EFFECT OF MEASUREMENT CONDITIONS AND ELECTRODES ON THE MAGNITUDE OF THE ELECTRICAL CHARACTERISTICS OF A SOLID SOLUTION OF THE KCl—KBr SYSTEM

V. A. GRISHUKOV

(Presented by the scientific seminar of the Faculty of Physics and Technology)

The available information on the study of the dielectric properties of solid solutions of the KCl—KBr system is contradictory. Thus, in the works of K. A. Vodopyanov and G. I. Galibina [1] and G. I. Potakhova [2] it was shown that, in solid solutions of the KCl—KBr system at room temperature, at different frequencies there is a dependence of the magnitude of the loss angle on the composition of the solid solutions. When the composition of the solid solution changes, the loss angle varies along a curve with a maximum in the region of approximately equal concentrations of the components. The magnitude of the maximum is greatest in the low-frequency region \((3 \cdot 10^5\ \text{Hz})\) and decreases as the frequency increases, so that at a frequency of \(10^7\ \text{Hz}\) the loss angle depends little on the composition of the solid solution. According to the data of G. I. Potakhova, an analogous dependence of \(\operatorname{tg}\delta\) on the composition of the solid solution is also observed at higher temperatures. The authors relate this type of dependence of the loss angle in mixed crystals to the structural features of these crystals.

Somewhat later, N. P. Bogoroditskii and B. A. Kulik [3] investigated the concentration dependence of the angle of dielectric losses of a solid solution of the KCl—KBr system and concluded that \(\operatorname{tg}\delta\) at a frequency of \(10^6\ \text{Hz}\) and at a temperature of \(200^\circ\text{C}\) assumes intermediate values between the values of \(\operatorname{tg}\delta\) for pure KCl and KBr.

Analyzing the results of the works cited above, it should be noted that the measurements were carried out under atmospheric conditions. B. N. Matsunashvili [4] showed that moisture has a strong influence on the values of dielectric losses. Consequently, it is possible that the influence of moisture was also present in the investigations of K. A. Vodopyanov.

It may be assumed that the hygroscopicity of the crystals of the KCl—KBr solid solution differs for different compositions and, in the case of maximum hygroscopicity for the equimolar composition, it may turn out that the change in the angle of dielectric losses with the composition of the solid solutions is due to the different hygroscopicity of the crystals.

In works [1—3], when measuring dielectric losses in solid solutions, different materials and methods of making electrical contact with the specimen were used. This also could have contributed to the difference in the concentration dependences of the angle of dielectric losses of the solid solutions.

The aim of the present work was: 1. To determine the influence of the electrode material and the method of applying them on the magnitude of the dielectric losses and electrical conductivity of the solid solutions, and to select the most suitable ...

same type of electrodes. 2. To investigate the influence of atmospheric moisture on the values of the dielectric-loss angle and electrical conductivity of solid solutions and to determine the reasons for the discrepancies between the experimental data of K. A. Vodopyanov and N. P. Bogoroditskii in the study of the dielectric-loss angle in solid solutions of KCl—KBr.

Selection of the electrode material and the method of applying them to the specimen

Extensive studies on the influence of the electrode material and the methods of applying them were carried out by B. N. Matsonashvili [4] and V. V. Panchenko [7].

The results of their studies showed that, when electrodes are applied by firing-in a paste, and also when aquadag (graphite) electrodes are applied, strong contamination of the specimens occurs and the conductivity of the crystals increases. In specimens with so-called optical contact, the dielectric losses proved to be lower than with all other electrodes. On this basis the author [4] concludes that electrodes with optical contact are the best. However, the results of the studies by V. V. Panchenko [7] indicate that, when air interlayers are present between the electrode and the specimen (when optical contact is used), a series capacitance appears, and the magnitude of the measured capacitance decreases and the value of \(\operatorname{tg}\delta\) decreases.

In the opinion of the author [7], the most reliable electrodes should be considered to be electrodes deposited in vacuum. A drawback of electrodes deposited by evaporation in vacuum is their relatively low conductivity, which can strongly affect the results of measurements of \(\operatorname{tg}\delta\) at high frequencies.

According to Artsybyshev [8], alkali-halide crystals at sufficiently high temperatures react with almost all metals, with the exception of chemically pure iron and platinum. V. V. Panchenko was unable to obtain good platinum electrodes, and no comparison was made between platinum electrodes and other types of electrodes.

In our laboratory, platinum electrodes were obtained by the method of cathodic sputtering. For the measurements, specimens were used in which the resistance of the electrode layer did not exceed 30–50 ohms. For comparison, specimens with aquadag electrodes and specimens with polished surfaces (optical contact) were tested.

The results of the studies showed that, for specimens of all compositions of the solid solution of the KCl—KBr system, as well as for the constituent components themselves, an increased value of \(\operatorname{tg}\delta\) and \(\sigma\) is characteristic when aquadag electrodes are used (Fig. 1, dashed lines), in comparison with specimens having sputtered platinum electrodes (Fig. 1, solid lines). Moreover, calculations show that the increase in \(\operatorname{tg}\delta\) in specimens with carbon electrodes is caused by an increase in the electrical conductivity in these specimens. Consequently, the overestimated values of \(\operatorname{tg}\delta\) and \(\sigma\) are most probably due to contamination of the specimens when aquadag is applied.

When measuring the dielectric losses of crystals with polished surfaces (optical contact), the values of \(\operatorname{tg}\delta\) proved to be two times lower than in crystals with platinum electrodes (Fig. 1, dash-dot lines). This confirms V. V. Panchenko’s supposition that, when electrodes with optical contact are used, the measured values of the specimen capacitance and \(\operatorname{tg}\delta\) may be underestimated.

Samples with platinum electrodes give better reproducibility of results when going from sample to sample. In measurements in the frequency range up to 100 kHz, no noticeable influence of electrode resistance on the values of \(\operatorname{tg}\delta\) was found.

Fig. 1. Temperature dependence of \(\operatorname{tg}\delta\) for crystals of solid solutions of composition 91 mole % KCl—9 mole % KBr with carbon electrodes (dotted lines), platinum electrodes (solid lines), and optical contact (dash-dotted lines).
1 — 50 Hz, 2 — 5000 Hz.

All this led to the use of platinum electrodes in the study of \(\operatorname{tg}\delta\), \(\sigma\), and \(\varepsilon\) of KCl—KBr solid solutions. In addition, platinum electrodes are mechanically stronger and make it possible to carry out repeated measurements on one and the same sample.

Study of the influence of moisture on the values of \(\operatorname{tg}\delta\) in solid solutions of the KCl—KBr system

The studies of B. N. Matsonashvili [4] established that the values of \(\operatorname{tg}\delta\) of hygroscopic samples under atmospheric conditions are overestimated at temperatures up to 200°C in the frequency region up to \(10^6\) Hz. These results call into question the assertion of K. A. Vodopyanov [8] that, at high frequencies, the influence of atmospheric moisture is not reflected in the values of \(\operatorname{tg}\delta\) of alkali halides and their solid solutions.

To clarify the influence of atmospheric moisture on the values of \(\operatorname{tg}\delta\) and \(\sigma\) in KCl—KBr solid solutions, measurements of these quantities were carried out in vacuum and in air.

In the low-temperature region, the values of \(\operatorname{tg}\delta\) for crystals measured in air proved to be much larger than the values of \(\operatorname{tg}\delta\) of these same crystals measured in vacuum (Fig. 2). At higher temperatures, the dielectric losses of crystals measured in air and in vacuum practically coincide. Such high dielectric losses in the low-temperature region may be due either

an increase in dielectric losses of a relaxation character, or due to an increase in conduction losses.

Measurement of electrical conductivity showed that the increase in \(\operatorname{tg}\delta\) in the low-temperature region is caused by conduction losses.

Fig. 2. Temperature dependence of \(\operatorname{tg}\delta\) for crystals of solid solutions of composition \(10\,\mathrm{M}\%\ \mathrm{KCl}—90\,\mathrm{M}\%\ \mathrm{KBr}\), measured in vacuum (solid lines) and in the atmosphere (dashed lines).
\(1 — 50\ \mathrm{Hz},\ 2 — 500\ \mathrm{Hz},\ 3 — 5000\ \mathrm{Hz}\)

At room temperature the crystals vigorously adsorb moisture, as a result of which the surface conductivity many times exceeds the bulk conductivity of the specimen. As the specimen is heated, the adsorbed moisture evaporates from the specimen and the surface conductivity decreases, while the bulk conductivity increases. However, the relationship between the decrease in surface conductivity and the growth of bulk conductivity is such that the total conductivity, and consequently also \(\operatorname{tg}\delta\) of the specimen, decreases with increasing temperature (Fig. 2).

At certain temperature values, at which the role of surface conductivity becomes insignificant, a bend is observed in the temperature dependence of \(\operatorname{tg}\delta\). With increasing frequency of the applied field, the bend point shifts into the region of higher temperatures.

The dependences of \(\operatorname{tg}\delta\) for crystals of the solid solution, measured in the atmosphere, on its composition have a maximum corresponding to a composition close to \(64\,\mathrm{M}\%\ \mathrm{KBr}\) in \(\mathrm{KCl}\) (Fig. 3), and have overestimated values in comparison with the values of \(\operatorname{tg}\delta\) measured in vacuum. As already noted above, the overestimated values of \(\operatorname{tg}\delta\) are due to the significant surface conductivity of the specimens.

The magnitude of the surface conductivity is determined by the thickness and properties of the moisture film covering the specimen. The thickness of the moisture film and its conductivity depend on the properties of the specimen on which it has formed—

… film is formed. The volume \(V\) of moisture adsorbed on the surface of the sample is determined by the equation of Brunauer’s polymolecular adsorption theory [9]

\[ V=\frac{V_m C P}{(P_0-P)\left[1+(C-1)\frac{P}{P_0}\right]}, \]

where \(V_m\) is the volume of adsorbed substance when the entire surface is covered with a monomolecular layer; \(C\) is a constant determined by the condition

\[ C \simeq e^{\frac{U_1-U_2}{RT}}, \]

where \(U_1\) is the adsorption of the first layer, and \(U_2\) is the heat of condensation.

Fig. 3. Dependence of \(\tg\delta\) on the composition of the solid solution of the KCl—KBr system for samples measured in an atmosphere at \(20^\circ\mathrm{C}\) (solid lines) and in vacuum (dashed lines).
\(1\)—500 Hz, \(2\)—5 kHz, \(3\)—50 kHz.

The volume of adsorbed moisture \(V\) depends: a) on the contact angle of wetting of the dielectric surface; b) on the degree of solubility of the dielectric in water. The former is determinative for dielectrics that do not contain water-soluble ions in their composition. The solid solution of the KCl—KBr system is readily soluble in water; therefore, the volume of adsorbed moisture will be determined by the degree of solubility of the solid solution in water.

Dissolution, like melting, represents a transition from an ordered crystalline state to a disordered one. These transitions are associated with an increase in the entropy of the system. During dissolution, rupture of the crystalline bonds of the ions occurs due to the penetration of solvent particles between the ions of the crystal lattice. This process is characterized by the heat of dissolution. An analogous rupture of bonds also occurs during the melting of solid crystalline bodies, but only at the expense of supplied heat. Therefore, an analogy may be drawn between dissolution and melting of the solid solution KCl—KBr.

From the melting diagram [10, p. 56] it is seen that, for the solid solution of the KCl—KBr system, the lowest melting temperature corresponds to the composition 64 M% KBr in KCl, i.e., to the composition at which the maximum value of \(\operatorname{tg}\delta\) is observed. Moreover, the melting temperature of KCl is higher than the melting temperature of KBr. Analogous phenomena should also be observed in the case of dissolution of crystals, which is confirmed by measurements of \(\operatorname{tg}\delta\) in solid solutions under atmospheric conditions. KCl, which has a greater ion-binding energy in comparison with KBr, adsorbs a smaller amount of moisture (owing to its lower solubility) than KBr. Solid solutions characterized by asymmetry of the crystal lattice have increased solubility in comparison with the solubility of the components, and hence adsorb a larger amount of moisture.

Fig. 4. Frequency dependence of \(\operatorname{tg}\delta\) for samples measured in atmosphere (solid lines) and in vacuum (dotted line).
1 — 24 M% KCl—76 M% KBr; 2 — 75 M% KCl—25 M% KBr.

It should be noted that the volume of adsorbed moisture, and consequently also the absolute values of \(\operatorname{tg}\delta\) and \(\sigma\), depend strongly on the relative humidity of the air at the moment of measurement and on the time during which the samples remain under atmospheric conditions before measurement.

Measurements of \(\operatorname{tg}\delta\) as a function of the frequency of the applied field show that the value of \(\operatorname{tg}\delta\) decreases as the frequency increases (Fig. 4). However, even at a frequency of \(10^5\) Hz the values of \(\operatorname{tg}\delta\) for samples measured under atmospheric conditions still considerably exceed the values of \(\operatorname{tg}\delta\) for samples measured in vacuum (Fig. 4). Extrapolation of the values of \(\operatorname{tg}\delta\) into the high-frequency region leads to the conclusion that the difference between the values of \(\operatorname{tg}\delta\) of samples measured in atmosphere and in vacuum practically disappears starting from frequencies of \(10^7\) Hz and higher.

According to the work of K. A. Vodop’yanov [1] and G. I. Potakhova [2], beginning with frequencies of \(10^7\) Hz and higher, the dielectric losses in solid solutions of the KCl—KBr system practically do not depend on the composition of the solid solution. As the frequency is decreased, \(\operatorname{tg}\delta\) in solid solutions increases along a curve with a maximum close to the equimolar composition.

The experiments carried out show that the explanation of such a dependence of the dielectric-loss angle must be associated with the different solubility of solid solutions in water and with the dependence of the value of \(\operatorname{tg}\delta\) in specimens containing adsorbed moisture on the frequency of the applied field.

REFERENCES

1. K. A. Vodopyanov, G. I. Galibina. Izv. TPI, 91, 269, 1956.
2. G. I. Potakhova. Dissertation, Tomsk, 1956.
3. N. P. Bogoroditskii, B. A. Kulik. ZhTF, 10, 2165, 1958.
4. B. N. Matsonashvili. Izv. AN SSSR, Phys. Ser., 22, No. 3, 1958.
5. G. I. Skanavi. Izv. AN SSSR, Phys. Ser., 22, No. 3, 1958. Discussion.
6. V. I. Odelevskii. Izv. AN SSSR, Phys. Ser., 24, No. 2, 1960. Discussion.
7. V. V. Panchenko. FTT, 6, issue 2, 1964.
8. K. A. Vodopyanov. Izv. AN SSSR, Phys. Ser., 24, No. 2, 1960. Discussion.
9. A. V. Tolpinskaya. Surface resistance of solid dielectrics. Author’s abstract, Leningrad, LPI, 1955.
10. A. A. Vorob’ev. Physical properties of ionic crystalline dielectrics, book 2, TSU Publishing House, Tomsk, 1961.