Xiaodong Liu

Demie Kepaptsoglou

Zhaohe Gao

Andrew Thomas

Krishnendu Maji

Emmanuel Guilmeau

Feridoon Azough

Quentin M Ramasse

Robert Freer

Controlling the Thermoelectric Properties of Nb-Doped TiO2 Ceramics through Engineering Defect Structures

Keywords: Thermoelectric, Nb doping, Magnéli, oxygen vacancies, twin boundaries

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Thermoelectric (TE) materials are able to directly convert heat energy into electrical energy, offering routes to contribute to energy sustainability and global environmental changes. The evaluation of a materials' TE performance is usually based on the dimensionless figure of merit, 𝑍𝑇 = ! ! " # 𝑇 , where 𝑆 is the Seebeck coefficient, 𝜎 is electrical conductivity, 𝜅 is thermal conductivity and T is the absolute temperature. To improve the TE performance and increase ZT of a candidate material, the power factor (𝑆 $ 𝜎) needs to be enhanced and/or thermal conductivity needs to be reduced, but coupling effects between the TE parameters makes this challenging.

Considerable efforts have been made to maximize ZT values; however, current commercial TE materials are predominantly based on rare, expensive and toxic elements, which hinders worldwide exploitation. Consequently, there is a growing demand for readily available, low cost, environmentally-friendly thermoelectric materials.

Oxide materials based on earth-abundant elements exhibit exceptional chemical and thermal stability at high temperatures under oxidizing environments; they show considerable potential as candidates for high temperature TE applications [START_REF] Backhaus-Ricoult | Semiconducting Large Bandgap Oxides as Potential Thermoelectric Materials for High-Temperature Power Generation?[END_REF][START_REF] Ohtaki | Recent Aspects of Oxide Thermoelectric Materials for Power Generation from Mid-to-High Temperature Heat Source[END_REF][START_REF] Koumoto | Oxide Thermoelectric Materials: A Nanostructuring Approach[END_REF][START_REF] Koumoto | Thermoelectric Ceramics for Energy Harvesting[END_REF] . A wide range of oxide thermoelectrics have been investigated; cobaltites (including NaCo 2 O 4 [START_REF] Terasaki | Large Thermoelectric Power in NaCo 2 O 4 Single Crystals[END_REF] , Ca 3 Co 4 O 9 [START_REF] Yu | Enhancing the Thermoelectric Performance of Calcium Cobaltite Ceramics by Tuning Composition and Processing[END_REF] , Ca 2 Co 2 O 5 [START_REF] Funahashi | Oxide Single Crystal with High Thermoelectric Performance in Air[END_REF] and Bi 2 Sr 2 Co 2 O y 8 ) are the most popular p-type TE materials. Amongst the corresponding n-type TE materials, SrTiO 3 [START_REF] Ekren | Enhancing the thermoelectric power factor of Sr 0.9 Nd 0.1 TiO 3 through control of the nanostructure and microstructure[END_REF] , CaMnO 3 10 , donor doped TiO 2 [START_REF] Xu | Doping Effects on Internally Coupled Seebeck Coefficient, Electrical, and Thermal Conductivities in Aluminum-Doped TiO 2[END_REF][START_REF] Zaitsev | Preparation and Characterization of Nanocrystalline Doped TiO 2[END_REF] , Magnéli phases (Ti n O 2n-1 [START_REF] Liu | Manipulation of Planar Oxygen Defect Arrangements in Multifunctional Magnèli Titanium Oxide Hybrid Systems: From Energy Conversion to Water Treatment[END_REF][START_REF] Portehault | Facile General Route toward Tunable Magnéli Nanostructures and Their Use as Thermoelectric Metal Oxide/Carbon Nanocomposites[END_REF] and Nb 12 O 29 [START_REF] Backhaus-Ricoult | Semiconducting Large Bandgap Oxides as Potential Thermoelectric Materials for High-Temperature Power Generation?[END_REF] ), In 2 O 3 [START_REF] Koumoto | Thermoelectric Ceramics for Energy Harvesting[END_REF][START_REF] Bérardan | In 2 O 3 :Ge, a Promising n-Type Thermoelectric Oxide Composite[END_REF] and tungsten bronze structured oxides (Ba 5.19 Nd 8.54 Ti 18 O 54 [START_REF] Azough | Ba 6-3x Nd 8+2x Ti 18 O 54 Tungsten Bronze: A New High-Temperature n-Type Oxide Thermoelectric[END_REF] and Ba 6 Ti 2 Nb 8 O 30 [START_REF] Jiang | The Structure and Thermoelectric Properties of Tungsten Bronze Ba 6 Ti 2 Nb 8 O 30[END_REF] ) show much promise. TiO 2 -based materials have been widely investigated for solar cell [START_REF] Tang | Incorporation of Graphenes in Nanostructured TiO 2 Films via Molecular Grafting for Dye-Sensitized Solar Cell Application[END_REF] , photovoltaic [START_REF] Wei | Design and Synthesis of TiO 2 Nanorod Assemblies and Their Application for Photovoltaic Devices[END_REF] and photocatalytic applications [START_REF] Williams | TiO 2 -Graphene Nanocomposites. UV-Assisted Photocatalytic Reduction of Graphene Oxide[END_REF] . For TE applications, rutile structured, TiO 2 ceramics are attractive because of the low cost of the raw materials and high temperature stability. However, the key obstacle to the exploitation of TiO 2 ceramics is their modest thermoelectric performance. In particular, the relatively high thermal conductivity (6-8 W m -1 K -1 for single crystal rutile [START_REF] Touloukian | Thermophysical Properties of Matter -The TPRC Data Series[END_REF] and 3-6 W m -1 K -1 for polycrystalline rutile [START_REF] Nam | A Gigantically Increased Ratio of Electrical to Thermal Conductivity and Synergistically Enhanced Thermoelectric Properties in Interface-Controlled TiO 2 -RGO Nanocomposites[END_REF] ) and low electrical conductivity limit the ZT value, to typically less than 0.001 at 1000 K [START_REF] Nam | A Gigantically Increased Ratio of Electrical to Thermal Conductivity and Synergistically Enhanced Thermoelectric Properties in Interface-Controlled TiO 2 -RGO Nanocomposites[END_REF] . Many strategies have been developed to improve the TE performance of TiO 2 -based ceramics, with donor doping the most common. Donors such as Nb, Al and Ta [START_REF] Xu | Doping Effects on Internally Coupled Seebeck Coefficient, Electrical, and Thermal Conductivities in Aluminum-Doped TiO 2[END_REF][START_REF] Zaitsev | Preparation and Characterization of Nanocrystalline Doped TiO 2[END_REF][START_REF] Backhaus-Ricoult | Levers for Thermoelectric Properties in Titania-Based Ceramics[END_REF] can increase the carrier concentration and mobility through reducing carrier localization; the mass/radii differences between donors and matrix can also be useful to enhance phonon scattering and thus reduce thermal conductivity. The effects of introducing high densities of oxygen vacancies and Magnéli phases have also been investigated, since the resulting crystallographic shear planes can act as phonon scattering centers, whilst not affecting carrier transport [START_REF] Liu | Manipulation of Planar Oxygen Defect Arrangements in Multifunctional Magnèli Titanium Oxide Hybrid Systems: From Energy Conversion to Water Treatment[END_REF][START_REF] Portehault | Facile General Route toward Tunable Magnéli Nanostructures and Their Use as Thermoelectric Metal Oxide/Carbon Nanocomposites[END_REF][START_REF] Harada | Thermoelectric Properties and Crystallographic Shear Structures in Titanium Oxides of the Magǹeli Phases[END_REF][START_REF] Fan | Preparation of Monophasic Titanium Sub-Oxides of Magnéli Phase with Enhanced Thermoelectric Performance[END_REF][START_REF] Mikami | Thermoelectric Properties of Nitrogen-Doped TiO 2-x Compounds[END_REF] . A variety of complex synthesis routes have been employed to develop nanostructures, including urea combustion [START_REF] Liu | Chemical Tuning of TiO 2 Nanoparticles and Sintered Compacts for Enhanced Thermoelectric Properties[END_REF] , sol-gel and high pressure and high temperature (HPHT) methods [START_REF] Liu | High-Thermoelectric Performance of TiO 2-x Fabricated under High Pressure at High Temperatures[END_REF] . Nevertheless, such complex synthesis methods can be expensive and are not ideal for large-scale application.

Guided by earlier work and using donor doping and a reducing atmosphere to control the type and concentration of defects, we present a facile, economical method to synthesize, in a single sintering step, n-type reduced, Nb-doped rutile structured TiO 2 with enhanced performance. We provide atom level details of Magnéli phases and shear structures. From a combination of dopants, oxygen vacancies and planar defects, the thermal conductivity was minimized. The charge transport properties were improved by a factor of two compared to pure rutile. We show the significant enhancement of ZT was a direct consequence of controlling the microstructure and defect structures of the material.

EXPERIMENTAL METHODS

Nb-doped TiO 2 thermoelectric ceramic samples were prepared by conventional mixed oxide route. The TiO 2 powder (Sigma Aldrich, >99.99%) and Nb 2 O 5 powder (Sigma Aldrich, >99.99%) were vibration milled with Propan-2-ol (Fisher Scientific®) and YSZ balls (Pi-kem) for 24 hours. The mixtures were dried in air at 363 K for 24 hours then calcined in air in a covered alumina crucible at 1373 K for 4 hours. To lower the sintering temperature and increase sample density, 0.81wt% manganese (II) carbonate (Sigma Aldrich, >99.99%) powder was added to the calcined powders and then re-milled and dried once more. The final powder was pressed in a 20 mm diameter disk-shaped die under a pressure of 50 MPa. The cylindrical pellets were packed in, and surrounded by, carbon flakes (Sigma Aldrich, >99.99%) in a 30 mm diameter alumina crucible with alumina lid. The assembly was sintered in a box furnace at 1523 K for 8 hours. The carbon flakes created a reducing atmosphere; the large volume of flakes to ceramic sample ensured that no more than 10% of flakes were consumed during each sintering run. The sample formulations and codes are listed in Table 1. intensity reduced with the increasing Nb content. These peaks do not match existing phases in the standard database; their origin will be discussed in the TEM section. However, in the spectra for TN30, TN45 and TN60 (samples with higher Nb contents), there is almost no trace of these unknown peaks (Figure 1b). Refined lattice parameters for the main rutile phase (Table 2 and (R Nb 5+ =0.64 Å) substituted for the smaller Ti 4+ (R Ti 4+ =0.605 Å) ions [START_REF] Shannon | Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides[END_REF] . average grain sizes varied between 7-13 μm, with a minimum for mid-range compositions of TN15 and TN30. (Figure S3 and Figure S4 show EBSD band contrast maps and grain size distributions). For samples TN5, TN10 and TN15, twin boundaries (marked with yellow dash lines) are present inside the grains, with rotation angles of approximately ~55° (TN5 -Figure 2b) and ~66° (TN10 -Figure 2d) respectively. A high density of wavy-shaped, domain structures are distributed inside the grains and on both sides of the twin boundaries; the dark stripes alternate with bright stripes, with intervals from approximately 170 nm to 300 nm (Figure 2b,d,f). The twin boundaries and domain structures were interlaced, forming a twiningdomain net-shape, complex structure. For samples TN30, TN45 and TN60, such sub-grain features did not develop but the concentration of pores increased. Some isolated micro-cracks occurred (marked with red arrows in Figure 2a -i), but the samples still exhibited high mechanical strength. In Nb is uniformly distributed inside the grains (Figure S6). The small dark areas represent Mnrich secondary phases at the grain boundaries; the different levels of darkness are due to different grain orientations and not compositional differences. Twins can be frequently be observed in TN60 samples. "coherent twin boundaries" (CTB), as there is no lattice misfit between the neighboring twin domains. Figure 7f represent twins with double CTBs; furthermore, we observed triple CTBs and even six CTBs inside the grains along the <111> R zone axis (Figure 7h and7i). In addition, the TB can also co-exist with defects (Figure 7g). Since the intervals of these CTBs vary from 1-7 nm, which is about 2-10 times the size of the phonon mean free path for TiO 2 (0.8 nm), the twin boundaries can act also as phonon scattering centers. Earlier studies [START_REF] Yu | Simultaneous Optimization of Electrical and Thermal Transport Properties of Bi 0[END_REF][START_REF] Mao | High Thermoelectric Power Factor in Cu-Ni Alloy Originate from Potential Barrier Scattering of Twin Boundaries[END_REF] demonstrated that twin boundaries can effectively scatter low energy carriers, without scattering the high energy carriers, so as to increase the Seebeck coefficient. states (TiO 2 and Ti 2 O 3 spectra have different peak shapes) [START_REF] Jackman | Photoelectron Spectroscopy Study of Stoichiometric and Reduced Anatase TiO 2 (101) Surfaces: The Effect of Subsurface Defects on Water Adsorption at near-Ambient Pressures[END_REF][START_REF] Kurtz | UHV-Cleaved Single Crystal Ti 2 O 3 (101̄2) by UPS and XPS[END_REF] . For all samples (TN5 to TN60), the [Ti 3+ ] content increases with increasing Nb doping (from 17.6% to 24.1%) (Table 3), indicating that higher Nb doping promotes the reduction process from Ti 4+ to Ti 3+ .

Table 1. Sample compositions and codes

According to Di Valentin et al. [START_REF] Di Valentin | Reduced and N-Type Doped TiO 2 : Nature of Ti 3+ Species[END_REF] , there are four types, or sources, of Ti 3+ species in TiO 2 , namely Ti 3+ introduced by F-or Nb-doping, Ti 3+ -OH associated with H-doping, Ti 3+ introduced with oxygen vacancies, and interstitial Ti 3+ . Two main Ti 3+ species can be generated in our Nbdoped TiO 2 ceramics. The first is due to Nb doping; the Ti 3+ ions can be generated by charge compensation (denoted as Ti 3+ (d)). The other is under-coordinated Ti 3+ species associated with oxygen vacancies generated by the reducing atmosphere treatment (denoted as Ti 3+ (v)). The two Ti 3+ species can be closely associated with the electrical conductivity by localized electrons, and will be discussed later in the transport property section.

For Nb3d spectra, the spin orbital splitting (∆ s.o. ) of Nb 3d 5/2 and 3d 3/2 core levels is ~2.6 eV [START_REF] Atashbar | XPS Study of Nb-Doped Oxygen Sensing TiO 2 Thin Films Prepared by Sol-Gel Method[END_REF] .

Asymmetry of the Nb 3d peaks also indicates the presence of both Nb 5+ and Nb 4+ states [START_REF] Darlinski | Angle-Resolved XPS Studies of Oxides at NbN, NbC, and Nb Surfaces[END_REF] . With increasing Nb content, the peak positions in all spectra are displaced to lower binding energy by The formula Ti shown as a function of temperature in Figure 9. The electrical conductivity is significantly higher than for pure rutile (additional reference sample, this study), and increases with increasing temperature for all samples (Figure 9a); the rate of increase of electrical conductivity at a specific temperature increases with increasing Nb content. Near room temperature (323 K), the electrical conductivity initially increased with Nb doping, achieving a maximum for TN30, but then decreases with increasing Nb content. Hall Effect measurements undertaken at room temperature provide carrier concentrations and mobility values (Table 5). The carrier concentrations follow a similar trend to electrical conductivity, initially increasing with Nb content and then decreasing dramatically. In contrast, carrier mobility decreases from lower content samples (TN5 -TN15) to higher Nb content samples (TN30-TN60); this can be attributed to the combination of intrinsic effects (doping and point defects) and also extrinsic effects (grain and other boundaries). However, at elevated temperatures, the electrical conductivity increases continuously with increasing Nb content. The trends for electrical conductivity at different temperatures can be explained in terms of the Ti 3+ species. Near room temperature, the electrical conductivity of lower Nb content samples (TN5-TN15) can be attributed to the additional electrons introduced by Nb doping (related to Ti 3+ (d)). However, from XPS (Table 4), the concentration of oxygen vacancies (related to Ti 3+ (v)) starts to decrease from TN30. Recent studies [START_REF] Cho | First-Principles Study of Point Defects in Rutile TiO 2-x[END_REF][START_REF] Perevalov | Electronic Structure of TiO 2 Rutile with Oxygen Vacancies: Ab Initio Simulations and Comparison with the Experiment[END_REF] suggest that defect states induced by oxygen vacancies have strong localization effect on electrons. As the effect reduces (at TN30), the electrical conductivity and carrier concentration are maximized at room temperature. For samples with even higher Nb content (TN45, TN60), the electrical conductivity decreased steadily. The reciprocal Arrhenius plots indicate that the activation energy for conduction is increased for higher Nb content samples (Figure S17). According to earlier studies [START_REF] Frederikse | Recent Studies on Rutile (TiO 2 )[END_REF][START_REF] Chester | Electron Spin Resonance in Semiconducting Rutile[END_REF] for Nbdoped rutile TiO 2 , the carriers tend to be self-trapped at Nb 4+ sites at low temperatures. With increasing temperature, the carriers are partially thermally activated to Ti sites and form Ti 3+ , and are eventually excited to the conduction band when enough energy is provided. Therefore, in the low temperature region, for higher Nb content samples, the higher content of Nb 4+ and Ti 3+

(Figure 8b) localizes more carriers, thereby significantly increasing the thermal activation energy. Furthermore, the shift of donor level towards the valence band with increasing Nb content has been confirmed by valence-band photoemission experiments [START_REF] Morris | Photoemission and STM Study of the Electronic Structure of Nb-Doped TiO 2[END_REF] ; the peak can further coalesce with the 4d peak of NbO 2 , which supports the model that activation energy increases with higher Nb doping.

At elevated temperatures, the changes in electrical conductivity can be attributed to different localization effects produced by the reduced cations. Whilst electrons are 'self-trapped' on cation sites at low temperatures, the additional energy available at higher temperatures dominates processes, increasing carrier concentration and electrical conductivity.

The negative Seebeck coefficients (Figure 9b) confirm n-type behavior for the Nb-doped TiO 2 ceramics. With increasing temperature (from 323 K to 873 K) the absolute Seebeck coefficients decrease for all samples, reaching a minimum value of approximately ~230 μV K -1 for TN60 at 873 K, which is still higher than for many similar compositions [START_REF] Liu | Bottom-up Assembly to Ag Nanoparticles Embedded Nb-Doped TiO 2 Nanobulks with Improved n-Type Thermoelectric Properties[END_REF][START_REF] Yuan | Investigation of the Thermoelectric Properties of Reduced Nb-Doped TiO 2-δ Ceramics[END_REF][START_REF] Yuan | Thermoelectric Properties of Nb-Doped TiO 2-δ Ceramics Reduced at Elevated Temperature[END_REF] . However, the Seebeck coefficient of -330 μV K -1 for TN30, obtained near room temperature (323 K), is the highest value amongst the samples. Indeed, at elevated temperatures, the Seebeck coefficients for TN30 samples are still high, and second only to TN5. As carrier concentration increases with Nb content, there is the expected decrease in mobility (Table 5) as noted previously.

Through the combination of the highest Seebeck coefficients and electrical conductivity near room temperature, TN30 exhibits the highest power factor (470 μW m -1 K -2 ) near room temperature (Figure 9c); this is the highest value reported for TiO 2 -based materials without the use of SPS processing. For all samples, except TN30, the power factor increases with increasing By the Wiedemann-Franz approximation, (ĸ total = ĸ lattice +ĸ electronic = ĸ lattice + LσT), the electronic and lattice thermal conductivity were determined as function of temperature (Figure 10b); L is the Lorenz factor (L = 2.44 × 10 -8 J 2 K -2 C -2 ), σ is electrical conductivity and T is temperature.

The electronic components increase with increasing Nb content, reaching a maximum fraction of 7.7% of ĸ total at 873 K for TN60. For all samples, lattice thermal conductivity is dominant and the changes in ĸ lattice as a function of both temperature and Nb content are consistent with those for ĸ total .

The lattice thermal conductivity can be described by the Debye-Callaway model:

𝜅 & = ' " $( ! ) ' ' " * + ( , 𝑇 , ∫ -# . $ / % (/ % 1%) ! dx 3 & * ⁄ 5 (1)
where 𝐾 6 is the Boltzmann constant, υ is sound velocity, ℏ is Planck's constant, 𝜃 7 is the Debye temperature, 𝑥 = ℏ9 ' " * is a dimensionless quantity, 𝜔 is the phonon frequency and 𝜏 : is the overall relaxation time, which depends upon the phonon scattering processes operating [START_REF] Ren | Contribution of Point Defects and Nano-Grains to Thermal Transport Behaviours of Oxide-Based Thermoelectrics[END_REF] (Equation S1 and S2). Compared to pure TiO 2 , the enhancement of phonon scattering in our material is mainly controlled by boundary scattering (grain boundaries, twin boundaries, anti-and mass fluctuations, increasing the disorder scattering parameter, promoting phonon scattering and reducing the overall relaxation time, and thus reducing lattice thermal conductivity. For higher Nb contents (TN30-TN60), the concentration of oxygen vacancies decreases with increasing Nb content (Table 4); therefore, the contribution of oxygen vacancies to the overall phonon scattering is reduced. However, lattice thermal conductivity decreases with increasing Nb content, which can be explained by the higher levels of point-defect scattering produced by the higher Nb doping.

Planar defect structures (twin boundaries and anti-phase boundaries) can also help to reduce lattice thermal conductivity by enhancing boundary scattering. It was noted that twin boundaries (TBs) are present inside the primary grains (Figure 7 and Figure S9), and that TBs occur more frequently in samples with higher Nb content (e.g. TN60). The interval between the multiple TBs varies from 1 nm to 10 nm, which is about 1.5 ~ 15 times the phonon mean free path for rutile TiO 2 . Again, these sizes are comparable with the phonon mean free path, implying that the TBs can effectively contribute to phonon scattering and thus help to reduce lattice thermal conductivity. Furthermore, a high density of dislocation was observed in TN60, which can similarly help to reduce thermal conductivity through phonon scattering [START_REF] Xin | Mg Vacancy and Dislocation Strains as Strong Phonon Scatterers in Mg 2 Si 1-x Sb x Thermoelectric Materials[END_REF][START_REF] Chen | Lattice Dislocations Enhancing Thermoelectric PbTe in Addition to Band Convergence[END_REF] . Furthermore, the maximum ZT values achieved in this study are comparable with Magnéli phase thermoelectric species [START_REF] Liu | Manipulation of Planar Oxygen Defect Arrangements in Multifunctional Magnèli Titanium Oxide Hybrid Systems: From Energy Conversion to Water Treatment[END_REF][START_REF] Portehault | Facile General Route toward Tunable Magnéli Nanostructures and Their Use as Thermoelectric Metal Oxide/Carbon Nanocomposites[END_REF][START_REF] Harada | Thermoelectric Properties and Crystallographic Shear Structures in Titanium Oxides of the Magǹeli Phases[END_REF] . Although marginally higher ZT values have been obtained for TiO 2 based thermoelectric ceramics, through a combination of more complex processing routes and co-doping, our approach is competitive and offers many advantages, not only because of the much simpler, easier and cheaper than alternative processing methods, but also because it provides a route and the potential for further enhancement of ZT values. With increasing Nb content, the electrical conductivity and power factor increased significantly, except for TN30; the highest power factor of 530 μW m -1 K -2 was obtained for TN60 at 823 K. At room temperature TN30 exhibited a very high-power factor of 470 μW m -1 K - 2 , the highest value reported for TiO 2 -based materials without the use of SPS processing.

Thermoelectric figure of merit (ZT

Through the use of Nb doping and a reducing atmosphere the samples contained considerable numbers of point defects and planar defects which contributed to phonon scattering, helping to reduce lattice thermal conductivity to a minimum of 2.6 W m -1 K -1 . Consequently, there was a 50% enhancement in the ZT value at room temperature and a maximum value of 0.17

ASSOCIATED CONTENT

Supporting Information

The following supporting information is available free of charge. (PDF)

Formulation: ( 1 5

 15 -x)TiO 2 -xNb 2 O Sample was analyzed using a Philips X'Pert X-ray diffractometer® (XRD) with Cu Kα radiation (λ = 1.540598 Å). Diffraction patterns were collected from 0° to 100°, with 0.033° step size. The lattice parameters were refined using Bruker TOPAS software. The microstructures were examined using a TESCAN MIRA LC FEG scanning electron microscope (SEM) equipped with an Oxford Instrument SDD energy dispersive X-ray (EDS) detector and an Oxford Instrument Symmetry electron backscattered diffraction (EBSD) detector.Specimens for TEM analysis were prepared by standard crushing and Focused Ion Beam (FIB) techniques. For the crushing methods, fragments were ground in an agate mortar and pestle dispersed in chloroform/ Propan-2-ol and dropped onto a holey carbon grid. FIB specimens were prepared using an FEI FEG Quanta 3D Dual Beam Focused Ion Beam system equipped with both FEG SEM column and a Ga ion source FIB column. Phase identification employed a 200 kV FEI Tecnai 20 analytical LaB6 TEM. The nano-scale structures were identified using high-resolution transmission electron microscopy (HRTEM) and scanning transmission electron microscopy (STEM), which were conducted with a 300 kV FEI Tecnai F30 analytical FEG TEM and a 200 kV Thermo Fisher Talos F200X FEG TEM equipped with a HAADF STEM detector and a Super-X EDXS detector. Atomically-resolved STEM images were acquired using an aberration-corrected dedicated scanning transmission electron microscope (100 kV Nion UltraSTEM100) equipped with high, middle, low-angle annular dark-field (HAADF, MAADF and LAADF) and an annular bright-field (ABF) STEM detectors. Crystal structure models, SAED pattern simulations and PXRD simulations were performed using CrystalMaker software.

Figure S2 )

 S2 Figure S2) increased with increasing Nb content, reflecting the expansion of the unit cell as Nb 5+

Figure 1 .

 1 Figure 1. (a) XRD patterns for the sintered samples; (b): Enlarged view of the region from 23° to

Figure 2 ,

 2 there is evidence of a secondary phase, bright in color at low levels of Nb, growing darker with increasing Nb content, segregating to the grain boundaries (circled blue in Figure2a -i). EDS line analyses of the secondary phases (FigureS5) indicated they were enriched in Mn and contain almost no Nb, being very close to a mixture of TiO 2 and MnTiO 3 . This may have originated from a low melting point eutectic between MnTiO 3 and TiO 2 , promoting a liquid phase and sintering at a lower temperature[START_REF] Liu | High-Thermoelectric Performance of TiO 2-x Fabricated under High Pressure at High Temperatures[END_REF] . BSE imaging and EDS analysis (FigureS6and FigureS7) showed no Ti or O segregation, but clear evidence of Nb segregation in samples with lower Nb contents (TN5-TN15); the darker grains are enriched with Nb while the lighter grains contain less Nb. High magnification EDS maps (FigureS7) for samples with lower Nb contents samples (e.g. TN10) indicated that the sub-grain features show the preference to grow in the lighter colored grains which have lower Nb content. By contrast, Nb is uniformly distributed inside the sub-grain domain structures, indicating that the sub-grain features do not affect the Nb distribution inside the grains. In samples with higher Nb contents (TN30-TN60),

Figure 2 .

 2 Figure 2. SEM Back-Scattered Electron (BSE) images of sintered TiO 2 samples: (a) TN5; (b)

Figure 3 .

 3 Figure 3. Experimental TEM selected area electron diffraction patterns for Magnéli phases along

Figure 4 .

 4 Figure 4. TEM analysis of TN15 sample: (a) TEM Bright field image of TN15 sample showing

Figure 5 .

 5 Figure 5. STEM analysis of the crystallographic shear structure in TN15 sample: (a) HAADF;

Figure 6 .

 6 Figure 6. STEM analysis of TN60 samples (averaged by non-rigid registration from a stack of

  Figure 7a, showing typical diffraction patterns for a twin structure[START_REF] Hrkac | Atomic Structure and Crystallography of Joints in SnO 2 Nanowire Networks[END_REF][START_REF] Zheng | Growth Twins in Nanocrystalline SnO 2 Thin Films by High-Resolution Transmission Electron Microscopy[END_REF][START_REF] Suzuki | High-Resolution Electron Microscopy of Lattice Defects in TiO 2 and SnO 2[END_REF][START_REF] Shen | On the Transformation Pathways of Alpha-PbO 2 -Type TiO 2 at the Twin Boundary of Rutile Bicrystals and the Origin of Rutile Bicrystals[END_REF] . The blue circles mark the

Figure 7 . 8 ;

 78 Figure 7. TEM analysis of TN60 samples: (a) TEM Bright field image of TN60 sample indicates

  (1-x) Nb x O (2-y) can be used to describe the level of Nb doping and oxygen vacancies. The oxygen deficiency (y) arises through Nb doping and the use of the reducing atmosphere which generates oxygen vacancies during sintering. By charge compensation, the concentrations of [Ti 3+ ]/[Ti 4+ ] and [Nb 5+ /Nb 4+ ] can be defined in terms of y for different levels of Nb (Table4). For lower Nb content (TN5 to TN15), there is no significant change in y with increasing Nb content (values of 0.081to 0.083), indicating similar concentrations of oxygen vacancies, which helps to explain the very similar microstructures (TN5 to TN15). Therefore, the effective formula for such samples (TN5 to TN15) is approximately Ti (1-x) Nb x O 1.918 . This is very close to Ti 12 O 23 (equivalent to TiO 1.917 ), consistent with the XRD and TEM SAED results for TN15 (Figure1and Figure3). In contrast for higher Nb content samples (TN30-TN60), the y values decrease with increasing Nb content, indicating that higher levels of Nb can suppress the formation of oxygen vacancies, which is consistent with the modelling work of Wang et al.[START_REF] Wang | Ab Initio Studies of Nb Doping Effect on the Formation of Oxygen Vacancy in Rutile TiO 2[END_REF] on oxygen vacancy formation in Nb-doped rutile TiO 2 .

Figure 9 .

 9 Figure 9. Transport Properties of Nb-doped TiO 2 ceramic samples as a function of temperature:

  Nb content. The highest power factor of 503 μW m -1 K -2 was achieved for TN60 sample at 873 K, approximately twice the value for pure rutile prepared in air/carbon atmosphere. The reproducibility of the power factor data is demonstrated in FigureS18, where data for sample TN60 are presented as an example.Thermal Properties. The temperature dependences of the total thermal conductivity (ĸ total ) for Nb-doped TiO 2 ceramic samples are shown in Figure10a; values range from 2.6 W m -1 K -1 to 4.4 W m -1 K -1 , and decrease with increasing Nb content and increasing temperature, reaching the lowest value of ~2.6 W m -1 K -1 for TN60 at 873 K. The collected ĸ total values for these Nb doped samples are consistently lower than the thermal conductivity of single crystal rutile 21 (6-8 W/m K) and polycrystalline rutile 22 (4-5 W m -1 K -1 ).

Figure 10 .

 10 Figure 10. Temperature-dependent thermal conductivity of Nb-doped TiO 2 ceramic samples: (a)

Figure 11 .

 11 Figure 11. Thermoelectric figure for rutile-based ceramics: (a) results from this study (ZT) as a

  at 873 K, equal to the highest reported for single Nb-doped TiO 2 ceramics; other studies relied on SPS or chemical processing. This work presents new understanding of the microstructural evolution of n-type TiO 2 and offers a simple, economical fabrication route to enhance the thermoelectric performance. The control of thermoelectric properties of TiO 2 achieved here by Nb doping through engineering the defect structures could guide the development of future oxide thermoelectric materials.

  Density data for Nb-doped TiO 2 ceramic samples; XRD spectra of mixed final powders after calcination; Lattice parameters for the main rutile phase in Nb-doped TiO 2 ceramics; SEM EBSD Band Contrast Maps of Nb-doped TiO 2 ceramics; Average grain sizes of Nb-doped TiO 2 ceramics; SEM EDS line and map analyses of Nb-doped TiO 2 ceramics of different Nb contents; Experimental TEM SAED patterns, BF images, DF images and HRTEM images for samples TN15 and TN60; Simulated unit cell model and XRD patterns for Ti 12 O 23 Magnéli phase; XPS survey spectra and Positions of the different fitted peaks in the HR XPS spectra; Calculated activation energy of bulk Nb-doped TiO 2 ceramics; Scattering processes and relaxation times.

RESULTS AND DISCUSSION Bulk Property and Phase Analysis. All

	the sintered bulk samples were of high density
	(>97% theoretical), dark grey in color with no visible cracks. The relative density decreased with
	increasing Nb content (Table S1 in Supporting Information (SI)).
	X-ray Diffraction spectra for the final calcined powders are shown in Figure S1a; they are
	predominantly tetragonal (Space Group P4 2 /mnm) TiO 2 rutile phase. For powders containing
	lower contents of Nb (TN5 to TN15), all peaks matched the TiO 2 rutile phase. For powders
	The element valence states were investigated by X-ray photoelectron spectroscopy (XPS) using containing higher content of Nb, there were additional peaks, which corresponded to TiNb 2 O 7
	High-Throughput XPS, ESCA2SR spectrometer (Scienta Omicron) with monochromatic Al Kα (Space Group A1 2 /m1). The intensities of the new peaks increased with the increasing Nb
	radiation (E source = 1486.69 eV). Survey scans were conducted at 0-1200 eV (binding energy). content, as the amount of the new phase increased.
	Higher resolution scans were recorded for Ti (2p) peaks, Nb (3d) peaks, O (1s) peaks and C (1s) XRD patterns for the Nb-doped TiO 2 ceramics are shown in Figure 1; they are dominated by
	peaks. Carbon (1s) peaks (284.8 eV) were used to calibrate the binding energy for all the spectra. tetragonal TiO 2 rutile (Space Group P4 2 /mnm). In contrast to the spectra for the calcined powders
	CasaXPS software was used to process and analyze the XPS data. for TN5, TN10 and TN15 (samples with lower Nb contents), new, high intensity peaks appeared
	The transport properties, Seebeck coefficients and electrical conductivity were determined close to the peaks for (110) and (011) at 2θ values of 26.9°, 28.02°, 28.40°, 35.4° and 35.9°; the
	using an Ulvac-Riko ZEM-3 operating in low pressure He atmosphere from room temperature to
	873 K. Hall effect measurements were carried out at room temperature using a Physical
	Properties Measurement System (PPMS; Quantum Design) under an applied magnetic field from
	-7 T to 7 T. Thermal conductivity was determined from density (ρ), thermal diffusivity (α) and
	heat capacity (C p ) values. Density was determined from mass and dimension measurements.
	Thermal diffusivity was measured by NETZCH LFA-427 in an Ar atmosphere from room
	temperature to 873 K. Heat capacity values were obtained by a NETZCH STA 449C in an Ar
	atmosphere from room temperature to 873 K.

Table 2 .

 2 Lattice parameters for the rutile phase in Nb-doped TiO 2 ceramics

	Sample	TN5	TN10	TN15	TN30	TN45	TN60
	a, b (Å)	4.5955	4.5980	4.5994	4.6055	4.6125	4.6210
	c (Å)	2.9570	2.9603	2.9629	2.9655	2.9685	2.9714

Scanning Electron Microscopy. SEM Back-Scattered Electron (BSE) images of Nb-doped TiO 2 ceramics are shown in Figure 2. All samples exhibit regular polygonal-shaped grains;

Table 3 andTable S2 .

 3S2 For Ti 2p spectra, the spin orbital splitting (∆ s.o. ) of Ti 2p 3/2 and 2p 1/2 core levels is ~5.6 eV 41 . Asymmetries are observed for Ti 2p peaks, indicating the presence of both Ti 4+ and Ti 3+

Table 3 .

 3 Component Analysis of XPS Spectra for Nb-doped TiO 2 samples.

	Sample	Ti2p 3/2 %		Nb3d 5/2 %
	Code	Ti 4+	Ti 3+	Nb 5+	Nb 4+
	TN5	82.4	17.6	78.3	21.7
	TN10	82.0	18.0	76.2	23.8
	TN15	80.7	19.3	76.4	23.6
	TN30	80.0	20.0	71.5	28.5
	TN45	78.5	21.5	70.9	29,1
	TN60	75.9	24.1	67.9	32.1

Table 4 .

 4 Values of x and y in the formula Ti (1-x) Nb x O (2-y) for Nb-doped TiO 2 samples The charge transport properties of Nb-doped TiO 2 ceramics are

	Values	TN5	TN10	TN15	TN30	TN45	TN60
	x	0.01	0.02	0.03	0.058	0.086	0.113
	y	0.083	0.081	0.082	0.073	0.068	0.069
	Charge transport properties.

Table 5 .

 5 Electrical conductivity (σ), carrier concentration (n) and carrier mobility (μ) of the Nb-

		doped TiO 2 ceramics at room temperature
	Sample	TN5	TN10	TN15	TN30	TN45	TN60
	σ (S cm -1 )	25.25	30.02	31.40	35.68	33.01	26.07
	n (10 20 cm -3 )	0.575	1.480	3.100	12.00	4.950	6.260
	μ (cm 2 V -1 s -1 )	2.774	1.268	0.633	0.186	0.416	0.260

  ). The resulting thermoelectric figure of merit, ZT values, for the Nb-doped TiO 2 ceramics are presented as function of temperature in Figure11a. Whilst TN30 exhibits the highest power factor of 470 μW m -1 K -2 at room temperature, the ZT value was only 0.04 due to the relatively high thermal conductivity; nevertheless, this is still the highest ZT value at room temperature. At elevated temperatures, the ZT values increase with increasing Nb content, to a maximum value of 0.17 for TN60 at 873 K. The ZT values from this study are presented graphically alongside data from other studies[START_REF] Backhaus-Ricoult | Semiconducting Large Bandgap Oxides as Potential Thermoelectric Materials for High-Temperature Power Generation?[END_REF][START_REF] Zaitsev | Preparation and Characterization of Nanocrystalline Doped TiO 2[END_REF][START_REF] Liu | Bottom-up Assembly to Ag Nanoparticles Embedded Nb-Doped TiO 2 Nanobulks with Improved n-Type Thermoelectric Properties[END_REF][START_REF] Yuan | Investigation of the Thermoelectric Properties of Reduced Nb-Doped TiO 2-δ Ceramics[END_REF][START_REF] Yuan | Thermoelectric Properties of Nb-Doped TiO 2-δ Ceramics Reduced at Elevated Temperature[END_REF][START_REF] Verchère | Optimum in the Thermoelectric Efficiency of Nanostructured Nb-Doped TiO 2 Ceramics: From Polarons to Nb-Nb Dimers[END_REF] for single Nb-doped TiO 2 based thermoelectric ceramics in Figure11b. The present results show approximately 50% enhancement in ZT at 373 K compared with earlier studies. Indeed, the maximum ZT value obtained in this study (0.17, 873 K) is the equal to the highest reported ZT value for single Nbdoped TiO 2 ceramics, where the earlier samples were prepared by spark plasma sintering 1 .

ACKNOWLEDGMENT

The authors are grateful to the EPSRC for the provision of funding for this work (EP/H043462, EP/I036230/1, EP/L014068/1, and EP/L017695/1 acknowledged by R.F.). The work was also supported by the Henry Royce Institute for Advanced Materials, funded through EPSRC Grants EP/R00661X/1, EP/S019367/1, EP/P025021/1, and EP/P025498/1. We gratefully acknowledge the support from X-ray facilities in the Department of Materials in the University of Manchester. X.L thanks China Scholarship Council for their financial support during his Ph.D. program. All research data supporting this work are directly available within this publication.

about 0.4 eV (from TN5 to TN60) (Table 3), and the [Nb 5+ /Nb 4+ ] ratio is reduced, confirming the reduction of Nb. phase boundaries and shear planes) and point defect scattering (dopants and vacancies). In samples with lower Nb contents (TN5-TN15), the presence of crystallographic shear structures (formed by the high density of oxygen vacancies) is one of the important factors for attaining lower lattice thermal conductivity. The Debye model (Equation 2) can be used to estimate the phonon mean free path from lattice thermal conductivity and sample density:

where 𝐶 @ is the specific heat capacity, ρ is density, υ is sound velocity (6.91×10 -3 m s -1 for rutile [START_REF] Mcqueen | Shock-Wave Compression and X-Ray Studies of Titanium Dioxide[END_REF] ) and l is phonon mean free path. For TN15 samples, the estimated phonon mean free path is approximately 0.52 nm at room temperature. This low value is mainly ascribed to the presence of crystallographic shear planes in the Magnéli phases (average CS spacing 1.65 nm to 2.13 nm), which are believed to contribute to phonon-boundary scattering and help reduce thermal transport [START_REF] Harada | Thermoelectric Properties and Crystallographic Shear Structures in Titanium Oxides of the Magǹeli Phases[END_REF][START_REF] Fan | Preparation of Monophasic Titanium Sub-Oxides of Magnéli Phase with Enhanced Thermoelectric Performance[END_REF] . The XPS data (Table 4) demonstrated that oxygen vacancy concentrations of samples with lower Nb contents (TN5-TN15) are essentially the same, and therefore the contributions to scattering by oxygen vacancies will be similar for TN5-TN15. Furthermore, the microstructures, and specifically grain sizes, of TN5-TN15 are not significantly different (Figure S3 and S4). Therefore, the reduction in lattice thermal conductivity with increasing Nb doping level (from TN5 to TN15) can be attributed to increased scattering from point defects generated by Nb doping. The presence of the Nb, having different size and mass to the host atoms can introduce local strain-stress and mass fluctuations, which can effectively enhance the scattering of phonons of a particular wavelength. The fluctuations can be described by the Debye-Callaway model, as given by Klemense (details in Supplementary Information). Here the size and mass of Nb 5+ (R Nb 5+ = 0.64 Å) are larger than those for Ti 4+ (R Ti 4+ = 0.605 Å). According to Equation S3, S4, S5 and S6, the substitution of Nb ions for Ti ions will introduce significant local strain-stress

AUTHOR INFORMATION

Corresponding Author *Email: Robert.Freer@manchester.ac.uk

Notes

There are no conflicts to declare.