DIELECTRIC LOSSES IN SOLID SOLUTIONS OF ALKALI-HALIDE CRYSTALS AT HIGH FREQUENCY

G. I. Potakhova

(Presented by Corresponding Member of the Academy of Sciences of the USSR V. D. Kuznetsov)

In investigations of dielectric losses in simple ionic crystals it has been established that the loss angle is a characteristic connected with all the physicochemical constants of the crystal [1]. The temperature and frequency dependences of the loss angle of simple crystals have been studied, as has the dependence of dielectric losses on the preliminary treatment of the crystals [2].

It is of interest to trace how the regularities in the variation of the loss angle, established in the study of simple crystals, change in the transition to solid solutions. In the electrophysics laboratory of the SFTI, the system of solid solutions KBr—KJ [1] and the initial concentrations of the KCl—NaCl system [2] were investigated. The present article gives the results of a continuation of the study of dielectric losses in solid solutions of other systems of alkali-halide crystals.

For the study of dielectric losses in crystals of solid solutions, the systems NaCl—NaBr, KCl—KBr, and KCl—RbCl were chosen.

In studying systems of alkali-halide crystals it was found that, as a result of the interaction of pairs of alkali-halide salts, both solid solutions and eutectics may form [3, 4], which is determined by the ratio of the molecular volumes and of the constants of the crystal lattices of the interacting components. A whole series of salts of alkali-halide crystals, on being fused together, form solid solutions, but upon lowering the temperature these solid solutions decompose [5]. Only a very limited number of pairs of salts, when they interact, give solid solutions that do not decompose at room temperatures [6]. The systems NaCl—NaBr, KCl—KBr, and KCl—RbCl are continuous solid solutions that do not decompose at room temperature over a long period of time [3—7]. These are the most stable solid solutions. Therefore, precisely these systems of alkali-halide crystals were chosen for the investigation of dielectric losses in solid solutions. Mixed crystals NaCl—NaBr, KCl—KBr, and KCl—RbCl were grown from the melt by the Kyropoulos method.

For the majority of the crystals investigated, X-ray analysis was carried out; it showed that the crystals under consideration are indeed solid solutions. X-ray diffraction [[unclear: text continues on next page]]

Fig. 1. Dependence of the loss angle in solid solutions on their composition

(a) \( \mathrm{KCl} \)–\( \mathrm{KBr} \): \( \tan\delta \cdot 10^{4} \) and \( \varepsilon \) versus composition; curves marked \(3 \cdot 10^{5}\), \(10^{6}\), and \(f = 10^{7}\,\mathrm{Hz}\).

(b) \( \mathrm{NaCl} \)–\( \mathrm{NaBr} \): \( \tan\delta \cdot 10^{4} \) versus composition; curves marked \(5 \cdot 10^{5}\), \(10^{5}\), and \(f = 10^{7}\,\mathrm{Hz}\).

(c) \( \mathrm{KBr} \)–\( \mathrm{KI} \): \( \tan\delta \cdot 10^{4} \) versus composition; curves marked \(10^{5}\) and \(f = 10^{7}\,\mathrm{Hz}\).

(d) \( \mathrm{KCl} \)–\( \mathrm{RbCl} \): \( \tan\delta \cdot 10^{4} \) versus composition; curves marked \(f = 3 \cdot 10^{5}\,\mathrm{Hz}\) and \(f = 10^{6}\,\mathrm{Hz}\).

the lattice constant of the crystals under investigation was determined.

Measurements of the loss angle were carried out by the resonance method of measuring resistance in the frequency range \(3 \cdot 10^5\)—\(10^7\) cps; at higher frequencies a variant of this method, improved by K. A. Vodop’yanov and V. F. Ivlev [8], was used.

The loss angle in the mixed crystals under investigation was measured at room temperature with mercury electrodes. In Fig. 1, together with the previously studied system KJ—KBr [1], the dependences obtained for the loss angle on the composition of the solid solutions studied are given for various frequencies of the electric field applied to the dielectric. The dependences of the loss angle in solid solutions on their composition are analogous for all the systems investigated: NaCl—NaBr, KCl—KBr, KCl—RbCl, and the previously studied system KJ—KBr. As a function of the composition of the solid solution, the loss angle varies along a curve with a maximum in the region of approximately equal concentrations of the two components. The magnitude of the maximum in the dependence of the loss angle on composition is greatest in the low-frequency region (\(3 \cdot 10^5\) cps) and decreases as the frequency increases. It is characteristic that in the high-frequency region, beginning with a frequency of the order of \(3 \cdot 10^6\) cps, no further decrease in the magnitude of the loss angle in the crystals is observed with increasing frequency: the curves characterizing the change in the loss angle as a function of the composition of the solid solutions coincide at applied-electric-field frequencies of \(10^7\) and \(3 \cdot 10^6\) cps. A further increase in frequency also does not lead to any noticeable change in the loss angle in the solid solutions (Fig. 2).

Fig. 2. Frequency dependences of the loss angle in a simple KCl single crystal (1) and in solid solutions 40 mol% KCl—60 mol% KBr (2) and 50 mol% KCl—50 mol% KBr (3).

Simultaneously with the measurement of the loss angle in the solid solutions, their dielectric constant was also measured. The dielectric constant for all the crystals investigated changes hardly at all with change in the frequency of the applied electric field. With change in the composition of the solid solutions, a very slight change in the dielectric constant is observed. In Fig. 1, for the KCl—KBr system, the change in their dielectric constant as a function of the composition of the solid solutions (at a frequency of \(10^7\) cps) is given simultaneously with the loss angle. As can be seen from the figure, the values of the dielectric constant of crystals with approximately equal concentrations of the two components are somewhat larger than the values of the dielectric constant of the initial components. For other crystals the values of \(\varepsilon\) are approximately equal to, or somewhat greater than, the values of the dielectric constant of the simple crystals.

To clarify the mechanism of losses in solid-solution crystals, measurements were carried out of the loss angle in them at various frequencies as a function of temperature.

In studying the temperature dependences of the loss angle, Wood’s alloy was used as the electrodes; it melts at temperatures of about \(70^\circ\mathrm{C}\), ensuring good contact of the electrodes with the specimen. The temperature was measured by means of a thermocouple placed in a special recess in the electrode located near the specimen under investigation. To measure the loss angle in the temperature interval \(20\text{--}240^\circ\mathrm{C}\), the specimen was placed in a heated quartz beaker, which did not disturb the symmetry of the setup. For measurements in the temperature interval \(20\text{--}300^\circ\mathrm{C}\), a crucible furnace was used.

Figure 3 gives the temperature dependences of the loss angle in mixed crystals of the NaCl—NaBr system at a frequency of \(10^6\) Hz. Figure 4 shows the change of the loss angle with temperature in a crystal of \(40\ \mathrm{mol}\%\ \mathrm{KCl}—60\ \mathrm{mol}\%\ \mathrm{KBr}\) over a wider temperature interval \((20\text{--}300^\circ\mathrm{C})\).

Fig. 3. Temperature dependences of the loss angle in solid solutions of the NaCl—NaBr system.

1. NaCl.
2. \(95\ \mathrm{mol}\%\ \mathrm{NaCl} — 5\ \mathrm{mol}\%\ \mathrm{NaBr}\).
3. \(80\ \mathrm{mol}\%\ \mathrm{NaCl} — 20\ \mathrm{mol}\%\ \mathrm{NaBr}\).
4. \(70\ \mathrm{mol}\%\ \mathrm{NaCl} — 30\ \mathrm{mol}\%\ \mathrm{NaBr}\).
5. \(40\ \mathrm{mol}\%\ \mathrm{NaCl} — 60\ \mathrm{mol}\%\ \mathrm{NaBr}\).
6. \(30\ \mathrm{mol}\%\ \mathrm{NaCl} — 70\ \mathrm{mol}\%\ \mathrm{NaBr}\).
7. \(5\ \mathrm{mol}\%\ \mathrm{NaCl} — 95\ \mathrm{mol}\%\ \mathrm{NaBr}\).

Fig. 4. Temperature dependence of the loss angle in the mixed crystal \(40\ \mathrm{mol}\%\ \mathrm{KCl}—60\ \mathrm{mol}\%\ \mathrm{KBr}\).

The temperature dependences of the loss angle in other mixed crystals (the KCl—KBr and KCl—RbCl systems) are similar to these, and therefore they are not given here. As can be seen from Figs. 3–4, the changes in the loss angle in all mixed crystals as a function of temperature are analogous: over a certain temperature interval the loss angle changes little with temperature, and then a sharp increase of the loss angle begins as the temperature is raised further. The temperature above which a noticeable increase of the loss angle is observed depends on the composition of the solid solution: the closer the composition of the crystal studied is to a composition with approximately equal concentrations of the components, the greater the concentration of the second component in the solid solution, the lower the temperature at which a sharp increase of the loss angle is observed.

Measurement of the temperature dependences of the loss angle in solid solutions at various frequencies showed that the temperature above which a large increase of the loss angle is observed also depends on the frequency. Figure 5 gives the temperature dependences of the loss angle in a crystal of \(50\ \mathrm{mol}\%\ \mathrm{KCl}—50\ \mathrm{mol}\%\ \mathrm{KBr}\), obtained at frequencies \(3\cdot10^5\), \(10^6\), and \(10^7\) Hz. As the frequency of the external electric field is increased, it is observed—

there is an increase in the temperature corresponding to the beginning of a noticeable rise in the loss angle in this crystal.

As can be seen from Fig. 3, in one and the same temperature interval the loss angle in crystals of solid solutions changes much more substantially—

Fig. 5. Temperature dependences of the loss angle in a crystal of 50 mol% KCl—50 mol% KBr at different frequencies:
1. $f = 3 \cdot 10^5$ Hz, 2. $f = 10^6$ Hz, 3. $f = 10^7$ Hz.

—than the loss angle in simple crystals of the initial components. Figure 6 shows the change in the loss angle in solid solutions of the NaCl—NaBr system as a function of composition at different temperatures at a frequency of $10^6$ Hz. The maximum values of the loss angle, corresponding to the loss angles in crystals with a higher content of the second component, increase very strongly with increasing temperature. As can be seen from Fig. 6, the loss angle in a crystal of 40 mol% NaCl—60 mol% NaBr at a temperature of 20°C exceeded the loss angle in NaCl by only a factor of 2.5, whereas at a temperature of 180°C it is approximately 8 times greater than the loss angle in NaCl at the same temperature. Similar regularities also occur for crystals of the other investigated systems (KCl—KBr and KCl—RbCl). The temperature and frequency dependences obtained for the loss angle in the solid-solution crystals under consideration are characteristic neither of ohmic nor of relaxation losses. To determine the role of conductivity in the process of energy loss in the crystals considered, their electrical conductivity was measured at several temperatures. From the obtained conductivity values of the crystals, the loss angle due to conductivity was calculated. The results of the measurements of the loss angle and conductivity are given in Table 1.

Fig. 6. Dependences of the loss angle in solid solutions of the NaCl—NaBr system on their composition, obtained at different temperatures at a frequency of $10^6$ Hz.

As can be seen from the table, in the region of relatively low temperatures, 100–150°C,

the loss angle measured directly is considerably greater than the loss angle calculated from the conductivity, while at temperatures of 160–200°C both values are of the same order. From this one may conclude that at high temperatures, in the temperature range where a noticeable increase of the loss angle with temperature is observed, the losses are determined mainly by conductivity.

Table 1

In the temperature range where the loss angle depends only weakly on temperature and the total losses exceed the conductivity losses, losses of another type will predominate. The same relationship between the total losses and the conductivity losses is also observed for simple crystals [2]. Taking into account that the frequency and temperature dependences of the loss angle in solid solutions and in simple single crystals are analogous, one may suppose that the loss mechanisms in them are also analogous. The losses in simple alkali-halide crystals are composed of conductivity losses and relaxation losses caused by the displacement, within limited volumes, of weakly bound ions of the crystal lattice [1].

In solid solutions, increased energy losses are observed in comparison with simple single crystals. The temperature and frequency dependences of the loss angle in solid solutions are characterized by a more substantial increase of $\operatorname{tg}\delta$ with decreasing frequency and increasing temperature than in the corresponding dependences for simple crystals.

For several specimens of solid solutions and simple single crystals of the initial components, spectral analysis was carried out. As a result of the spectral analysis, it was found that in the crystals of the solid solutions there existed only those impurities which were also found in the simple crystals of the initial components. Therefore the deviations of the temperature and frequency dependences of the loss angle in solid solutions, as compared with the analogous dependences for simple crystals, cannot be explained by the influence of any extraneous impurities or contaminations. Such an explanation is also contradicted by the fact that the changes in the loss angle as a function of the composition of the solid solution, and the deviations of the frequency and temperature dependences from the dependences for simple crystals, obey definite regularities: the greater the concentration of the second component in the composition of the solid solution, the more the loss angle in it differs, in absolute value, from the loss angle in the crystal-

in the initial components, and the temperature and frequency dependences differ significantly from similar dependences for simple crystals.

All this indicates that the different changes in the loss angle in solid solutions and in simple crystals, and the substantially different magnitudes of the loss angle in them, must be associated with the structural features of solid solutions.

As is known, the crystal lattice of solid solutions is looser than the lattice of simple single crystals, differing from the crystal lattice of simple single crystals by the presence of systematic distortions—microdeformations. Microdeformations arise in the crystal lattice of solid solutions in the region of a site occupied by an ion of the second component, as a result of the fact that the sites of the crystal lattice of solid solutions are occupied by ions with different radii. The number of such microdeformations increases as the concentration of the second component in the solid solution increases [9—10].

Distortions of the crystal lattice facilitate the tearing of ions from equilibrium positions owing to a decrease in the disruption energy of the crystal lattice [11].

This causes an increase in the number of ions participating in conduction, and an increase in the number of weakly bound ions whose motion occurs in limited volumes of the crystal lattice. Therefore, increased energy losses are observed in solid solutions. Since the number of distortions in the crystal lattice of solid solutions increases with increasing concentration of the second component, which is accompanied by an increase in the number of weakly bound and free ions, all the regularities in the deviations of the dependences of the loss angle in solid solutions from the analogous dependences for simple crystals are understandable.

The dependence of the loss angle of solid solutions on their composition, in accordance with the structural features of solid solutions, can be explained as follows: as the concentration of the second component increases, the number of microdeformations of the crystal lattice increases; the number of weakly bound ions increases, the displacement of which under the action of an electric field gives rise to relaxation losses; and the number of ions participating in conduction and producing ohmic losses increases. Therefore, we observe an increase in the loss angle as the concentration of the second component increases. The conductivity of solid solutions is increased, which is understandable, since the disruption energy of a crystal lattice with foreign impurities is reduced in comparison with the disruption energy of a crystal lattice without impurities. And the conduction loss angle increases as the frequency decreases. This explains the increase in the maximum of \(\operatorname{tg}\delta\) in its dependence on the composition of solid solutions as the wavelength increases. The earlier rise of the loss angle in solid solutions as a function of temperature is also associated with the increased conduction losses in solid solutions. The higher the concentration of the second component, the more distorted the crystal lattice, the greater the conduction losses, the larger their share in the total energy losses in the crystal; thus, at a lower temperature the conduction losses become predominant, and we find the sharp temperature dependence of the loss angle characteristic of ohmic losses.

It is of interest to note that analogous regularities in the change of the loss angle as a function of composition and temperature are also observed for solid solutions of ceramic-type materials [12—13].

In the study of alkali-halide single crystals, a quite definite correspondence was established in the change of the loss angle and a whole series of physicochemical characteristics of these crystals: the angle

losses increases with increasing distance between ions in the crystal lattice, and with decreasing lattice energy, melting temperature, heat of formation, etc., of the crystals [1].

Upon transition to solid solutions, a change in these regularities is observed. The lattice constant of solid solutions, depending on their composition, changes approximately linearly (the additivity rule is approximately fulfilled for the change in the lattice parameter of solid solutions). The energy of the crystal lattice changes in the same way. But the melting temperature of solid solutions, depending on composition, changes along a curve with a minimum. For single crystals of alkali-halide salts, a parallel change is observed in the melting temperature and the energy of the crystal lattice. The mechanical characteristics of single crystals of alkali-halide salts, such as Brinell hardness, yield pressure, and microhardness, increase as the distance between ions in the crystal lattice decreases [14, 15]. For solid solutions there is no analogy in the change of the mechanical characteristics and their lattice constant: the lattice constant changes, depending on composition, approximately linearly, whereas the mechanical characteristics follow a curve with a maximum [16, 17].

Consequently, the regularities in the change of the physicochemical characteristics of solid solutions differ from the regularities in the change of these characteristics of simple single crystals. The loss angle in solid solutions changes, depending on composition, along a curve with a maximum. Thus, the change in the loss angle in solid solutions proceeds parallel to the change in their mechanical characteristics and oppositely to the change in their melting temperature. The loss angle changes in exactly the same way in simple single crystals. But in the case of solid solutions there is no such relation in the change of the loss angle and the lattice constant as is observed for simple single crystals [1].

A similar change in the regularities established for single crystals is also observed in measurements of the electric strength of solid solutions of alkali-halide crystals. In this connection there exists the viewpoint [18] that the electric strength in the case of solid solutions is determined not by the energy of the crystal lattice, but by the heat absorbed in the formation of the solid solution. For the change in the loss angle in solid solutions as a function of composition, an analogy is also observed with the change in the heat absorbed in the formation of these solid solutions: depending on the composition of the solid solution, the heat \(Q\) also changes along a curve with a maximum. In addition, even a certain quantitative correspondence is observed in the changes of \(\tg \delta\) and \(Q\). The largest maximum of the loss angle as a function of the composition of solid solutions at a frequency of \(10^6\) cps is observed for the KBr—KI system; the greatest amount of heat is absorbed in the formation of the equimolecular solution of precisely this system \(\left(700\ \frac{\text{kcal}}{\text{mole}}\right)\). The maximum value of the loss angle in the NaCl—NaBr system is approximately 3 times, and in the KCl—KBr system 2 times, greater than the loss angle in the initial components, and the heat in the formation of equimolecular solid solutions of these systems is also smaller \(\left(335\ \frac{\text{kcal}}{\text{mole}}\right)\) and \(235\ \frac{\text{kcal}}{\text{mole}}\) for NaCl—NaBr and KCl—KBr, respectively). The smallest increase in the loss angle is observed for the KCl—RbCl system. For this system there is also observed the smallest heat of formation of the equimolecular solid solution [6, 7].

Over time, the heat absorbed during the formation of the solid solution changes. The decomposition of the solid solution is accompanied by a change in the flow pressure [16], the electric strength [17], and the loss angle [18].

On the basis of a study of dielectric losses in solid solutions of alkali-halide crystals, the following conclusions may be drawn:

1. The mechanism of losses in crystals of solid solutions is analogous to the mechanism of losses in simple crystals: the losses consist of ohmic and relaxation losses associated with the displacement, under the action of an electric field, of free and weakly bound ions over large distances and within limited volumes.

2. The losses in crystals of solid solutions are increased in comparison with the losses in simple crystals, which is connected with the structural features of solid solutions, whose crystal lattice is distorted.

3. The regularities in the variation of the physicochemical characteristics of solid solutions differ from the regularities in the variation of these characteristics in simple single crystals, which is also due to the structural features of solid solutions.

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