DIELECTRIC LOSSES

IN ALKALI-HALIDE CRYSTALS

AT HIGH FREQUENCY AND THEIR THERMOCHEMICAL

CHARACTERISTICS

A. A. VOROB’EV, K. A. VODOP’YANOV

Dielectric losses in solid dielectrics are theoretically explained as the result of processes caused chiefly by impurities and by disturbances in the homogeneity of the structure. The structure of the dielectric itself, in the theory of losses, is either not taken into account at all or is taken into account as a secondary factor.

Losses in dielectrics are explained by taking into account the phenomena of high-voltage polarization, which are likewise associated with structural disturbances and impurities.

Such a construction of the theory of losses is probably correct in describing phenomena in polycrystalline and amorphous dielectrics, with their complex and disturbed structure. Such an approach is hardly correct when considering the phenomenon of losses in solid crystalline dielectrics with a small number of defects in the crystal lattice.

It is of interest to take into account the influence of the structural elements of the crystal lattice and of the physicochemical characteristics of the substance on the magnitude of the dielectric-loss angle.

The experiments of A. K. Krasin [1] did not reveal any influence of conduction electrons on the magnitude of the dielectric constant.

The experiments of M. A. Krivov [2] revealed an increase in losses under photoconductivity of X-rayed rock salt by only 30–35%.

Thus, it should be considered that losses in solid dielectrics are substantially connected with the motion of ions in them and with the ionic structure of the dielectric. Table 1 gives some physicochemical characteristics of crystals of alkali-halide salts.

It is evident from Table 1 that the dielectric constant \(\varepsilon\) is considerably higher than the optical component \(\varepsilon_{\sim}\). Consequently, in alkali-halide crystals, along with electronic polarization, ionic polarization plays an essential role.

As is evident from the table, \(\varepsilon_{\sim}\) varies regularly with the change in the ion radius. This is explained by the fact that \(\varepsilon_{\sim}\) is determined by the magnitude of the ion radius and by electronic polarizability.

The total dielectric constant \(\varepsilon\), with variable cation and constant anion, as a rule decreases with increasing cation radius. With constant cation and variable anion, no regular change in \(\varepsilon\) is observed.

Ionic polarization increases with decreasing cation radius at constant anion and also increases with decreasing anion radius at constant cation. Since \(\varepsilon\) is determined by the electronic and ionic components of polarization, the absence in some cases of a regular change in \(\varepsilon\) is apparently due to the fact that sometimes the electronic component plays a greater role than the ionic one.

One of the most important characteristics of a dielectric crystal is the dependence of its electrical conductivity on temperature. Experimen-

tally measured electrical conductivity \(\sigma\) of ionic crystals is described by a two-term formula:

\[ \sigma = A_1 e^{-\frac{U_1}{kT}} + A_2 e^{-\frac{U_2}{kT}}, \]

where \(U_1\) and \(U_2\) are activation energies.

Lehfeldt [3] believes that at low temperatures \(\sigma\) of crystals is due to impurity ions, and at high temperatures to dissociated ions of the lattice. The activation energy \(U_2\) of impurity ions is smaller than \(U_1\), that of the ions of the basic lattice.

Table 1

Academician A. F. Ioffe [4] believes that the electrical conductivity of crystals, both at low and at high temperatures, is due to ions of the lattice itself. At low temperatures the current carriers are metal ions, and at high temperatures both metal ions and, predominantly, halide ions.

It follows from the table that for alkali-halide crystals the activation energies \(U_1\) and \(U_2\) decrease with increasing anion radius at a constant cation radius. This indicates a direct connection between the conductivity of ionic crystals and the energy binding the ions in the lattice sites. Impurity ions in this case play a secondary role.

One of the authors of this article, together with E. K. Zavadovskaya [5], proposed a physical explanation of the electrical form of breakdown of alkali-halide crystals. It was suggested that the responsible factor in the electrical breakdown of an ionic crystal is the energy of the bond between its structural elements. It has been established [6] that the electric strength of a compound increases with an increase in the heat of formation and the heat of sublimation, that is, with an increase in the chemical stability of the compound. The connection of the electric strength of a dielectric crystal with its physicochemical characteristics (table) has important

importance for elucidating the mechanism of phenomena occurring in crystals that are in an electric field.

Until recently, no reliable values had been obtained for the loss angle in alkali-halide crystals, chiefly because of the absence of perfected methods for measuring small loss angles. Meanwhile, establishing a connection between the loss angle and the physicochemical properties in alkali-halide crystals is of great importance for the physical substantiation of the mechanism of dielectric losses not only in ionic crystals, but also in the large group of solid inorganic dielectrics, which are of great practical importance. We were able to establish such a connection for certain ionic crystals through the use of a more accurate method for measuring $\operatorname{tg}\delta$, developed by one of us [7].

Figures 1–3 give the results of measurements of $\operatorname{tg}\delta$ for crystals of NaCl, KCl, KBr, and KI at a frequency of $10^6$ cycles, carried out by one of the authors. The dependence of $\operatorname{tg}\delta$ on the activation energy, lattice energy, lattice constant, heat of formation, and heat of sublimation for crystals of alkali-halide salts is plotted.

Fig. 1. $U$—activation energy, $E$—lattice energy

It follows from Fig. 1 that $\operatorname{tg}\delta$ is connected with the potential barrier separating the lattice particles. With an increase in the activation energy, $\operatorname{tg}\delta$ decreases. The magnitude of the potential barrier depends on the lattice energy; therefore it is natural to expect that, with an increase in the lattice energy, $\operatorname{tg}\delta$ should decrease. This is confirmed experimentally (Fig. 1). On the other hand, the lattice energy is a function of the distance between particles, that is, of the lattice constant. With an increase in the lattice constant, the lattice energy decreases; consequently, the value of $\operatorname{tg}\delta$ should increase. This is in agreement with our experimental data (Fig. 2).

From Fig. 3 it is seen that $\operatorname{tg}\delta$ of the crystals decreases with an increase in the heat of formation and the heat of sublimation.

On the basis of the dependences obtained, it may be concluded that the dielectric losses of alkali-halide crystals are determined by the chemical composition and the strength of the chemical compound, that is, the loss angle is a characteristic of the principal substance and its structure, while impurities play a secondary role.

The mechanism of dielectric losses in ionic crystals appears to us as follows. Under the influence of an external action (electri-

...chemical, thermal, etc.) in the crystal there occurs an increase in the number of weakly bound ions having different activation energies. A comparatively small number of ions possessing the higher activation energy, under the influence of an electric field, will execute translational motion in the crystal, creating a through conduction current. The greater part of the ions, having the lower activation energy, under the action of an alternating

Fig. 2. Lattice constant

electric field will execute a reciprocating displacement within a limited volume, giving rise to dielectric losses of a relaxation character. The smaller the lattice energy, the greater will be the number of weakly bound ions responsible for relaxation dielectric losses.

Fig. 3. $\Theta_1$—heat of formation of the solid compound.
$\Theta_2$—heat of sublimation

Mixed crystals consisting of components having different crystal-lattice constants have a loosened structure. This facilitates the thermal dissociation of ions and causes an increase in $\operatorname{tg}\delta$.

The dielectric losses of a system of solid solutions of isomorphic crystals KI—KBr were investigated. Mixed crystals of the syste...

the KI—KBr systems at all points of the phase diagram are solid solutions with a melting temperature lower than the melting temperatures of their constituent components. Consequently, in these crystals the chemical stability, lattice energy, and heat of formation must have lower values than in the lattices of the components. This, in turn, should increase the loss angle. In Fig. 4 it is shown that $\operatorname{tg}\delta$ in mixed crystals of the KI—KBr system at a frequency of $10^6$ cycles is indeed greater than in its constituents.

Fig. 4

The relation found between the electrical properties of a dielectric crystal and its physicochemical data should facilitate the search for new dielectrics possessing high electrical properties.

CITED LITERATURE

1. Krasin A. K. DAN, 2, No. 6 (1934).
2. Krivov M. A. Tr. SIBFTI, 28, 347 (1949).
3. Lehefeldt W. z. f. Phys. 85, 717 (1939).
4. Physics of Dielectrics. STTI, 1932, Kobeko P. P. Amorphous Substances, (1952).
5. Vorob’ev A. A. and Zavadovskaya E. K. DAN, 81, No. 3 (1951); DAN, 82, No. 4 (1952); Izvestiya Tomskogo politekhnicheskogo instituta, vol. 73, 3 (1952).
6. Vorob’ev A. A. and Zavadovskaya E. K. Izvestiya Tomskogo politekhnicheskogo instituta, vol. 71, 3 (1952).
7. Vodop’yanov K. A. and Ivlev V. F. ZhTF, 8, 1521 (1938).