Atomic-scale control of TiO₆ octahedra through solution chemistry towards giant dielectric response

Abstract

The structures of many important functional oxides contain networks of metal-oxygen polyhedral units i.e.MO_n. The correlation between the configurations and connectivities of these MO_n to properties is essentially important to be well established to conduct the design, synthesis and application of new MO_n-based functional materials. In this paper, we report on an atomic-scale solution-chemistry approach that for the first time enables TiO₆ octahedral network control starting from metastable brookite TiO₂ through simultaneously tuning pH values and interfering ions (Fe³⁺, Sc³⁺ and Sm³⁺). The relationship between solution chemistry and the resultant configuration/connectivity of TiO₆ octahedra in TiO₂ and lepidocrocite titanate is mapped out. Apart from differing crystalline phases and morphologies, atomic-scale TiO₆ octahedral control also endows numerous defect dipoles for giant dielectric responses. The structural and property evolutions are well interpreted by the associated H⁺/OH⁻ species in solution and/or defect states associated with Fe³⁺ occupation within TiO₆ octahedra. This work therefore provides fundamental new insights into controlling TiO₆ octahedral arrangement essential for atomic-scale structure-property design.

Introduction

The crystal structures and functional properties of metal oxide materials are directly affected by the arrangement of their constituent MO_n polyhedral building blocks^1,2. Atomic-scale control over these arrangements is extremely important because 1: controlling the way to link MO_n polyhedra together favors the creation of novel nanostructures, with a wide variety of particle sizes, crystal structures and morphologies³; 2: control of the local distortions and defect chemistry of the constituent MO_n polyhedra can alter electrical properties such as local dipole moments and macroscopic polarization⁴; and 3: both the individual MO_n configurations and their connectivities can profoundly affect the growth kinetics of metal oxides. Reliable control of the above factors enables the design of new solid-state materials and the associated development of novel practical applications.

TiO₆-octahedral-based functional materials, e.g. several typical Ti-containing oxides (TiO₂ and layer-structured titanates), exhibit versatile properties e.g. photovoltaic, electrochemical, catalytic and dielectric properties^5,6,7,8. These functional oxides are built of the same fundamental TiO₆ polyhedral building units (see e.g.Figure 1a) but connected differently⁹. The gaining of the necessary control over the local TiO₆ octahedral arrangement is essential for property tailoring. Although a multitude of efforts have been devoted, the usual synthesis routes do not allow simultaneous control over structural/phase evolution, defect chemistry and resultant properties of the materials produced¹⁰. Otherwise, the synthetic strategies have to involve extremely complicated procedures and/or insurmountable challenges arising from using capping complexes that invariably either obscure the desired structural configurations or undermine surface reactivity. To date, only a few examples (mainly perovskites) refer to TiO₆ octahedral tilting, rotating and/or distortions², which are only fabricated in non-solution ways and what's more, these have to be subject to thermally/dynamically nonequilibrium states e.g. via sintering under high temperatures/pressures¹¹, or based on external strains/stimulus¹², or forming local intergrowth with non-stoichiometry¹³. As such, the control of TiO₆ octahedral arrangements from equilibrium-state solution chemistries, i.e. the connectivities and configurations thereto on the atomic-scale level, remains unsuccessful. As a result, an investigation on TiO₆ octahedral evolutions and the relationships between TiO₆ octahedral arrangements and the resultant structures/properties is still missing.

Figure 1

Representations of the connectivity and configurations of TiO₆ octahedra and their control under solution reaction conditions allowing crystalline phase and morphology evolutions in TiO₂ and layer-structured Lepidocrocite-type titanate.

(a) The connectivity and configurations of TiO₆ octahedra in brookite, anatase and lepidocrocite-type titanate. The arrows denote the axial directions (e.g. x, y and z) of the crystal structure. The blue dashed lines and circles denote edge-sharing and vertex/corner-sharing connections, respectively. The white frames demonstrate the configurations in a TiO₆ octahedron corresponding to respective structures, where the same (different) colors mean the same (different) length of Ti–O bonds. (b) TiO₆ octahedral modification through pH controlling giving rise to the structural evolution (XRD patterns and SEM/TEM images). (c) SEM (left: R_Fe = 5%–20%) and TEM/HRTEM (right: R_Fe = 5% and 15%) images of as-prepared lepidocrocite-type titanate for the TiO₆ octahedral modification controlled through the introduction of interfering (Fe³⁺) ions. Inset in c-right are the Fourier-transform diffraction patterns corresponding to the HRTEM.

There remains an urgent and ongoing need for new synthetic strategies enabling control over TiO₆ octahedral configurations and connectivities. To this end, we herein report on a new, facile solution-chemistry approach with which the relationship between the synthesis variables and the resultant TiO₆ octahedral networks is mapped out in terms of controlling simultaneously the pH values of solutions and interfering/blocking ions (Fe³⁺, Sc³⁺ and Sm³⁺). On the one hand, the interaction between H⁺/OH⁻ groups and TiO₆ octahedral networks could respond to a strong negative/positive voltage and exhibit a large increase in electrical capacitance and subsequent variation in TiO₆ octahedral arrangements¹⁴. The kinetics of nucleation/growth in solutions can thus be manipulated¹⁵, as theoretically predicted¹⁶, by the presence of H⁺/OH⁻ species since they influence the surface energies and surface tension, leading to variations in morphology and phase stability of TiO₂. On the other hand, interfering/blocking ions could permit the local environment of the TiO₆ octahedra to be altered¹⁷, introduce local chemical defects and change the local chemical potential energy of the particular TiO₆ octahedra involved^10,18. Likewise, introducing interfering ions could probably cause local distortion, even breaking the local symmetry of the TiO₆ octahedra, giving rise to new local polarization states.

In the light of the two synthetic variables for tuning TiO₆ octahedral configurations and connectivities described above, this paper presents the atomic-scale control of TiO₆ octahedra in several typical titanium-containing oxides (e.g. TiO₂ and layer-structured lepidocrocite-type titanate) from solutions and builds the correlation between TiO₆ octahedral control and structures/properties.

Results

Like many other functional titanium-containing oxides, TiO₂ (anatase, brookite and rutile) and titanates are all built out of the same basic structural unit, TiO₆ octahedron. Figure 1a shows the arrangements of TiO₆ octahedra in brookite, anatase and lepidocrocite-type titanate, showing distinctly different TiO₆ octahedral configurations (i.e., different Ti–O bond lengths and angles) and connectivities (i.e., edge-sharing and vertex/corner-sharing connections). Depending on the local arrangements of TiO₆ octahedra, the resultant oxides have different crystal structures. This can be considerably influenced by the reaction parameters, solution pH and the concentration of interfering ions, during the solution synthesis.

TiO₆ octahedral connectivity and configurations controlled through pH tuning

The connectivity types as well as the local configurations of the individual TiO₆ octahedra are strongly influenced by pH value (pH = 1 ~ 14) without interfering ions. Thereby, as a result of the TiO₆ octahedral control under different pH conditions, the corresponding crystalline nanophases, morphologies/microstructures show considerable diversity (Figure 1b). The reaction condition of pH ≤ 6.0 usually gives anatase TiO₂ nanophases (Figures 1b, S1) with edge-sharing connectivity of TiO₆ octahedra (Figure 1a). The average crystallite sizes of the resultant compounds are estimated to be between 8.2 nm (pH = 1) and 21 nm (pH = 6) from the strongest diffraction line (101) for anatase using Scherrer equation, consistent with TEM result. It is interesting that rutile TiO₂ seems able to exist only with pH range of 2.0–3.0 (S1). A high pH value, by contrast, promotes vertex-sharing connectivity of the TiO₆ octahedra (Figure 1a) as evidenced by the appearance of brookite phase (Figure 1b) particularly with pH value of 10.5, which still gives a mixture of spindle-shaped brookite and square-like anatase phases. Pure brookite phase was achieved when pH value is varied between 12.0 and 14.0, as confirmed by the structural refinements (S2–S4). While, the resultant morphologies are highly pH-sensitive, i.e., flower-shaped assemblies with a dimension of ~2 μm at pH = 12.5 and well-dispersed spindle-shaped brookite particles with dimensions around 300 nm along the axial direction and 100 nm along the cross-sectional direction at pH = 13.5. When the pH value is beyond 14.0, a new secondary phase with the strongest diffraction at 2θ = 9.8° appears in addition to the dominant brookite phase (Figure 1b and S5), presenting two different morphologies: spindle-shaped brookite and rod-like layered titanates with scrolled TiO₆ frameworks. This new phase is related to a type of sodium-containing titanate (EDS in S5) that has a corner/edge-sharing TiO₆ octahedral connectivity (Figure 1a)¹⁹. Upon further increase of the alkalinity (OH⁻), brookite is always the major phase unless extremely high alkali conditions such as the (OH⁻) concentration 5 M reported for lepidocrocite-type titanate nanotubes (TNTs)²⁰. Unfortunately, such an extremely high alkalinity would not be favorable to control the TiO₆ octahedral units, nor the size, morphology and chemical compositions of the final products.

It is noted that only a few papers to date report obtaining pure brookite TiO₂. Usually, it coexists easily with anatase, implying the difficulty in the formation of pure brookite TiO₂ phase^21,22. Even in this work, pure brookite TiO₂ is limited to a relatively narrow pH value range. For this reason, the subsequent control over the configurations and connectivity of TiO₆ octahedra using interfering ions will be based on high-purity brookite. As a matter of fact, all the nanophases/structures can be achieved by changing synthesis conditions from the starting brookite TiO₂, so we note here that the controlling process can be generally considered as a process of TiO₆ octahedral modification.

TiO₆ octahedral connectivity and configurations controlled through the interfering ions

Dominant nanophase evolution

The introduction of interfering Fe³⁺ ions at pH = 12.5 leads to a nanophase transformation from brookite to anatase and/or lepidocrocite-type titanate, i.e. the TiO₆ octahedra were modified. Pure-phase brookite was obtained when pH = 12.5 without interfering Fe³⁺ ion, while a small amount of Fe³⁺ ions, e.g.R_Fe = 5%, results in anatase TiO₂ formation (S6 and S7), which is confirmed by the decreased intensity of the (121) to the (120) peak (see the detailed explanation in Figure S8), the appearance of a Raman peak at 515 cm⁻¹ (S8) corresponding to anatase²³, also the inhomogeneous morphologies observed (S7). The ratio of the brookite to the anatase phase is about 79: 21 in this specific case, estimated via XRD refinement (S9). When the R_Fe increases up to or beyond 10%, the TiO₆ octahedral configuration and connectivity are mainly of lepidocrocite-type titanate form rather than anatase, suggesting that interfering Fe³⁺ ion favors the former. It is apparent that the interfering Fe³⁺ ion behavior differs by contrast with previous work where Fe³⁺ ions may either be stably doped into the anatase/rutile phase^17,18, or a transformation from anatase to rutile was deduced¹⁰. Most importantly, the interfering ions seem to be dispatched into lepidocrocite-type titanate rather than remaining in brookite (S10).

As discussed above, interfering Fe³⁺ ions play an important, but still limited, role in the control of TiO₆ octahedral configurations and connectivity for pH ≤ 12.5 because (i) both brookite and lepidocrocite-type titanate phases always coexist even at R_Fe = 20% (S6) and (ii) the morphologies were different due to the two-phase coexistence (S7). However, if the pH value is increased slightly up to 13.5, only a small amount of interfering Fe³⁺ ions (e.g., R_Fe = 5%) is required to achieve pure-phase sodium-containing titanate (clearly indicated by XRD (S11) and EDS (S12)) without a trace of either the brookite or anatase phase. Pure-phase lepidocrocite-type titanate can always be achieved over a broad Fe³⁺ amount range of R_Fe = 5–20% (S11). Note that without interfering Fe³⁺ ions, it is impossible to form the lepidocrocite-type titanate. Further increasing the pH value, e.g. beyond pH = 14, however, is not suitable for the control of TiO₆ octahedral configurations and connectivity as the Fe³⁺ no longer behaves like an interfering ion as described above, instead forming iron-based oxide phases (S13).

Dominant microstructure evolution

Apart from the control of the connectivity and configurations of TiO₆ octahedral units to achieve lepidocrocite-type titanate nanophases, the interfering Fe³⁺ ions also lead to macro/microscopic morphological and structural evolution. The SEM/TEM images (Figure 1c) demonstrate a distinct transformation in morphology from tubular structures to sheet-like nanoparticles with increasing R_Fe. Relatively low R_Fe (e.g. 5%) advances the formation and further rearrangement of distorted and scrolled TiO₆ octahedral frameworks to form lepidocrocite-type titanate tubular structures. A typical tube possesses inner/outer diameter of around 50/120 nm and a length of up to several microns. These tubes are apparently different from those titanate nanotubes (TNTs) reported previously that were characterized by scrolling-up of 3–4 layered structures with inner/outer diameter of several/tens nanometers²⁴. The resultant tubes in this work are highly crystallized with lattice spacings of 0.362 nm and 0.669 nm, corresponding to the (110) and (020) planes of the lepidocrocite-type titanates (Figure 1c-inset). Although TNTs have been well explored under concentrated alkali conditions (e.g., 10 M NaOH)²⁴, we have not seen any report with respect to such titanate tubes to date, especially obtained with such a lower pH value.

After the intermediate stage where the lepidocrocite-type titanates show a mixture of short rod-like and round particles (e.g., R_Fe = 10%), the lepidocrocite-type titanate tubes are completely transformed into small-scale nanosheets when the R_Fe increases up to 15% (Figure 1c). These nanosheets are ~50 nm in the two-dimensional plane and highly crystallized with a d value of 0.362 nm that belongs to the (110) plane. Such a sheet-like morphology remains unchanged even when R_Fe reaches 20% (Figure 1c). We note that utilization of other interfering ions with different sizes (or charges) may greatly influence the resulting structures such as the cases of Sc³⁺ (S14) and Sm³⁺ (S15), 5% of which could form pure-phase lepidocrocite titanate with nanosheet shapes.

Microstructure identification

To examine the crystalline structures and locally TiO₆ octahedral variations, spectroscopic techniques were used. For Raman, nine vibrations (Figure 2a) for all titanates were detected around 187, 279, 387, 442, 567, 663, 703, 785 and 906 cm⁻¹, which match fairly well the structure with the orthorhombic layered lepidocrocite titanate (Figures 1a, 3b), a type of protonic acid ^19,20. Nonetheless, the lengths of the Ti–O bonds and the symmetry of the corresponding octahedra are greatly changed, as indicated by apparent Raman shifts towards lower wavenumbers at 442 and 703 cm⁻¹. The Raman band at 663 cm⁻¹, with the same origin as the A_g mode of 703 cm⁻¹, is associated with the bending of TiO₆ octahedral layers during the formation of lepidocrocite-type titanates via scrolling of Ti–O networks²⁵. With increasing R_Fe, this band gradually disappears, reflecting the transformation from titanate tubes to nanosheets. Systematic shift of Ti–O vibrations with increasing R_Fe is also reflected by FT-IR spectra (Figure 2b), e.g., a Ti–O vibration shifting from 679 to 657 cm⁻¹. While, the vibration of interlayered Ti–O–Na bonds¹⁹ at 899 cm⁻¹ does not show any shifts with increasing the R_Fe but only weakens gradually, indicating that a small amount of Fe³⁺ would be dispatched to the interlayer sites to occupy the original Na⁺ locations. EPR (Figure 2c, a detailed EPR is also see Figure S16) signal of g_eff = 4.3, a characteristic of isolated Fe³⁺ ions, is related to Fe³⁺ cations into an orthorhombic structure. Its decrease indicates that the diffusion of Fe³⁺ ions is progressed from their initial location at the oxide lattice towards the surface/interface/interlayer¹⁸. Consequently, gradual weakening of this signal also implies that a part of dopant Fe³⁺ ions was transported to the interlayered sites as those Fe³⁺ doped tetra-titanate bulks (K₂Ti₄O₉), where Fe³⁺ ions occupy the sites of interlayered K⁺ ions²⁶.

Figure 2

Spectroscopic characterizations of lepidocrocite-type titanates with varying R_Fe.

(a) Raman spectra. (b) Furrier-Transition infrared (FT-IR) spectra. (c) Electron paramagnetic resonance (EPR) spectra. The curve from top to bottom denotes the spectrum of R_Fe = 5%, 10%, 15%, 20%, respectively.

Figure 3

(a) Thermogravimetric (TG) and (b) Crystal structure of lepidocrocite-type titanate. a-inset is the differentiated TG (DTG) curve (black) of R_Fe = 15% and fitting results (colored). b-right shows the chemical coordination of TiO₆ octahedron where the numbers denote the lengths (unit: Å) of Ti-O bonds.

For layered lepidocrocite titanate, a predominant characteristic is that interlayer ions are exchangeable with a variety of inorganic cations or organic groups²⁷. One may thus assume that interlayer spaces can accommodate Na⁺ and/or H⁺ to compensate the charge neutralization. In terms of TG-DTG analysis (Figures 3a, S17), all the lepidocrocite-type titanates followed a similar three-fold dehydration process. For instance, the titanate formed at R_Fe = 15% loses 13 wt% of its total weight due to the dehydration of physisorbed water at 106°C, of chemisorbed water at 169°C and of interlayer protons at ~206°C, corresponding to weight losses of 5.4 wt%, 2.4 wt% and 5.2 wt%, respectively. Furthermore, ICP-AES measurement (Table S1) suggests the molar ratio of Fe to Ti coincides with their initial nominal ratios. With increasing R_Fe, the numbers of interlayer protons increased, accompanied by a slight decrease in the molar ratio of Na to (Fe+Ti) when R_Fe is beyond 15%. This, consistent with FT-IR and EPR, confirms that a small amount of Fe³⁺ dopants are probably dispatched into the interlayer Na⁺ sites. As a result, the structural components of the present lepidocrocite-type titanate can be expressed by the general formula , where the Na⁺ ions and/or protons (H⁺ or [H₃O]⁺) or even Fe³⁺ cations co-occupy the inter-layer regions between the main framework of the TiO₆ octahedra, as schematically shown in Figure 3b.

Mapping TiO₆ octahedral connectivity and configurations under solutions for tunable nanophases and nanostructures

To achieve a comprehensive understanding of how to control the configurations and connectivities of TiO₆ octahedra, experiments under a broad range of pH conditions in conjunction with a given R_Fe were performed, giving rise to tunable nanophases and nanostructures. When fixing R_Fe = 5%, solution reaction with a high alkalinity (pH = 14) leads to the occurrence of α-Fe₂O₃. While, low pH conditions (pH < 3.0) generally caused a significant loss of Fe³⁺ because of high solvency. A single-phase Fe³⁺ doped anatase would therefore form in the conditions of either weak alkalinity (pH = 9.0) or acidity (pH = 3.0). The pH values in between (S13) that, indeed, are the optimum pH conditions for growing Fe³⁺ doped anatase TiO₂ nanocrystals²⁸.

Once R_Fe reached 10%, a relatively high alkalinity leads to the coexistence of two (pH = 12.0) or three nano-phases (pH = 10.5) like anatase, titanate and brookite (S18). Nevertheless, the Fe-based oxide, e.g. α-Fe₂O₃, also appears even at a weak alkalinity of pH = 9.0, meaning that a high R_Fe and a relatively low pH value cause the formation of Fe-based oxides. A map outlining the nanophases and nanostructure evolution achieved is shown in Figure 4. This map provides a feasible and controllable route for the configurations and connectivity of TiO₆ octahedral units controlled via pH values and Fe³⁺ dopant concentrations.

Figure 4

Map of TiO₆ octahedral modification through simultaneously controlling over the solution pH values and doping levels of interfering Fe³⁺ ions.

Effect of the structural evolutions on the giant dielectric responses

Giant dielectric permittivities (ε′) of ~10⁴ were obtained at room temperature for all the lepidocrocite-type titanates (Figure 5a): ε′ decreases with increasing frequency and then turns flat in the higher frequency range. With increasing R_Fe, the lepidocrocite-type titanate shows a higher and frequency-independent ε′. Most strikingly, the titanate with R_Fe = 15% showed a ε′ of larger than 10⁴ over a wide frequency range up to 10⁵ Hz. Beyond R_Fe = 15%, the dielectric permittivity drops to a lower level with the fall threshold value at a relatively lower frequency. All titanates exhibit a similar Debye-like relaxation feature in ε″ curves²⁹. This relaxation peak shifts towards the higher frequencies with increasing R_Fe, reaching a maximum value of 76.2 kHz for R_Fe = 15%. Afterwards, the peak, for the lepidocrocite-type titanate with R_Fe = 20%, shifts slightly towards lower frequency. The relaxation time (τ) is also estimated to be 395, 64, 4.2 and 9.4 μs for the lepidocrocite-type titanates of R_Fe = 5–20% by using the equation according to the relaxation peak position (f_p) on ε″. These dielectric responses, with their fittings (capacitance |C| and Bode drawings in Figure S20) by taking grain boundary contributions into account, are related to structurally heterogeneous contributions from the grain and grain boundary regions³⁰ as suggested by the impedance measurements (S19), which yields grain resistivities of 64 kΩ.cm, 23 kΩ.cm, 12 kΩ.cm and 14 kΩ.cm for the lepidocrocite-type titanates with R_Fe = 5–20%, while the resistivities for the grain boundaries are all beyond 10 MΩ, at least three orders of magnitude higher than that of the corresponding grains.

Figure 5

Dielectric characterizations for Fe³⁺ doped lepidocrocite-type titanates with varying R_Fe.

(a) Frequency dependences of dielectric permittivities (real part ε′ and imaginary part ε″) measured at room temperature as well as the fitting curves (solid lines). (b) Arrhenius plots of grain conductivities (ln σ_g) versus measured temperatures (1/T). Solid lines denote the fitting results using Arrhenius law , where E_a is the activation energy, k_B the Boltzmann constant, σ₀ a constant related to the density of charge carriers and T the absolute temperature. Fitting the plots yields the E_a for lepidocrocite-type titanates with R_Fe = 5–20%. (c) Frequency dependences of normalized peaks, tanδ/tanδ_max and M″/M″_max of lepidocrocite-type titanates with R_Fe = 5% at given temperatures.

To gain insight into the underlying polarization mechanism, temperature-dependent conductivities (ln σ_g) were also recorded. Figure 5b summarizes the variations in ln σ_gvs. 1/T over the measured temperature region, which all show a well-defined linear characteristic in Arrhenius law²⁹. Fitting the ln σ_g plots gives the activation energies (E_a) of 0.81, 0.73, 0.57 and 0.64 eV for the lepidocrocite-type titanates with R_Fe = 5–20%. Obviously, the lepidocrocite-type titanate of R_Fe = 15% possesses the smallest E_a, which can be associated with the optimum dielectric permittivity that will be addressed later. Further, M″/M″_max combining with tanδ/tanδ_max, an effective approach, was employed to determine the dynamic nature of polaronic particles. It is well-established that, the peak positions of the two curves for a delocalized or long-range transport must be overlapped^31,32. Figure 5c clearly suggests a localized or short-range character for the polaronic particles as the peak position of the M″/M″_max and tanδ/tanδ_max curves is apparently not overlapped.

Discussion

Structural evolution by TiO₆ octahedral modification

TiO₂ (anatase, rutile and brookite) and lepidocrocite-type titanate are constructed of basic TiO₆ octahedral structural units. Previous work suggests that TiO₂ formation involves an intermediate titanate state followed by a deionization (e.g. Na⁺ and/or H⁺ ions) process^22,33. Cations/anions during solution chemistry greatly affect surface charges and tensions, which in turn promote releasing Na⁺/H⁺ from titanate precursor to form TiO₆ octahedra and further enable TiO₆ octahedral reconstruction in terms of edge/vertex sharing to form brookite, anatase or rutile^33,34,35. These TiO₆ octahedral units themselves are structurally distorted and further become highly polarized when interacting with cations/anions, resulting in reconfigurations and reconnections in the solution reactions.

Generally, introducing heteroatom doping will affect the surrounding solution around heteroatom-containing TiO₆ octahedra while resulting in defect states that could change the polarity of the TiO₆ octahedra. The driving forces of the TiO₆ octahedra control are closely related to the degree of tolerance of the defects for TiO₆ octahedra in different crystalline polymorphs, which is intrinsically linked to the local environment of the Ti atoms, as well as the types of introduced interfering ions.

Brookite→Anatase

The TiO₂ phase transformation from brookite to anatase promoted by the interfering Fe³⁺ ions can be ascribed to the differing structural arrangements of TiO₆ octahedra between brookite and anatase. TiO₆ octahedra in the anatase share edges along all three directions in a zigzag manner, while in the brookite, they become more complicated: TiO₆ octahedra only share edges along the c direction, but alternately share vertices and edges along both a and b directions (Figures 1a, 6). When trivalent iron ions (Fe³⁺) are substitutionally doped into TiO₂, defect states such as oxygen vacancies should be spontaneously introduced to maintain charge neutrality³⁶. Meanwhile, the octahedra become highly distorted and polarized, which results in local fluctuations in structure and energy. Thus, sharing one more O atom (i.e., sharing two O atoms totally) with the neighboring TiO₆ octahedron would be a better way to accomplish the defect compensation for the octahedra with Fe³⁺ situated, i.e., through edge-sharing connections. Once the edge-sharing connection for two octahedra happens, local fluctuations around the octahedra with Fe³⁺ situated in the solution would favor edge-sharing connections for more octahedra to develop into the three-dimensional anatase nanostructures. This statement complies well with the predictions made by density functional theory (DFT) using the generalized gradient approximation taking into account the Hubbard level (GGA+U)^37,38, where convincing evidence that the presence of Fe³⁺ could strongly reduce the formation energy of defect states for anatase is provided. As a result, the TiO₆ octahedra involving Fe³⁺ ions, in order to tolerate the defect states, will restack and turn themselves into anatase from brookite. An indirect evidence for DFT prediction is that interfering Fe³⁺ ions result in band-gap narrowing, in good agreement with experimental results (S21). The TiO₆ octahedral modification with the phase evolution from brookite to anatase in the solution seems not obeying traditional crystal chemical theory where edge-sharing connection generally leads to cation-cation repulsions and then structural destabilization³⁹. In fact, this is because the interfering Fe³⁺ ions play the key role in TiO₆ octahedra modification, which allows a better tolerance of defect states in anatase. Perhaps this is why it is so difficult to synthesize high-quality brookite. We have not found any report to date to successfully introduce dopant ions into brookite structure.

Figure 6

Schematic representations of the structural evolutions with varying the TiO₆ octahedral connectivity and configuration.

(a) brookite TiO₂. (b) lepidocrocite titanate. (c) anatase TiO₂. Two rings denote the reversible circles of phase transformation and the corresponding directions are marked by arrows. The blue dashed ring and lines denote the vertex-sharing and edge-sharing connections of TiO₆ octahedra, respectively.

Brookite→Titanate

The crystal structure of lepidocrocite-type titanate consists of two-dimensional corrugated skeleton layers of edge- and corner-sharing TiO₆ octahedra (Figures 1a, 6c). The six Ti-O bonds in an octahedron can be classified into 3 pairs, since each pair in opposite directions has same length (Figures 1a, 3b). To this, the polarity (or symmetry) of the octahedra for lepidocrocite-type titanate should be lower (higher) than that for brookite but higher (lower) than that for anatase, since in brookite the lengths of six Ti–O bonds are all different, while in anatase four of them are short and two of them are long (Figure 1a)⁹. The substitutional Fe³⁺ ions, combined with those defects induced by interfering Fe³⁺ ions, further intensify the polarity and distortions of the TiO₆ octahedra. When the concentrations of OH⁻ and Na⁺ ions in the solution are high enough, those TiO₆ octahedra would need to slightly rotate and change the lengths of the Ti–O bonds to release the local strain, because: (i) lepidocrocite-type titanate has a relatively high similarity to brookite in TiO₆ octahedral connectivity, which allows the control to be easily accomplished with only a small variation in energy; and (ii) OH⁻ and Na⁺ ions, as well as protons (H⁺ and/or [H₃O]⁺) in the solution can bond to the TiO₆ octahedra to compensate the charge neutrality and minimize the lattice relaxation, further stabilizing the octahedral skeletons. For lepidocrocite-type titanate, interlayer confined ions (Na⁺ ions and protons) are weakly bonded to the Ti-O skeletons, which are thus sufficiently flexible to be even altered and replaced²⁷. When heterovalent Fe³⁺ ions were introduced, layer-structured titanate can tune the interlayer spacing to compensate for both the defect states and host-guest mismatching that are induced by the substitution of Fe³⁺ for Ti⁴⁺, accompanied with the accommodation of more Na⁺ ions and protons (H⁺ and/or [H₃O]⁺) into the interlayers, for charge balance and TiO₆ octahedral skeleton stabilization. This is why the contents of Na⁺ ions and the hydrated groups are slightly increased with increasing R_Fe as indicated by ICP and TG. By contrast, for brookite TiO₂, due to the absence of lattice Na⁺/H⁺ ions, charge neutrality can only be compensated by those defect states (e.g. vacancies), spontaneously leading to structural instability for the Ti–O networks and thus recombination of TiO₆ octahedra^10,40.

Nanotube→Nanosheet (titanate)

Previous studies on several types of titanates indicate that a layered crystal structure is an important prerequisite for nanotube formation⁴¹. Differently, the formation of doped lepidocrocite-type titanate nanotubes here is a consequence of the interfering ions (Fe³⁺) that play a key role in TiO₆ octahedral modification. Substitution of Ti⁴⁺ with the smaller-size and lower-valent Fe³⁺ gives rise to charge imbalance as well as internal strain in the TiO₆ octahedra and even bending of Ti–O skeleton layers in order to compensate the elevated surface tension and free energy^42,43. However, when R_Fe is relatively high, the TiO₆ octahedra cannot accommodate so many Fe³⁺ counterparts and defect states. As a result, partial Fe³⁺ ions are situated at the interlayer sites of the original Na⁺ species. Since these Fe³⁺ ions are much smaller in size than that of the interlayered Na⁺ species, the spacing of the interlayer would slightly reduce, somewhat like the protonated sodium titanate after acid rinsing²⁰. At this stage, the electrical repulsive interaction between two Ti–O skeleton layers would dramatically accelerate to produce relatively high Coulomb repulsive energy, which directly results in layered structure collapse as indicated by a theoretical study⁴³. The occupational competition between the skeletal Fe³⁺ and the interlayered Fe³⁺ allows lepidocrocite-type titanate nanotubes to completely convert into the nanosheets.

Associated with the TiO₆ octahedral control, the structurally mutual evolution between brookite, anatase and lepidocrocite-type titanate can be achieved through appropriately controlling the synthetic conditions of solution chemistries. The TiO₆ octahedra in the as-prepared lepidocrocite-type titanates could be modified in the solution reactions and convert to anatase or brookite by deionizing, i.e., releasing Na⁺ (and/or doped Fe³⁺) species and protons (S22), which has been accepted as an important route for TiO₂ synthesis.³⁵ Conversely, Ti–O bonds in TiO₂, as indicated from previous work, could react with the concentrated alkali, leading to lamellar fragments of Ti–O frameworks and finally reconstruct into titanates^43,44. In summary, the mutual evolution between TiO₂ and lepidocrocite-type titanate is the result of TiO₆ octahedral modification, which can be well controlled in solution chemistries, as schematically demonstrated in Figure 6.

TiO₆ octahedral modification for optimum giant dielectric response

Microstructure- and morphology-related physical and chemical properties of solids are of significant importance in fabricating functional nanostructures⁴⁵. The dielectric properties of nano-based materials could be directly related to the microstructure of the solid, i.e. the nanoscale bulk and interfaces, where the solid can be defective or even polarized as a result of surface defect dipoles and/or surface charges, which are expected to be even larger when heteroatoms are involved. Earlier structural analysis identified that substitutional Fe³⁺ ions greatly influence the local environment and polarity of TiO₆ octahedra thereby altering the macroscopic morphology. Since Fe³⁺ is slightly smaller in both size and valence than Ti⁴⁺, substitution of Fe³⁺ for Ti⁴⁺ would force local shrinkage of the lattice, resulting in local strain across a few atomic distances. Meanwhile, local disorder/distortion surrounding the Fe³⁺ will also appear due to dopant-host mismatching like many other doping cases^46,47. That is, introducing Fe³⁺ could cause a local charge imbalance, leading to a polaronic-like distortion³¹. As a result, defect dipoles induced by e.g. ion-defect pairs, local defects or distortion would form to act as the available polaronic species, making a contribution to the high dielectric permittivity observed^8,30,48. These defect dipoles, with short-range behaviour, are unable to catch up with the oscillation of the externally applied electric field, causing a quick decrease in ε′ at relatively high frequencies. Apparently, the number of these defect dipoles is proportional to R_Fe and its transport nature is determined by R_Fe, i.e., intrinsically linked to the TiO₆ octahedral modification and microstructural nature.

It is well established that the transformation from lepidocrocite-type titanate nanotubes to nanosheets is a result of TiO₆ octahedral control caused by the incorporation of interfering Fe³⁺ ions. Here, R_Fe has two impacts: one is an increase in the number of defect dipoles and the other is that hydrated groups (associated with protons, H⁺ and/or [H₃O]⁺, etc.) and heavy Fe³⁺ instead of Na⁺ ions are partially dispatched into the interlayers. Our previous study indicates that inter-layered Na⁺ ions in sodium titanate nanotubes can easily migrate to induce charges at the interfaces and the conductivity of sodium-rich lepidocrocite-type titanate is one or two orders of magnitude higher than that of the protonated lepidocrocite-type titanate with more hydrated groups⁴⁴. Thus, inter-layered Na⁺ ions in Fe³⁺ doped lepidocrocite-type titanates would not be expected to hinder the polaronic transport. Comparatively, hydrated groups are strongly bonded to TiO₆ octahedral skeleton layers and meanwhile Fe³⁺ is too heavy to migrate, both of which thus act as a giant barrier to obstruct the polaronic transport⁴⁹. Consequently, the competition of the above two aspects gives rise to the shortest τ, smallest grain σ_g and E_a, responsible for the optimum dielectric property. It should be noted that the giant dielectric response is not related to those space charges induced by the electronic hopping from possibly delocalized 3d¹ of Ti³⁺ as there is no trace of Ti³⁺ detected by EPR (Figure 2c) and XPS (S23).

The primary goal of this work is to establish the structure/property correlation via atomic-scale control over the connectivity and configurations of TiO₆ octahedra through solution chemistry. Further, when taking into consideration the fact that nearly all of the metal-oxide materials obtained are constructed by metal-oxygen polyhedral (MO_n) units, one can envisage atomic-scale reaction mechanisms for synthesizing metal-oxide nanostructures, which is expected to remain an important and exciting subject for future studies, a judicious choice that enables simple bottom-up fabrication of structurally more complex metal-oxides or multifunctional materials and devices.

Methods

Sample Preparation

The synthesis of titanium-based oxide nanostructures was performed by solution chemistry using the following procedure: 0.04 mol TiOSO₄ (Ourchem, 99%) was dissolved into 100 mL deionized water to form solution (I). 0.025 mol NaOH (Sinoreagent, 99.9%) was dissolved into 100 mL deionized water to form solution (II). Subsequently, solution (I) was slowly added into solution (II) while stirring. The resultant white suspension was thoroughly filtered and then dispersed in water to form a precursor solution through magnetic-ultrasonic stirring for 12 h. 2 M NaOH or H₂SO₄ (Sinoreagent, 99.9%) solution was then added to adjust the pH value. The resultant precursor solutions were then sealed in Teflon-lined stainless steel autoclaves and reacted at 220°C for 48 h for precipitation and crystallisation. The reaction products were filtered, washed with distilled water and dried in air to get the final samples.

Using a similar synthesis procedure, interfering Fe³⁺ ions (also the Sc³⁺ and Sm³⁺ ions for investigating the effects from different sizes of interfering ions), were then incorporated into the titanium-based oxide nanostructures to control the configurations and connectivity of the TiO₆ octahedral units in an attempt to control the microstructures and properties of the resultant Ti-based oxides. The Fe³⁺-doped titanium-based nanostructures were achieved via the dissolution of the appropriate relative amount of TiOSO₄ and Fe₂(SO₄)₃ (Sinoreagent, 99.9%) into 100 mL of deionized water to give a total mole amount of 0.04 with mole ratios R_Fe = Fe/(Fe + Ti) with values of 5%, 10%, 15% and 20%, respectively. The remaining synthesis procedures were the same as outlined above for the un-doped titanium-based nanostructures. The preparation procedure of titanium-based nanostructures with doping other interfering ions i.e. Sc³⁺ and Sm³⁺ is similar to the case of Fe³⁺.

Sample Characterizations

The chemical compositions of the resultant samples were determined by inductively coupled plasma-atomic emission spectrometry (ICP-AES). The phase purity and crystallinity of the samples were characterised by X-ray diffraction (XRD, Rigaku Dmax2500, Cu Kα radiation, λ = 0.15418 nm). Ni powders were chosen as an internal standard for the determination of the peak positions. The average crystallite size, D, was calculated via the Scherrer formula, D = 0.9λ/(βcosθ), where λ is the X-ray wavelength employed, θ is the diffraction angle and β is defined as the half width after subtracting instrumental broadening. Structural refinements on the XRD patterns were performed using the Rietveld method. The particle size, morphology and microstructures of the samples were characterized using field emission scanning electron microscopy (SEM, JEOL JSM-6700), transmission electron microscopy (TEM, JEOL JEM-2010). Energy-dispersive X-ray spectroscopy (EDS) data were collected on INCA Energy 450 EDXA system.

Optical diffuse reflectance spectra of the samples were collected at room temperature via a Lambda 900 UV-vis spectrometer. Raman spectra of the final products were obtained on a UV-vis Raman System (Renishaw 1000) with an excitation wavelength of 532 nm. Their infrared optical spectra were also collected by a Perkin-Elmer IR spectrophotometer. Thermal analysis of the samples was performed by thermogravimetric (TG) analysis (Netzsch STA449C). The valence and defect states were studied by X-ray photoelectron spectroscopy (XPS, ESCA-LAB MKII spectrometer) and electron paramagnetic resonance (EPR, Bruker BioSpin EPR) at a microwave frequency of 9.86 GHz.

Electrical and dielectric measurements

The samples were also hot-pressed at a pressure of 12 MPa at 200°C for 30 min to make pellets with a diameter/thickness of 12/1.5 mm. Both sides of the pellets were then coated with Ag-based conductive electrodes and dried under infrared radiation. Alternative current (AC) impedance measurements were carried out using a precision LCR meter (Agilent 4294A) over a frequency (f) range from 40 Hz to 5 MHz at selected temperatures to obtain the complex impedance , where Z′(ω) and Z″ (ω) are real and imaginary parts, respectively. The complex dielectric permittivity ε*(ω) was then extracted based on the relation , where ω(= 2πf) is the angular frequency and C₀ = ε₀S/L represents the vacuum capacitance of a capacitor with an area of S and a thickness of L. These impedance parameters were also modeled using the least-squares refinement program EQUIVCRT to obtain an equivalent circuit through which the equivalent grain and grain boundary conductivity can be deduced.