TiO6 Octahedron Research Articles

Quantitative Unraveling of Exsolved Heteroboundaries for High-Temperature Electrocatalysis.

The application of perovskite oxide for high-temperature electrocatalysis is hindered by its limited activity. Exsolution is a smart strategy that allows the enrichment of the perovskite's surface with highly reactive phases, yielding heteroboundaries. However, the identification of the exact catalytic role of this complex architecture is still elusive. Here we presented a quantitative analysis of the CO2 electroreduction reactivity of a series of perovskite thin film platforms (La0.4Ca0.4Ti0.94Ni0.06O3, LCTN) boosted by exsolved heteropical nanoparticles (particularly for Ni and NiO). The cross-scale electrochemical characterizations, together with density functional theory (DFT) modelings, have shown clear evidence that the boundary length of the NP/perovskite interface is strictly correlated with the CO2RR activity. The intrinsic reaction rate per active site at the NiO/LCTN boundary demonstrates a highest turnover frequency (TOF) of 7.05 ± 0.75 × 104 s-1 at 800 °C, which is 2.5 times and 4 orders of magnitude better than that of Ni/LCTN and LCTN, respectively. The ab initio molecular dynamics (AIMD) proves that the CO2 absorption at the NiO/LCTN boundary leverages a bidentate carbonate modality with a reduced dissociation energy barrier. Moreover, a multifold enhancement in oxygen exchange rate was confirmed, which correlated to the facilitated oxygen ion hopping between adjacent TiO6 octahedrons. Further near-ambient pressure X-ray photoelectron spectroscopy (NAP-XPS) during CO2 electrolysis on model electrolyzers reveals the crucial role of the NiO/LCTN boundary in stabilizing oxidized carbon intermediates, raising the onset potential threshold of adventitious carbon as well as preventing its build-up.

Tailoring the structural and optical properties of lead-free Na0.5(Bi1-xSmx)0.5TiO3 multifunctional ceramics by Sm-doping

In this study, the effects of Sm3+-content on the structural and optical properties of the Na0.5(Bi1-xSmx)0.5TiO3 multifunctional lead-free system were investigated using x-ray diffraction (XRD), ultraviolet-visible (UV-Vis), Raman spectroscopy and photoluminescence (PL) spectroscopy. The Na0.5(Bi1-xSmx)0.5TiO3 (x = 0.000, 0.005, 0.010, 0.015, and 0.020) ceramics were synthesized by the solid-state reaction method with subsequent annealing. The Rietveld method was used to refine the XRD data. The results of these refinements indicated that pure NBT (Na0.5Bi0.5TiO3) and the Sm3+-doped samples showed the coexistence of the rhombohedral (R3c) and tetragonal (P4bm) phases in different fractions, which depend on the Sm3+-content. The UV-Vis data revealed that the optical band gap of the Na0.5(Bi1-xSmx)0.5TiO3 samples monotonically decreases with increasing Sm3+-content, providing evidence of replacement of Bi3+- by Sm3+-ions. Furthermore, Raman spectroscopy confirmed that substitution of Bi3+- by Sm3+-ions leads to a shortening of the Na/Bi-O bond length. It was demonstrated that this behavior is responsible for the increase in the local symmetry of the TiO6 octahedron and the consequent decrease in the ratio between both rhombohedral and tetragonal phases, as observed by the XRD data. The findings from the PL data revealed typical emissions corresponding to transitions between the 4G5/2 → 6Hj (j = 5/2, 7/2, 9/2, 11/2, 13/2) states of the Sm3+-ion. Additionally, the presence of non-radiative recombination processes was found to depend on both laser pumping power and Sm3+-content.

Differences in the Ti4+/Ti3+ Redox Reactions between Li4Ti5O12 and LiTi2(PO4)3 Observed By Soft X-Ray Spectroscopy

Clarification of the redox reaction in electrode materials for Li-ion batteries is essential to obtain strategies to improve the performances such as charge-discharge capacity, voltage and cyclability. We focus on the difference in voltage, i.e., redox potential between Li4Ti5O12 (LTO) and LiTi2(PO4)3 (LTP). Spinel-type LTO with a redox potential around 1.5 V vs Li/Li+ is one of the anode materials [1], while the main redox potential of LTP (NASICON-type structure) is around 2.4 V vs Li/Li+ [2]. Although the difference in redox potential is as large as ~0.9 V, it has been thought to be that Ti4+/Ti3+ redox couple is identical for both LTO and LTP. Here, we demonstrate the electronic-structure analysis of LTO and LTP by using soft X-ray absorption spectroscopy (XAS) and soft X-ray photoemission spectroscopy (XPS). Operando Ti L 2,3-edge XAS by use of an all-solid-state cell [3,4] successfully revealed reversible Ti4+/Ti3+ redox reactions by discharge/charge for both materials, but the XAS line shapes were different. By analyzing the spectra using multiplet calculation [5], differences in the crystal-field splitting for the TiO6 octahedron and O 2p -> Ti 3d charge-transfer (CT) effect were found. The different CT effect was also confirmed by Ti 2p-3d resonant XPS measurements for the initial-state LTO and LTP samples. Moreover, the difference in redox potential is mostly explained by the energy levels of the pre-edge structures in the O K-edge XAS calibrated with the O 1s XPS spectra. In the presentation, the understandings of the spectroscopic results will be discussed in detail.

Optimized hybrid improper ferroelectricity of (Ca1-xNdx)3Ti2O7 ceramics based on soft doping effects

Low remnant polarization and high coercive field are the main factors limiting the practical application of Ca3Ti2O7-based hybrid improper ferroelectric ceramics. Based on sol-gel method and soft doping effect, (Ca1-xNdx)3Ti2O7 (x=0.003) ceramics with higher remnant polarization of ∼3.53 μC/cm2 and lower coercive field of ∼91 kV/cm were obtained. More interestingly, thanks to the large distortion amplitude of TiO6 octahedron and effective suppression of defects such as oxygen vacancies caused by Nd3+ as a donor dopant, the remnant polarization of (Ca1-xNdx)3Ti2O7 (x = 0.003 and 0.006) ceramics measured at 10 Hz using the DHM mode were as high as 7.33 μC/cm2 and 5.85 μC/cm2. These findings prove that the soft doping at A sites of Ca3Ti2O7 material is a simple and effective strategy to enhance its hybrid improper ferroelectricity.

Infrared spectroscopy of nanocrystalline anatase (TiO2) particles under the neutron irradiation

Bands structure of nanocrystalline anatase (TiO2) particles was investigated before and after neutron irradiation (1.6 × 1015n·cm−2, 8 × 1015n·cm−2, 4 × 1016n·cm−2 and 2 × 1017n·cm−2) using FTIR spectroscopy. The peaks expressing Ti – O and Ti – O – Ti stretching oscillations before and after neutron irradiation were explained with appropriate wavenumber in the infrared (IR) absorption spectra. The new peaks observed in the IR spectra as a result of neutron transmutations were analyzed with V – O or V – O – H deformation oscillations of the newly formed V isotope. Simultaneously, deformation vibration of the TiO6 octahedron were detected on the nanoparticle surface. Moreover, the effect of neutron irradiation on the surface activity of anatase nanoparticles and amorphization processes in nanocrystals were explained by their corresponding IR spectra.

Local structure analysis of Bi0.5Na0.5TiO3–BaTiO3 solid solutions

Abstract Solid solutions of Bi0.5Na0.5TiO3 (BNT) and BaTiO3 (BT) with ABO3-type perovskite system is known to possess good ferroelectric properties. A local structural analysis and an electronic structure analysis of high-quality BNT-BT solid solutions were performed using synchrotron radiation X-rays to clarify the mechanism of the enhanced ferroelectric properties. The BNT-BT solid solution undergoes a series of phase transitions to tetragonal structures with space groups P4bm and P4mm. The local structure analysis revealed reduced off-center shift of A-site atoms resulting of the BT substitution. The local structure obtained by high-energy X-ray total scattering is consistent with the electronic structure obtained by X-ray absorption spectroscopy.

The optical and ferroelectric properties of Fe-doped hybrid improper ferroelectricity Ca3Ti2O7 via experimental and density functional theory study

The magnetoelectric multiferroic materials with ferroelectric and magnetic orders have great attributed attention in the field of magnetoelectric memories and magnetic resonance devices. Here, we systematically investigated the optical and multiferroic properties of Fe-doped hybrid improper ferroelectricity Ca3Ti2O7 prepared by sol-gel method. The distortion of TiO6 octahedron changes with the content of oxygen vacancy introduced by Fe doping, thus realizing the adjustment of remnant ferroelectric polarization of the samples. The slight blue shift of the Raman band at 667 cm−1 reflected the introduces of oxygen vacancies by Fe doping. The optical bandgaps of the doped samples were reduced after doping, agreeing with the results of the first-principles calculations. With the introduction of Fe3+, the magnetism increases gradually. The first-principles calculation shows that magnetism origins from the Fe-3d and their surrounding O-2p orbitals. The Fe-doping Ca3Ti2O7 materials realizing the introduction of magnetic properties while regulating its ferroelectric properties are expected to be applied in magnetoelectric memories, optoelectronic devices spintronics and magnetic response devices.

Lead free high Tc piezoelectric Sr2Nb2O7-La2Ti2O7 solid solution: A structural, dielectric ferroelectric and piezoelectric studies

The ferroelectric and piezoelectric properties of Sr2Nb2O7–La2Ti2O7 (SNB-LT) solid solution ceramics have been studied. The La and Ti ions were substituted into the Sr2Nb2O7 (SNB) lattice and their resultant phase of SNB-LT has lattice distortion. The Rietveld refinement parameters from the XRD patterns corroborate a solid solution of Sr2Nb2O7–La2Ti2O7. The addition of La3+ and Ti4+ dampens the SNB intra-structural phase. Raman spectroscopy confirmed the internal lattice relaxation due to the Ti(Nb)O6 octahedron in the lattice. At 2×106 Hz, the dielectric permittivity of SNB-LT-1, SNB-LT-2, and SNB-LT-3 is 17.2, 17.5, and 21.3, respectively, with σac conductivity in the order of 10−5 S/m. With an increase in Ti(Nb)O6 distortion, the piezoelectric coefficient of SNB-LT-1, SNB-LT-2, and SNB-LT-3 increases linearly as 6.3, 8.1, and 9.3 pC/N. The temperature-dependent ferroelectric polarization of SNB-LT-1, SNB-LT-2, and SNB-LT-3 has been tested, and a substantial rise in polarization has been demonstrated up to 120 °C. At 120 °C, the SNBLT solid solution showed a two-fold increase in remnant polarization.

Potassium Titanate Supported Atomically Dispersed Palladium for Catalytic Oxidation.

Single-atom catalysts based on noble metals provide efficient atomic utilization along with enhanced reactivity. Herein, a convenient strategy to construct atomically dispersed palladium catalyst on layered potassium titanate (KTO), which has enhanced interaction between the TiO6 layer and the palladium atoms, is presented. Due to the presence of K+ ions in the interlayers of KTO, the TiO6 octahedron layers have negative charge, which increases the interaction between Pd atoms and the substrate, thus preventing their agglomeration. In addition, the provision of charge of K+ ion makes the molecular oxygen in the system easier to be activated and promotes catalytic oxidation activity.

Structural and electrical properties of bismuth sodium titanate ceramic

Single-phase lead-free Bi0.5Na0.5TiO3 (BNT) perovskite ferroelectric ceramic was produced using a solid-state reaction method. A detailed investigation of the structural and electrical properties of BNT ceramic is conferred. According to phase analysis employing Rietveld refined X-Ray diffraction, the crystal structure is single phase with rhombohedral (R3C) symmetry. Raman spectra measurement also confirms the rhombohedral structure of BNT by originating numerous peaks from the TiO6 octahedron. The ferroelectric character of the BNT sample was established by a hysteresis loop measurement of polarisation vs electric field (P-E). The remnant polarisation (Pr) and coercive field (Ec) have characteristic values of 1.63 μC/cm2 and 29.91 kV/cm, respectively. The ferroelectric phase change is seen in the temperature-dependent dielectric research, with a transition temperature of 323°C. The compound possessed a low value of tanδ even at a high temperature (500°C) at 1 MHz. The prepared sample exhibited excellent dielectric characteristics from room temperature to high temperatures, making it ideal for various applications.

Phase Evolution and Local Piezoelectric Response of Sn‐Doped BaTiO3 Ceramics

Multiphase coexistence is the key to rendering samples with superior piezoelectric properties for BaTiO3 ceramics. Ba(Ti1−xSnx)O3 (BTS, x = 0.0–0.30) ceramics are prepared by the traditional solid‐state method. Orthorhombic (O) and tetragonal (T) phases are visually observed to coexist only in the ceramics with the low‐doping of Sn (x = 0.025–0.075) by electron backscattered diffraction (EBSD). The O phase percentage increases from 13.90% to 75.10%, therefore enhancing their piezoelectric response over the decreasing T phase. Further increase of x turns the BTS to rhombohedral (R) and cubic (C) phases, while cathodoluminescence (CL) analysis detects significant redshifts of the defect peak, which is mainly due to the change of phase structure. The phase transition can lead to the change of Ti–O6 octahedron, thereby affecting the charge transfer between and . High piezoelectric responses can be achieved by the coexistence of O and T phases, which facilitates the rotation of ferroelectric domains. These results are beneficial to understanding the relationship between the microstructure and piezoelectric properties of BTS ceramics, and also indicate that CL can be a useful tool for phase identification.

Enhanced electrochemical performance of MgFe2O4/SrTiO3 and MgFe2O4/SiO2 nanocomposite structures

MgFe2O4/SrTiO3 and MgFe2O4/SiO2 nanocomposites were prepared via a modified sol-gel auto combustion method. X-ray diffraction (XRD) patterns confirmed the formation of both MgFe2O4/SrTiO3 and MgFe2O4/SiO2 nanocomposite structures. Williamson-Hall analyses showed that MgFe2O4/SrTiO3 had a crystallite size of 18 nm, while it was 17 nm for MgFe2O4/SiO2. It was found that the lattice constant for MgFe2O4/SiO2 was longer than that for MgFe2O4/SrTiO3; thus, the cell volume was larger for MgFe2O4/SiO2 nanocomposite. Fourier transform infrared (FTIR) spectra for MgFe2O4/SrTiO3 and MgFe2O4/SiO2 nanocomposites revealed absorption bands corresponding to bending vibrations of the TiO6 octahedron and Si―O―Si with symmetric and antisymmetric stretching vibrations. The electrochemical characteristics showed that MgFe2O4/SrTiO3 and MgFe2O4/SiO2 nanocomposites exhibited similar initial discharge capacity values, while MgFe2O4/SrTiO3 had a higher coulombic efficiency of 64.1%. After 100 cycles, MgFe2O4/SrTiO3 delivered a discharge capacity of 311 mAh g−1, larger than MgFe2O4/SiO2. Furthermore, MgFe2O4/SrTiO3 nanocomposite demonstrated significantly improved high rate capability, with a capacity of 330 mAh g−1 and 65% retention of the 2nd cycle, compared to MgFe2O4/SiO2 (with a capacity of 252 mAh g−1 and 42% retention of the 2nd cycle) after the current density was returned to 100 mA g−1.

Growth, Structure and Optical Characterization of Rb3Ti3P5O20 Single Crystal.

Phosphate crystals attract much attention on account of their rich crystal structures and excellent physical and chemical properties. Herein, Rb3Ti3P5O20 single crystals were grown by the high temperature solution method using Rb2CO3 and NH4H2PO4 as the fluxes. This crystal, with non-centrosymmetric Pca21 space group, presents a three-dimensional framework structure composed of [TiO6] octahedron, [PO4] tetrahedra, and [P2O7] dimers. The electronic structure was measured via X-ray photoelectron spectroscopy. The measurements found that Rb3Ti3P5O20 has stronger Ti–O ionic bonding properties and weaker P–O covalent bonding properties compared to RbTiOPO4. Optical measurements indicated that Rb3Ti3P5O20 has a 3.54 eV band gap and a wide transmission range (0.33–4.5 μm). Theoretical calculations showed that Rb3Ti3P5O20 crystals have a moderate birefringence of 0.079 at 1064 nm. In addition, the relationship of the structure–property was studied using first-principles method. The results demonstrated that TiO6 octahedron played a significant role for the optical properties.

Structural, electronic, and optical properties of rare-earth-doped SrTiO3 perovskite: A first-principles study

The doping effect of the addition of rare earth elements (Pr, Nd, and Sm) on the mechanical and dielectric properties of the strontium titanate perovskite SrTiO3 was investigated using density functional theory (DFT). The introduction of rare earth elements modifies the structural properties and the charge distribution. Distortion of the Ti–O6 octahedron results in a decreasing trend in the mechanical and electronic properties with increasing nuclear charge numbers of Pr (59), Nd (60), and Sm (62). Rare earth element substitutions move the Fermi-level into the conduction band and change the absorption spectrum by adding peaks at 0.1–0.4 eV.

Unprecedented Superhigh‐Rate and Ultrastable Anode for High‐Power Battery via Cationic Disordering

AbstractHigh‐power lithium‐ion batteries (LIBs) are critical for power‐intensive applications; however, their development is largely hindered by the lack of anode materials that have stability and high capacity at high charging/discharging rates. Herein, a cationic disordering strategy is reported to build an ideal high‐power anode with boosted intercalation kinetics and a stable framework. A novel titanium niobate (TiNb2O7) anode with unique predistorted Nb(Ti)O6 octahedrons (pd‐TNO) is developed by introducing cation disorder, which allows ultrafast Li+ storage within seconds and exceptional stability over long cycling at high rates. The pd‐TNO delivers an outstanding specific capacity of 153 mAh g−1 at 100 C, 20 times higher than that of conventional TNO anodes without cationic disordering, and retains 42.8% of the capacity after 15,000 cycles. Using the pd‐TNO anode, a high‐power LIB with an unprecedented power density of 91,197 W kg−1 at 200 C, which is approximately eight times higher than that of the advanced commercial high‐power anode Li4Ti5O12 (11,813 W kg−1 at 50 C), is demonstrated. Importantly, the pd‐TNO is prepared under ambient conditions via a high‐throughput process, and it exhibits considerable potential for scalability for practical applications.

Enhanced electrical properties of (Bi0.2Na0.2Ba0.2Ca0.2Sr0.2)TiO3 high-entropy ceramics prepared by hydrothermal method

In this study, (Bi0.2Na0.2Ba0.2Ca0.2Sr0.2)TiO3 (BNBCST) high-entropy ceramics (HECs) were prepared by using hydrothermal-synthesized powders. According to the characterizations of microstructure and crystal structure, the BNBCST HECs sintered at 1180–1220 °C exhibit a great chemical homogeneity and a single tetragonal phase. Compared to BNT, the chemical element disorder at A-site of BNBCST results in a large lattice distortion, which effectively disturbs the symmetry of the TiO6 octahedron and leads to dielectric relaxation as well as enhanced energy storage performance in HECs. The dielectric, ferroelectric and energy storage performances are density dependent. For the sample sintered at 1200 °C, a dielectric constant of 3788 and a recoverable energy storage density (under 127 kV/cm) of 1.37 J/cm3 can be achieved. This work shows that powder preparation by hydrothermal method is a promising approach to fabricate high-entropy ferroelectric ceramics and the prepared BNBCST is a practicable alternative for electrical energy storage applications.

Zn2SnxTi1–xO4 Continuous Solid-Solution Photocatalyst for Efficient Photocatalytic CO2 Conversion into Solar Fuels

Solid-solution materials exhibit promising photocatalytic performance for complete photocatalytic conversion of carbon dioxide (CO2) and water (H2O) into solar fuels and oxygen (O2). In this study, Zn2SnxTi1–xO4 (0 ≤ x ≤ 1) solid-solution photocatalysts with an inverse spinel structure were prepared using the molten-salt-assisted method. The Zn2SnxTi1–xO4 solid-solution photocatalyst effectively enhanced CO2 photoreduction due to the increase in optical excitation centers, including SnO4 tetrahedrons, ZnO6, and TiO6 octahedrons. Numerous photoexcited centers generated sufficient photogenerated carriers to increase the overall redox reaction rate of H2O and CO2. In situ Fourier transform infrared spectroscopy analysis revealed that the distortion of the structural unit of the Zn2SnxTi1–xO4 solid solution not only improved the separation of photogenerated charges but also promoted the activation of CO2 molecules on the catalyst surface. Moreover, the reduction in the effective mass of photogenerated carriers in the Zn2SnxTi1–xO4 solid solution enables their fast migration, which results in excellent carrier movement. This synergistic effect leads to enhanced photoactivity of Zn2SnxTi1–xO4 for CO2 reduction.

Synchrotron based x-ray absorption spectroscopy investigation and temperature dependent ferroelectric properties of Ni doped BaTiO3 nanostructures

In this report, the local structure geometry of BaTi1-xNixO3 (0.0 ≤ x ≤ 0.06) ceramics has been studied through synchrotron based x-ray-absorption spectroscopy, measured at the Ti K, Ba L3 and Ni K-edges at room temperature. The x-ray absorption near edge spectroscopy (XANES) at Ti K-edge confirms the TiO6 octahedron geometry of Ti atom due hybridization between Ti(3d)-O(2p) orbitals and signifies the non-centrosymmetric nature of BaTiO3 samples. However, Ti–O off-center displacement (non-centrosymmetric) is disturbed under the effect of Ni doping as a result of oxygen vacancies formation. More interestingly, XANES studies at Ni K-edge ensure successful substitution of Ni in BaTiO3 as Ni2+ ions. Extended x-ray absorption fine structure (EXAFS) data at Ni K-edge have been fitted to estimate pertinent local structural parameters of the Ni–O, Ni–Ba, Ni–Ti and Ni–Ni shells (viz. bond lengths and disorder parameters) and it also reveal that the structural disorders around the Ti sites in the doped BaTiO3 expand with Ni doping. The mixed-valence states of titanium ion, i.e., Ti4+ and Ti3+ in the doped samples were established with the x-ray photoelectron spectroscopy (XPS). Moreover, XPS divulges the creation of oxygen vacancies due to Ni doping in BaTiO3 matrix. The complementary information about the lattice vibration is analyzed through Raman studies that approve the softening of the transverse optical (TO) mode present at 515 cm−1. The temperature dependent ferroelectric studies affirm that the ferroelectricity vanishes in the doped samples due to the decrement in the off-center displacement between the Ti4+ and O2− ions in the TiO6 octahedral geometry. Differential thermal analysis (DTA) exhibits a ferroelectric tetragonal to para-electric cubic phase transition in the pristine as well as Ni doped BaTiO3 samples.

Presence of Delocalized Ti 3d Electrons in Ultrathin Single-Crystal SrTiO3.

Strontium titanate (STO), with a wide spectrum of emergent properties such as ferroelectricity and superconductivity, has received significant attention in the community of strongly correlated materials. In the strain-free STO film grown on the SrRuO3 buffer layer, the existing polar nanoregions can facilitate room-temperature ferroelectricity when the STO film thickness approaches 10 nm. Here we show that around this thickness scale, the freestanding STO films without the influence of a substrate show the tetragonal structure at room temperature, contrasting with the cubic structure seen in bulk form. The spectroscopic measurements reveal the modified Ti-O orbital hybridization that causes the Ti ion to deviate from its nominal 4+ valency (3d0 configuration) with excess delocalized 3d electrons. Additionally, the Ti ion in TiO6 octahedron exhibits an off-center displacement. The inherent symmetry lowering in ultrathin freestanding films offers an alternative way to achieve tunable electronic structures that are of paramount importance for future technological applications.

Molten salt synthesis and characterization of 1D sodium hexatitanate nanowires

The synthesis of Na2Ti6O13 nanowires (NTNW) was performed at chemical interaction between rutile nanopowder with sodium chloride flux on the surface of molten aluminum under air. Synthesis of NTNW proceeds at two stages reaction at the three-phase boundary “gaseous medium (air)/molten salt/molten metal (Al)” under the quasi-autocatalytic mechanism.SEM, micro-Raman spectroscopy, X-Rays photoelectron spectroscopy, electron dispersive spectroscopy, and XRD are used to characterise NTNWs.The composition and morphology of NTNW can be controlled by experiment parameters. The increasing of synthesis temperature up to 850 °C allows getting single-phase product. Further increase in temperature up to 950 °C leads to increase in sodium concentration in NTNW. The ratio between the length and diameter of NTNW reaches 50.During high-temperature MS synthesis at 850–950 °C NTNW with some reduced Ti3+ were obtained. When the temperature of sodium hexatitanate nanorods and nanowires synthesis in molten salt media elevated to 950 °C, the amount of reduced Ti3+ atoms increased, giving a Ti3+/Ti4+ surface atomic ratio of 0.112.The sodium hexatitanate nanorods mainly formed by TiO6 octahedrons connected with corner-shared OO bridge bands wherein Na ions stay between layers. This position of Na+ ions is prospective for possible application of sodium hexatitanates in sodium-ion batteries.