and vacancies. This creates a possibility for cation order–disorder phenomena. The energetics of cation ordering in SBN, approximated by the end components, SN and BN, and PN were investigated by first principles calculations, initially with focus on the paraelectric structures. A supercell approach was used to sample ten different possible cation configurations, as an approximation to the true, possibly disordered structure. A thermodynamic model was developed for cation interchange in tungsten bronzes, and this model predicts that cation ordering in the three compositions SN, BN and PN behave qualitatively different as a function of temperature. Importantly, it was concluded that Ba-rich, ferroelectric SBN compositions will probably be more strongly affected by the thermal history than Sr-rich relaxor compositions. The next step in the investigation was the underlying mechanism behind the ferroelectric transition in SBN and PN. First-principles phonon calculations revealed an unstable polar mode in all the ten configurations of both SN and BN. The mode is similar to the soft mode causing spontaneous polarization in perovskite ferroelectrics such as BaTiO3 and KNbO3. Some of the configurations were also found to have a second instability, a mode consisting of octahedral tilting in the xy plane of the TTB structure. In contrast to many ferroelectrics, this was not found to reduce the polarization, even for severely distorted structures. The possibilities for octahedral tilting are limited in the rigid TTB structure, and the structural framework cannot completely adapt to the different size of the Sr2+ and Ba2+ cations. This leaves Sr2+ with enough space so that it can displace under the application of an electric field, which is suggested to contribute to the diffuse dielectric response of Sr-rich SBN. In the case of PN, X-ray and neutron diffraction experiments were performed in order to provide reliable data on the ferroelectric crystal structure. Refinement of the cation distribution made it possible to concentrate further first principles calculation on only four relevant cation configurations, for which energies and spontaneous polarization were calculated. The polarization was found to be large and surprisingly robust against cation disorder. Nudged elastic band calculations were performed for the ferroelastic switching in PN, and high transition barriers were found. This is a likely reason why the observed spontaneous polarization in PN is lower than the calculated value. SBN and PN are “unfilled” TTBs with cation–vacancy disorder. A number of “filled” TTBs were also examined computationally, both to isolate the order–disorder effects from other phenomena, and to extend the project to more general TTB materials. The series K4R2Nb10O30 with R = La, . . . , Gd, Bi was studied by first-principles phonon calculations, and it was found that while all are subject to the same polar instability as unfilled SBN, the size of the R3+ cation has a profound effect on an in-plane polar instability similar to the one found in PN. When R = Bi, this instability dominates and results in a net in-plane polarization. Comparison with materials where K is replaced by Tl revealed that the in-plane polarization is closely connected to the presence of lone pair cations on the perovskite-like A1 sites in the TTB structure. It is suggested that this is the mechanism behind the morphotropic phase boundary in the lead barium niobate system, for which very high piezoelectric response is achieved. TTBs with partially reduced Nb are electrically conducting and have recently been shown to be promising for thermoelectric applications. (Sr, Ba)6Nb10O30, the filled counterpart to the ferroelectric SBN system, has an interesting metal–insulator transition as the composition changes from the Ba to the Sr end component. As metallic systems are more challenging for DFT calculations than insulators, attention was given to the choice of functional used for (Sr, Ba)6Nb10O30. The DFT+U approach was used, after calibration against computationally much more expensive hybrid functional calculations. Structural optimizations and phonon calculations were then performed, along with an analysis of the electronic structure. Consistent with experiments, filled Ba6Nb10O30 was found to be dynamically stable in the tetragonal aristotype symmetry, while filled Sr6Nb10O30 has multiple instabilities which lead to an orthorhombic ground state with octahedral tilting and a larger unit cell. The electronic structure calculations were however inconclusive with respect to the metal–insulator transition associated with this structural distortion. The final part of the thesis deals with the rhombohedral polymorph of PN, r- PN. At room temperature, PN is only metastable in the TTB structure, with r-PN being the thermodynamically stable structure. This polymorph has previously been thought to have less interesting properties, with little or no piezoelectric response. The previously reported space group symmetry, R3m, is polar, and initial calculations of the spontaneous polarization based on structural data from literature demonstrated a fairly high polarization. A polar–nonpolar phase transition, which could possibly be ferroelectric, was also observed by high-temperature X-ray diffraction, so it was decided to investigate further whether r-PN could have attractive functional properties. X-ray and neutron diffraction experiments were conducted in order to provide a better description of the crystal structure of r-PN at room temperature. This led to a complete re-investigation of the crystal structure, and it was concluded based on experimental and computational investigations that the space group symmetry of r-PN is R3, and not R3m as previously reported. At the same time, the improved description of the crystal structure led to significantly less exciting predictions of spontaneous polarization, and additional dielectric characterization demonstrated that while the material indeed shows a polar–nonpolar phase transition at a high temperature of 780 ◦C, the structural transition has no impact on the dielectric permittivity and the material is not ferroelectric. Finally, this work is a significant contribution to a platform for computational investigation of ferroelectric tungsten bronzes. It has been established that the ferroelectric polarization in the well known SBN system is driven by an unstable phonon similar to what is found in ferroelectric perovskites, and is suggested to be a general feature for most Nb-based TTBs. Only in certain cases, such as when the A1 site is occupied by a lone pair cation, the out of plane polarization mechanism is suppressed by a different driving force, leading to in-plane polarization.