On the Nature of the Temperature Dependence of Dielectric Losses during the Polarization of Ionic Compounds

N. P. Bogoroditskii

The nature of the temperature dependence of $\tg \delta$ in inorganic dielectrics is of great importance from the standpoint of the practical use of materials; moreover, the form of this dependence makes it possible, to a certain extent, to judge the very mechanism of dielectric losses.

In numerous works devoted to this question, it is noted that in some temperature interval $\tg \delta$ does not depend on temperature, or that $\tg \delta$ increases continuously with temperature, or, finally, that $\tg \delta$ has an extremal value at a definite temperature. Skanavi [1] summarized the views that had existed and proposed distinguishing, for glasses:

a) structural dielectric losses, which do not depend on temperature;
b) relaxation dielectric losses;
c) conductivity losses.

Recently, in connection with the sharply increased requirements concerning the electrical properties of high-frequency insulation, the need has arisen for a more thorough study of the dielectric losses of ionic compounds at high frequencies.

For this purpose we have again studied the dielectric losses of a number of simple borate and silicate glasses, as well as of the highest-quality types of high-frequency ceramics.

Method of Investigation

The following were subjected to study: borate glasses—pure boric anhydride; sodium borate glasses at different ratios of $\mathrm{B_2O_3}$ and $\mathrm{Na_2O}$; barium borate glasses; technical alkali-free barium silicate and lead silicate glasses. In addition, certain ceramic materials with comparatively low electrical characteristics were investigated: radio porcelain, insulating porcelain, and the highest-quality types of ceramics with a high content of the crystalline phase—steatite, ultraporcelain, spinel, and celsian ceramics. Experimental samples of borate glasses were prepared by melting in a platinum crucible using chemically pure reagents (boric acid, barium hydroxide hydrate, sodium carbonate). The molten glass was poured onto a cast-iron plate heated to $300^\circ$, with a recess 30–40 mm in diameter and 1.5–2.0 mm deep. The resulting disk-shaped samples were annealed for 10–12 hours. After annealing, the samples were ground using kerosene or turpentine. The electrodes were silver applied by firing (for silicate glasses) and polished silver disks, which in the process

measurements were pressed tightly by a spring against the surface of the sample (for boron glasses).

The ceramic specimens were prepared by the usual ceramic technology, using technical raw materials, and had the form of disks 20–30 mm in diameter and 1.5–2.0 mm thick. Silver applied by firing served as the electrodes.

Dielectric losses at radio frequencies were measured with a Q-meter and an IP-3 instrument, as well as with an apparatus for measuring losses by the method of measuring reactance. At low frequencies the measurements were made with ML-E and MT-K bridges. In measurements at low temperatures the samples were placed in a vacuum flask, which was cooled in a Dewar vessel.

Results of the Experiments and Their Discussion

The temperature dependence of \(\operatorname{tg}\delta\) of boron glass shown in Fig. 1 indicates a noticeably smaller value of the dielectric losses in comparison with the literature data, and also the presence of an increase of \(\operatorname{tg}\delta\) with temperature, in contrast to earlier data.

In Figs. 2, 3, and 4 the dependences of \(\operatorname{tg}\delta\) on temperature are presented for boron-alkali and boron-barium glasses. It should again be noted that there is a noticeable increase in dielectric losses in the temperature range for which this dependence had previously, erroneously, not been observed.

Fig. 1

A different character of the dependences of \(\operatorname{tg}\delta\) on temperature is observed for silicate glasses. In Figs. 5 and 6 the temperature dependences of \(\operatorname{tg}\delta\) are given for alkali-free barium silicate and lead silicate glasses. In this case a minimum of losses is found, as was also observed in the work of V. A. Ioffe [3]. Here, too, the independence of \(\operatorname{tg}\delta\) from temperature is again not confirmed.

In the investigation of ceramic materials it was likewise established in all cases that there is no temperature region in which the losses do not depend on temperature. In Fig. 7 the temperature dependence over a wide temperature interval is presented for insulating porcelain and radio porcelain. In Figs. 8, 9, 10, and 11 the dependences of \(\operatorname{tg}\delta\) and \(\varepsilon\) on temperature are shown for steatite and rutile ceramics according to the data of Hippel [4].

Fig. 2

Fig. 3

Fig. 4

Fig. 5

In Fig. 12 are given the temperature dependences of $\operatorname{tg}\delta$ at $f = 1 \cdot 10^6$ Hz for a number of ceramic materials used in domestic industry.

Generalizing the experimental material set forth above, one may assert that, over a wide range of temperatures and frequencies, dielectric losses during the polarization of ionic compounds are caused by one and the same

Fig. 6

Fig. 7

phenomenon—the disturbance of the thermal motion of ions under the action of an electric field, which manifests itself the more sharply the closer the period of the electric field and the relaxation time of the particles coincide. In this connection it must be borne in mind that the particles execute complex thermal motions—

Fig. 8

Fig. 9

jumps in space from one equilibrium position to another and vibration (rotation) with the so-called natural frequency of oscillation of the particles.

At low frequencies, the thermal motion of ions affects dielectric losses almost in the same way as it affects through electrical conductivity,

which is why a sharp increase of $\operatorname{tg}\delta$ with temperature is observed, beginning from its low values. As the frequency is raised, the electric field has less and less time to orient the ions during their thermal jumps, and $\operatorname{tg}\delta$ changes with temperature less and less. Figs. 8 and 10

Fig. 10

Fig. 11

show that at a frequency \(f=10^{10}\) cps the temperature dependence of \(\operatorname{tg}\delta\) of radio ceramics is almost not observed. From this point of view, the fans of curves \(\operatorname{tg}\delta=f(t^\circ)\) and \(\varepsilon=f(t^\circ)\) at different frequencies are quite natural.

In connection with the above, it is hardly expedient to divide dielectric losses in ionic compounds, as Skanavi does (Fig. 14, 1), into three components. It may be assumed that the data on the independence of \(\operatorname{tg}\delta\) from temperature were due to insufficient accuracy of the measuring instruments used about 20 years ago [2, 5].

Fig. 12

Fig. 13

Dielectric losses caused by the phenomenon of relaxation (the weakening of the thermal motion of ions or dipoles by an electric field), according to the established terminology, are usually characterized by the presence of frequency and temperature maxima. However, it should not be overlooked that relaxation processes, in one form or another, inevitably accompany the polarization of a dielectric associated with the thermal motion of particles. From this point of view, losses due to electrical conductivity and losses at ultrahigh frequencies, which are sometimes called resonant,

may be regarded as particular cases of relaxation losses, although the indicated mechanisms of dielectric losses are accompanied by new phenomena.

As is known, the dielectric $\operatorname{tg}\delta$ in electrical-conductivity losses changes markedly with frequency and temperature.

As for dielectric losses at ultrahigh frequencies, a large body of experimental material shows that, up to

\[ f = 2 - 3 \cdot 10^{10}\ \text{cps}, \]

$\operatorname{tg}\delta$ of the most diverse dielectrics increases, while the dielectric constant decreases. An increase in the dielectric constant at ultrahigh frequencies has been found only for a few dielectrics, in particular for certain gases.

On the basis of the foregoing, it seems to us that dielectric losses can be reduced mainly to the following physical processes:

1. The phenomenon of relaxation during polarization, associated with the thermal motion of particles and manifested at low frequencies, radio frequencies, and ultrahigh frequencies; it is characteristic of the solid, liquid, and even gaseous states of matter.

2. The phenomenon of relaxation during electrical conduction, likewise associated with the thermal motion of particles.

3. The phenomenon of ionization of a substance, usually a gas, either free or distributed in a solid body, manifested in electric fields of increased intensity.

The author expresses gratitude to Candidate of Chemical Sciences O. V. Mazurin and engineer L. P. Chikhanova, who participated in the experimental work on the study of the electrical properties of glass.

References

1. Skanavi, G. I. Dielectric Polarization and Losses in Glasses and Ceramic Materials with High Dielectric Constant. Gosenergoizdat, 1952.
2. Bogoroditskii, N. P. and Fridberg, I. L. ZhTF, 7, 18—19, 1952.
3. Ioffe, V. A. ZhTF, 22, 4, 1952.
4. Hippel, A. Dielectric Materials and Applications, 1954.
5. Skanavi, G. I. ZhTF, 7, 10, 1937.

Leningrad Electrotechnical Institute
named after V. I. Ulyanov—Lenin.