Thermodynamic Characteristics of Zinc Niobates Zn₃Nb₂O₈, ZnNb₂O₆, and Zn₂Nb₃₄O₈₇. p–x Diagram of the ZnO–Nb₂O₅ System

Abstract

Vapor formation in the ZnO–Nb₂O₅ system in the range 1223–1465 K was studied by Knudsen effusion mass spectrometry. Over the entire range of condensed phase compositions, the saturated vapor above the system consists of zinc atoms, oxygen molecules, and a small amount of ZnO molecules. The absolute component partial vapor pressures and activities were calculated. The р–х section of the global р–Т–х phase diagram at 1353 and 1443 K was plotted. The second-law and third-law values were determined of the standard enthalpies of selected heterophase reactions and the standard enthalpies of formation zinc niobates: ${{\Delta }_{f}}H_{{298}}^{^\circ }$(Zn₃Nb₂O₈) = –2992.0 ± 30.2 kJ/mol, ${{\Delta }_{f}}H_{{298}}^{^\circ }$(ZnNb₂O₆) = –2292.4 ± 19.9 kJ/mol, and ${{\Delta }_{f}}H_{{298}}^{^\circ }$(Zn₂Nb₃₄O₈₇) = –33056.1 ± 15.0 kJ/mol, and their enthalpies of formation from simple oxides: (Zn₃Nb₂O₈) = –50.0 ± 20.0 kJ/mol, (ZnNb₂O₆) = –40.5 ± 15.0 kJ/mol, and (Zn₂Nb₃₄O₈₇) = –90.9 ± 15.0 kJ/mol.

INTRODUCTION

Systems comprising wide-gap oxide semiconductors SnO₂ (3.54 eV) and ZnO (3.37 eV) are in the focus due to their optical, electrophysical, catalytic, and sensing properties. These compounds belong to the family of transparent conducting oxides (TCOs). TCO films are used as transparent contact layers for LEDs and solar cells and as displays. ZnO- and SnO₂-based nanomaterials have unique sensing and catalytic activities and high photosensitivity to UV radiation; they are used as field-effect transistors, emission displays, and luminescent materials. However, pure ZnO and SnO₂ have rather limited applications due to their high electrical resistance; therefore, they are almost always doped with donor impurities (Al, Ga, Nb, Ta, and other). In addition to the increased interest in physical properties of ZnO-based films and diverse nanomaterials doped with tantalum and niobium [1–9], the ZnO–Ta₂O₅ and ZnO–Nb₂O₅ systems have recently gained increased attention due to the mixed oxides ZnTa₂O₆, Zn₃Ta₂O₈, ZnNb₂O₆, and Zn₃Nb₂O₈ existing therein. Ceramics based on those compounds are promising materials in microwave electronics. The combination of a high dielectric constant, a high electrical Q-factor, and a low temperature coefficient of dielectric constant makes Zn–Nb–Ta–O ceramics useful for substrates of microwave microcircuits, dielectric resonators or filters in the microwave range [10–13]. Zn₃Ta₂O₈, Zn₃Nb₂O₈, and their combinations can be used as low-voltage cathodoluminescent phosphors in field-emission displays or vacuum luminescent displays [14–16]. Various compositions of ZnO–Ta₂O₅ and ZnO–Nb₂O₅ systems are used in heterogeneous organic catalysis and photocatalysis to degrade toxic organics in the environment [17, 18].

The physical and physicochemical properties of any oxide material strongly depend on the preparation method used and its parameters. There are two main approaches to the preparation of oxide materials. One involves gas-phase processes, while the second uses solutions. The solution methods, as the gas-phase methods, too, often employ high temperatures (up to 1400°С), as the material prepared from solution is subjected to long-term high-temperature annealing in order to obtain the required properties. Therefore, for the controlled synthesis of polyfunctional oxide materials with tailored cationic and anionic compositions, it is extremely important that their thermodynamic characteristics be known and vaporization thermodynamics be studied. We should emphasize that the key matters must be the determination of the vapor composition, absolute values of partial vapor pressures, mainly oxygen partial pressures, the standard enthalpies of formation of complex oxides and the Gibbs energies of formation of solid solutions; and the construction of the р–х and р–Т sections of global р–Т–х phase diagrams of oxide systems. The Т–х diagrams of the ZnO–Ta₂O₅ and ZnO–Nb₂O₅ systems have been studied in sufficient detail.

EXPERIMENTAL

Our high-temperature studies of the vaporization and thermodynamic properties of the ZnO–Nb₂O₅ system over the entire range of compositions were performed by Knudsen effusion mass spectrometry on an MS 1301 instrument. Quartz effusion cells with the vaporization-to-effusion surface area ratio of ~100 were used. The Knudsen cell was heated by a resistance furnace; temperature was measured by a Pt/Pt(Rh) thermocouple and maintained accurate to ±1^оС.

According to Dayal [19], the ZnO–Nb₂O₅ quasi-binary system forms three complex oxides, namely, Zn₃Nb₂O₈ (3 : 1), ZnNb₂O₆ (1 : 1), and Zn₂Nb₃₄O₈₇ (2 : 17). Up to 1085°С, these oxides are in equilibrium with four heterogeneous fields: [ZnO + Zn₃Nb₂O₈] (I), [Zn₃Nb₂O₈ + ZnNb₂O₆] (II), [ZnNb₂O₆ + Zn₂Nb₃₄O₈₇] (III), and [Zn₂Nb₃₄O₈₇ + Nb₂O₅] (IV). Below 1085°С, the (2 : 17) compound is unstable; the other two are separated by three heterogeneous fields: [ZnO + Zn₃Nb₂O₈] (I), [Zn₃Nb₂O₈ + ZnNb₂O₆] (II), and [ZnNb₂O₆ + Nb₂O₅] (V). The (1 : 1) and (3 : 1) compounds melt congruently at 1312 and 1405°С, respectively, and the (2 : 17) compound melts incongruently with the peritectic temperature 1415°С. At 1350°С zinc niobate (1 : 1) undergoes polymorphic transition from the low-temperature phase α-ZnNb₂O₆ to the high-temperature phase β-ZnNb₂O₆.

The vaporization thermodynamics of the ZnO–Nb₂O₅ system has not been studied up to now, while the vaporization of its constituent individual oxides is described in detail in numerous documents [20–23]. According to those works, zinc oxide vaporization is congruent; the saturated vapor consists mostly of Zn atoms and dioxygen molecules О₂. This nature of the saturated vapor, despite its simplicity, makes it problematic to use platinum Knudsen cells in mass-spectrometric studies because they dissolve zinc [24–26]. It is for this reason that the vaporization of oxides and oxide systems where the vapor contains metal atoms is always accompanied by an uncontrolled monotonic decrease in metal partial pressure and an increase in oxygen pressure [25, 26]. However, the review of literature on the ZnO–SiO₂, Nb₂O₅–SiO₂, and ZnO–Nb₂O₅–SiO₂ phase diagrams [27, 28] showed that quartz Knudsen cells can be used to study the ZnO–Nb₂O₅ system in the range 1200–1400 K. The constancy of the measured ion currents during vaporization in the heterogeneous phase regions of the system, as well as the absence of zinc silicate in nonvolatile residues after evaporation according to X-ray powder diffraction data, proves that silicon oxide can be used as an inert material relative to the system under study in this temperature range.

The sublimation of niobium oxide Nb₂O₅ in the range 1100–1400°С is incongruent, with oxygen molecules transferred to the vapor phase and various condensed oxides formed, whose compositions lie in the range Nb₁₂O₂₉–Nb₅₃O₁₃₂ [29–34]. The lower volatility of niobium oxide compared to that of zinc oxide allows us to consider the system during vaporization in the range 1200–1500 K in the frame of a two-component system as

$${{N}_{{{\text{ZnO}}}}} + {{N}_{{{\text{N}}{{{\text{b}}}_{{\text{2}}}}{{{\text{O}}}_{{\text{5}}}}}}} = {\text{ }}1,$$

(1)

where N_ZnO (${{N}_{{{\text{Nb}}}}}_{{_{2}{{{\text{O}}}_{5}}}}$) is zinc oxide (niobium oxide) mole fraction.

ZnO–Nb₂O₅ samples containing 90, 75, 60, 50, 40, and 11 mol % ZnO were used in vaporization experiments. The first four of these samples were prepared by annealing homogenized mixtures of pure niobium oxide and zinc oxide in platinum crucibles under air at T = 1173 K for 30 h; the purity and phase composition of the samples were monitored by X-ray powder diffraction and X-ray fluorescence analysis. The 11 mol % ZnO sample was prepared immediately in the course of a mass-spectrometric experiment by annealing a thoroughly homogenized ZnNb₂O₆ + Nb₂O₅ sample containing 88.9 mol % Nb₂O₅ in the effusion cell at Т > 1360 K.

RESULTS AND DISCUSSION

The requirements imposed on the experimental work where quartz effusion chambers are used did not allow us to determine the component partial vapor pressures over all phase areas of the ZnO–Nb₂O₅ system in one isothermal evaporation experiment [35]. We performed three isothermal partial sublimation experiments on I, II, and V phase systems at Т = 1353 K and four similar experiments on I–IV phase systems at Т = 1443 K. The thus-performed sublimation study and the known thermodynamic characteristics of zinc oxide [20–23] indicate that the saturated vapor of the system consists mostly of zinc atoms and oxygen molecules. However, Grade et al. [36] detected ZnO molecules in the vapor phase, with the partial pressure almost three orders of magnitude lower than the pressure of the major components. The partial pressures of zinc atoms and oxygen molecules were calculated by the Hertz–Knudsen equation subject to the congruent sublimation of zinc oxide in the settings of an effusion experiment:

$$({{p}_{{{\text{Zn}}}}}{\text{/}}\sqrt {{{M}_{{{\text{Zn}}}}}} ){\text{/}}({{p}_{{{{{\text{O}}}_{2}}}}}{\text{/}}\sqrt {{{M}_{{\text{O}}}}_{{_{2}}}} ) = 2.$$

(2)

The results of these calculations appear in Tables 1 and 2. Table 1 also lists the partial vapor pressures upon zinc oxide sublimation in a closed space, where the vaporization process fulfills the equality of gas and condensed phase compositions:

$${{p}_{{{\text{Zn}}}}}{\text{/}}{{p}_{{{{{\text{O}}}_{2}}}}} = 2.$$

(3)

Table 1. Component partial vapor pressures over the ZnO–Nb₂O₅ system, T = 1353 K

Table 2. Component partial vapor pressures over the ZnO–Nb₂O₅ system, T = 1443 K

In so doing, we used the equilibrium constants of the reaction

$${\text{ZnO(g)}} = {\text{Zn(g)}} + 0.5{{{\text{O}}}_{2}}$$

(4)

that we calculated using experimental data borrowed from [36]. The thus-determined partial pressures were used to plot the р–х section of the global р–Т–х phase diagram (Figs. 1 and 2) at 1353 and 1443 K.

Fig. 1.

р–х diagram of the ZnO–Nb₂O₅ system at Т = 1353 K.

Fig. 2.

р–х diagram of the ZnO–Nb₂O₅ system at Т = 1443 K.

In order to determine the standard enthalpies of formation of zinc niobates, we calculated the enthalpies of the following heterophase reactions:

$${\text{ZnO(cr}}) = {\text{Zn(g}}) + 0.5{{{\text{O}}}_{2}},$$

(5)

$${\text{Z}}{{{\text{n}}}_{{\text{3}}}}{\text{N}}{{{\text{b}}}_{{\text{2}}}}{{{\text{O}}}_{{\text{8}}}}{\text{(cr}}) = {\text{ZnN}}{{{\text{b}}}_{{\text{2}}}}{{{\text{O}}}_{{\text{6}}}}{\text{(cr)}} + 2{\text{Zn(g}}) + {{{\text{O}}}_{2}},$$

(6)

$${\text{ZnN}}{{{\text{b}}}_{{\text{2}}}}{{{\text{O}}}_{{\text{6}}}}{\text{(cr}}) = {\text{N}}{{{\text{b}}}_{{\text{2}}}}{{{\text{O}}}_{{\text{5}}}}{\text{(cr}}) + {\text{Zn(g}}) + 0.5{{{\text{O}}}_{2}},$$

(7)

$$\begin{gathered} {\text{ZnN}}{{{\text{b}}}_{{\text{2}}}}{{{\text{O}}}_{{\text{6}}}}{\text{(cr}}){\text{ }} = 1{\text{/}}17{\text{Z}}{{{\text{n}}}_{{\text{2}}}}{\text{N}}{{{\text{b}}}_{{{\text{34}}}}}{{{\text{O}}}_{{{\text{87}}}}}{\text{(cr}}) \\ + \,\,15{\text{/}}17{\text{Zn(g) }} + {\text{ }}15{\text{/}}34{{{\text{O}}}_{2}}, \\ \end{gathered} $$

(8)

$$\begin{gathered} {\text{Z}}{{{\text{n}}}_{{\text{2}}}}{\text{N}}{{{\text{b}}}_{{{\text{34}}}}}{{{\text{O}}}_{{{\text{87}}}}}{\text{(cr}}) \\ = 17{\text{N}}{{{\text{b}}}_{{\text{2}}}}{{{\text{O}}}_{{\text{5}}}}{\text{(cr}}) + 2{\text{Zn(g)}} + {{{\text{O}}}_{2}}. \\ \end{gathered} $$

(9)

The second-law and third-law enthalpies of reactions (5)–(9) were determined. To determine the second-law value, we studied temperature-dependent values proportional to the equilibrium constants of reactions (5)–(9), which were written as k*(5, 7) = (I_ZnT)^1.5, k*(6, 9) = (I_ZnT)³, and k*(8) = (I_ZnT)^45/34 by virtue of the congruent sublimation of zinc oxide.

The standard enthalpies of reactions (5)–(9) were calculated by the reaction isobar equation by the least-squares method (Table 3).

Table 3.   Standard enthalpies of heterophase reactions (kJ/mol)

Here, we should emphasize that those enthalpies can have a certain systematic error associated with the enrichment of the surface layer of the system under study with non-volatile niobium oxide Nb₂O₅ in the process of vaporization and possible attendant hampering of zinc oxide sublimation. It is possible that niobium pentoxide would retain its original stoichiometric composition in these experiments, as vaporization in the system takes place at a relatively high oxygen pressure (Tables 1, 2). The enthalpies of reactions (5)–(9) were referred to 298.15 K using the known heat capacity values: $c_{p}^{^\circ }$(Zn_g) = 20.79 J/(mol K), $c_{p}^{^\circ }$(О_2g) = 29.35 J/(mol K), $c_{p}^{^\circ }$(ZnO_cr) = 40.25 J/(mol K) [38, 39], and $c_{p}^{^\circ }$(Nb₂O_5cr) = 131.95 J/(mol K) [37, 38]; and the heat capacities of mixed oxides calculated according to the Neumann–Kopp rule: $c_{p}^{^\circ }$(Zn₃NbO_8cr) = 252.7 J/(mol K), $c_{p}^{^\circ }$(ZnNbO_6cr) = 172.2 J/(mol K), and $c_{p}^{^\circ }$(Zn₂Nb₃₄O_87cr) = 2323.65 J/(mol K) on the assumption of their temperature independence. The standard enthalpies of these reactions referred to 298.15 K appear in Table 4.

Table 4. Second-law and third-law standard enthalpies ${{\Delta }_{r}}H_{{298}}^{^\circ }$ of heterophase reactions (kJ/mol)

The standard enthalpies of heterophase reactions (5)–(9) were also calculated by the third law of thermodynamics. In the calculations, used were the experimentally determined absolute partial vapor pressures of zinc atoms and oxygen molecules at T = 1353 and 1443 K (Table 1); known entropies of components of these reactions at T = 298.15 K: S°(Zn_g) = 160.88 J/(mol K) [37, 38], S°(ZnО_g) = 37.89 J/(mol K) [38, 39], S°(О_2g) = 205.03 J/(mol K) [37, 38], and S°(Nb₂О_5cr) = 137.10 J/(mol K) [37, 38]; and the entropies of mixed oxides calculated as means of the Kelley and Latimer increments [39–42]: S°(Zn₃Nb₂O_8cr) = 274.0 J/(mol K), S°(ZnNb₂O_6cr) = 181.7 J/(mol K), and S°(Zn₂Nb₃₄O_87cr) = 2422.5 J/(mol K). The thus-determined standard enthalpies of reactions (5)–(9) are as follows:

${{\Delta }_{r}}H_{{1353\,\,{\text{K}}}}^{^\circ }$(5) = 494.2 ± 20.0 kJ/mol, ${{\Delta }_{r}}H_{{1353\,\,{\text{K}}}}^{^\circ }$(6) = 981.5 ± 25.0 kJ/mol, ${{\Delta }_{r}}H_{{1353\,\,{\text{K}}}}^{^\circ }$(7) = 524.1 ± 20.0 kJ/mol, ${{\Delta }_{r}}H_{{1443\,\,{\text{K}}}}^{^\circ }$(8) = 463.1 ± 20.1 kJ/mol, and ${{\Delta }_{r}}H_{{1443\,\,{\text{K}}}}^{^\circ }$(9) = 1067.1 ± 25.0 kJ/mol. Table 4 lists the enthalpies referred to 298.15 K. The uncertainty in the third-law enthalpies is due mainly to the accuracies of determination of equilibrium constants and estimation of entropy changes of heterophase reactions. Thermodynamic analysis showed that these factors have roughly equivalent contributions. The recommended values of the enthalpies of reactions (5)–(9) obtained as arithmetic means of the second-law and third-law values also appear in Table 3. This is because, in this experimental work, it is difficult to give preference to any method for determining the values of enthalpies. The total uncertainty for the recommended values was calculated according to the law of addition of random variables.

We used the recommended values of the enthalpies of reactions (5)–(9) and borrowed the standard enthalpies of formation ${{\Delta }_{f}}H_{{298}}^{^\circ }$(Nb₂О_5cr) = –1897.0 kJ/mol [37, 38] and ${{\Delta }_{f}}H_{{298}}^{^\circ }$(Zn_g) = 130.7 kJ/mol [37, 38] to calculate, by the Hess law, the standard enthalpies of formation of zinc niobates from constituent elements and from simple oxides (Tables 4, 5). Our value of the standard enthalpy of formation of crystalline zinc oxide correlates with the published values, and this may serve to validate the correctness of our study. We should mention here a rather low relative accuracy of the calculations of standard enthalpies of formation of zinc niobates from simple oxides using the thermodynamic cycle. This is due to the calculation method used, in which the determined small value (the enthalpy of formation of a mixed oxide from simple oxides) is calculated as the algebraic sum of several large values (the standard enthalpies of formation from elements). For this reason, the standard enthalpies of formation of zinc niobates from simple oxides were also calculated from the Gibbs energies of formation of zinc niobates from simple oxides [43] and the absolute entropies of components of reaction (10):

$$n{\text{Zn}}{{{\text{O}}}_{{{\text{cr}}}}} + m{\text{N}}{{{\text{b}}}_{{\text{2}}}}{{{\text{O}}}_{{{\text{5cr}}}}} = n{\text{ZnO}}m{\text{N}}{{{\text{b}}}_{{\text{2}}}}{{{\text{O}}}_{{{\text{5cr}}}}},$$

(10)

$${{\Delta }_{f}}G_{T}^{^\circ }(n{\text{ZnO}}m{\text{N}}{{{\text{b}}}_{{\text{2}}}}{{{\text{O}}}_{{{\text{5cr}}}}}) = RT\ln (a_{{{\text{ZnO}}}}^{n}a_{{{\text{N}}{{{\text{b}}}_{{\text{2}}}}{{{\text{O}}}_{{\text{5}}}}}}^{m}).$$

(11)

Table 5. Standard enthalpies of formation of zinc niobates (kJ/mol)

The niobium oxide activities necessary for the calculations were found from Eq. (11), according to which relationships can be written to calculate niobium oxide activities in all heterogeneous areas of the ZnO–Nb₂O₅ system at T = 1353 K:

$${{({{a}_{{{\text{ZnO}}}}}{{a}_{{{\text{N}}{{{\text{b}}}_{{\text{2}}}}{{{\text{O}}}_{{\text{5}}}}}}})}_{{\text{V}}}} = {{({{a}_{{{\text{ZnO}}}}})}_{{\text{V}}}} = {\text{ }}{{({{a}_{{{\text{ZnO}}}}}{{a}_{{{\text{N}}{{{\text{b}}}_{{\text{2}}}}{{{\text{O}}}_{{\text{5}}}}}}})}_{{{\text{II}}}}},~~$$

(12)

$${{({{a}_{{{\text{N}}{{{\text{b}}}_{{\text{2}}}}{{{\text{O}}}_{{\text{5}}}}}}})}_{{{\text{II}}}}} = {\text{ (}}{{a}_{{{\text{ZnO}}}}}{{{\text{)}}}_{{\text{V}}}}{\text{/(}}{{a}_{{{\text{ZnO}}}}}{{{\text{)}}}_{{{\text{II}}}}},$$

(13)

$${{(a_{{{\text{ZnO}}}}^{3}{{a}_{{{\text{N}}{{{\text{b}}}_{{\text{2}}}}{{{\text{O}}}_{{\text{5}}}}}}})}_{{\text{I}}}} = {{({{a}_{{{\text{N}}{{{\text{b}}}_{{\text{2}}}}{{{\text{O}}}_{{\text{5}}}}}}})}_{{\text{I}}}} = {{(a_{{{\text{ZnO}}}}^{3}{{a}_{{{\text{N}}{{{\text{b}}}_{{\text{2}}}}{{{\text{O}}}_{{\text{5}}}}}}})}_{{{\text{II}}}}},$$

(14)

$${{({{a}_{{{\text{N}}{{{\text{b}}}_{{\text{2}}}}{{{\text{O}}}_{{\text{5}}}}}}})}_{{\text{I}}}} = {{{\text{(}}a_{{{\text{ZnO}}}}^{3}{{a}_{{{\text{N}}{{{\text{b}}}_{{\text{2}}}}{{{\text{O}}}_{{\text{5}}}}}}}{\text{)}}}_{{{\text{II}}}}},$$

(15)

and at T = 1443 K:

$${{(a_{{{\text{ZnO}}}}^{2}a_{{{\text{N}}{{{\text{b}}}_{{\text{2}}}}{{{\text{O}}}_{{\text{5}}}}}}^{{17}})}_{{{\text{IV}}}}} = {{(a_{{{\text{ZnO}}}}^{2})}_{{{\text{IV}}}}} = {{(a_{{{\text{ZnO}}}}^{2}a_{{{\text{N}}{{{\text{b}}}_{{\text{2}}}}{{{\text{O}}}_{{\text{5}}}}}}^{{17}})}_{{{\text{III}}}}},$$

(16)

$${{(a_{{{\text{N}}{{{\text{b}}}_{{\text{2}}}}{{{\text{O}}}_{{\text{5}}}}}}^{{{\text{17}}}})}_{{{\text{III}}}}} = {{{\text{(}}a_{{{\text{ZnO}}}}^{2}{\text{)}}}_{{{\text{IV}}}}}{\text{/(}}a_{{{\text{ZnO}}}}^{2}{{{\text{)}}}_{{{\text{III}}}}},$$

(17)

$${{({{a}_{{{\text{ZnO}}}}}{{a}_{{{\text{N}}{{{\text{b}}}_{{\text{2}}}}{{{\text{O}}}_{{\text{5}}}}}}})}_{{{\text{III}}}}} = {{({{a}_{{{\text{ZnO}}}}}{{a}_{{{\text{N}}{{{\text{b}}}_{{\text{2}}}}{{{\text{O}}}_{{\text{5}}}}}}})}_{{{\text{II}}}}},$$

(18)

$${{({{a}_{{{\text{N}}{{{\text{b}}}_{{\text{2}}}}{{{\text{O}}}_{{\text{5}}}}}}})}_{{{\text{II}}}}} = {{({{a}_{{{\text{ZnO}}}}}{{a}_{{{\text{N}}{{{\text{b}}}_{{\text{2}}}}{{{\text{O}}}_{{\text{5}}}}}}})}_{{{\text{III}}}}}{\text{/(}}{{a}_{{{\text{ZnO}}}}}{{{\text{)}}}_{{{\text{II}}}}}.$$

(19)

The calculated niobium oxide activities in the areas [ZnO + Zn₃Nb₂O₈] (I), [Zn₃Nb₂O₈ + ZnNb₂O₆] (II), and [ZnNb₂O₆ + Zn₂Nb₃₄O₈₇] (III) and the experimentally determined zinc oxide activities (Tables 1, 2) enabled us to determine the standard Gibbs energies of zinc niobates. Once the absolute entropies of zinc [37, 38] and niobium [37, 38] simple oxides and of mixed oxides estimated according to Kelley and Latimer [39–42] were known (see above), we could determine the enthalpies of formation of zinc niobates from simple oxides (Table 6). The uncertainty in the thus-calculated enthalpies arises from estimates of the entropies of mixed oxides and our accepted condition of the temperature-independent entropy change of zinc niobates formation reactions from simple oxides. The enthalpies of formation were referred to 298.15 K in the same manner as the enthalpies of reactions (5)–(9) were.

Table 6. Gibbs energies and enthalpies of formation of zinc niobates from simple oxides (kJ/mol)

The consistency of the values of standard enthalpies of formation of zinc niobates found by three independent methods (calculated from the second and third laws of thermodynamics and from the Gibbs energy of formation) signifies the correctness of our studies performed to determine component partial vapor pressures and activities.

CONCLUSIONS

The thermodynamic characteristics of the ZnO–Nb₂O₅ system determined in this study can be very useful in the manufacture of dielectric ceramics with high physical characteristics, which can be an alternative to the more expensive tantalum oxide ceramics. As mentioned above, zinc niobates are distinguished by high sensing sensitivity to hydrogen [2], and the hydrogen gas selectivity strongly depends on the single-phase state of the material, e.g., ZnNb₂O₆, whose preparation and performance with the maintenance of the initial characteristics is impossible unless the main thermodynamic characteristics of the sensor are known.