Physical Chemistry

V. I. Lavrent’ev, Corresponding Member of the Academy of Sciences of the USSR, Ya. I. Gerasimov, and T. N. Rezukhina

Thermodynamic Characteristics of Niobium Oxides

(Equilibrium with Hydrogen and Electrochemical Measurements)

In the niobium–oxygen system there exist, at least, three oxides: Nb₂O₅, with a homogeneity range from NbO₂.₅ to NbO₂.₄*, NbO₂, and NbO, with very narrow homogeneity ranges (¹–⁷). The equilibrium conditions in the reduction of Nb₂O₅ to NbO₂ by hydrogen and carbon monoxide have been studied in works (³–⁷). However, the results of works (³,⁴) are not free from errors associated with the influence of thermal diffusion; in work (⁵) only approximate values of the equilibrium constants are given. Work (⁶) is known to us only from a brief description in the monograph (²²), where values of the equilibrium constants are absent. In the later work (⁷), the equilibrium of niobium pentoxide with hydrogen was measured only for one temperature. The equilibrium of the lower oxides of niobium with hydrogen apparently has not been studied by anyone. In the present work the equilibrium reduction of niobium pentoxide to NbO was investigated, and the e.m.f. of a galvanic cell containing the lower niobium oxide NbO and metallic niobium was measured. In the work, niobium pentoxide (99.9% Nb₂O₅) and metallic niobium (98.6% Nb; 0.08% Fe; 0.06% Ti; 0.10% Pb; 0.04% Si; 0.12% C) were used.

![Figure 1 schematic not reproduced]

Fig. 1. Reduction isotherms of Nb₂O₅ for temperatures:
a — 1207°, b — 1400°, c — 1550°

The equilibrium of niobium oxides with hydrogen in the temperature interval 1200–1550° C was studied by the circulation method in an apparatus described in (⁸). The sample under investigation, in the form of a pellet, was placed in a molybdenum short-circuit furnace on a platinum support so that the pellet touched the platinum in a few places. The gross composition of the reduction products was determined from the gain in weight of the preparation upon ignition in air to Nb₂O₅; the phase composition was determined by X-ray diffraction. Two stages of reduction of Nb₂O₅ were investigated:

\[ 2.5\,\mathrm{NbO}_{2.4} + \mathrm{H}_2 \rightarrow 2.5\,\mathrm{NbO}_2 + \mathrm{H}_2\mathrm{O}, \tag{I} \]

\[ \mathrm{NbO}_2 + \mathrm{H}_2 \rightarrow \mathrm{NbO} + \mathrm{H}_2\mathrm{O}. \tag{II} \]

The values of the equilibrium constants \(K_p = P_{\mathrm{H_2O}} / P_{\mathrm{H_2}}\) are presented in Table 1 and in Fig. 1. In the composition range from NbO₂.₄ to NbO₂.₅, the values of \(K_p\) increase rapidly and cannot be measured sufficiently accurately in our apparatus. The logarithmic polytherms of the equilibrium constants for the two stages

* Nb₂O₅ remains homogeneous within the limits from NbO₂.₅ to NbO₂.₃₉ according to (¹) and from NbO₂.₅ to NbO₂.₄₂ according to (⁶).

the reduction of Nb₂O₅ (Fig. 2) are described (with an accuracy of ±0.2% for the first and ±0.3% for the second) by the following equations:

\[ \lg K_{\mathrm{p}_1}=-15050/4.575T+1.3306 \qquad (1480-1673^\circ\mathrm{K}), \]

\[ \lg K_{\mathrm{p}_{\mathrm{II}}}=-29490/4.575T+1.3334 \qquad (1673-1823^\circ\mathrm{K}), \]

whence

\[ \Delta G^0_{\mathrm{I}}(\mathrm{cal})=15050-6.087T,\qquad \Delta G^0_{\mathrm{II}}(\mathrm{cal})=29490-6.10T. \]

Combining reactions I and II with the reaction of formation of water vapor

\[ \mathrm{H_2+\tfrac12 O_2 \to H_2O(g)}, \qquad (\mathrm{III}), \]

whose isobaric potential according to Chipman \((^9)\) is expressed by the equation

\[ \Delta G^0_{\mathrm{III}}(\mathrm{cal})= -59251+2.006\,T\lg T-7.5\cdot10^{-5}T^2+4.08\cdot10^5T^{-1}+6.8085\,T, \]

and using literature data on the heat capacities of NbO₂ and NbO according to \((^{10})\) and for O₂ according to \((^{11})\), one can calculate \(\Delta G^0_{\mathrm{VI}}\) (respectively \(\Delta H^0_{\mathrm{IV}}\) and \(\Delta H^0_{\mathrm{V}}\)) for the reactions of formation of NbO₂.₄ and NbO₂ at 298.2°K for the reactions

Fig. 2

\[ \mathrm{NbO_2+\tfrac15 O_2 \to NbO_{2.4}}, \qquad (\mathrm{IV}) \]

\[ \mathrm{NbO+\tfrac12 O_2 \to NbO_2}, \qquad (\mathrm{V}) \]

\[ \Delta G^0_{\mathrm{IV}}=-26.2\ \mathrm{kcal};\quad \Delta H^0_{\mathrm{IV}}=-28.1\ \mathrm{kcal};\quad \Delta S^0_{\mathrm{IV}}=-6.36\ \mathrm{e.u.};\quad \Delta G^0_{\mathrm{V}}= \]

\[ =-87.33\ \mathrm{kcal};\quad \Delta H^0_{\mathrm{V}}=-94.95\ \mathrm{kcal};\quad \Delta S^0_{\mathrm{V}}=-25.57\ \mathrm{e.u.} \]

For the reaction of formation of Nb₂O₅ from NbO₂:

\[ \mathrm{2NbO_2+\tfrac12 O_2 \to Nb_2O_5} \qquad (\mathrm{VI}) \]

linearly extrapolating from the composition NbO₂.₄ to NbO₂.₅, we obtain at 298.2°K:

\[ \Delta H^0_{\mathrm{VI}}=-70.25\ \mathrm{kcal};\quad \Delta G^0_{\mathrm{VI}}=-65.5\ \mathrm{kcal};\quad \Delta S^0_{\mathrm{VI}}=-15.91\ \mathrm{e.u.}^{*} \]

We were unable to carry out equilibrium reduction of niobium oxides by hydrogen to the metal. Therefore, to determine the thermodynamic functions of the lower niobium oxide NbO, the emf method was used. Measurements of the cell \(E\)

\[ \mathrm{Pt}\mid \mathrm{Fe,\,Fe_{0.95}O}\mid \begin{array}{c} \text{solid}\\[-2pt] \text{electrolyte} \end{array} \mid \mathrm{NbO,\,Nb}\mid \mathrm{Pt} \qquad (\mathrm{A}) \]

were carried out in an apparatus described in \((^{12})\), in the temperature interval 841–1073°C. Mixed crystals in the ThO₂—La₂O₃ system were used as the solid electrolyte in the experiments. In individual cases, after carrying out an experiment with cell A, the electrolyte pellet was used to measure the \(E\) of the cell

\[ \mathrm{Pt}\mid \mathrm{Fe_3O_4,\,Fe_{0.95}O}\mid \begin{array}{c} \text{solid}\\[-2pt] \text{electrolyte} \end{array} \mid \mathrm{Fe_{0.95}O,\,Fe}\mid \mathrm{Pt} \qquad (\mathrm{B}) \]

\[ ^{*} \]
The calculation of \(\Delta G^0_{\mathrm{VI}}\) (respectively \(\Delta H^0_{\mathrm{VI}}\) and \(\Delta S^0_{\mathrm{VI}}\)) under the assumption that reduction of Nb₂O₅ proceeds according to the reaction

\[ \mathrm{Nb_2O_5+H_2 \to 2NbO_2+H_2O} \]

gives for 298.2°K:

\[ \Delta H^0_{\mathrm{VI}}=-70.5\ \mathrm{kcal};\quad \Delta G^0_{\mathrm{VI}}=-65.9\ \mathrm{kcal};\quad \Delta S^0_{\mathrm{VI}}=-15.6\ \mathrm{kcal}. \]

As an example, we give the values of \(E\) of cell B obtained for one experiment:

Fig. 3

The agreement of the values obtained with the literature data \((^{13})\) confirms the correctness of the choice of electrolyte*. The reference electrode \((\mathrm{Fe}_{0,95}\mathrm{O},\ \mathrm{Fe})\) and the electrolyte were prepared as described in \((^{12})\). The electrode under investigation was prepared by pressing pellets from a mixture of calculated amounts of Nb and \(\mathrm{Nb}_2\mathrm{O}_5\), followed by annealing them at \(1700^\circ\mathrm{C}\) for 3 h in vacuum.

For the equilibrium e.m.f. of cell A, the following values were obtained, corresponding to the change in the isobaric potential \((\Delta G^0_{\mathrm{VII}}=-2FE)\) of the reaction

\[ \mathrm{Fe}_{0,95}\mathrm{O}+\mathrm{Nb}\longrightarrow 0,95\mathrm{Fe}+\mathrm{NbO}, \tag{VII} \]

From the data presented and from Fig. 3 it is seen that the greatest deviation from the linear dependence of \(E\) on \(T\) does not exceed \(\pm 0,008\) V, i.e., about 1,2% of the measured quantity. The experimental data in the temperature interval studied are described (with an accuracy of \(\pm 0,7\%\)) by the equation \(\Delta G^0_{\mathrm{VII}}\) (cal) \(=-34500+3,15T\). Using \(\Delta G^0_T\) of the reactions \(\mathrm{Fe}_{0,95}\mathrm{O}+\mathrm{CO}\to0,95\mathrm{Fe}+\mathrm{CO}_2\) \((^{14})\) and \(\mathrm{CO}+\frac{1}{2}\mathrm{O}_2\to\mathrm{CO}_2\) \((^{15})\), and the temperature dependence of the heat capacities of NbO according to \((^{10})\), Nb and \(\mathrm{O}_2\) according to \((^{11})\), one can calculate for the reaction of formation of NbO:

\[ \mathrm{Nb}+\frac{1}{2}\mathrm{O}_2\to\mathrm{NbO}, \tag{VIII} \]

\[ \Delta G^0_{\mathrm{VIII}}(\mathrm{cal})=-98450-0,564T\lg T-0,63\cdot10^{-3}T^2-0,08\cdot10^5T^{-1} +22,10T\ (298—1346^\circ\mathrm{K}), \]

Table 1

* In preliminary experiments it was established that mixed crystals in the \(\mathrm{ZrO}_2\)—CaO system could not serve as the electrolyte because of penetration of the electrode material (apparently, Nb, NbO) into the electrolyte, although for other cells investigated in \((^{12},\ ^{13})\) this electrolyte proved suitable.

whence, for 298.2°K: \(\Delta G^0_{\mathrm{VIII}}=-92.36\) kcal; \(\Delta H^0_{\mathrm{VIII}}=-98.39\) kcal; \(\Delta S^0_{\mathrm{VIII}}=-20.19\) e.u. Combining reactions V, VI, and VIII, one can calculate for the reaction of formation of \(\mathrm{Nb_2O_5}\) from the elements:

\[ 2\mathrm{Nb}+\frac{5}{2}\mathrm{O_2}\to \mathrm{Nb_2O_5} \tag{IX} \]

at 298.2°K: \(\Delta H^0_{\mathrm{IX}}=-456.9\) kcal; \(\Delta G^0_{\mathrm{IX}}=-424.9\) kcal; \(\Delta S^0_{\mathrm{IX}}=-107.43\) e.u. and for the reaction of formation of \(\mathrm{NbO_2}\) from the elements:

\[ \mathrm{Nb}+\mathrm{O_2}\to \mathrm{NbO_2} \tag{X} \]

at 298.2°K: \(\Delta H^0_{\mathrm{X}}=-193.3\) kcal; \(\Delta G^0_{\mathrm{X}}=-179.7\) kcal; \(\Delta S^0_{\mathrm{X}}=-45.76\) e.u.

Table 2

In Table 2, for comparison, \(\Delta H^0_{298}\) and \(\Delta S^0_{298}\) of reactions V, VI, VIII, IX, and X are presented according to the data of various authors: \(\Delta H^0_{298}\)—calorimetric values obtained \((^{18—21})\), and \(\Delta S^0_{298}\)—calculated using entropies at 298.2°K: \(S^0_{\mathrm{Nb}}=8.73\) \((^{11})\); \(S^0_{\mathrm{NbO}}=11.5\) \((^{11})\); \(S^0_{\mathrm{NbO_2}}=13.07\) \((^{16})\); \(S^0_{\mathrm{Nb_2O_5}}=32.8\) \((^{11})\) and \(S^0_{\mathrm{O_2}}=49.02\) \((^{11})\).

Received
30 XI 1960

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