Photoelectron Spectroscopy Study of the Optical and Electrical Properties of Cr/Cu/Mn Tri-Doped Bismuth Niobate Pyrochlore

Abstract

The multielement pyrochlore of the composition Bi_1.57Mn_1/3Cr_1/3Cu_1/3Nb₂O_9−Δ (sp. gr. Fd-3m:2, 10.4724 Å) containing transition element atoms—chromium, manganese and copper in equimolar amounts—was synthesized for the first time using the solid-phase reaction method. The microstructure of the ceramics is grainless and has low porosity. The sample is characterized by reflection in the red (705 nm) color region. The band gap for the direct allowed transition in the sample is 1.68 eV. The parameters of the Bi5d, Nb3d, Сr2p, Mn2p, and Cu2p X-ray photoelectron spectroscopy (XPS) spectra for the mixed pyrochlore are compared with the parameters of transition element oxides. For the complex pyrochlore, a characteristic shift in the Bi4f and Nb3d spectra to the region of lower energies by 0.15 and 0.60 eV, respectively, is observed. According to the XPS Cu2p and Mn2p spectra of pyrochlore, copper, and manganese cations are in a mixed charge state; they mainly have an effective charge of +2/+3, and the Cr2p spectrum is a superposition of the spectra of chromium ions in the charge state of +3, +4, +6. At 24 °С, the permittivity of the sample in the frequency range (10⁴–10⁶ Hz) weakly depends on the frequency and is equal to ~100, the dielectric loss tangent is 0.017. The activation energy of conductivity is equal to 0.41 eV. The specific electrical conductivity of Bi_1.57Cr_1/3Cu_1/3Mn_1/3Nb₂O_9−Δ increases with the temperature increasing from 1.8 × 10⁻⁵ Ohm⁻¹·m⁻¹ (24 °С) to 0.1 Ohm⁻¹·m⁻¹ (330 °С). Nyquist curves for the sample are modeled by equivalent electrical circuits.

1. Introduction

The inexhaustible interest in synthetic pyrochlores is due to their broad spectrum of practically useful properties, among which are superconducting, electro-optical, photocatalytic, and dielectric properties [1,2,3,4]. Bismuth-containing pyrochlores attract close attention from scientists due to their excellent dielectric properties—high permittivity, low values of dielectric losses and temperature coefficient of capacitance, multiple dielectric relaxation, as well as due to the low synthesis temperature and chemical compatibility with low-melting metal electrodes. The combination of practically significant properties of pyrochlores determines the prospect of their use in multilayer ceramic capacitors and microwave electronic devices [5,6,7]. The tolerance of the crystal structure of pyrochlores to iso- and heterovalent substitutions of cations and oxygen vacancies allows one to significantly vary the chemical composition and study its effect on the physicochemical properties of the compounds [8,9,10,11,12,13]. The crystal structure of cubic pyrochlore A₂B₂O₇ (Fd-3m) is formed by two interpenetrating cation sublattices, A₂O and B₂O₆ [14,15]. The octahedra of the basic structure B₂O₆, located around the points of the diamond network, form a tetrahedral framework linked at the vertices. The framework of regular octahedra contains extensive voids, which accommodate two or more large cations A and one additional atom O’ for each formula unit (BO₃)₂ of the framework. Relatively small B cations (Ta⁵⁺, Nb⁵⁺, Ti⁴⁺) are coordinated in the octahedra, and large A ions (Ca²⁺, Bi³⁺) are located in a distorted eight-vertex network formed by the oxygen atoms of the A₂O and B₂O₆ sublattices. Classical two-component pyrochlores, A⁺³₂B⁺⁴₂O₇ and A⁺²₂B⁺⁵₂O₇, are formed by a combination of different-valent cations +3/+4 and +2/+5. Attempts to synthesize pyrochlores with a combination of cations +3/+5 or +2/+4 fail because they do not satisfy the stability criterion of pyrochlores. In this regard, pyrochlores formed by bismuth(III) and niobium(V)/tantalum(V) cations are not known. However, the doping of bismuth orthoniobate BiNbO₄ with transition element cations stabilizes the structure of cubic pyrochlore. A feature of such pyrochlores is the mixed arrangement of transition element cations in two cation sublattices, predominantly in the octahedral one, and is the reason for the relaxation properties of the ceramics [16,17]. Among bismuth-containing pyrochlores, doped bismuth niobates exhibit good dielectric properties. According to most authors, the special dielectric properties are due to the significant polarizability of niobium–oxygen octahedra and the low-porosity grain-free microstructure of the solid solutions. In [18], it was shown that Bi_2−xLa_xMg_2/3Nb_4/3O₇ (x = 0.25) ceramics exhibit a comparatively high permittivity of 141 and a dielectric loss tangent of 0.1. A high permittivity of 167–204 and low dielectric losses of ~10⁻⁴–10⁻³ (1 MHz, 28 °C) were demonstrated by Bi_3+(5/2)xMg_2−xNb_3−(3/2)xO_14−x (0.14 ≤ x ≤ 0.22) ceramics [19]. High values of permittivity ε = 69–171 and low values of dielectric loss tangent of ~10⁻³ (30 °C, 1 MHz) were demonstrated by (Bi_3.36Mg_0.64−xCa_x)(Mg_1.28Nb_2.72)O_13.76 (0 ≤ x ≤ 0.7) ceramics of complex composition [20].

Of particular interest, from the point of view of the mutual influence of cations on each other and on the functional properties of the compound as a whole, is the study of the physicochemical properties of multi-element pyrochlores doped with several transition 3d elements. In this paper, we present the results of a study of the electrical and optical properties of oxide pyrochlore based on bismuth niobate doped with copper, chromium, and manganese cations in equimolar amounts. The electrical properties of monodoped pyrochlores based on bismuth niobate containing manganese, chromium or copper have not been sufficiently studied. Information on the properties of chromium or copper-containing pyrochlores based on bismuth niobate is unknown. According to work [21], pyrochlore Bi₂CrNb₂O_9+y with a unit cell parameter of 10.459(2) Å can be synthesized. In [22], the crystal structure of chromium-containing pyrochlore Bi_2−x(CrTa)O_7−y (a = 10.451 Å) was refined using powder neutron and synchrotron X-ray diffraction data. In [23], it was shown that in the composition of pyrochlore Bi₂CrTa₂O_9+Δ (Fd-3m:2, 10.45523(3) Å), the ions are in the charge states of Bi(III), Ta(V), Cr(III). According to the results of [23], the porous sample noticeably adsorbs moisture, exhibits a permittivity of 16 and dielectric losses of 0.017 at room temperature and a frequency of 1 MHz. At temperatures above 400 °C, ion transfer dominates in the sample, which is manifested in a decrease in the activation energy of conductivity to 0.78 eV. A detailed study of pyrochlores in the Bi₂O₃-Nb₂O₅-Mn₂O₃ system was carried out in [9], where it was established that the system contains a significant concentration region of manganese-containing pyrochlores with a deficiency of bismuth(III) cations, in which 14–30% of the A-positions are occupied by Mn²⁺ ions. X-ray powder diffraction data confirmed that all Bi–Mn–Nb–O pyrochlores are formed with structural displacements, as was found for similar pyrochlores with Mn replaced by Zn, Fe or Co. According to [9], the disordering of the displacement is crystallographically similar to that for Bi_1.5Zn_0.92Nb_1.5O_6.92, which has a similar concentration of small B-type ions in the A-positions. EELS spectra of manganese-containing pyrochlores showed the presence of Mn²⁺ and Mn³⁺ ions. The authors showed that at 300 K and 1 MHz, the relative permittivity of Bi_1.6Mn_1.2Nb_1.2O₇ was 128, and the dielectric loss was 0.05. Low-temperature dielectric relaxation, such as that observed for Bi_1.5Zn_0.92Nb_1.5O_6.92 and other bismuth-based pyrochlores, was not observed.

This paper presents the results of a study of the optical and electrical properties of multi-element pyrochlore Bi_2−хMn_1/3Cr_1/3Cu_1/3Nb₂O_9−Δ as a potential photocatalyst and a compound with semiconductor properties.

2. Experimental Part

Oxides of bismuth(III), niobium(V), copper(II), chromium(III), manganese(III) were used as precursors for the synthesis of Bi_2−хMn_1/3Cr_1/3Cu_1/3Nb₂O_9−Δ (x = 0, 0.43) by the standard ceramic method in stoichiometric quantities according to the solid-phase reaction equation. For example, the synthesis of Bi_1.57Mn_1/3Cr_1/3Cu_1/3Nb₂O_9−Δ sample (3.8808 g) was carried out from analytical-grade oxides, Bi₂O₃ (2.0000 g), Nb₂O₅ (1.4534 g), CuO (0.1450 g), Cr₂O₃ (0.1385 g), Mn₂O₃ (0.1439 g), produced by the factory Red Chemist and the Ural Chemical Reagents Plant. The mixture of oxides was homogenized and ground for one hour in an agate mortar, and then the homogeneous mixture was pressed in the form of disks and calcined in four stages at temperatures of 650 (15 h), 850 (15 h), 950 (15 h), and 1050 °C (15 h) to obtain a single-phase sample. At each calcination stage, the reaction mixture was again homogenized and compacted for better contact of the ceramic grains. The phase purity of the prepared sample was confirmed using a Shimadzu 6000 X-ray diffractometer using Cu_Kα radiation in the 2-theta range of 10–80° at a scanning rate of 2.0 deg/min. The microstructure of the sample was studied using scanning electron microscopy (SEM). Spot chemical analysis of the sample composition was performed using energy-dispersive spectroscopy (SEM-EDS) (Tescan VEGA 3LMN scanning electron microscope, Brno, Czech Republic; INCA Energy 450 energy-dispersive spectrometer, Oxford Instruments, Abingdon, UK). The electrical properties were studied on a silver-coated sample. A silver layer was applied to the ends of the sample (2.5 mm thick, 13.2 mm in diameter) in the form of a disk. The conductive layer on the sample was formed by burning silver paste at a temperature of 600 °C for an hour. A temperature of 600 °C is necessary for the decomposition of silver paste (silver oxide (I)) to silver and the removal of organic impurities. Impedance studies were carried out using a Z-1000P impedance meter in the frequency range from 25 Hz to 5 MHz and a temperature from 24 to 450 °C. The X-ray photoelectron spectroscopy (XPS) apparatus is a Thermo Scientific ESCALAB 250Xi X-ray spectrometer, Waltham, MA, USA. The energy broadening of the XPS spectrometer, i.e., the minimum distance between two separated peaks, is 0.8 eV. The binding energy determination accuracy is 0.1 eV. An Al_Kα X-ray tube (1486.6 eV) was used as the source of ionizing radiation. An ion and electron charge compensation system was used to neutralize the sample charge. All spectral lines were calibrated relative to the C1s peak at 284.6 eV. The experimental data were processed using the ESCALAB 250 Xi program. The figures show the results of the decomposition of the spectral dependences into individual peaks, modeled using Gauss–Lorentz curves. The spectra of metals were used to analyze the chemical composition of the sample surface.

The diffuse reflectance spectrum was recorded in the range of 200–800 nm using a UV-2550 spectrophotometer, Shimadzu, Kyoto, Japan, with a spectral step of 1 nm. Halogen and deuterium lamps were used as radiation sources. The spectrum was obtained for the substance in a barium sulfate matrix. The scattering spectrum from a pure barium sulfate matrix was subtracted from the resulting spectrum. The Kubelka–Munk theory was used to quantitatively describe the diffuse scattering spectra. The value of Eg was determined by the position of the fundamental absorption edge according to the Tauc equation (hνF(r))^1/n = A(hν − Eg), where Eg is the band gap, h is the Planck constant, ν is the oscillation frequency of the electromagnetic waves, F(r) = (1 − r)²/2r is the Kubelka–Munk function, and A is a constant. The value of the exponent for direct allowed transitions is n = 1/2. The diffuse scattering spectra are reconstructed in Tauc coordinates: (hνF(r))² from E(eV). The value of Eg was determined by extrapolating the linear section of the Tauc curve to the energy axis.

3. Results and Discussion

We previously synthesized a sample whose chemical composition is described by the formula Bi₂Cr_1/3Cu_1/3Mn_1/3Nb₂O_9+Δ. As the X-ray phase analysis showed, the synthesized sample was non-single-phase and contained bismuth orthoniobate α-BiNbO₄ (sp. gr. Pnna) as an impurity in an amount of 21.5 mol. % (Figure S1). As shown in [24], quantitative consideration of the impurity content and the creation of a vacant bismuth sublattice proportional to the amount of the impurity phase allows single-phase pyrochlore to be synthesized. Thus, the quantitative composition of non-stoichiometric pyrochlore Bi_1.57Cr_1/3Cu_1/3Mn_1/3Nb₂O_9−Δ was obtained. According to X-ray phase analysis (Figure 1), the sample crystallizes in the cubic pyrochlore structural type (sp. gr. Fd-3m:2). Figure 1 shows the consistency indices in the Rietveld analysis. The R_Br-Bragg factor is used to assess the quality of the refined structural model. At high modeling accuracy, its value tends to zero. The R_wp-weighted profile factor, is responsible for the correspondence of the experimental and calculated X-ray diffraction patterns. The R_p-profile factor reflects the quality of refinement of the entire diffraction pattern by points, including the background. The R_exp-expected weighted profile factor is used to assess the reliability of the refinement and the correctness of the selected model. The GOF indicator is used to assess the quality of fitting the calculated profile to the experimental data. The fit is of good quality when this indicator is close to one. As the R-factors show, there is good agreement between the experimental and calculated X-ray diffraction patterns for the structural model of cubic pyrochlore.

As a result of the calculation, the unit cell parameter of pyrochlore Bi_1.57Cr_1/3Cu_1/3Mn_1/3Nb₂O_9−Δ was obtained as 10.4724 Å (sp. gr. Fd-3m:2). The unit cell parameter of the synthesized pyrochlore is comparable with the unit cell parameter for monodoped chromium pyrochlores of the composition Bi₂CrNb₂O_9+y 10.459 Å and Bi_1.6Cr_0.8Ta_1.6O_7.6 (sp. gr. Fd-3m:2, 10.45523 Å, Z = 8 (No. 227) [21,22], but closer to the unit cell parameter of Bi_1.6Mn²⁺_0.4(Mn³⁺_0.8Nb_1.2)O₇, (#227), 10.478 Å), although the stoichiometric coefficient at the bismuth atoms is underestimated [9].

The surface morphology of the sample was investigated using scanning electron microscopy (Figure 2). The figure shows that the sample has a low-porosity, monolithic microstructure without clearly defined grain boundaries. Elemental mapping of the sample surface showed (Figure 3) the presence of all cations indicated in the chemical formula of the sample composition and their uniform distribution over the sample surface. EDS analysis showed that the quantitative ratios of elements in the synthesized sample correspond to the specified theoretical composition. According to the calculation based on energy-dispersive X-ray spectroscopy data (EDS), the chemical composition of the experimental sample is described by the chemical formula, Bi_1.60Cr_0.34Cu_0.32Mn_0.30Nb₂O_9−Δ.

The diffuse reflectance spectrum of the Bi_1.57Cr_1/3Cu_1/3Mn_1/3Nb₂O_9−Δ sample is shown in Figure 4.

The band gap (Eg) of complex pyrochlore for direct allowed electron transitions was estimated from the diffuse reflectance spectrum (Figure 4). As Figure 4a shows, the sample is characterized by reflection in the red (705 nm) range. Apparently, reflection in the red range is associated with the red-brown color of the sample, which is typical for compounds containing copper cations. As calculations showed, the band gap for the direct allowed transition in the sample is 1.68 eV (Figure 4b), which determines the prospect of using materials based on multi-element pyrochlores as photoabsorbing elements in solar batteries. The band gap width of known niobium pyrochlores is quite high compared to the value obtained for multi-element pyrochlore. In [25], the dependence of the band gap width of pyrochlores on Sn(IV) was established; it was shown that oxidation of tin(II) to tin(IV) increases the band gap width from 2.38 eV in Sn²⁺_1.62(Nb_1.86Sn⁴⁺_0.14)O_6.55 to 3.38 eV in Sn⁴⁺_1.62(Nb_1.86Sn⁴⁺_0.14)O_8.17. For pyrochlores (Bi_1.5Mg_0.5)(Nb_1.5Mg_0.5)O₇ and (Bi_1.5Na_0.5)(Nb_1.5Mg_0.5)O₇, a decrease in the direct values of the band gap width from 3.21 to 3.15 eV with an increase in the sodium content was recorded [26]. A decrease in the energy of the band gap for the direct transition was observed with an increase in ruthenium in pyrochlores Bi_1.5Mg_0.375Cu_0.375Nb_1.5−xRu_xO_7−d: from 2.40 (x = 0) to 2.10 eV (x = 0.5) [27]. Much larger band gap values are found in niobium pyrochlores of the Bi₂MNbO₇ (M = Al, Ga, In) composition. These values are approximately 2.9, 2.75 and 2.7 eV, respectively [28].

XPS spectra of pyrochlore doped with copper, chromium, and manganese atoms are shown in Figure 5. The energy position of the absorption bands in the spectra is presented in

Table 1. Energy positions of XPS spectra components of the Bi_1.57Cr_1/3Cu_1/3Mn_1/3Nb₂O_9−Δ.

Peak	Energy (eV)
Bi4f7/2	158.85
Bi4f5/2	164.18
Nb3d5/2	206.43
Nb3d3/2	209.19
Cr2p3/2	576.49
Cr2p1/2	586.02
Mn2p3/2	641.35
Mn2p1/2	653.28
Сu2p3/2	934.02
Cu2p sat	941.86
Сu2p1/2	954.14
Cu2p sat	961.76

. The spectra of the oxide precursors are given for comparison. Figure 5a shows the XPS spectra in a wide energy range, and Figure 5b–f show the spectral dependences in the region of the Bi5d, Nb3d, Cr2p, Mn2p and Cu2p ionization thresholds of the sample.

Comparison of the XPS spectra of the studied Bi_1.57Cr_1/3Cu_1/3Mn_1/3Nb₂O_9−Δ sample and Bi₂O₃ oxide (Figure 5b) showed that the energy position of the Bi4f_7/2 band has a characteristic shift to the low-energy region compared to the binding energy in the trivalent oxide Bi₂O₃. The shift in the Bi4f spectrum to the low-energy region (by 0.15 ± 0.10 eV) means a decrease in the effective charge of bismuth ions in pyrochlore Bi_1.57Cr_1/3Cu_1/3Mn_1/3Nb₂O_9+Δ compared to the charge of bismuth in bismuth(III) oxide. In this case, the oxidation state of bismuth ions in pyrochlores is +(3-δ). A low-energy shift was also determined for the Nb 3d_5/2 spectrum (by 0.60 eV) compared to the binding energy in niobium oxide Nb₂O₅, which indicates a decrease in the oxidation state of niobium cations to +(5-δ). We associate the decrease in the effective charge of bismuth and niobium cations with the distribution of some of the low-charge cations of transition elements in the niobium and bismuth positions, which is confirmed by XRD data. A significant shift in the Nb3d spectrum compared to the Bi4f spectrum indicates a pronounced preference of 3d metal cations for the octahedral Nb(V) positions, and not bismuth(III). This conclusion is completely logical, since this distribution is consistent with the size factor and polarization properties of transition element cations.

A comparison of the Mn2p spectrum of pyrochlore with the spectra of the previously studied oxides MnO [29], Mn₂O₃ [30], and MnO₂ [31] shows that the Mn2p spectrum for Bi_1.57Cr_1/3Cu_1/3Mn_1/3Nb₂O_9−Δ correlates to a greater extent with the spectra of Mn₂O₃ and MnO in terms of energy position. The positions of the peaks in the Mn2p spectra of pyrochlore and the oxide Mn₂O₃ practically coincide, with the subspectra Mn 2p_3/2 and Mn 2p_1/2 appearing at 641 eV and 653 eV, which corresponds to Mn(III) ions. The presence of Mn(II) cations in the composition of pyrochlore is acceptable, since the blurred, diffuse Mn2p spectra of pyrochlore can represent a superposition of energetically closely spaced spectra from Mn(II) (640.5 eV) and Mn(III) (641 eV) ions. The Cr 2p spectra of pyrochlore and chromium oxides [32,33] are shown in Figure 5e. The shift in the pyrochlore spectrum relative to the Cr 2p spectrum of Cr₂O₃ oxide to the high-energy region and the insufficient selectivity of the broadband spectrum of pyrochlore give us reason to believe that the chromium cations in pyrochlore have an average charge state different from +3. It is necessary to assume that the Cr 2p spectrum of pyrochlore represents a superposition of subspectra from chromium cations in the charge state +3, +4, +6. The energy position of the main peaks in the Cu 2p spectrum of pyrochlore (934 and 954 eV) is more consistent with the spectrum of CuO [34]. In the spectrum, Cu 2p clearly shows satellite peaks in the ranges of 938–945 and 960–965 eV, characteristic of Cu(II) cations. At the same time, the low-energy broadening in the spectrum at 932 eV and 952 eV, coinciding with the absorption bands of Cu₂O, may indicate the presence of a small proportions of copper cations in the charge state Cu(I). In this regard, we suggest that copper cations in pyrochlore may be in the mixed valence state Cu(II,I). The presence of copper cations(I) is not entirely clear at this stage of the study. This may stabilize the crystal structure of pyrochlore by heterovalent doping, since it is more advantageous for copper cations (I) to occupy the positions of bismuth(III) rather than niobium(V), taking into account size and charge factors. The possibility of changing the charge state of transition element cations in pyrochlore arose due to the presence of dopants with a variable oxidation state. It may be assumed that electron exchange is possible in pyrochlores doped with 3d elements, i.e., the transfer of electrons from one cation to another, resulting in a decrease in the oxidation state of one cation and an increase in the other. In this case, when transferring electrons to copper(II) cations, chromium(III) or manganese(II) ions may increase their charge. According to the XPS analysis data, we estimated the pyrochlore formula as Bi_1.41Mn_0.40Cr_0.37Cu_0.37Nb₂O_9.78, which correlates with the initial composition, Bi_1.53Mn_1/3Cr_1/3Cu_1/3Nb₂O₉.

Electrical Properties

The electrical properties of the Bi_1.57Cr_1/3Cu_1/3Mn_1/3Nb₂O_9−Δ sample were studied in the temperature range of 24–350 °C in a frequency range of 25 Hz–5 MHz (Figure 6). Figure 6 shows the frequency dependences of the impedance modulus (Figure 6a) and the phase angle (Figure 6b) as a function of temperature. As Figure 6a shows, the impedance modulus of the sample depends on the frequency in a complex way; at low frequencies (up to 5 × 10³), the end-to-end conductivity dominates, which is manifested by the frequency independence of the impedance modulus. In the high-frequency region, capacitive currents prevail. The change in the phase angle due to the frequency correlates with the frequency dependence of the impedance modulus (Figure 6b). It can be seen that at room temperature and in the low-frequency range, the phase angle has a zero value, which corresponds to the manifestation of active resistance caused by the ionic conductivity of the sample. With increasing temperature (from 275 °C) the end-to-end conductivity prevails over capacitive conductivity in the entire frequency range, which is reflected in the frequency independence of the impedance modulus. At high frequencies, the phase angle maintains a value of 90°, indicating the flow of predominantly biased currents. Such behavior of the modulus and phase angle indicates that the sample under study exhibits semiconductor properties.

Figure 7a,b show the frequency dependences of the relative permittivity and the dielectric loss tangent. On some curves (Figure 7a,b), some points are missing on the graphs. This is due to strong interference at low frequencies and high temperatures due to the ongoing electrode process. We tried to reflect the experimental data as much as possible, so we did not neglect fragmentary curves. The relative permittivity of the sample in a wide temperature range (up to 250 °C) maintains a constant value of ~100 (the average high-frequency permittivity is 95) (Figure 7a). In a narrow frequency range, the permittivity weakly depends on frequency (10⁴–10⁶ Hz). The increase in permittivity with decreasing frequency and increasing temperature can be associated with an increasing contribution of end-to-end conductivity. The temperature dependences of the dielectric loss tangent are almost parallel and linearly depend on the frequency, and the loss tangent values are inversely proportional to the frequency (Figure 7b). The sample exhibits a minimum value of 2 × 10⁻² dielectric loss tangent at a frequency of 5 × 10⁷ Hz and 24 °С. With increasing temperature and frequency, dielectric losses increase, which is associated with electron polarization.

The obtained values of permittivity and dielectric loss tangent for Bi_1.57Cr_1/3Cu_1/3Mn_1/3Nb₂O_9−Δ are comparable with the electrical characteristics for complex bismuth niobates doped with 3d element cations, for example, Bi_1.5MgNb_1.5O₇ (ε = 120, 1 MHz, tan δ = 0.001) [35] and Bi_1.5ZnNb_1.5O₇ (ε = 130, tan δ = 0.001) [36], Bi_1.6Ni_0.77Nb_1.43O_6.55 (ε = 127, 1 MHz) [37] and Bi₂Ni_2/3Nb_4/3O₇ (ε = 122, 1 MHz, tan δ = 0.001) [38]. The dielectric loss tangent at room temperature and a frequency of 1 MHz is low and takes the value of 0.002 as for most niobium pyrochlores [37,38,39]. The temperature dependence of the through conductivity of the sample is shown in Figure 5f. The calculation of the activation energy of conductivity in the sample showed a fairly low value of Ea = 0.41 eV [17], typical of many copper-containing semiconductors, characterized by the hopping mechanism of electrical conductivity. The specific electrical conductivity of Bi_1.57Cr_1/3Cu_1/3Mn_1/3Nb₂O_9−Δ changes with increasing temperature from 1.8 × 10⁻⁵ Ohm⁻¹·m⁻¹ (24 °C) to 1.0 × 10⁻¹ Ohm⁻¹·m⁻¹ (330 °C). Meanwhile, for nickel pyrochlore based on bismuth niobate Bi₂NiNb₂O₉, the values of specific electrical conductivity are small and vary from 2.5 × 10⁻⁶ Ohm⁻¹·m⁻¹ (325 °C) to 6.3 × 10⁻⁵ Ohm⁻¹·m⁻¹ (410 °C) [40,41].

Based on the analysis of the shape of the hodographs (Figure 8) (Nyquist plots), an equivalent electrical circuit was modeled that simulates the electrical behavior of the sample in the high-temperature range [42]. When modeling the impedance of the sample using the ZView program, an accurate equivalent circuit was built.

Table 2. Parameters of the equivalent circuit for the temperature range of 24–250 °С.

t, °C	R, Ω	C, pF	TCPE	PCPE	χ2 × 104
24	7.79 × 105	49.8	8.99 × 10−10	0.615	3
50	2.64 × 105	48.4	1.2 × 10−9	0.613	3
75	94,729	47.5	1.16 × 10−9	0.647	3
100	38,539	47.6	1.89 × 10−9	0.627	4
125	17,268	46.5	1.31 × 10−9	0.670	3.6
150	8520	45.3	1.22 × 10−9	0.692	2
175	4406	45.1	1.46 × 10−9	0.687	2.6
200	2456	46.4	3.55 × 10−9	0.625	1.2
225	1450	44.4	4.40 × 10−9	0.625	1
250	821	34.7	1.008 × 10−9	0.751	0.5

shows the parameters of the ES for temperatures from 24 to 250 °С.

The accuracy of the electrical model can be judged by the χ² criterion (column 6 in Table 2) and visually judged in Figure 8. This figure shows the impedance hodographs (Nyquist plots). The dots mark the experimental impedance values, and the lines are obtained using the ZView program when approximating the experimental data with an equivalent circuit. The equivalent circuit of the sample can be considered as a parallel-connected capacitor C and a two-terminal network “R–CPE”. The capacitor models the high-frequency part of the impedance, and the two-terminal network is responsible for the low-frequency part of the impedance. Thus, the studied sample exhibits semiconductor properties and is characterized by significant electrical conductivity at room and elevated temperatures, which is typical for most copper-containing preparations, shows high values of permittivity and low dielectric losses. Meanwhile, the low bandgap value indicates the prospect of using multielement pyrochlore as a photocatalyst.

4. Conclusions

The possibility of solid-phase synthesis of multi-element cubic pyrochlore Bi_1.57Cr_1/3Cu_1/3Mn_1/3Nb₂O_9−Δ with a deficient bismuth sublattice is demonstrated. The sample is characterized by a dense microstructure with unclear grain boundary outlines. The sample is promising as a photocatalyst, exhibiting a low band gap of 1.68 eV. According to XPS data, a low-energy shift in the Bi4f and Nb3d spectra by 0.15 and 0.60 eV, respectively, is recorded, which is associated with an uneven distribution of transition 3d elements in the position of bismuth(III) and niobium(V) cations. According to the XPS Cu 2p/Mn 2p spectra, copper and manganese cations in pyrochlore have an effective charge of +2/+3, respectively, the Cr 2p spectrum is a superposition of spectra from chromium ions in the charge state of +3, +4, +6. At 24 °C, the permittivity is 95, and the dielectric loss tangent is 0.017. The activation energy of conductivity is 0.41 eV. The specific electrical conductivity of Bi_1.57Cr_1/3Cu_1/3Mn_1/3Nb₂O_9−Δ increases with temperature from 1.8 × 10⁻⁵ Ohm⁻¹·m⁻¹ (24 °C) to 0.1 Ohm⁻¹·m⁻¹ (330 °C). Based on the analysis of the hodograph shape, an equivalent electrical circuit is modeled that simulates the electrical behavior of the sample in the high-temperature range. The ES of the sample can be considered as a parallel-connected capacitor C and a two-terminal network “R–CPE”.