Exhaustive Study of Electrical Conductivity in the MNb2−x TixO6–0.5x (M = Mg, Ca, Zn; x = 0, 0.1, 0.2) Columbites

The CaNb2O6 and ZnNb2O6 columbites (Sp.gr. Pbcn) were studied as oxygen ion conductors both theoretically and experimentally. A theoretical approach included geometrical-topological analysis, bond valence site energy (BVSE) and density functional theory (DFT) calculations. The BVSE approach showed the possibility of pure oxygen ions diffusion with migration energies less than 0.45 eV in both compounds. However, DFT calculations indicated the possibility of diffusion of both anions and cations. The single-phases columbites were synthesized by the Pechini method for accurately determine charge carriers type and investigated by impedance spectroscopy, by the Tubandt method, which confirmed the absence of cationic conductivity, and measured the electrical conductivity as a function of oxygen partial pressures. The CaNb2O6 sample was characterized by the pure oxygen-ionic conductivity ∼2 × 10−6 S cm–1 at 800 °C (E a = 0.82 eV), while the ZnNb2O6 had a similar conductivity value due to mixed ionic-electronic contribution (E a = 0.83 eV). The electromotive force method also showed the predominance of the ionic type of conductivity in CaNb2O6, while ZnNb2O6 has a mixed conductivity with ion transport number of about 0.4. Additionally, we synthesized Ti-doped samples MNb2−x Ti x O6–0.5x (M = Mg, Ca; x = 0.1, 0.2) to study the doping effect on conducting properties.

5][6][7] The conductivity in NiNb 2 O 6 and MnNb 2 O 6 was experimentally studied, and the mixed ion-electronic conductivity was found to be about 10 −5 S cm −1 at 800 °C. 4,6Later, the oxygen vacancy formation energies were calculated and the electronic density of states was theoretically examined for five columbites MNb 2 O 6 (M = Mn, Fe, Co, Ni, Cu), suggesting CuNb 2 O 6 as a potential mixed electronic-ionic conductor. 5The pure oxygen ion conductivity about 10 −5 S cm −1 at 800 °C was recently proved both theoretically and experimentally in the magnocolumbites Mg 1−x Li x Nb 2 O 6-x (x = 0, 0.1, 0.2). 7 In this paper, we explored the conductivity in a group of MNb 2−x Ti x O 6-0.5x columbites (M = Mg, Ca, Zn; x = 0, 0.1, 0.2), by assuming the ionic conductivity due to structural and chemical similarity with Ni-, Mn-, Cu-and Mg-columbites.The conductivity of CaNb 2 O 6 was previously studied in Singh et al. by impedance spectrometry. 8From the frequency dependence of the permittivity, it was indirectly established that the conductivity is due to ion hopping.Here, we comprehensively studied the conductivity using a combined theoretical and experimental approach.The theoretical treatment consisted of geometrical-topological (GT) analysis, bond valence site energy (BVSE) and density functional theory (DFT) calculations.Experimental measurement of conductivity in pure and doped compounds was carried out by: (1) impedance spectroscopy to determine the total conductivity; (2) the conductivity measurements under varying of the oxygen partial pressure by electrochemical method to determine the fraction of ionic conductivity; (3) the Tubandt method to determine charge carriers type (4) the measurements of ion transport number by the electromotive force (EMF) method.To evaluate the effect of doping on conductivity the titanium-doped samples were synthesized (MgNb 1.9 Ti 0.1 O 5.95 -MNT 0.1 O, MgNb 1.8 Ti 0.2 O 5.9 -MNT 0.2 O, CaNb 1.9 Ti 0.1 O 5.95 -CNT 0.1 O, CaNb 1.8 Ti 0.2 O 5.9 -CNT 0.2 O).As a result, pure oxygen-ionic conductivity was found in the Ca-columbite of σ > 2•10 −6 S cm −1 at 800 °C, while Zn-columbite has mixed ionic and electronic conductivity with the total value close to CaNb 2 O 6 .

Experimental
Theoretical evaluation of ionic transport.-Geometrical-topological(GT) analysis.-GTanalysis based on the partition of the crystal space into convex Voronoi polyhedra and fulfilled in the ToposPro program package. 9Voronoi polyhedra completely fill the crystal space, the vertices of the polyhedra are possible voids as the furthest points from lattice atoms, and the edges are channels connecting them.The system of all vertices and edges of the Voronoi polyhedra forms a Voronoi net showing possible ion migration paths. 10However, not all voids and channels may be geometrically suitable for oxygen ion migration.To exclude outlying pathways, we applied criterion r chan (min), which was determined as in the case of magnocolumbites. 7We used tabular values of Shannon ionic radii of working ion and environmental ions for calculations.Consequently, the values of the threshold criteria were r chan (min) ⩾ 1.99 Å for CNO and r chan (min) ⩾ 1.89 Å for ZNO.BVSE modeling.-Themigration energy (E m ) for oxygen and M 2+ ions was calculated using the BVSE method implemented in softBV. 11,12Ions with the lowest E m value were considered as working ions.The BVSE method as applied to ionic conductors has the idea of calculating the deviation of the bond valence sum from the oxidation state of working ion.Regions of the crystal space with minimal deviations (less than 15%) are considered accessible for the working ion diffusion.
DFT calculations.-Themigration energy for oxygen and M 2+ ions was computed within the DFT approach 13 using the Nudged Elastic z E-mail: eliztimofeeva@mail.ruBand (NEB) method as it implemented in the VASP package. 14The Generalized Gradient Approximation (GGA) exchange-correlation functional in the form of Perdew-Burke-Ernzerhof (PBE) 15 was utilised.All settings for structural relaxation and NEB calculations were kept the same as for magnocolumbite. 7The supercell size was 1 × 2 × 2 for the NEB calculation providing cell sizes greater than 10 Å in each direction. 16The input files for the NEB calculations were prepared by using the PATHFINDER script (https://pathfinder.batterymaterials.info/).
We also estimated the oxygen vacancy formation energy E v (O) by using the following formula: 5,17-23 where E defect and E bulktotal energies of the structure with an introduced oxygen vacancy and of the bulk structure, respectively; E O2the total energy of the O 2 molecule.To calculate E defect , one neutral oxygen atom was removed from the 1 × 2 × 2 supercell, which corresponds to 1.04 % vacancies, and the relaxation of all atomic positions was performed.
The electron densities of states (DOS) and band structure for the CNO and ZNO were computed with the hybrid HSE03 exchangecorrelation functional [24][25][26] and the Gaussian smearing method. 7he mechanical properties were evaluated by calculating the single-crystal elastic constants.Polycrystalline elastic moduli: the bulk modulus B, the shear modulus G, Young's modulus E, and the Poisson's ratio ν, were estimated within the Voigt-Reuss-Hill approximation. 27nthesis and characterization.-Allcompounds were synthesized by Pechini method with the sintering procedure as described in the previous work. 28The following sintering procedure was used.The stoichiometric mixture of the hydrated metal nitrates (99.9% purity) was heated up to the melting point, then the Nb 2 O 5 and TiO 2 (anatase modification) powder (50-100 nm in size) and citric acid were added.After further heating and stirring a gel-like phase burnt out and turned into a powder.The obtained powders were pressed into pellets and calcined at 650 °С (1 h), 1000 °C (5 h), 1100 °C (20 h), 1250 °C (5 h) with intermediate grinding (for 30 min) and repelleting.The calcinations of the samples were carried out in corundum crucibles.
The phase and elemental analysis were characterized by X-ray diffraction (XRD), scanning electron microscopy in backscattered electron regime (BSE-SEM) and the energy dispersive X-ray (EDX) analysis using the same devices and conditions as were described in the previous work. 7The FullProf software package was used for modeling of XRD patterns.Diffuse reflectance spectra were recorded by a Schimadzu UV-2600i spectrophotometer with an ISR-2600 integrated sphere and the corresponding Tauc plot was constructed. 7Additionally, the pellets' density was estimated by the hydrostatic weighing method.The total porosity (%) was calculated as (ρ xrd -ρ app )/ρ xrd × 100%, where ρ xrdtheoretical density from XRD data, ρ appthe apparent density. 29For the apparent density calculation was used the dried mass of pellet m dry , the water-saturated pellet m sat , the hydrostatic mass of the water-saturated pellet in the water m hydr , water density ρ water at experiment temperature.The formula can be shown as ρ app = m dry /(m satm hydr )*ρ water . 29ectrical study.-Electricaldata were obtained by impedance spectroscopy method (E7-28 immitance analyser) using two-point technique.Both faces of the pellets were coated with silver paste and annealed at 700 °C for 30 min.The measurement parameters were as follows: 0.5 V, 25 °C-750 °C (a cool mode), 25-10 7 Hz, in air.
The conductivity was measured under varying pO 2 , that was set by the electrochemical method as described in Schulz et al. 30 The partial oxygen pressure was monitored using an oxygen ion pump and measured using a Zirconia-M automatic electrochemical sensor (https://zirconiaproject.wordpress.com).The studies were carried out in the pO 2 = 0.21÷10 −20 atm range and the 500−900 °C temperature range with a 100 °C heating step and long exposure (about 36 h) to achieve equilibrium in the sample−gas-phase system at T = const and p(O 2 ) = const.
Experimental procedure of Tubandt Method.-TheTubandt method 31,32 was used to study the effective transport numbers.The tripartite cell was constructed from three equally weighted discs/ pellets in series as follows: where Pt electrodes were shaped as plates.Preliminarily, each pellet/ disc and the overall cell were weighted.The experiments were performed at 800 °C.The amount of current Q passing through the cell was varied between 25 C and 100 C. Tripartite cell was put into a furnace and heated to the required temperature, then the cell was electrified (U = const = 300 V).The typical current through the cell was 0.1 mA.After about 40 h of exposure, the compositions were naturally cooled to room temperature and disassembled.At the end of the experiment, the cell's sections (discs) were weighted again.Further, using Faraday's law and considering that Δm (-) is equal to the mass carried by the current charges from the cathode to the anode part, we calculated the ion transport numbers: where Δmmass change, M ionmolar weight of ion, z ionion charge, F -Faraday constant, Qthe total amount of electricity passed through an electrochemical system.The phase composition of the near-electrode layers was determined by XRD method and then the possible ionic charge carrier was proposed.
Experimental procedure of electromotive force method.-Ionictransport numbers were measured by the EMF method in a concentration cell in the temperature range of 400 °C to 800 °C for pure MNO, CNO, ZNO. 33,34Oxygen transport numbers were determined by the pO 2 gradient, for which the pressure of atmospheric air (pO 2 = 0.21 atm) was compared with the pressure of supplied oxygen (pO 2 = 1 atm).The measurement samples were pellets similar to those used to measure electrical conductivity by impedance spectroscopy.The samples were placed in the measuring furnace in such a way that its ends fit tightly to the tube separating the two gas chambers.The sum of ion transport numbers averaged over the pO 2 gradient was calculated using the formula: where Σt ion -the sum of ionic transport numbers; E А/А and E В/Аmeasured EMF values without pO 2 gradient and with pO 2 gradient (mV); R -universal gas constant (J/[mol,K]); T -temperature (K); F -the Faraday constant (C/mol); ′ pO 2 and ¢¢ pO 2 -the partial pressures of oxygen in the tank and in air, respectively.

Results and Discussion
Structural investigation.-Thesingle-phase CNO and ZNO ceramics with the columbite structure (Pbcn space group) were obtained (Fig. 1).ZNO is characterized by larger crystallized agglomerates (2-5 μm size) compared to CNO (1-2 μm).The obtained ceramics have compositions closed to the initial stoichiometry (Table S1).The insignificant diversity in the composition is caused by rough surface of the ceramics.Lattice parameters were calculated from Rietveld refinement of the XRD patterns (Table S2).
We also estimated density using the hydrostatic weighing method.In the literature, various densities of ceramic columbites from 81 to 90% are given, 1,4 but a significant increase in density up to 97% is observed with the addition of dopant. 6,36The closed porosity (porosity in tablet volume) of the pure MNO, CNO, and ZNO synthesized by us was 8%-13% (Table S3), and an decrease in porosity by 5% is visible in the example of titanium-doped MNO samples.Previously, we were able to increase the density of MNO by adding copper additives, but such samples became mixed conductors.Our further research will be aimed at finding additives that significantly increase the densities of MNO and CNO, but while maintaining the ionic type of conductivity.We also recalculated the dependence of the sample density on the conductivity, assuming that the samples are absolutely dense, and found that the order of conductivity for pure ZNO-СNO-MNO and doping compounds is conserved (Fig. S3).samples were measured through the reflectance spectra (Fig. 3).For MNT x O, the band gap for direct electron transition E g dir decrease from 4.25 (x = 0) to 3.72 (x = 0.2) eV.For CNT x O E g dir remains in the same level (4.14-4.16eV) within titanium concentration up to x = 0.2.The E g indir of pristine CNO is equal to 3.94 eV (Fig. 3d) close to 4.17 eV as bulk and 3.53 eV as nanosized sample in other works. 37,38The indirect band gap E g indir for ZNO corresponds to 3.75 eV (Fig. 3c), close to 3.87 eV found by Zhao et al. 39 Calculations and comparison with literary data.-From the DFT-HSE03 calculations CNO and ZNO were found to be indirect band gap semiconductors (Fig. S4) with corresponding E g indir of 4.89 and 4.69 eV (Table I).It should be noted that difference between E g value of indirect and direct transition is negligible.The major contribution to the formation of the valence and conduction band is due to overlapping Nb d and O p states.The other orbitals give a minor contribution to electronic structure.It is known that PBE functional underestimates band gap value while hybrid exchangecorrelation functionals might overestimate it.Accordingly, the DFT results within local spin density approximation performed by Duman et al 40 for CNO yielded E g dir = 3.50 eV.ZNO has E g indir = 3.50 eV within the PBE approximation according to Zhao et al 39 or E g indir = 3.53 eV from the DFT+U results. 41deling of ionic conductivity.-Thepossible oxygen-ion migration pathways in the CNO and ZNO columbites were found using GT analysis (Fig. S5a).The 3D ion migration map was obtained in the structures.The minimum channel sizes are shown in Table I.
Next, we calculated the migration energies of oxygen and divalent cations (Ca 2+ , Zn 2+ ) using the BVSE approach.The simulation indicated the probability of oxygen diffusion only, with the layer (2D) migration (Table I, Fig. S5b).Further, we calculated the migration energies within DFT-NEB approach and revealed that 2D oxygen diffusion is likely in CaNb 2 O 6 (Table I) while the 3D oxygen migration is possible in ZnNb 2 O 6 .However, according to the DFT results, the 1D migration of divalent cations is also possible due to comparable migration energies with oxygen (Table I, Fig. 4).
The average value of oxygen vacancy formation energies for CaNb 2 O 6 and ZnNb 2 O 6 are 5.64 eV and 4.62 eV, respectively (Table I).The E v value of CNO is close to the typical values for columbites and other oxygen-ion conductors, while ZNO has quite low values of E v . 5,23,42[45] Experimental electrical properties for CNO and ZNO.-The electrical properties of ceramics were studied by the electrochemical impedance technique.The impedance spectra for CNO and ZNO recorded at 700 °C-800 °C temperatures were shown in Fig. S6.The spectra of these samples are fitted by R-CPE equivalent circuit and are characterized by bulk resistance (C p = 10 −11 F).According to the Jonscher power law, fitting of the frequency dependence on Table I.The GT, BVSE, DFT results for pure MNO (data taken from Morkhova et al. 7 ), CNO and ZNO.

Compound
Migration map; r chan (min), Å conductivity is the same as in the previous work. 7The transition motion of charge carrier (oxygen ions) with sudden hopping type in the low temperature range (T < 700 °C) and oxygen diffusion by jumping over the sites (at T ⩾ 700 °C) was detected (Fig. S7).
The conductivity as function of temperature was estimated in air.The data are presented in Fig. 5.The conductivity increases in the series of ZNO-CNO-MNO 7 (Fig. 5).The activation energy for all samples close to each other.
The Tubandt method was used to determine the nature of the charge carriers in the CNO and ZNO samples.The assumption of cationic (Ca 2+ or Zn 2+ ) conductivity in these samples can be confirmed by weighing the products of electrolytic decomposition deposited on the electrodes and measuring the amount of electricity required to cause such decomposition.The weight of the electrodes would change with the appearance of cationic conductivity.In addition, the current passage would cause parts of the composition to stick together.In our cases, there was no change in the mass of a single pellets or overall composition.The XRD studies of the surface of all the pellets in contact with the platinum electrodes showed that in all cases no impurity phases were formed.Thus, no evidence was obtained for the involvement of Ca 2+ or Zn 2+ ions in ionic conduction.
The conductivity was also measured as function of oxygen partial pressure in the temperatures range of 600-900 °C, similarly to previous measurements in magnocolumbites. 7The conductivity isotherms of CNO sample are presented on the Fig. 6a.They show  region of pO 2 -independent plateau over a wide range of temperature and partial oxygen pressure (pO 2 = 0.21 ÷ 10 −17 atm), associated to the dominant oxygen-ionic transport.However, a negative slope is observed on the conductivity curves at low pO 2 due to the contribution of the n-type electron conduction.We assume a possible defect formation mechanism similar to that in the Orera et al. 4 At low oxygen partial pressures, n-type conductivity predominates probably due to the reduction of Nb +5 to Nb +4 according to the equation: Then the equilibrium constant of such a quasi-reaction will be calculated as: . The CNO sample is characterized by an increase in the electronic conductivity contribution at low pO 2 values with increasing temperature, which is accompanied by a change in the slope from −1/10 to −1/4.The deviation of the conductivity slope from −1/6 may be due to impact of nonstoichiometry and temperature-dependent grow of electronic carrier concentration. 46he conductivity isotherms for the ZNO sample (Fig. 6b) show the similar behavior as for CNO at low and intermediate pO 2 values.However, for the ZNO sample the electronic contribution to the conductivity remains the same for all temperatures.The character of the conductivity slope that is observed at high (the slope is ca.−0.23) and low pO 2 (the slope is ca.−0.25), may be explained by the contribution of n-type conductivity.Perhaps, this difference is due to the stability of the coordination number for calcium (CN = 6), whereas for zinc the tetrahedral polyhedra is most preferred (CN = 4).Thus, as the partial pressure of oxygen decreases, the formation of electronic defects process can be accelerated according to Eq. 4 for the ZNO sample.At the same time, this process is reversible for both compounds: after pumping out, when the partial oxygen pressure returned to the air value (pO 2 = 0.21 atm), the resistance also returned to its original value.
The dependence of the transport number on temperature is presented in Fig. 7.The t ion values observed in MNO and CNO are between the range of 0.6 to 0.8, confirming their similar nature of conductivity with predominantly ionic contribution.While the transport numbers measured for ZNO are approximately 0.4, that indicates a mixed type of conductivity.Agreement is also observed with the theoretically and experimentally determined E g value, which is lowest for ZNO.It is worth considering that the error of the EMF method reaches 20% since it depends sensitively on the electrode polarization resistance as well as the conduction properties of the studied materials. 34,47perimental electrical properties for MNT x O and CNT x O (x = 0.1, 0.2).-Impedance spectra for MNT x O and CNT x O are fitted by R-CPE equivalent circuit as their matrices (Figs.S8-S9).However, different electrical behaviour was detected for them.For MNT x O, an increase in Ti 4+ content led to a decrease in conductivity, while for CNT x O the opposite trend was observed (Fig. 8).For Ti-doped MNO the decrease in conductivity may result from a decrease in cell volume and a free space, available for ion diffusion (Table S1).Vice versa, Ti doping of CNO resulted in increased cell volume (Table S1).Earlier, a good correlation between crystal free space and ion migration barriers was established. 48

Conclusions
The CaNb 2 O 6 , ZnNb 2 O 6 columbites and Ti-doped samples MNb 2-x Ti x O 6-0.5x (M = Mg, Ca; x = 0, 0.1, 0.2) were explored as ion conductors.BVSE method predicted pure 2D oxygen ion conductivity in CNO and ZNO columbites while DFT indicated the possible contribution of divalent cations to the diffusion process.ECS Advances, 2024 3 024504 However, the Tubandt method refuted the cationic diffusion and conductivity dependence in different oxygen pressure confirmed the oxygen conductivity for CNO and the mixed (electronic n-type and oxygen) conductivity for ZNO.The EMF method also demonstrated the ionic type of conductivity in CNO and MNO, while the oxygen transport numbers for ZNO were in the range of 0.3-0.4.The Tidoping in CNO and MNO results in the formation of columbites with low amounts of admixtures.The heterovalent titanium doping leads to grow electronic contribution to the conductivity.The band gap value decreased for MNTO from 4.25 to 3.72 eV with the grow of Ti content while the band gap of CNTO remains in the same level of 4.14-4.16eV.Thus, the exclusively anionic type of conductivity dominates in pure MNO and CNO, while ZNO and Ti-doped structures have mixed ion-electronic conductivity.

Figure 1 .
Figure 1.Results of Rietveld analysis of the XRD patterns and BSE-SEM images of the surfaces for (a) CNO and (b) ZNO.

Figure 3 .
Figure 3. Absorption spectra (a), (b) and Tauc plots for direct electron transition (insets) for (a) MNT x O and (b) CNT x O, and for indirect electron transition for (c) ZNO and (d) CNT x O.

Figure 4 .
Figure 4. Migration maps of divalent cations (a) and anions (b) in ZNO with the corresponding migration energies of working ions from the DFT-NEB approach.

Figure 6 .
Figure 6.Dependencies of conductivity of CNO (a) and ZNO (b) ceramics on the partial oxygen pressure at 600 -900 °С.Slopes at low partial pressures are highlighted with black lines.

Figure 7 .
Figure 7.The temperature dependences of ionic transport numbers for MNO, CNO and ZNO from EMF method.

Table II .
7echanical properties from DFT for MNO, CNO and ZNO.The conductivity of the MNO,7CNO, and ZNO ceramics as a function of inverse temperature in air.