Structure, disorder, and oxygen vacancies in ferroelectric tetragonal tungsten bronzes
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Ferroelectric materials are widely used materials in electronics due to their spontaneous and switchable polarization. The most common ferroelectric material on the market today is the lead-based perovskite PbZr1-xTixO3 (PZT), and due to environmental concerns with lead there is an ongoing research effort to replace PZT with lead-free alternatives. Ferroelectric tetragonal tungsten bronzes (TTBs) is a family of materials which has not received much attention in this respect. The crystal structure of TTBs is unique in that it has four cation sites of different size and solid solutions of TTBs are readily formed. As a result, a large part of the periodic table can be used as a playground to develop new compositions. Disorder is inherent in TTBs because of the many similar cation and anion sites. Additionally, TTBs are prone to structural disorder such as incommensurate tilt patterns. Moreover, oxygen vacancies are also known to influence the physical properties of TTBs as well as transition metal oxides in general. The TTB structure has five symmetry inequivalent oxygen sites where oxygen vacancies can be localized, but the influence of oxygen vacancies on the physical properties of TTBs have so far not received much attention. The motivation for this work was to elucidate the relationships between structure, disorder, and oxygen vacancies in TTBs, which are keys for tailoring the functional properties. In this work, a combination of experiments and first principles calculations were combined to study crystal structure, disorder and oxygen vacancies in TTBs using the well-known lead-free ferroelectric TTBs strontium barium niobate (SrxBa1-xNb2O6, SBN) and barium sodium niobate (Ba2NaNb5O15, BNN) as two model systems. In the first part of the work, the effect of thermally induced cation-cation vacancy disorder was studied in four different SBN compositions (SBN25, SBN33, SBN50 and SBN61, where the number denotes the strontium content x). Dense SBN ceramics prepared by conventional solid-state synthesis were annealed in air at varying temperatures and subsequently quenched to room temperature. The Curie temperature was determined by dielectric spectroscopy, and for all the SBN materials, TC increased with higher quenching temperature. Measurements of electric field-polarization hysteresis loops of SBN33 revealed ferroelectric hardening with higher quenching temperature. The variation in the thermal history caused also structural changes, specifically a contraction of the a lattice parameter and a minor elongation of the c parameter of the TTB unit cell. These effects were discussed in relation to recent first principles calculations of the energy landscape of the cation vacancy configurations and experimental evidence of thermally induced cation/vacancy disordering. The crystal structure of the ferroelastic and ferroelectric BNN has been debated. In the second part of the thesis, the crystal structure of BNN was reexamined by ambient powder X-ray diffraction (XRD) combined with density functional theory (DFT) calculations. The room temperature space group observed by XRD was Cmm2with significant cation disorder on the Ba and Na cation sublattices. The structural evolution and the ferroelectric and ferroelastic phase transitions were studied by high-temperature X-ray diffraction and dilatometry. The ferroelectric phase transition at 570 °C is of first order and cause the unit cell of BNN to expand in the polar c direction, while the ferroelastic distortion starting at 270 °C takes place in the ab plane and does not affect the polarization. These two phase transitions were not observed to be coupled, making BNN a ferroic material with two primary and uncoupled order parameters. DFT calculations of different polymorphs of BNN revealed small energy differences between structures of different symmetries, including the energetics of cation disorder. The Cmm2 structure was found to have the same energy as the ferroelectric P4bm structure, while the tilted Bbm2 structure was identified as the DFT ground state, indicating that the cation sublattice stays in the high symmetry disordered state while the sublattice of NbO6 octahedra display tilting. In the third part of the work, oxygen vacancy formation in BNN and SBN was studied by DFT calculations. The oxygen vacancy formation energy in the case of BNN with a non-polar reference state varied in the range 3.15-4.04 eV for the five different sites. The lowest value was observed for the perovskite-like equatorial lattice site, in agreement with experimental studies of other TTB materials. Relaxation effects dominated over the predicted bond strengths from Crystal Orbital Hamiltonian Population (COHP) analysis. The oxygen vacancies caused delocalized electronic states in the Nb 4d bands, and a dramatic lowering of the ferroelectric polarization. The network of NbO6-octahedra accommodated the oxygen vacancies by forming long-range tilt patterns. These tilt patterns lowered the polarization even after the oxygen was reinserted at the vacancy site, which could explain why oxygen vacancies, incommensurate tilting, and relaxor behavior often coexist in TTBs. Calculations for SBN was performed for SBN20 with three different Sr-vacancy configurations on the A1 sublattice. The formation energy in case of non-polar SBN varied in the range 4.03-5.51 eV, considerably higher than for BNN and in god accordance with experimental data for SBN. Electrostatic interactions from cation vacancy-oxygen vacancy interactions have little effect on the formation enthalpies. In the final part of the work, the stability of quaternary BNN relative to the ternary competing phases NaNbO3 (NN) and BaNb2O6 (BN) was studied using DFT calculations. The calculations demonstrated that BNN is metastable with respect to NN and BN at 0 K. A thermodynamic model for the stability of BNN was presented that takes both configurational and vibrational entropy into consideration. The model for the configurational entropy due to cation-disorder in BNN is compared with experimental data for the formation of BNN. The configurational entropy was found to be the major contributor in stabilizing BNN with respect to the competing phases, but not large enough to be the sole contributor. The vibrational entropy was calculated using a finite displacement method to compute harmonic phonons. While these calculations are inconclusive, it is suggested that the low-frequency modes related to tilting of NbO6 octahedra will stabilize BNN through vibrational entropy. Finally, the metastable nature of tetragonal tungsten bronze niobates at low temperatures were also discussed using examples from the Materials Project database. The nature of the crystal structure of TTBs give rise to several different type of disorder, which can affect the ferroelectric properties of TTBs. In this work, it was demonstrated that cation disordering and oxygen vacancy formation can be introduced by thermal treatments and affect both the crystal structure and the ferroelectric properties. TTBs have the possibility to display complex tilt patterns, and due to small energetic differences between these tilt patterns, small perturbations can have a strong influence on what is observed in experiments. It was also proposed that entropy stabilization is a general feature of TTBs, mainly due to the configurational entropy introduced by cation disorder, but it was also suggested that vibrational entropy from octahedral tilting also contributes to the stabilization.