IONIC ELECTRICAL CONDUCTIVITY OF SINGLE CRYSTALS OF SOLID SOLUTIONS AND MECHANICAL MIXTURES OF ALKALI-HALIDE COMPOUNDS

Z. I. Druzhinina, E. K. Zavadovskaya, G. V. Stebnitskaya

(Presented by the Scientific Seminar on Dielectrics)

Many electrical properties of crystals are determined by the lattice energy and the heat of formation. It has been established experimentally that the electrical strength of alkali-halide salts increases with increasing lattice energy [1].

From the magnitude of the heat of formation of a chemical compound one can judge the stability of the compound and its electrical properties [2].

It was of interest to investigate the regularities governing the electrical conductivity of solid solutions of alkali-halide compounds. The electrical conductivity of solid dielectrics, in particular crystals of alkali-halide salts, has been studied by many authors [3, 4, 5]. However, we are not aware of studies of the temperature dependence of the electrical conductivity of solid solutions of alkali-halide salts with quantitative variation of the composition of the solution, or of mechanical mixtures of alkali-halide salts.

The electrical conductivity of crystals is divided into intrinsic conductivity, due to the motion of the principal ions of the crystal lattice, which is more clearly manifested at high temperatures, and conductivity due to impurity ions and weakly bound ions in defective sites, manifested in the region of comparatively low temperatures.

When interstitial-type impurities are introduced, the electrical conductivity of a crystal, determined by the motion of current carriers in the interstices, increases, because the number of current carriers increases and their liberation energy decreases as a result of the disturbance of the lattice by impurities and the decrease in the binding energy between the particles of the crystal. The electrical conductivity due to the transition of ions from one vacant site to another, as occurs for substitutional solid solutions, does not increase appreciably with a small introduction of impurities. But with a large introduction of impurities, some of the current carriers will be located in the interstices; this will cause an increase in the number of current carriers and a decrease in the binding energy between the particles of the crystal, as a result of which the electrical conductivity will increase.

We measured the electrical conductivity of substitutional solid solutions of the systems potassium chloride + rubidium chloride and potassium chloride + potassium bromide in order to determine the influence of the stability of a chemical compound on electrical conductivity.

Single crystals of the indicated solid solutions, pressed specimens made from ground single crystals, and pressed specimens representing mechanical mixtures of the previously indicated systems, taken in various percentage ratios, were investigated.

The specimens studied were obtained by growth from the melt by the Czochralski method and were brought to the required thickness by grinding on glass wetted with a saturated solution of the given composition. The specimens had a thickness of 2 mm, which was measured with a micrometer to an accuracy of 0.01 mm. The quality of the specimens was checked with a microscope.

Table

To measure the electrical conductivity of the specimens, they were placed between flat nickel electrodes with rounded edges in a special crystal holder, which was then placed in a furnace. The temperature of the specimen was measured with a thermocouple (platinum–platinum-rhodium). Heating of the specimen and its cooling were carried out at a rate of 2° per minute. The current passing through the specimen was measured with a galvanometer by the direct-deflection method at a field strength in the specimen of 50 V/mm. Measurements of the current flowing in the specimen were made during its heating and cooling.

The dependence of electrical conductivity on temperature was measured for single crystals of solid solutions of potassium chloride—rubidium chloride of various compositions (see table).

Figure 1 shows the dependence of the logarithm of electrical conductivity on temperature for single crystals of solid solutions of the potassium chloride—rubidium chloride system. The break in the straight-line increase

Fig. 1. Dependence of the logarithm of electrical conductivity on temperature for single crystals of the potassium chloride—rubidium chloride system (high-temperature region).

of the logarithm of electrical conductivity with increasing temperature and the increase in the slope of the straight line show that in the region of comparatively low temperatures, up to the break point, the current is carried by charges with a lower activation energy than at temperatures above the break point.

From the graphs on which the results of the indicated measurements are presented, the values of the activation energies corresponding to various percentage ratios of the solid solutions of the potassium chloride—rubidium chloride system were calculated.

Figure 2 presents the change in the electrical conductivity and activation energy of single crystals of solid solutions of the potassium chlo-

lithium—rubidium chloride. With a change in their composition, the electrical conductivity of single crystals of solid solutions changes along a curve with a maximum, depending on the composition of the solid solutions. Correspondingly, the low-temperature activation energy, as a function of the composition of the single crystals, changes along a curve with a minimum. The activation energy has the smallest values, and the electrical conductivity the largest values, in the region of nearly equal contents of the components of the solid solutions.

The study of the potassium chloride—rubidium chloride system was carried out on specimens prepared by various methods: single crystals grown from the melt; specimens pressed from pulverized single crystals grown from the melt; and pressed specimens that were a mechanical mixture of potassium chloride and potassium bromide.

The results of the study of single crystals of solid solutions of the potassium chloride—potassium bromide system are presented in Fig. 3, from which it is seen that, when the composition of the solid solution is changed, a decrease in the activation energy corresponds to an increase in the electrical conductivity of the solid solutions.

An attempt to determine the regularity in the change of the electrical conductivity of single crystals of solid solutions with a change in their composition in the region of higher temperatures was not successful. No definite dependence of the magnitude of the activation energy and of the electrical conductivity on the quantitative ratio of the components of the solid solution at temperatures of 530–600 degrees, corresponding to the region of high-temperature electrical conductivity, was obtained.

This circumstance can possibly be explained by the fact that, when the temperature dependence of the electrical conductivity of single crystals of solid solutions changes, their aging takes place.

We observed the aging of single crystals as a function of the time of their storage over two months on specimens of solid solutions of the potassium chloride—potassium bromide system, taken in equal ratios: 50 mol% potassium chloride and 50 mol% potassium bromide. The results of measurements of the electrical conductivity of the indicated single crystals are presented in Fig. 4.

With an increase in the storage time, the electrical conductivity of single crystals of the potassium chloride—potassium bromide solid solution decreases. According to the data of Rombakh and Zhemchuzhnyi [6], and of Kurnakov and Zhemchuzhnyi [7], it follows that with time the heat of formation of the solid solution decreases and the system passes into a more stable state. This is accompanied by a decrease in the magnitude of the electrical conductivity.

The least stable are single crystals with approximately equal contents of the components. The decomposition of solid solutions is accompanied by a decrease in the heat of formation, an increase in the stability of the system, and a decrease in the electrical conductivity.

In our work we took into account the possibility of aging of the specimens and subjected to study specimens prepared 2–3 days before the measurement.

The results of the conducted investigation of the electrical conductivity of single crystals of solid solutions of the potassium chloride—rubidium chloride and potassium chloride—potassium bromide systems can be explained as follows: with an increase in the amount of the second component of the single crystals, the stability of the system decreases, which can be judged indirectly from the increase, for such specimens, in the heat of formation. In Fig. 5 the change in the magnitude of the heat of formation and, correspondingly, of the electrical strength with a change in the percentage ...

component ratios for single crystals of the potassium chloride—potassium bromide system.

A decrease in the stability of the system promotes a decrease in the activation energy of the ions and an increase in the electrical conductivity of samples of the corresponding composition.

Fig. 2. Dependence of the logarithm of electrical conductivity at \(t = 100^\circ\) and of the low-temperature activation energy in the temperature interval \((50—400^\circ)\) on composition for single crystals of solid solutions of potassium chloride—rubidium chloride.

Fig. 3. Dependence of the logarithm of electrical conductivity at \(t = 300^\circ\) and of the activation energy in the temperature interval \((100—400^\circ)\) on the composition of single crystals of solid solutions of potassium chloride—potassium bromide.

The investigation of the electrical conductivity of the potassium chloride—potassium bromide system was carried out on pressed samples prepared from

of pulverized single crystals or from a mechanical mixture of potassium chloride and potassium bromide in various percentage ratios.

Figure 6 presents the dependences of the logarithm of electrical conductivity and of the activation energy on composition for the potassium chloride—potassium bromide system in specimens pressed from pulverized single crystals of solid solutions.

The greatest value of the electrical conductivity and the smallest value of the activation energy are found in specimens containing nearly equal amounts of both components.

Figure 7 presents the dependence of the logarithm of electrical conductivity on temperature for specimens pressed from a mechanical mixture of powders of potassium chloride and potassium bromide. For pressed specimens, the usual character of the dependence of electrical conductivity

Fig. 4. Dependence of the electrical conductivity of single crystals of a solid solution of 50% potassium chloride—50% potassium bromide on the storage time of the specimens \((t = 300^\circ\mathrm{C})\).

on temperature is observed, as for other dielectrics with ionic electrical conductivity.

Figure 8 gives the dependence of the logarithm of electrical conductivity on composition for specimens pressed from powders of potassium chloride and potassium bromide (mechanical mixture). In the temperature range from 200 to 400°, a considerable decrease in the activation energy is observed with an increase in the quantitative ratio of the second component. Corresponding to the decrease in activation energy, the electrical conductivity of the specimens increases. At a certain quantitative ratio of potassium chloride and potassium bromide powders, a maximum of the logarithm of electrical conductivity and a minimum of the activation energy are observed.

Figure 9 shows the dependence of the logarithm of electrical conductivity on the percentage ratio of potassium chloride and potassium bromide powders in pressed specimens at a temperature of 400° and at a temperature of 600°. The latter corresponds to the high-temperature region

Fig. 5. Dependence of the electric strength and of the difference in heats of dissolution in water of a mechanical mixture and a solid solution on composition for single crystals of the potassium chloride—potassium bromide system.

Fig. 6. Dependence of the logarithm of electrical conductivity at \(t = 200^\circ\)C and of the activation energy in the temperature interval \((200\text{—}400^\circ\text{C})\) on composition for specimens pressed from powdered single crystals of solid solutions potassium bromide—potassium chloride.

Fig. 7. Dependence of the logarithm of electrical conductivity on temperature for specimens prepared by pressing from mixtures of the potassium chloride—potassium bromide system.

Fig. 8. Dependence of the logarithm of electrical conductivity at the bend point and of the activation energy in the temperature range (200–400 degrees) on composition for specimens prepared from mixtures of powders of potassium chloride—potassium bromide.

ionic electrical conductivity. The value of the electrical conductivity is also given at various temperatures at which a break is observed in the temperature dependence of the logarithm of the electrical conductivity on passing from the low-temperature to the high-temperature region for each composition of the specimens studied.

In all the cases shown in Fig. 9, a maximum in the electrical conductivity of the pressed specimens is observed when the amounts of both components are nearly equal. In the higher-temperature region, the dependence

Fig. 9. Dependence of the logarithm of electrical conductivity on composition for specimens pressed from a mixture of powders of potassium chloride—potassium bromide.
× — after the break point, \(t = 600^\circ\); ○ — before the break point, \(t = 400^\circ\);
\(\Delta\) — at the break point.

of the electrical conductivity on the composition of the pressed specimens is expressed more weakly, which may be explained, as was already indicated above, by the influence of aging of the specimens at high temperatures on their intrinsic electrical conductivity.

The temperature dependence of the electrical conductivity of pressed specimens prepared from crushed single crystals of solid solutions and from powders representing a mechanical mixture of potassium chloride and potassium bromide obeys the same laws as does the electrical conductivity of single crystals of solid solutions of alkali-halide salts.

The identical regularities in the temperature behavior of the electrical conductivity of solid solutions and of specimens prepared from mechanical mixtures of powders of alkali-halide salts are probably explained by the fact that, upon heating, the solid solutions decompose. In mechanical mixtures, upon heating, diffusion and transport of matter by the current occur, accompanied to some extent by the formation of solid solutions.

The dependence of electrical conductivity on composition observed for single crystals of solid solutions is also preserved for specimens prepared by pressing from powders of crushed single crystals and from a mechanical mixture.

REFERENCES

1. Vorob’ev A. A. and Zavadovskaya E. K. DAN SSSR, XXXI, 3, 375, 1951.
2. Vorob’ev A. A., Zavadovskaya E. K. and Trubitsyn A. M. DAN, SSSR, 100, 6, 1065, 1955.
3. Seitz V. UFN 18, no. 4, 542, 1937.

1. Ioffe, A. F. Collection dedicated to the 30th anniversary of the Great October Socialist Revolution, part 1, p. 305, Publishing House of the Academy of Sciences of the USSR, 1937.
2. W. Lehfeldt, Zs. f. Phys., 85, 11–12, 1933.
3. Zhemchuzhnyi, S. I., and Fedorov, F. News of the St. Petersburg Polytechnic Institute, vol. XII, Section of Engineering, Natural Science, and Mathematics, issue 1, 349, 1909.
4. Kurnakov, N. S., and Zhemchuzhnyi, S. F. Collected Selected Works of N. S. Kurnakov, vol. 1, 186, ONTI, 1938.

1. Izv. TPI, vol. 95.

ERRATA

Izv. TPI, vol. 95.