Physical Chemistry

S. F. Pal’guev, S. V. Karpachev, A. D. Neuimin, and Z. S. Volchenkova

Transition of Electronic Conductivity to Ionic Conductivity as a Function of the Composition of Solid Solutions of Oxides

(Presented by Academician A. N. Frumkin on June 6, 1960)

At 1000°C, solid solutions in the system CeO₂—ZrO₂ are practically electronic conductors (¹). On the other hand, solid solutions of the oxides ZrO₂—CaO possess purely ionic conductivity, and only oxygen ions are mobile (²–⁴). In order to determine how the introduction of calcium oxide into the mixed oxides \((\mathrm{Ce}, \mathrm{Zr})\mathrm{O}_2\) affects their electrical conductivity, we measured it and determined the nature of the conductivity for a series of samples of compositions \((0.75\,\mathrm{CeO}_2 \cdot 0.25\,\mathrm{ZrO}_2) + \mathrm{CaO}\). The composition \(0.75\,\mathrm{CeO}_2 \cdot 0.25\,\mathrm{ZrO}_2\) was taken as one of the components because, for it, the maximum electrical conductivity in the CeO₂—ZrO₂ system had been found (¹).

The samples were prepared from CeO₂ (chemically pure), ZrO₂ (chemically pure for analysis), and calcium carbonate (chemically pure for analysis). The method of preparing the samples and measuring their electrical conductivity was analogous to that described in (¹). For each sample, the temperature dependences of electrical conductivity were determined in the interval 500–1000°, on the basis of which its activation energy was calculated. The nature of the conductivity was determined by the method of measuring the e.m.f. The essence of the method is as follows. It is known (⁵,⁶) that the e.m.f. of a cell whose electrolyte possesses, along with ionic conductivity, also electronic conductivity (irrespective of whether it is of the \(n\)- or \(p\)-type) is determined by the equation \(E = [1 - (\bar t_e + \bar t_0)] E_0\), where \(E\) is the measured electromotive force of the cell; \(\bar t_e\) and \(\bar t_0\) are the mean, over the electrolyte, transport numbers of electrons and holes, respectively; \(E_0\) is the thermodynamic value of the electromotive force of the cell under investigation (i.e., in the absence of electronic and hole conductivity in the solid electrolyte). To estimate the magnitude \((\bar t_e + \bar t_0)\), i.e., the fraction of electronic conductivity in the electrolyte, it is sufficient to measure the e.m.f. of a cell incorporating the electrolyte under study and compare it with the thermodynamically calculated value. Naturally, for this purpose such an electrochemical cell must be assembled that the thermodynamic value of its e.m.f. can be calculated. We used two types of cells:

\[ (\mathrm{Pt}),\quad \begin{array}{c} \mathrm{O}_2\\ p_1 \end{array} \left|\, \text{solid electrolyte} \,\right| \begin{array}{c} \mathrm{O}_2\\ p_2 \end{array} ,\quad (\mathrm{Pt}) \tag{I} \]

\[ \mathrm{Me}',\, \mathrm{Me}'(\mathrm{O}) \,|\, \text{solid electrolyte} \,|\, \mathrm{Me}''(\mathrm{O}),\, \mathrm{Me}'' \tag{II} \]

In the indicated cells the e.m.f. is determined by the oxygen pressures at the electrodes. The thermodynamic value of their e.m.f. can be calculated from the relation: \(E_0 = \dfrac{RT}{4F} \ln \dfrac{p_2}{p_1}\). Here \(p_1\) and \(p_2\) are the oxygen pressures on the left and right sides of the cell, respectively. Since, during operation with cell (I), the solid electrolyte is in contact with oxygen, whereas in case (II) it is in vacuum, by comparing the results obtained for both cells one can determine the dependence of the electronic (hole) conductivity of the electrolyte on the partial pressure of oxygen in the gas phase, which in a number of cases is of great interest.

A cell of type (I) is shown in Fig. 1. The solid electrolyte (5), with platinum electrodes applied to its ends, is clamped between two quartz tubes (9 and 10), which serve to supply gases to the electrodes. The electrodes ...

come into contact with platinum tips (7 and 8), to which platinum current leads (11 and 12) are welded. The plate of solid electrolyte is carefully

Fig. 1

ground to the quartz tube (3), whereby separation of the electrode spaces is achieved. The quartz tubes (9 and 10) are fixed in heads (13 and 14) made of molybdenum glass. The heads, by means of ground joints, hold the entire system inside the quartz tube (2), which is placed in an electric furnace (1). The thermocouple junction (6) is in the immediate vicinity of the specimen. The arrows show the scheme for supplying gases with oxygen partial pressures that usually differ by a factor of 5–10.

Measurements on cell (I) make it possible to estimate the fraction of ionic conductivity with an accuracy of 2–3%.

The design of a cell of type (II) is analogous. It has no separation of the electrode spaces; therefore there is no system for supplying gases to the electrodes. The oxygen partial pressures above the electrodes are determined here by the dissociation vapor pressures of the corresponding oxides. For this purpose we used mixtures of Fe, FeO and Cu, Cu\(_2\)O \((^2)\). The accuracy of measurements on a cell of this type decreases as the fraction of electronic conductivity increases.

Fig. 2

Figure 2 gives the results of measurements of electrical conductivity at 1000°. The change in activation energy with composition is also shown there. Table 1 presents the results of studies of the nature of the conductivity of the ternary system considered by us and of the initial oxides.

As follows from Table 1 and Fig. 2, despite the fact that the ionic conductivity increases, the total electrical conductivity in the system decreases for small additions of calcium oxide. Meanwhile, as experiment \((^3)\) shows, additions of calcium oxide separately to zirconium dioxide, and also to cerium dioxide, cause only an increase in electrical conductivity; moreover, the solid solutions formed in this case also have the larger fraction of ionic conductivity the higher their CaO content \((^7)\). An explanation of these experimental results can be given on the basis of the following considerations.

It is known \((^{8,9})\) that upon heating solid solutions CeO\(_2\)—ZrO\(_2\) a relatively small but noticeable decrease in weight is observed. Ob-

Table 1

* The samples were prepared from specially purified cerium dioxide with an impurity content of not more than 0.01%.

** Measurements were carried out in a cell of type (II). With time these values decreased.

As is evident, it occurs as a result of the loss of oxygen belonging to cerium. Therefore it may be assumed that part of the cerium in the solid solution $\mathrm{CeO_2}$—$\mathrm{ZrO_2}$ is in the trivalent state. The appearance of appreciable amounts of trivalent cerium ions together with tetravalent ones may be the cause of the occurrence of considerable electronic conductivity. In this connection, the decrease in electronic conductivity associated with an increase in the calcium oxide content can be explained by a lowering of the degree of reduction of tetravalent cerium owing to the presence of calcium oxide in the solid solution. The current carriers of the ionic component of conductivity in the ternary solutions $\mathrm{CeO_2}$—$\mathrm{ZrO_2}$—CaO must be oxygen ions, as is the case in the $\mathrm{ZrO_2}$—CaO system ($^{3,4}$).

In general, oxygen-ion conductivity may be expected in solid solutions of oxides of metals of different valence, formed according to the substitution–subtraction type and having a cubic crystal lattice (usually of the fluorite type). Because of the different valence of the cations, vacancies are present in the anion part of the crystal lattice of the solid solution, through which migration of oxygen ions can occur. As X-ray structural studies have shown, in the ternary $\mathrm{CeO_2}$—$\mathrm{ZrO_2}$—CaO system we are dealing with an analogous case: over the range of compositions from 0 to 40 mol.% CaO there is a continuous series of solid solutions. Moreover, they retain the fluorite-type crystal lattice possessed by the solid solution 0.75 $\mathrm{CeO_2}\cdot$0.25 $\mathrm{ZrO_2}$.

From this point of view it is easy to explain the experimentally observed change in the character of the conductivity of our samples as a function of CaO content. Solid solutions of $\mathrm{ZrO_2}$ in $\mathrm{CeO_2}$ that contain no calcium oxide practically have no ionic conductivity, since the number of oxygen-ion vacancies in their crystal lattice is very small. On the other hand, for the reason indicated above, their electronic conductivity is large. As the CaO content in the solid solution increases, the fraction of ionic conductivity continuously increases, reaching practically 100% in samples with 20–40 mol.% CaO, when the number of defects in the anion part of the lattice is large.

Since under these limiting conditions the values of the electrical conductivity are close to one another, we have an interesting case of a gradual transition of electronic conductivity into ionic conductivity, rather than a relative increase in ionic conductivity with an unchanged electronic component. The presence of a minimum in the electrical conductivity is probably connected here with the following circumstance. When calcium oxide is introduced into the lattice of a solid solution of cerium and zirconium dioxides, a deficiency of oxygen ions arises in it. The latter is accompanied by a certain distortion of it, i.e., is connected

with an expenditure of energy. The presence of trivalent cerium in these solid solutions acts in the same direction, and with increasing CaO content trivalent cerium will tend to pass into tetravalent cerium (in an oxidizing atmosphere). This decreases the concentration of electron sources (Ce³⁺), and the fraction of electronic conductivity drops rapidly. Although the fraction of ionic conductivity also increases in this case, the number of oxygen vacancies is evidently still too small to ensure appreciable electrical conductivity. Therefore, up to a content of 8 mol. % CaO in the samples, the total electrical conductivity decreases. Only at higher contents of calcium oxide in the solid solutions does the ionic conductivity increase so much that it outweighs the continuing decrease (already relatively small) of the electronic component—and the electrical conductivity begins to rise.

The fact that the electronic conductivity of the CeO₂—ZrO₂ solid solutions is caused by partial reduction of Ce⁴⁺ to Ce³⁺ in them is also confirmed by the fact that CeO₂ and ZrO₂ separately have considerably larger fractions of ionic conductivity than their solid solutions. During the formation of solid solutions, the ionic conductivities existing in pure CeO₂ and ZrO₂ apparently remain, but they are practically not perceived, since the electrical conductivity of the solid solutions is several orders of magnitude higher than that of the pure oxides (¹).

The data presented in Table 1 were obtained from measurements in a cell of type (I), i.e., under conditions in which the solid electrolyte was in contact with gases having relatively high partial pressures of oxygen (1.0–0.2 atm). Under these conditions, at a content of 20–40 mol. % CaO in the solid solution, the ionic conductivity is close to 100%. If the measurements were carried out at very low oxygen pressures: 10⁻⁷–10⁻²⁵ atm (in a cell of type II), then even for these solid solutions the electronic conductivity completely predominates. It should be noted that in the latter measurements the samples changed their color and, after the experiment, literally fell apart, which indicates very considerable reduction of cerium.

The fraction of ionic conductivity in the oxide system studied depends noticeably on temperature, and it is maximal at 750°. The increase in ionic conductivity with increasing temperature is due to an increase in ion mobility, while its decrease at higher temperatures is due to the thermal decomposition of cerium dioxide to Ce₂O₃. The latter, as follows from Table 1, decreases with increasing calcium oxide content in the solid solution, for the reasons considered above.

The experimentally observed change in the activation energy of electrical conductivity (Fig. 1) is in agreement with the mechanism described above.

In the system studied, the electrical conductivity increases right up to the limiting content of calcium oxide in the solid solution (40 mol. %). This permits one to assume that, in contrast to ZrO₂—CaO solid solutions (³), here the interaction between defects of the crystal lattice (oxygen vacancies), if it exists, has no noticeable effect on the electrical conductivity, and the latter is determined mainly by the number of these defects.

The decrease in electrical conductivity with increasing CaO content above 40 mol. % is apparently connected with the presence of free calcium oxide.

Institute of Electrochemistry
Ural Branch of the Academy of Sciences of the USSR

Received
6 VI 1960

CITED LITERATURE

¹ S. F. Pal’guev, Z. S. Volchenkova, ZhFKh, 34, no. 2 (1960).
² K. Kiukkola, C. Wagner, J. Electrochem. Soc., 104, 379 (1958).
³ Z. S. Volchenkova, S. F. Pal’guev, Tr. Inst. Elektrokhimii, vol. 1, Ural Branch of the Academy of Sciences of the USSR, 1960.
⁴ W. D. Kingery, J. Pappis, M. E. Doty, D. C. Hill, J. Am. Ceram. Soc., 42, 393 (1959).
⁵ C. Wagner, Z. Phys. Chem., 21, Abt. B, 25 (1933).
⁶ S. V. Karpachev, S. F. Pal’guev, Tr. Inst. Elektrokhimii, vol. 1, Ural Branch of the Academy of Sciences of the USSR, 1960.
⁷ S. F. Pal’guev, A. D. Neuimin, Tr. Inst. Elektrokhimii, vol. 1, Ural Branch of the Academy of Sciences of the USSR, 1960.
⁸ H. Vartenberg, W. Gurr, J. Am. Ceram. Soc., 196, 374 (1931).
⁹ S. F. Pal’guev, S. I. Alyamovskii, Z. S. Volchenkova, ZhNKh, 4, 2571 (1959).