Characterization of Tunneled Wide Band Gap Mixed Conductors: The Na2O-Ga2O3-TiO2 System

This article focuses on the Na2O-Ga2O3-TiO2 system, which is barely explored in the study of transparent conductive oxides (TCOs). NaxGa4+xTin−4−xO2n−2 (n = 5, 6, and 7 and x ≈ 0.7–0.8) materials were characterized using neutron powder diffraction and aberration-corrected scanning transmission electron microscopy. Activation energy, as a function of different structures depending on tunnel size, shows a significant improvement in Na+ ion conduction from hexagonal to octagonal tunnels. New insights into the relationship between the crystal structure and the transport properties of TCOs, which are crucial for the design and development of new optoelectronic devices, are provided.


Introduction
Transparent conductive oxides (TCOs) are a specific field of wide band gap semiconductors, which are traditionally recognized for their high conductivity and transparency in the visible range [1,2]. In recent years, significant efforts have been made to continually upgrade optoelectronic devices, largely dependent on the study and development of new TCOs [3][4][5][6]. One such example is Ga 2 O 3 , specifically its β-polymorph, which has gained attention due to its unique properties, including a wide band gap of 4.9 eV, a high electric breakdown field of 8 MV/cm and high thermal and chemical stability [7,8].
Several Ga-based materials have been studied for their remarkable applications, particularly in the development of transparent electrodes and optoelectronic devices. For example, the homologous series Ga 2 O 3 (ZnO) m [9], as well as Ga 3−x In 3 Ti x O 9+x/2 [10], In-Ga-Zn-O [11], and Ga-Sn/Sb-Zn-O [12,13] systems, have been extensively researched. In all these systems, small variations in the composition of the cationic sublattice can cause significant changes in their electronic configuration and properties. In this article, we focus on the Na 2 O-Ga 2 O 3 -TiO 2 system, which has barely been explored. Moreover, one advantage is the replacement of Ga, a critical element [14], by abundant and non-toxic elements such as Na and Ti.
Specifically, we investigate the n = 5, 6, and 7 members of the Na x Ga 4+x Ti n−4−x O 2n−2 (x ≈ 0.7-0.8) homologous series. Chandrasekhar et al. [15] synthesized and characterized the Na 0.7 Ga 4.7 Ti 0.29 O 8 phase, which was later confirmed by Amoroso et al. [16] 2 of 10 in their phase stability studies. Michue et al. described the synthesis and characterization by single-crystal X-ray diffraction (XRD) of the next two phases of the series, Na 0.8 Ga 4.8 Ti 1.2 O 10 [17,18] and Na 0.8 Ga 4.8 Ti 2.2 O 12 [19]. The structure of these oxides can be described as an ordered intergrowth of β-Ga 2 O 3 -type chains and Ga/Ti octahedra for the n = 5 (hereinafter referred to as NGT1O) and n = 6 (NGT2O) members, with a monoclinic C2/m space group. Because of this intergrowth, hexagonal tunnels are formed for the NGT1O compound and octagonal for NGT2O. However, the structure of n = 7 material (NGT3O) presents both edge-sharing and corner-sharing (Ga,Ti)O 6 octahedra, as well as corner-sharing GaO 4 tetrahedra with an orthorhombic Pbam space group. In all cases, Na + ions are located in the tunnels of the structure. Our previous study [20] confirmed the structure of these materials by X-ray diffraction and aberration-corrected scanning transmission electron microscopy (STEM). Cathodoluminescence and photoluminescence response for the first two samples (NGT1O and 2) is essentially composed of a broad luminescence band centered around 2.2-2.3 eV, whereas the NGT3O sample's luminescence is composed of an intense band centered at 1.6 eV [20]. Furthermore, the band gap values obtained for each phase were Eg1 = 4.2 eV, Eg2 = 4.1 eV, and Eg3 = 3.5 eV, showing a decrease in energy values as the Ti content increases [20]. In addition, because these materials contain Na + situated in one-dimensional tunnels, a preliminary analysis of the potential of utilizing them as anode material has been explored using complex impedance. The characterization of materials with Na in their composition is a non-trivial task. Light and mobile elements made the use of conventional characterization techniques, such as XRD, more difficult. In this sense, techniques such as neutron diffraction and aberration-corrected transmission electron microscopy become essential techniques for the study of materials with light elements at the atomic level.
In this work, we report an extensive and detailed characterization of these materials using neutron diffraction, transmission electron microscopy, and complex impedance as a first step in the study of these materials as possible candidates in potential sodium ion anodes [21][22][23]. This, added to their interesting optical and photocatalytic and biomaterial properties reported before [24,25], makes these materials potential multifunctional oxides of technological interest in the field of optoelectronics.

Materials and Methods
Na x Ga 4+x Ti n−4−x O 2n−2 (n = 5, 6 and 7; x ≈ 0.7-0.8) powders were prepared by a solid-state reaction using the following starting reagents: Na 2 CO 3 (99.5%, Aldrich, St. Louis, MO, USA), Ga 2 O 3 (99.99%, Aldrich, St. Louis, MO, USA) and TiO 2 (99.9%, Aldrich, St. Louis, MO, USA). The powders were pressed into pellets and heated up to 1225 • C inside an alumina crucible using sacrificial powders to avoid contamination and prevent sodium losses. The reaction times were 48 h for the so-called NGT1O (n = 5) and NGT3O (n = 7) and 14 h for NGT2O (n = 6). After that, the crucible was quenched in air. Morphological characterization by transmission electron microscopy (TEM) did not present any particular morphology.
Cationic quantification was performed using a JEOL Superprobe JXA-8900M (JEOL, Tokyo, Japan) microscope, equipped with five wavelength dispersive X-ray spectrometers (WDS), allowing analysis over a sample diameter of 5-10 µm. The voltage and current used in the analysis of the Na-Ga-Ti-O samples were 20 kV and 50 nA, respectively.
Atomic resolution transmission electron microscopy was performed on a JEOL JEM GRANDARM 300F (JEOL, Tokyo, Japan) equipped with cold FEG and double Cs correctors operating at 300 kV and a JEOL JEM-ARM 200cF (JEOL, Tokyo, Japan) equipped with a cold FEG and probe Cs-corrected operating at 200 kV. High-angle annular dark-field (HAADF) images were recorded using a nominal camera length of 100 mm and inner and . For (S)TEM observations, the samples thus prepared were crushed in an agate mortar and ultrasonically dispersed in n-butanol and then transferred to carbon-coated copper grids. A structural characterization by X-ray diffraction of the samples investigated here was performed in our previous work [20].
The electrical measurements were performed by pressing powders of NGTO under 6 kbar, into pellets of 8 mm diameter and around 1 mm thickness, and sintering at 1225 • C. For the a.c. electrical conductivity measurements, blocking electrodes were deposited on both sides of the as-pelletized samples using platinum paint (previously dried at 500 • C) in the 573-753 K temperature range. The a.c. conductivity data were obtained using a frequency analyzer (Solartron 1260) coupled with a dielectric interface (Model 1296A) over a frequency range of 1 MHz-0.1 Hz and under oscillation voltages of 50 mV. Analysis of impedance spectra was performed using Zview 3.5f software (Scribner Associates) by fitting the data to appropriate equivalent circuits in order to resolve the impedance response into bulk, grain-boundary and electrode contributions.

Results and Discussion
In the first step, we assessed the precise structure of the Na-Ga-Ti oxides by neutron diffraction to gain a deeper insight into their structure and composition. Because the scattering lengths of Ga and Ti atoms are too distinct (bGa = 7.288 fm; bTi = −3.438 fm), they were solved by NPD and thus we obtained the Ga/Ti ratio in each polyhedron of the structure. Moreover, this technique allows determining of the oxygen and the Na content. The details of the analysis of the neutron diffraction data are described herein for NGT1O and NGT3O.
For NGT1O, the NPD pattern was refined using the monoclinic isostructural oxide, Na 0.7 Ga 4.7 Ti 0.29 O 8 [15] with a C2/m space group as a starting structural model. Figure 1a shows the results of the final NPD data fitting, whereas the corresponding structural parameters and distances are included in Tables 1 and S1 in the Supplementary Materials, respectively. The isotropic temperature factors were also refined, except for the Na + cation, for which an anisotropic factor was refined. The refinement of occupancy factors of the oxygen atoms does not reveal anionic vacancies; therefore, these factors were fixed during the refinement. The structure, schematically represented in Figure 1b, can be described on the basis of an ordered intergrowth of β-Ga 2 O 3 type chains (formed by octahedral and tetrahedral sites, colored in red) and (Ga/Ti)O 6 octahedra (colored in yellow).     The tetrahedral and octahedral sites were forced to be fully occupied but no constraint was imposed on the Ga: Ti ratio. The refinement shows that all tetrahedra are exclusively occupied by Ga (Ga1) whereas the octahedra ((M)2,3; M = Ga/Ti)) reveal the presence of both Ga and Ti with higher Ga concentrations. The distribution of Ga and Ti among octahedra is summarized in Table 1. Furthermore, the refinement shows that Na + ions occupy approximately 40% of the total 4a Wyckoff position. The easy mobility of Na + in the tunnel is reflected in the anisotropic factor temperature ( Table 1) indicating that the Na + ions are delocalized on the tunnel, which could suggest its potential use as an ionic conductor. The cell parameters obtained from the NPD refinement are: a = 12.36138 (8) Table S2) very similar to those found in β-Ga 2 O 3 (average distance = 1.839 Å). The corner-shared octahedra M3O 6 is nearly regular but, on the contrary, the edge-shared octahedra M2O 6 is quite distorted (see distances in Table S1 in Supplementary Materials). However, the presence of Ga and Ti in the octahedral sites does not significantly modify the Ga-O distances in an octahedral environment compared to the β-Ga 2 O 3 (average distance Ga-O = 1.993 Å).
The NPD study of the NGT3O was performed assuming, as an initial model, the orthorhombic isostructural oxide Na 1−x Ti 2+x Ga 5−x O 12 (x = 0.2) with Pbam space group. [19]. The result of the final NPD data fitted is depicted in Figure 2a, whereas the corresponding structural parameters and distances are summarized in Tables 2 and S2 ( Again, the refinement shows that all tetrahedra are exclusively occupied by Ga (Ga1) whereas the octahedra reveal the presence of Ti and Ga (see Table 2). The M4 octahedron is quite regular and is occupied preferably by Ga (85%), colored yellow in Figure 2b, as previously found in Na 0.80 Ga 4.66 Ti 0.34 O 8 (NGT1O). However, M2,3 octahedra are quite distorted (see distances in Table S2 in the Supplementary Materials) and a distinct Ga:Ti ratio is present, in contrast to those observed in Na 0.80 Ga 4.66 Ti 0.34 O 8 that have the same Ga:Ti concentration. Whereas the M2 site is richer in Ga (83%), the M3 site is occupied mainly by Ti (89%), colored green in Figure 2b. This distribution of Ga and Ti in the different polyhedra of the framework, obtained from the refinement of the neutron diffraction pattern as well as all average distances (M-O), is in good agreement with that proposed for Na 1−x Ti 2+x Ga 5−x O 12 (x = 0.2) [19].  Again, the refinement shows that all tetrahedra are exclusively occupied by Ga whereas the octahedra reveal the presence of Ti and Ga (see Table 2). The M4 octah is quite regular and is occupied preferably by Ga (85%), colored yellow in Figure  previously found in Na0.80Ga4.66Ti0.34O8 (NGT1O). However, M2,3 octahedra are qu torted (see distances in Table S2 in the Supplementary Materials) and a distinct Ga:T is present, in contrast to those observed in Na0.80Ga4.66Ti0.34O8 that have the same concentration. Whereas the M2 site is richer in Ga (83%), the M3 site is occupied m by Ti (89%), colored green in Figure 2b. This distribution of Ga and Ti in the di polyhedra of the framework, obtained from the refinement of the neutron diffractio tern as well as all average distances (M-O), is in good agreement with that propos Na1−xTi2+xGa5−xO12 (x = 0.2) [19].
Unfortunately, the NPD pattern of NGT2O prepared for the neutron diffracti periment shows a very weak presence of NGT1O and NaTi2Ga5O12 [30] as impuritie LeBail-type refinement, shown in Figure S1a    Unfortunately, the NPD pattern of NGT2O prepared for the neutron diffraction experiment shows a very weak presence of NGT1O and NaTi 2 Ga 5 O 12 [30] as impurities. The LeBail-type refinement, shown in Figure S1a  The overall sodium, gallium and titanium content was also analyzed by WDS, (Table S3, see Supplementary Materials). The Ga:Ti ratio obtained for the NGT1O and NGT3O phases is in good agreement with that obtained by NPD refinement. However, a slight difference can be observed in the Na + content due to the possible correlation between Na + occupancy and the temperature factors because of its mobility in the tunnel. This mobility of Na + indicates that this material could be a potential candidate for use in Na + ion anodes. The activation energy of Na + will be explored further by complex impedance spectroscopy.
The close structural features between the phases of this series require an in-depth and detailed structural study using transmission electron microscopy (TEM). As these materials can be used as potential ionic conductors, a more detailed analysis along the directions where the tunnels of the structure are observed has been carried out. Figure 3a,b shows representative STEM-HAADF images of a characteristic crystal of the NGT1O phase along the [010] zone axis and NGT3O along [001], respectively. In the STEM-HAADF image corresponding to NGT1O (Figure 3a), β-Ga 2 O 3 chains (represented by red circles in the image) are clearly seen, intergrowing in an ordered way with GaO 6 or TiO 6 columns (marked with dark yellow circles), giving rise to an irregular hexagonal tunnel of the dimensions 4.5 × 3.5 Å. Despite the difference in the Z values of each cation (Z Ga = 31 and Z Ti = 22), any difference in contrast is practically indistinguishable, due to the multiple occupation of cations at this position and the low concentration of Ti (see the refinement by NPD for this oxide). A similar characterization has been done for NGT3O (Figure 3b). Figure S1b in the Supplementary Materials shows a STEM-HAADF image corresponding to NGT2O along the [010] zone axis. In all the images, the cell parameters and the tunnel sizes, where the Na + is located, are indicated. Moreover, all the observed crystals are apparently ordered, so the presence of extensive defects can be ruled out, as well as disordered intergrowths with other members of the series. A more detailed characterization of the NGT2O and NGT3O phases by STEM-HAADF and ABF together with EELS spectroscopy was performed in our previous work [20].
of Na indicates that this material could be a potential candidate for use in Na ion anodes The activation energy of Na + will be explored further by complex impedance spectros copy.
The close structural features between the phases of this series require an in-depth an detailed structural study using transmission electron microscopy (TEM). As these mater als can be used as potential ionic conductors, a more detailed analysis along the direction where the tunnels of the structure are observed has been carried out. Figure 3a,b show representative STEM-HAADF images of a characteristic crystal of the NGT1O phase alon the [010] zone axis and NGT3O along [001], respectively. In the STEM-HAADF image cor responding to NGT1O (Figure 3a), β-Ga2O3 chains (represented by red circles in the im age) are clearly seen, intergrowing in an ordered way with GaO6 or TiO6 columns (marke with dark yellow circles), giving rise to an irregular hexagonal tunnel of the dimension 4.5 × 3.5 Å. Despite the difference in the Z values of each cation (ZGa = 31 and ZTi = 22), an difference in contrast is practically indistinguishable, due to the multiple occupation o cations at this position and the low concentration of Ti (see the refinement by NPD for thi oxide). A similar characterization has been done for NGT3O (Figure 3b). Figure S1b in th Supplementary Materials shows a STEM-HAADF image corresponding to NGT2O alon the [010] zone axis. In all the images, the cell parameters and the tunnel sizes, where th Na + is located, are indicated. Moreover, all the observed crystals are apparently ordered so the presence of extensive defects can be ruled out, as well as disordered intergrowth with other members of the series. A more detailed characterization of the NGT2O an NGT3O phases by STEM-HAADF and ABF together with EELS spectroscopy was per formed in our previous work [20]. Because these materials present one-dimensional tunnels where Na + is placed, a char acterization by impedance spectroscopy has been carried out to study their transpor properties. As only NGT1O and NGT3O samples are single phases we have focused th analysis on these two members. Onoda et al. [31], in their study by NMR of the 23 Na nucle observed an increase in Na + mobility as a function of temperature, suggesting its possibl use as a candidate for Na + ion batteries. Figure 4a-  Because these materials present one-dimensional tunnels where Na + is placed, a characterization by impedance spectroscopy has been carried out to study their transport properties. As only NGT1O and NGT3O samples are single phases we have focused the analysis on these two members. Onoda et al. [31], in their study by NMR of the 23 Na nuclei, observed an increase in Na + mobility as a function of temperature, suggesting its possible use as a candidate for Na + ion batteries. Figure 4a-f shows, as an example, the complex impedance diagrams at three different and representative temperatures for NGT1O and NGT3O compounds. In sample NGT1O, there are two overlapping semicircles and a small tail tilted on the x-axis. For sample NGT3O, a curve with a well-defined semicircle followed by a semicircle that does not end up closing is obtained. Along with the impedance measurements, the equivalent circuits used to fit the data are also shown. In addition, the data obtained from the simulations for the indicated fits are plotted in Figure 4a-f. It is worth mentioning that, over the entire working temperature range (500-753 K), the experimental data can be adjusted to a circuit, as shown in Figure 4a Tables S4 and S5 in the Supplementary Materials. imental data can be adjusted to a circuit, as shown in Figure 4a,d, for the two measured compounds. The capacitance values of all the samples obtained are of the order of ~10 −11 F in the case of the first semicircle, which makes it possible to associate them with a phenomenon taking place in the bulk of the material. At middle frequencies, 10 -11 -10 −8 F·cm −1 values are obtained which are interpreted as being due to grain boundaries and, at the lowest frequencies, 10 −7 -10 −5 F·cm −1 values are typical of sample-electrode interface effects. The values of capacitance and resistivity for all temperatures measured are included in Tables S4 and S5 in the Supplementary Materials. From the resistance values obtained from the simulation, the values of the bulk conductivity were calculated. Fitting to an Arrhenius-type behavior, log(σT) as a function of 1/T, the activation energies (Ea) of the conduction processes can be calculated. The experimental data are plotted in Figure 5, together with the line fittings.   From the resistance values obtained from the simulation, the values of the bulk conductivity were calculated. Fitting to an Arrhenius-type behavior, log(σT) as a function of 1/T, the activation energies (Ea) of the conduction processes can be calculated. The experimental data are plotted in Figure 5, together with the line fittings. The Ea values obtained were 1.10 and 0.88 eV for the NGT1O and NGT3O oxides, respectively. As can be seen, there is a significant decrease in the activation energy as the series member increases, indicating that the change from a hexagonal to an octagonal tunnel is especially important. A second factor to be considered would be the amount of sodium per unit formula, being slightly lower in the case of NGT3O, perhaps allowing more mobility along the tunnel in a hopping-type mechanism. The result for the NGT1O sample is higher than that obtained by Hasegawa et al. (0.39-0.57 eV) [32]. However, it should be pointed out that in their work, they have managed to synthesize the sample in an oriented manner along the tunnel direction, which would justify this lower value of activation energy. The values obtained for these compounds are characteristic of one-dimensional Na + conductors and close to the ones reported in the literature. For example, values between The Ea values obtained were 1.10 and 0.88 eV for the NGT1O and NGT3O oxides, respectively. As can be seen, there is a significant decrease in the activation energy as the series member increases, indicating that the change from a hexagonal to an octagonal tunnel is especially important. A second factor to be considered would be the amount of sodium per unit formula, being slightly lower in the case of NGT3O, perhaps allowing more mobility along the tunnel in a hopping-type mechanism. The result for the NGT1O sample is higher than that obtained by Hasegawa et al. (0.39-0.57 eV) [32]. However, it should be pointed out that in their work, they have managed to synthesize the sample in an oriented manner along the tunnel direction, which would justify this lower value of activation energy. The values obtained for these compounds are characteristic of one-dimensional Na + conductors and close to the ones reported in the literature. For example, values between 0.73 to 1.0 eV can be found for Na 2 Co 8 (PO 4 ) 6 , Na 8 M 4 (P 2 O 7 ) 4 (M = Mn, Co, Ni) or NaGe 2 (PO 4 ) 3 [33][34][35].

Conclusions
In the present work, three members of the homologous series Na x Ga 4+x Ti n−4−x O 2n−2 (n = 5, 6 and 7 with x ≈ 0.7-0.8) have been synthesized. According to the study performed by powder neutron diffraction, it can be concluded that both NGT1O and NGT2O samples crystallize in the C2/m space group as intergrowths of β-Ga 2 O 3 chains and Ga/Ti octahedra. The NGT3O sample crystallized in the Pbam space group and its structure can be described as being formed by both edge-sharing and corner-sharing (Ga,Ti)O 6 octahedra, as well as corner-sharing GaO 4 tetrahedra. In all cases, the structure contains tunnels where the Na + cation is placed. This information, combined with aberration-corrected scanning transmission electron microscopy, has allowed us to obtain a global and atomic-scale structural confirmation of these materials. Critical and precise information about atomic coordinates and the chemical composition and occupancy of each atomic position together with a direct visualization of the tunnel size for the NGT1O and NGT3O oxides were obtained. This information is crucial to the study of the transport properties of these materials. The activation energies corresponding to each sample obtained by using impedance spectroscopy were: 1.10 and 0.88 eV for NGT1O and NGT3O, respectively. These values demonstrate a clear structure-properties relationship, with tunnel size being a key factor in Na + ion transport, making these materials functional oxides of technological interest.