Crystal, Optical, Thermal and Dielectric Properties, XPS, and NEXAFS of Magnesium-Doped Nickel–Bismuth Stibate Pyrochlore

Abstract

The article presents the results of a study of the properties of a new pyrochlore (Bi_2.7Mg_0.46Ni_0.70Sb₂O_10+Δ) using X-ray powder diffraction analysis, high-temperature X-ray powder diffraction and thermal analysis, diffuse reflectance spectroscopy, impedance spectroscopy, and X-ray spectroscopy methods (XPS, NEXAFS). The Ni/Mg codoped bismuth stibate pyrochlore was synthesized using the solid-phase method. The best results of the Rietveld structure refinement were achieved for the disordered pyrochlore model (sp. gr. Fd-3m:2, a = 10.47574(6) Å). The results of modeling the cation distribution over crystallographic positions are presented. The thermal expansion coefficient (TEC) of pyrochlore increases monotonically from 6.8 × 10⁻⁶ °C⁻¹ (30 °C) to 9.8 × 10⁻⁶ °C⁻¹ (810 °C). Above 1080 °C, thermal dissociation of pyrochlore occurs with the formation of (Mg/Ni)Sb₂O₆ and two cubic phases. At temperatures below 200 °C, the sample exhibits primarily capacitive impedance. The sample capacitance (~17 pF) is independent of temperature and frequency up to 200 °C. The high-frequency relative permittivity and dielectric loss tangent are 30.5 and 5 × 10⁻⁴ (24 °C, 5 × 10⁴ Hz). The activation energy for conductivity is 0.99 eV. The analysis of NEXAFS and XPS spectra allowed for the determination of the charge state of the metal cations: Bi + (3-δ), Sb + (5-δ), Ni/Mg + 2.

1. Introduction

Oxide pyrochlores are a large class of compounds with diverse physicochemical properties of practical and theoretical significance [1,2,3,4,5,6]. The prevalence of pyrochlores in various fields of application is explained by the stability of the pyrochlore structure to oxygen vacancies and hetero and isovalent cationic substitutions. This allows for the study of reproducible effects associated with macrodoping. The composition of pyrochlore is represented by the chemical formula A₂B₂O₇ (sp. gr. Fd-3m) [7]. Binary pyrochlores A⁺³₂B⁺⁴₂O₇ and A⁺²₂B⁺⁵₂O₇ are formed by A/B cations in oxidation states +3/+4 and +2/+5, respectively. The existence of pyrochlores with a combination of cations with valence +3/+5 or +2/+4 has not been established. At the same time, doping with 3d transition elements stabilizes the structure of pyrochlores for cations in the oxidation states +3/+5 [8,9,10]. In this particular case, mixed pyrochlores are formed with a partially vacant sublattice of A cations and dopants distributed in both cation sublattices. Studies have shown that the octahedral sublattice is completely filled, while an insignificant fraction (up to 30 at.%) of doped cations is distributed in the sublattice of A cations [7,8,9,10]. Such a mixed distribution of cations is generally reproducible and does not depend on the synthesis conditions, which indicates that the distribution of cations in the A sublattice is not random, but is associated with the limited capacity of the octahedral sublattice. Previously, we carried out a number of studies of the properties of bismuth-containing pyrochlores based on bismuth niobate and tantalate. As shown in [11,12,13], bismuth-containing pyrochlores doped with 3d-elements exhibit predominantly semiconductor and dielectric properties [14,15]. It was previously established that nickel pyrochlores are capable of demonstrating high permittivity values. For example, the permittivity of Bi_1.6Ni_2/3−yNb_4/3+yO_6.4+3y/2 varied from 127 to 168 with a change in the y coefficient from −0.1 to 0.1 [15]. Similar values of permittivity 122 and dielectric loss tangent ~0.001 at a frequency of 1 MHz were demonstrated by Bi₂Ni_2/3Nb_4/3O₇ ceramics [3]. Nickel-containing tantalum pyrochlores showed low values of permittivity of 44.85 (RT, 10⁵ Hz) [16] for Bi₃Ni_1.4Ta₃O_13.4, and for Bi₂NiTa₂O₉ the permittivity did not exceed 32 at 30 °C and 1 MHz [17]. Replacing nickel(II) ions with magnesium(II) ions led to a decrease in the permittivity. According to the data [18], for Bi_1.4(Mg_1−xNi_x)_0.7Ta_1.4O_6.3 (x ≤ 0.7) ceramics, the permittivity and dielectric loss tangent are 24–28 (x(Mg) = 0.7–0.3) and ~0.002 (RT, 1 MHz). As shown in the literature review, niobium pyrochlores usually have higher dielectric properties compared to tantalum ones. This phenomenon can be explained by the grain-free microstructure and the highest polarizability of Nb-O bonds in octahedra compared to the rigid and short Ta-O bonds in compact and more symmetric Ta-O octahedra. In addition, the results of the literature review show that the replacement of tantalum(V)/niobium(V) ions with transition 3d ions leads to insignificant changes in the dielectric parameters [3,15,16,17,18]. Thus, it can be concluded that the polarizability of the octahedral framework, or more precisely the nature of the atoms forming the niobium/tantalum framework, mainly determines the dielectric properties of ceramics. Antimony pyrochlores monodoped with 3d-elements (Cr, Fe, Mn, Ni, Co, Zn) are currently being actively studied [13,19,20,21,22]; they are promising, first of all, as catalysts. Therefore, the aim of our work was to study the properties of a new nickel–magnesium pyrochlore based on bismuth stibate. This study reveals the role of substituting nickel/magnesium ions for antimony(V) cations on the dielectric, structural, and thermal properties of the ceramic. This study compares key physicochemical properties of magnesium/zinc-containing pyrochlores based on bismuth stibate. One of the advantages of magnesium-containing pyrochlores over zinc-containing ones is their thermal stability compared to zinc-containing ones, as well as their higher relative permittivity.

2. Experimental Section

Solid-phase synthesis of the Bi_2.7Mg_0.46Ni_0.70Sb₂O_10+Δ sample was carried out from bismuth(III), antimony(III), nickel(II), and magnesium(II) oxides using the procedure described in detail in [23]. High-temperature X-ray diffraction analysis of the sample was performed by powder high-temperature X-ray diffraction (HTXRD) using a Rigaku Ultima IV diffractometer (RIGAKU Corporation, Tokyo, Japan) (Co_Kα) with a thermo-attachment in the range 25–1200 °C with steps of 30 °C. The unit cell parameters were calculated using the Pauli approach using the Topas 5.0, Bruker, Karlsruhe, Germany software package [24]. The microstructure and chemical composition of the sample were studied using scanning electron microscopy and energy-dispersive spectroscopy (Tescan VEGA 3LMN scanning electron microscope and INCA Energy 450 energy-dispersive spectrometer, TESKAN, Brno, Czech Republic). Electrical characteristics of the sample were measured using a Z-1000P impedance meter (Elins, Minsk, Belarus) at 25 Hz–10 MHz and 24–450 °C. Thermal analysis of the sample was performed using an STA 409 PC Luxx synchronous thermal analyzer (Netzsch, Selb, Germany) at a heating rate of 10 K/min. Air was used as a purge gas, and an empty crucible was used as a standard. The enthalpy and thermal effect temperatures were processed using NETZSCH Proteus software (v. 8.0.3, NETZSCH-Gerätebau GmbH, Selb, Germany). NEXAFS spectra were obtained using the total electron yield (TEY) method. XPS analysis was performed on a Thermo Scientific ESCALAB 250Xi X-ray spectrometer (Thermo Fishes Scientific, East Grinstead, UK) with an AlKα X-ray tube (1486.6 eV). All peaks were calibrated relative to the C1s peak at 284.4 eV. The ESCALAB 250 Xi spectrometer software v.5.35, Thermo Fishes Scientific, East Grinstead, UK was used to process the experimental data. Diffuse reflectance spectra were recorded in the 200–1200 nm range using a UV-2550 spectrophotometer (Shimadzu, Tokyo, Japan).

3. Results and Discussion

3.1. Thermal Stability, Microstructure, and Crystal Structure

Scanning electron microscopy (SEM) results showed that the synthesized Bi_2.7Mg_0.46Ni_0.70Sb₂O_10+Δ sample is characterized by a low-porosity microstructure, with grain sizes, according to SEM data, ranging from 0.5 to 2.5 μm. The grains of the oxide ceramics are non-uniform in size. Zinc-containing pyrochlore is dominated by large grains [23], which are significantly larger than those of magnesium ceramics and range from 0.25 to 4 µm. The wide range of grain sizes in the ceramics may be due to the high synthesis temperature, close to the melting point of the material, at which small grains coalesce into larger ones. The atoms of the elements composing the oxide ceramic are uniformly distributed over the sample’s surface (Figure 1). According to EDS spectra, the chemical composition of the synthesized ceramic satisfies its nominal composition and is described by the stoichiometric formula Bi_2.7Mg_0.46Ni_0.69Sb_1.95O_10+Δ.

Thermal stability studies of the synthesized pyrochlore Bi_2.7Mg_0.46Ni_0.70Sb₂O_10+Δ were conducted using thermogravimetry and differential scanning calorimetry in the temperature range of 500–1200 °C. The obtained results revealed a change in sample mass above 1080 °C, indicating preservation of the stoichiometry of the pyrochlore phase during synthesis (Figure 2). As shown by the mass change curve (green), the sample mass decreases above 1080 °C by no more than 0.8 wt.%, which may be due to bismuth loss [17,18].

According to X-ray diffraction analysis (Figure 3), the sample synthesized at 1050 °C is single-phase and crystallizes in the cubic pyrochlore structural type. When refining the crystal structure, the ideal pyrochlore structure (sp. gr. Fd-3m) [7] was adopted as the initial model of the crystal structure, and the occupancy was determined in accordance with the stoichiometry of the composition. In order to provide the most accurate description of the X-ray diffraction profile, a model of disordered pyrochlore was considered. In this model the bismuth atoms are displaced to the 96g position, and the oxygen atoms are distributed over 48f and 8a with incomplete occupancy. The distribution of nickel(II) and magnesium(II) cations was varied over the bismuth and antimony positions. Six variants of filling the crystallographic positions are considered: 1—nickel and magnesium cations are distributed only in antimony positions; 2—only nickel(II) cations are located in bismuth positions in the amount of 16 at.% of the total amount of nickel; 3—only nickel(II) cations are located in bismuth positions in the amount of 16 at.% of the total amount of nickel and magnesium; 4—only magnesium cations are located in bismuth positions in the amount of 16 at.% of the total amount of magnesium and nickel; 5—magnesium and nickel cations are located in bismuth positions equally, in the amount of 8 at.% of the total amount of nickel and magnesium; 6—with the loss of bismuth and distribution of nickel and magnesium cations in antimony positions. The modeling results and refinement parameters for all variants are presented in

Table 1. Variants of cation distribution by crystallographic positions and refinement parameters obtained by the Rietveld method based on powder data, as well as atomic parameters of Ni-doped bismuth magnesium stibate.

1 option—[Bi1.71□0.29][Mg0.29Ni0.44Sb1.27]O6.87□0.13 = Bi2.7Mg 0.46Ni0.70Sb2O10.85
a (Å) α, β, γ (˚) V (Å 3) Dcalc (g/cm3)		10.47461(6) 90, 90, 90 1149.248(19) 7.562(5)	RB, % Rwp, % Rp, % Rexp, % GOF		0.494 5.14 3.76 3.05 1.69
Atom	Wyckoff site	x	y	z	SOF	Biso,Å2
Bi	96g	0	0.02150(14)	−0.01508(14)	0.1424(8)	0.98(7)
Sb	16b	0.5000	0.5000	0.5000	0.633	0.20(5)
Mg	16b	0.5000	0.5000	0.5000	0.1455	0.20(5)
Ni	16b	0.5000	0.5000	0.5000	0.2215	0.20(5)
O1	48f	0.1250	0.1250	0.4268(5)	1	1.45(18)
O2	8a	0.1250	0.1250	0.1250	0.87(3)	1.45(18)
2 option—[Bi1.71Ni0.07□0.22][ Mg 0.30Ni0.39Sb1.31]O6.99□0.11 = [Bi2.7Ni0.11][Mg 0.47Ni0.61Sb2.07]O11.04
a (Å) α, β, γ (˚) V (Å 3) Dcalc (g/cm3)		10.47471(6) 90, 90, 90 1149.2812(19) 7.662(5)	RB, % Rwp, % Rp, % Rexp, % GOF		1.393 5.19 3.82 3.05 1.70
Atom	Wyckoff site	x	y	z	SOF	Biso,Å2
Bi	96g	0	0.02151(13)	−0.02151(13)	0.1424(8)	0.30(7)
Ni	96g	0	0.02151(13)	−0.02151(13)	0.006(8)	0.30(7)
Sb	16b	0.5000	0.5000	0.5000	0.656	−0.14(5)
Ni	16b	0.5000	0.5000	0.5000	0.193	−0.14(5)
Mg	16b	0.5000	0.5000	0.5000	0.151	−0.14(5)
O1	48f	0.1250	0.1250	0.4247(6)	1	1.11(19)
O2	8a	0.1250	0.1250	0.1250	0.99(3)	1.11(19)
3 option—[Bi1.82Ni 0.12□0.06][ Mg 0.31Ni0.34Sb1.35]O7.0 = [Bi2.7Ni 0.18][ Mg 0.46Ni0.50Sb2]O10.38
a (Å) α, β, γ (˚) V (Å 3) Dcalc (g/cm3)		10.47536(6) 90, 90, 90 1149.49(2) 7.981(5)	RB, % Rwp, % Rp, % Rexp, % GOF		0.98 5.05 3.66 3.05 1.66
Atom	Wyckoff site	x	y	z	SOF	Biso,Å2
Bi	96g	0	0.02099(16)	−0.02099(2)	0.1514	1.57(8)
Ni	96g	0	0.02099(16)	−0.02099(2)	0.0104	1.57(8)
Sb	16b	0.5000	0.5000	0.5000	0.6729	−0.10(4)
Ni	16b	0.5000	0.5000	0.5000	0.1726	−0.10(4)
Mg	16b	0.5000	0.5000	0.5000	0.1545	−0.10(4)
O1	48f	0.1250	0.1250	0.4265(5)	1	1.22(16)
O2	8a	0.1250	0.1250	0.1250	1.00(3)	1.22(16)
4 option—[Bi1.82Mg 0.12□0.06][ Mg 0.18Ni0.47Sb1.34]O7 = [Bi2.73 Mg 0.18][ Mg 0.27Ni0.7Sb2.01]O10.5
a (Å) α, β, γ (˚) V (Å 3) Dcalc (g/cm3)		10.47566(6) 90, 90, 90 1149.59(2) 7.981(1)	RB, % Rwp, % Rp, % Rexp, % GOF		0.713 5.02 3.63 3.05 1.65
Atom	Wyckoff site	x	y	z	SOF	Biso,Å2
Bi	96g	0	0.02122(15)	−0.02122(15)	0.1514	1.16(7)
Mg	96g	0	0.02122(15)	−0.02122(15)	0.0104	1.16(7)
Sb	16b	0.5000	0.5000	0.5000	0.6729	0.00(4)
Ni	16b	0.5000	0.5000	0.5000	0.235	0.00(4)
Mg	16b	0.5000	0.5000	0.5000	0.0921	0.00(4)
O1	48f	0.1250	0.1250	0.4268(5)	1	0.95(15)
O2	8a	0.1250	0.1250	0.1250	1	0.95(15)
5 option—[Bi1.82Mg0.06Ni0.06□0.06][Mg0.24Ni0.41Sb1.3458]O7.00 = [Bi2.70Mg0.09Ni0.09][Mg 0.36Ni0.61Sb2]O10.38
a (Å) α, β, γ (˚) V (Å 3) Dcalc (g/cm3)		10.47576(6) 90, 90, 90 1149.63(2) 8.02280(14)	RB, % Rwp, % Rp, % Rexp, % GOF		0.810 5.03 3.65 3.05 1.65
Atom	Wyckoff site	x	y	z	SOF	Biso,Å2
Bi	96g	0	0.02119(15)	−0.02119(15)	0.1514(8)	1.23(7)
Mg	96g	0	0.02119(15)	−0.02119(15)	0.0052	1.23(7)
Ni	96g	0	0.02119(15)	−0.02119(15)	0.0052	1.23(7)
Sb	16b	0.5000	0.5000	0.5000	0.6729	0.37(4)
Ni	16b	0.5000	0.5000	0.5000	0.2038	0.07(4)
Mg	16b	0.5000	0.5000	0.5000	0.1233	0.07(4)
O1	48f	0.1250	0.1250	0.4272(5)	1	0.89(15)
O2	8a	0.1250	0.1250	0.1250	1.00(3)	0.89(15)
6 option—[Bi1.80□0.20][Mg 0.26Ni0.34Sb1.4]O6.91 = [Bi2.70][Mg 0.39Ni0.51Sb2.1]O10.365
a (Å) α, β, γ (˚) V (Å 3) Dcalc (g/cm3)		10.47574(6) 90, 90, 90 1149.62(2) 7.90(2)	RB, % Rwp, % Rp, % Rexp, % GOF		0.810 5.02 3.64 3.05 0.607
Atom	Wyckoff site	x	y	z	SOF	Biso,Å2
Bi	96g	0	0.02125(15)	−0.02115(15)	0.1501(8)	1.05(9)
Sb	16b	0.5000	0.5000	0.5000	0.7	0.23(5)
Ni	16b	0.5000	0.5000	0.5000	0.17	0.23(5)
Mg	16b	0.5000	0.5000	0.5000	0.13	0.23(5)
O1	48f	0.1250	0.1250	0.4271(5)	1	0.73(17)
O2	8a	0.1250	0.1250	0.1250	0.91(3)	0.73(17)

. Calculations showed that models 1, 5, and 6 demonstrated the best results in terms of thermal parameters and refinement parameters. Overall, the variation in fitting parameters across all models is minimal, and a single crystal is required for more accurate modeling. Structural aspects in comparison with the nature of bonds, vacancies and energetics can be further confirmed by DFT modeling within the framework of the synthetic growth concept and other levels of theory [25,26].

The geometric parameters of the structure for distribution variant 6, in which the spread of thermal parameters is minimal, are presented below. The analysis of the fitting results suggests that the bismuth sublattice is partially vacant in all models. In models 2 and 3, negative isotropic displacement parameters were obtained for the cations at position 16b, with the latter being even more negative for model 3. The very fact that such thermal atomic parameters were obtained indicates that the placement of only nickel(II) cations in the bismuth sublattice is unacceptable, and the result only worsens with increasing nickel(II) content. A comparison with similar model 4, which assumes the placement of only magnesium(II) cations, shows that the atomic displacement parameters remain unsatisfactory, but are no longer negative. Thus, it is shown that the distribution of magnesium(II) cations within the bismuth(III) sublattice is preferable to that of nickel(II). Furthermore, a mixed distribution of nickel and magnesium in the bismuth and antimony sublattices is probable.

The unit cell parameter of nickel pyrochlore Bi_2.7Mg_0.46Ni_0.70Sb₂O_10+Δ is 10.47574(6) Å. The unit cell parameter of pyrochlore Bi_2.7Zn_0.46Ni_0.70Sb₂O_10+Δ is a = 10.46442(5) Å, which is slightly smaller than that of pyrochlore with magnesium, despite the fact that the cationic radius of magnesium(II) is smaller than that of zinc(II) (R(Zn²⁺) = 0.074 nm, R(Mg²⁺) = 0.072 nm) [23]. This difference may be due to the distribution of a larger number of zinc cations at the bismuth position compared to magnesium. In the work [20] for pyrochlores described by the formula Bi_2−xNi_xNi_2/3−ySb_4/3+yO_7±δ, x = 0.1–0.35, y = 0–0.1, the unit cell parameter changes in the range of 10.44–10.47 Å, which is consistent with our data.

The final results of the refinement of the pyrochlore structure for the Bi_2.7Mg_0.46Ni_0.70Sb₂O_10+Δ composition by the Rietveld method in the Fd-3m:2 space group (227) are given in Table 1, variant 6. Model 6 of the structure plausibly describes the distribution of atoms among crystallographic sites, but is not the final model. Model 6 exhibits relatively small differences in the thermal parameters of the atoms, and the stoichiometric coefficient of the oxygen atom is closest to the calculated index, taking into account the formal valences of the atoms. The experimental, calculated, and difference X-ray diffraction patterns are shown in Figure 3. The atomic parameters and selected bond lengths of Bi_2.7Mg_0.46Ni_0.70Sb₂O_10+Δ are given in

Table 2. Selected bond lengths in the structure of Bi_2.7Mg_0.46Ni_0.70Sb₂O_10+Δ..

Bond	Length (Å)
Bi1–O1 × 2	2.2898(4)
–O1 × 2	2.3590(4)
–O1 × 2	2.640(4)
–O2 × 2	2.895(4)
<Bi1VIII–O>	2.55
Sb1–O1 × 6	2.003(19)
<Sb1VI–O>	2.00

. The modeling results indicate that the antimony(V)/nickel(II)/magnesium(II) cations form a regular oxygen octahedron, in which all M–O bonds in the octahedron have a length of approximately 2.003 Å (Table 2), close to that of octahedral polyhedra in tantalum/niobium pyrochlores [3,15,16,17,18].

The coordination polyhedron of bismuth atoms is a distorted octahedron, BiO₈. Individual interatomic distances in the BiO₈ polyhedron are pairwise identical and range from 2.2898(4) to 2.895(4) Å (Table 2). It is interesting to note that the BiO₈ polyhedron in antimony pyrochlore is more symmetrical and compact than that in niobium/tantalum pyrochlore [3,15,16,17,18]. This is evidenced by the alignment and small spread of Bi-O bond lengths in antimony pyrochlore compared to tantalum/niobium pyrochlore.

3.2. Thermal Expansion

The thermal expansion of nickel- and magnesium-containing antimony pyrochlore was studied in the temperature range of 30–1200 °C with a 30 °C increment (Figure 4a,

Table 3. TECs (×10⁶ °C⁻¹) of Bi_2.7Mg_0.46Ni_0.70Sb₂O_10+Δ along crystallographic axes at different temperatures.

T, °C	30	90	150	210	270	330	390	450	510	570	630	690	750	810
TECs (×106 °C−1)	6.82	7.06	7.29	7.53	7.76	7.99	8.22	8.46	8.70	8.92	9.15	9.38	9.61	9.84
<30-990>	8.34

) using high-temperature X-ray diffraction data, as well as the phase composition of the sample after annealing at 1200 °C (Figure 4b). The temperature dependence of the pyrochlore unit cell parameter is shown in Figure 4c. Up to 1080 °C, the unit cell parameter a of pyrochlore increases almost linearly from 10.47543 Å (30 °C) to 10.55078 Å (1080 °C), indicating the absence of phase transitions in this temperature range. The thermal stability of pyrochlore is confirmed by high-temperature X-ray diffraction data, according to which reflections of impurity phases appear in the X-ray diffraction patterns at a temperature of 1170 °C (Figure 4a). As can be seen from Figure 4c, a distinctive feature of the thermal behavior of antimony pyrochlore in the high-temperature region (above 1080 °C) is the duplication of the unit cell parameter. According to high-temperature X-ray diffraction data, the sample contains two cubic phases (sp. gr. Fd-3m), including the pyrochlore phase (Figure 4d). The doubling of the peaks can be clearly observed only at high angles, since the unit cell parameters of the cubic phases change only slightly: 10.5239 and 10.5249 Å. The peculiar behavior of bismuth-containing antimony pyrochlore is associated with its thermal dissociation at temperatures near 1080 °C. The thermal analysis curve, showing a slight mass loss in the sample, also indicates this thermal decomposition. According to data [23], zinc-containing pyrochlore is less stable (up to 1070 °C) than magnesium-containing pyrochlore, which is confirmed by thermogravimetry and high-temperature X-ray diffraction data. It is interesting to note that 1080 °C is also critical for tantalum pyrochlores. The cause of this extreme behavior is the same as in the case of bismuth evaporation, which affects the pyrochlore stoichiometry and is reflected in the unit cell parameter. The nature of the second cubic phase is still unclear. The content of the two cubic phases in a sample heated to 1140 °C was estimated at 49.88 and 50.12 at.%. A comparative assessment of the content of two cubic phases in antimony pyrochlores Bi_2.7Zn_0.46Ni_0.70Sb₂O_10+Δ/Bi_2.7Mg_0.46Ni_0.70Sb₂O_10+Δ, heated to 1170 °C, was carried out. According to the calculation, the content of the non-pyrochlore cubic phase at 1170 °C is almost the same in the samples, amounting to 50.2/50.12 mol.%, and demonstrates independence from the nature of the dopant. X-ray diffraction analysis of the sample at room temperature showed that the phase composition of the ceramics is represented by several phases: two cubic phases belonging to the Fd-3m space group, as well as a magnesium/nickel stibate phase (Mg/Ni)Sb₂O₆ (sp. gr. P42/mnm). The presence of nickel/magnesium stibate indicates the loss of bismuth upon heating of the sample, which is characteristic of the high-temperature dissociation of bismuth niobate/tantalate-based pyrochlores and indicates signs of a similar onset of thermal dissociation of bismuth-containing pyrochlores. The low content of thermal decomposition products indicates the low intensity of the bismuth evaporation process at 1200 °C, as evidenced by Figure 2, which shows that the mass loss of the sample calcined at 1200 °C does not exceed 0.8 at.% of the total mass of the sample. A simple calculation shows that the gross composition of the sample after calcination at 1200 °C, provided that only bismuth is removed, does not change much and corresponds to the conditional formula Bi_2.66Mg_0.46Ni_0.70Sb₂O_10+Δ..

Based on the polynomial approximation of the temperature dependence of the unit cell parameter, the values of the coefficient of thermal expansion (TEC), α, were calculated at different temperatures (Table 3, Figure 4e).

Analysis of the thermal behavior of Bi_2.7Zn_0.46Ni_0.70Sb₂O_10+Δ/Bi_2.7Mg_0.46Ni_0.70Sb₂O_10+Δ showed that antimony pyrochlores belong to isotropically expanding materials [23]. The coefficient of thermal expansion for Bi_2.7Zn_0.46Ni_0.70Sb₂O_10+Δ/Bi_2.7Mg_0.46Ni_0.70Sb₂O_10+Δ varies from 7.1 to 9.3 × 10⁻⁶/from 6.8 to 9.8 × 10^-6 °C⁻¹ in the temperature range of 30–810 °C, the average TEC values in this temperature range are almost the same 8.2 × 10⁻⁶/8.3 × 10⁻⁶ °C⁻¹. Interestingly, magnesium–nickel pyrochlore exhibits the greatest thermal expansion at high temperatures compared to zinc–nickel pyrochlore. This can be explained by the ionicity and bond length of Mg-O compared to Zn-O. The lower structural flexibility of zinc-containing pyrochlores may explain their reduced thermal stability. For nickel pyrochlore Bi₂NiTa₂O₉, the average TEC value in the range of 30–990 °C is 6.02 × 10⁻⁶ °C⁻¹ [17]. The lower TEC values for Bi₂NiTa₂O₉ indicate that, with similar bond lengths in the octahedron, the Ta-O bond is more rigid than the Sb-O bond, despite the fact that the covalency of the Sb-O bond is greater than that of Ta-O. Apparently, the reason for the greatest thermal expansion lies in the internal structure of antimony pyrochlore. The isotropy of the thermal behavior and the average TEC (8.3 × 10⁻⁶ °C⁻¹) of antimony pyrochlore are typical of compounds with a framework structure, confirming the thesis of the rigidity of the bonds of framework structures.

3.3. Optical and Dielectric Properties

The band gap (Eg) of antimony pyrochlore for direct allowed electron transitions was estimated using diffuse reflectance spectra. The approximation quality is higher for direct electron transitions. Meanwhile, the band widths calculated for n = 1 and n = 1/2 are almost identical. The calculations showed that the band gap for direct allowed transitions in the sample is 2.41 eV (Figure 5), corresponding to absorption in the 515 nm wavelength range. The band gap of the studied ceramics is typical for dielectrics and is close to the energy of solar radiation reaching the surface of our planet and having a maximum intensity (2.1–2.5 eV). This suggests the potential for using these materials as light-absorbing elements in solar cells.

The electrical properties of the Bi_2.7Mg_0.46Ni_0.70Sb₂O_10+Δ sample were studied in the temperature range of 24–450 °C at a frequency of 25 Hz–6 MHz (Figure 6). Figure 6a,b show the frequency dependences of the impedance modulus and phase angle as functions of temperature. The change in phase angle as a function of frequency and temperature is shown in Figure 6b. As can be seen, at room temperature, the phase angle is close to a right angle, confirming the conclusion about the manifestation of reactance caused by the capacitive current. At high frequencies, the phase angle remains at 90°, indicating the flow of predominantly bias currents. As Figure 6a shows, the impedance modulus of the sample remains virtually unchanged up to 200 °C (150 °C for Bi_2.7Zn_0.46Ni_0.70Sb₂O_10+Δ) over the entire frequency range and is proportional to the field frequency, indicating the flow of a capacitive current in the sample. As the temperature increases, through conductivity- the end-to-end conductivity begins to prevail over capacitive conductivity, which is reflected in the frequency independence of the impedance modulus, especially noticeable in the low-frequency region. As noted above, the sample exhibits capacitive conductivity, as a result of which the slope of the impedance modulus line is 45° with high accuracy (Figure 6c). In this case, $\left|Z\right|={\displaystyle \frac{1}{\omega C_p}}$, where $\omega =2\pi f$ is the angular frequency in units of rad/s; f—is the frequency in Hz; Cp—is the capacitance for the parallel equivalent circuit.

After taking the logarithm, we obtain a frequency dependence in the form of a straight line [27]:

$$log\left|Z\right|=-\log \left(2\pi f\right)-log{C}_p$$

(1)

Dependence (1) is observed experimentally, as shown in Figure 6a. All isotherms in this figure have coinciding high-frequency asymptotes, indicating the independence of capacitance from frequency and temperature. The formula for the approximating line for low-temperature data is as follows:

$$log\left|Z\right|=A+B·log\omega ,$$

(2)

where the values of parameters A and B are shown in Figure 6c. Comparing Formulas (1) and (2), we obtain: $log{C}_p=-A$. Thus, $C_p={10}^{-A}F={10}^{12-A}pF={10}^{1.226\pm 0.002}={10}^{0.002}{10}^{1.226}$. The relative error is 0.5%. The sample capacitance is Cp = (16.83 ± 0.08) pF. We determine the relative permittivity using the formula:

$$\epsilon =144·{\displaystyle \frac{h\left(mm\right)·C\left(pF\right)}{D^2\left(mm\right)}}=144·{\displaystyle \frac{2·16.83}{{12.6}^2}}\approx 30.5$$

(3)

The main error is related to the accuracy of measuring the sample’s geometric dimensions and is equal to 8%. It is interesting to note that the sample exhibits a constant relative permittivity of ~30 (26 for Bi_2.7Zn_0.46Ni_0.70Sb₂O_10+Δ) throughout the entire frequency range (up to 6 × 10⁶ Hz) at temperatures from room temperature to 200 °C (150 °C). With increasing temperature, the frequency range of independent permittivity narrows. The dielectric loss tangent at 24 °C does not exceed 2 × 10⁻² over the entire frequency range, and at a frequency of 5 × 10⁴ Hz it is minimal and equal to 5 × 10⁻⁴. The temperature dependence of the through conductivity of the sample is shown in Figure 6f. As a result of the calculation, the values of the activation energy of conductivity in the Bi_2.7Zn_0.46Ni_0.70Sb₂O_10+Δ/Bi_2.7Mg_0.46Ni_0.70Sb₂O_10+Δ samples were obtained as 1.30(5)/0.99(4) eV, respectively. The end-to-end conductivity of pyrochlore changes with increasing temperature from 2.5 × 10⁻⁷ Ohm⁻¹ ·m⁻¹ (230 °C) to 3.2 × 10⁻⁴ Ohm⁻¹ ·m⁻¹ (450 °C). The electrical conductivity values are close to those of nickel pyrochlore Bi₂NiTa₂O₉, the specific electrical conductivity varies from 3.2 × 10⁻⁷ Ohm⁻¹ ·m⁻¹ (350 °C) to 1 × 10⁵ Ohm⁻¹ ·m⁻¹ (450 °C), and for solid solutions Bi_1.4(Mg_1–xNi_x)_0.7Ta_1.4O_6.3 it varies from 2 × 10⁻⁷ Ohm⁻¹·m⁻¹ (370 °C) to 1.2 × 10⁻⁵ Ohm⁻¹·m⁻¹ (440 °C) [17,18].

3.4. XPS and NEXAFS

The charge state of cations in pyrochlore was studied using X-ray spectroscopy. Figure 7a,b–e show the survey and Bi4f, Sb3d, Mg1s, and Ni2p XPS spectra of the investigated sample, respectively. The chemical composition of the sample surfaces was analyzed based on the spectra of metals. The figures show the results of decomposition of spectral dependences into individual peaks modeled by Gaussian–Lorentzian curves, and background lines by Shirley or smart approximation. The shape of the peaks in the Bi4f XPS spectra of pyrochlore and Bi₂O₃ oxide (Figure 7b) clearly indicates that all bismuth cations are in the same charge state, as there is no peak splitting or distortion. The energy position of the pyrochlore peaks has a characteristic shift (ΔE = 0.2 eV) toward lower energies compared to the binding energy in trivalent Bi₂O₃ oxide. For this reason, it was concluded that the bismuth cations in antimonite have the same effective charge of +(3-δ). The decrease in the effective charge state may be associated with the introduction of low-charge cations of 3d-elements into the cationic sublattice of bismuth.

Figure 7c shows that the Sb3d XPS spectra overlap with the oxygen spectra. Meanwhile, the Sb3d_3/2 component at 539.6 eV can be distinguished, and its shape indicates the same charge state of antimony ions in the ceramics. In the literature [28,29,30], the distribution of binding energy values for antimony ions of different valences is observed. The difference between the binding energies of the Sb3d_3/2 lines found for Sb₂O₃ and Sb₂O₅ varies in the range of 0.6–1.0 eV and, accordingly, the states of Sb³⁺ and Sb⁵⁺ can be well separated by the XPS method. According to the literature data, the spread of binding energy values for Sb³⁺/Sb⁵⁺ is 539.4–540.0 eV [28], 539.3–540.2 eV [29], and 539.5–540.5 eV [30]. In the present experiment, the binding energy of the Sb3d3/2 peak is 539.6 eV, thereby indicating a charge state of +(5-δ) for antimony. A similar comparative analysis of the energy position of the peak was conducted for the Mg1s XPS spectrum of the pyrochlore sample (Figure 7d) and MgO [31], which allows us to assume that the charge state of these atoms is +2. The Ni2p XPS spectra of nickel oxides and antimony pyrochlore are shown in Figure 7e. Comparison of the pyrochlore spectra with the NiO spectrum obtained by us and the Ni₂O₃ spectrum known from the literature [32] allows us to conclude that all nickel cations are in the same charge state. The energy position of the XPS Ni2p spectrum of pyrochlore is more consistent with the Ni₂O₃ spectrum. However, the NEXAFS Ni2p spectra of pyrochlore and NiO oxide (Figure 7f) practically coincide in energy position and spectral details. Experimental NEXAFS Ni2p spectra of Ni₂O₃ are not available in the literature. However, the calculated spectra of trivalent nickel clearly differ from those of the pyrochlore studied here [33]. This difference led to the conclusion that the nickel cations in pyrochlore are divalent.

4. Conclusions

A low-porosity nickel- and magnesium-containing bismuth antimonate, Bi_2.7Mg_0.46Ni_0.70Sb₂O_10+Δ, was synthesized for the first time by the solid-phase method and characterized in detail. The structure was refined using the Rietveld method. The pyrochlore crystal structure is disordered, and the bismuth sublattice is partially vacant. The average thermal expansion coefficient (TEC) is 8.3 × 10⁻⁶ °C⁻¹ for the temperature range of 30–810 °C. Above 1080 °C, pyrochlore thermally dissociates to form bismuth-free phases of the MSb₂O₆ (M-Ni, Mg) type. Above 1080 °C, reflections of two cubic phases are recorded, one of which is the pyrochlore phase. The relative high-frequency permittivity is independent of frequency and temperature up to 200 °C and has a value of 30.5, while the dielectric loss tangent is low, equal to 5 × 10⁻⁴. The calculation of the conductivity activation energy in the sample yielded a value of 0.99 eV. According to X-ray spectroscopy data, the charge state of the metal cations is traditional.