DIELECTRIC LOSSES, ELECTRIC STRENGTH OF ALKALI-HALIDE CRYSTALS, AND LATTICE ENERGY

K. A. VODOPYANOV, A. A. VOROBYEV, and M. A. KRIVOV

The electric strength of alkali-halide crystals, as was shown earlier [1], is connected with the energy of the crystal lattice: as the latter increases, the electric strength increases in a regular manner. Between the degree of binding of the lattice particles, which can be judged from the lattice energy, the activation energy, the melting temperature, the heat of formation, and other energetic characteristics of the substance, and the electric strength of alkali-halide crystals, there exists a quite definite dependence. With increasing forces of interaction between the particles and the strength of their fixation in the lattice, the electric strength of the crystal increases. Further investigations [2] showed the presence of a regular relation between another most important characteristic of a substance—dielectric losses—and quantities characterizing the strength of the bonds between the particles of the lattice. As the lattice energy increases, the tangent of the dielectric-loss angle decreases monotonically.

Fig. 1. Dependence of $\operatorname{tg}\delta$ and the electric strength of crystals on the activation energy (a) and lattice energy (b), $(f = 10^6\ \text{Hz})$.

The dependence of the electric strength and the tangent of the dielectric-loss angle on the value of the lattice energy and the activation energy, calculated from the electrical conductivity of the crystal, is presented in Fig. 1. The experimental data given in Fig. 1 show that, with increasing activation energy (a) and lattice energy (b), the electric strength of the crystals increases, while the tangent of the dielectric-loss angle decreases.

A similar picture can also be observed in Fig. 2, on which experimental data are plotted for the electric strength and the tangent of the dielectric-loss angle of crystals as functions of the heat of formation of the solid compound (a) and of the melting temperature (b).

In all the graphs presented we observe one and the same regularity: an increase in the dielectric-loss angle in crystals is accompanied by a decrease in their electric strength.

If, for crystals of sodium chloride and of potassium chloride, bromide, and iodide, one plots from experimental data a graph of the change in the tangent of the dielectric-loss angle as a function of the electric strength of the same crystals, the picture shown in Fig. 3 is obtained.

Fig. 2. Dependence of \(tg\delta\) and the electric strength of crystals on the heat of formation of the solid compound (a) and the melting temperature (b), \((f = 10^6\ \text{Hz})\).

Thus, a decrease in the bonding of particles in the lattice leads to an increase in dielectric losses and to a decrease in the electric strength of the structure.

Fig. 3. Dependence between \(tg\delta\) and the electric strength of crystals, \((f = 10^6\ \text{Hz})\).

Figure 4 gives the temperature dependence of the course of change of the tangent of the dielectric-loss angle for some crystals of alkali-halide salts. The course of the curves shows that, as the lattice energy of the crystals decreases, the tangent of the loss angle increases. In systems with smaller

Fig. 4. Temperature dependence of \(tg\delta\) for crystals of alkali-halide salts, \((f = 10^6\ \text{Hz})\).

with lattice energy, the rapid increase of the loss tangent begins earlier and proceeds faster as the temperature is raised.

The relation between dielectric losses and electric strength can also be traced in mixed crystals of alkali-halide salts. Experiments have shown that if, as the amount of admixture of one salt in another is increased, the tangent of the dielectric-loss angle increases, then the electric strength of such crystals decreases in a regular manner. At a certain ratio of the amounts of the salts being mixed, the tangent of the loss angle passes through a maximum, the peak of which corresponds to a minimum of electric strength. This can be observed in the potassium bromide—potassium iodide system; the course of the change in the tangent of the loss angle for a frequency of \(10^6\) cps and the electric strength, as functions of the concentration of the components, are plotted in Fig. 5. The values of the electric strength of the system are plotted according to the data of N. B. Bogdanova [3].

Fig. 5. Values of \(tg\delta\) and electric strength for mixed crystals of the KBr—KI system
\((f = 10^6\ \text{cps})\).

Figure 6 shows the temperature dependence of the tangent of the dielectric-loss angle for the system under study. The tangent of the dielectric-loss angle for mixed crystals increases more sharply with increasing temperature than in pure crystals.

Figure 7 presents the temperature dependence of the tangent of the dielectric-loss angle and of the electric strength of rock-salt crystals. A comparison of the curves for the tangent of the loss angle and for electric strength shows that the weakening of the bonds between the ions of the lattice as the temperature is raised is accompanied by an increase in the tangent of the loss angle and a decrease in the electric strength of the crystal.

It is seen from Fig. 7 that up to a temperature of about \(200^\circ\text{C}\) the tangent of the dielectric-loss angle and the breakdown voltage of rock salt depend little on temperature. It is believed that in this temperature interval breakdown

has an electrical form [4]. At higher temperatures, when the breakdown voltage decreases strongly with increasing temperature, breakdown has a thermal form.

Fig. 6. Temperature dependence of \(\operatorname{tg}\delta\) for mixed crystals of the KBr–KI system \((f = 10^6\ \text{Hz})\).

However, the observed regularity may also have another explanation. At low temperatures the energy of interaction of particles in the lattice changes little with increasing temperature; the bonds in the lattice remain strong, as a result of which no change in the electrical characteristics of the crystal is noticeable as the temperature rises. At higher temperatures

Fig. 7. Dependence of \(\operatorname{tg}\delta\) and electric strength on temperature for a rock-salt crystal \((f = 10^6\ \text{Hz})\).

the lattice constant increases, the bonds between particles weaken, and the energy of interaction of the particles decreases. The decrease in lattice energy, in accordance with the regularity presented in Fig. 1, is accompanied by an increase in the dielectric-loss angle and a decrease in the electric strength of the crystal.

Thus, between the dielectric losses and the electric strength of alkali-halide salt crystals one may observe a quite definite regularity, explained by the fact that both of these phenomena

dielectric losses and breakdown—depend on the lattice energy of the crystal and are ultimately determined by the strength of the bonds between the particles in the crystal.

References

1. Vorob'ev A. A. Tr. SFTI V, 3, 234, 1939.
2. Vorob'ev A. A. and Vol'fkovich K. A. DAN SSSR, 94, 429—432, 1954.
3. Bogdanova N. ZhETF, 14, 30—31, 1944.
4. Physics of Dielectrics (edited by L. F. Wal'ter). GTTI, 1932.