Discussion on Dielectric Losses

A. A. Vorob'ev.—The data of K. A. Vodop'yanov are of interest, since they make it possible to draw a parallel between dielectric losses and electrical breakdown. The correlation here is far-reaching and is of interest. The increase in $\varepsilon$ also fits into the general picture. In all probability, the fundamental structure is involved here, and not impurities and additional ions. It is desirable that these measurements be continued.

The term structural losses is outdated, since it obscures the physical processes.

As for the freezing-in of ionic charges, at one time we studied this together with Venderovich. It proved possible to freeze in a charge for a long time and in simple structures.

V. I. Odelevskii.—1) On the types of dielectric losses. Structural losses were first introduced by P. P. Kobeko. Skanaev introduced this concept for those losses that do not depend on temperature. The term “structural losses” should be eliminated, as having no physical meaning.

2) Concerning the report of N. P. Bogoroditskii. One cannot agree with the unification of relaxation losses, conductivity losses, and resonance losses proposed by Bogoroditskii. Losses are divided into conductivity losses, relaxation (dipole) losses, and resonance losses.

3) On the report of R. L. Müller. In calculating the activation energy, R. L. Müller takes into account only Coulomb forces, but does not take into account repulsive and polarization forces.

V. N. Kessenikh.—At this conference a very large and wide-ranging body of material has been presented.

It has been established beyond dispute that a group of conductivity losses really exists objectively; this has been confirmed by the classical dependence of $\operatorname{tg}\delta$ on temperature and frequency, obtained by Vorozhdov for fused quartz. Therefore there are no grounds for assigning conductivity losses to relaxation losses, and no grounds for eliminating the term relaxation losses.

Relaxation oscillations occur in all radio circuits—these are transient processes, a simple exponential dependence on time. Therefore Bogoroditskii had some grounds for assigning conductivity losses to relaxation losses. I agree with Skanaev that dipole relaxation, associated with rotation, and a more complex relaxation (the works of Vodop'yanov and his students) should be distinguished.

Structural losses are vulnerable; this term is intermediate; everything that was not understood was assigned to it. It is inadvisable to use this term.

The existence of a type of loss independent of frequency has been demonstrated experimentally in Vodop’yanov’s works.

Can one construct a model that reproduces, over a broad range of frequencies, independence from frequency? Such a system cannot be constructed in the form of a purely electrical circuit consisting of capacitance, inductance, and resistance, in the presence of a reactive component. But, by applying an oscillatory model with fluctuation processes, one could explain this independence.

In the remarks made by T. Matzonashvili, it is unclear whether, first of all, it can be asserted that the weakly expressed maxima really exist. Is there not here a formation of space charges due to the geometry of the specimen? Could certain features of the operation of the \(Q\)-meter also have had an effect here? There have been cases when, in measurements at high frequencies, in a specimen with a silver electrode deposited by cathodic sputtering, an apparent change in \(\varepsilon\) by almost a factor of 2 was observed. The cause of this phenomenon turned out to be the switching-off of the outer part of the electrodes as a result of the skin effect.

G. I. Skanavi.—V. I. Odelevsky’s report is very interesting. In it the questions of dielectric losses in glasses are touched upon in substance. It is shown that in a number of cases maxima of \(\operatorname{tg}\delta\) can be obtained where previously they had not been obtained.

The attempt to consider a model of the molecular structure of glass is of interest. But this method of calculation is far from perfect, although it does give estimated values.

Odelevsky’s model develops the question in greater detail and makes it possible to draw certain physical conclusions, although it does not make it possible to calculate the magnitudes. The fact of an increase in electrical conductivity, which was considered by Müller, is very interesting, but this model does not make it possible to carry out quantitative calculations.

The remarks on K. A. Vodop’yanov’s report may be reduced to the following: it would be very good if the losses were so simply determined by the energy of the lattice. But for the time being it is difficult to imagine a simple relation between the energy of the lattice and \(\operatorname{tg}\delta\). The dependence of \(\operatorname{tg}\delta\) on the energy of the lattice does not yet make it possible either to calculate or to represent the physical processes that take place, and therefore the connection between \(\operatorname{tg}\delta\) and the energy of the lattice gives nothing in practical terms. In measuring \(\operatorname{tg}\delta\) of crystals, a special role is played by the care of the measurements, the purity of the specimen, and the measurement conditions. But experimentally it is always easier to determine \(\operatorname{tg}\delta\) and the electric strength \(E_{\mathrm{br}}\) than the lattice energy for complex crystals. How can one establish that in the measurements all those precautions of which Matzonashvili spoke were indeed taken into account? With regard to the temperature curves, the question arises whether there are losses that do not depend on temperature. Over a large temperature interval, as has been established, the losses do not depend on temperature. There is no theory for such losses. The same applies to the dependence on frequency.

What Vodop’yanov said concerning relaxation losses is unclear. If \(\lambda \simeq\) the wavelength of infrared rays, then relaxation losses are obtained. But if the field changes with a frequency of \(10^8\ \mathrm{sec}^{-1}\), then there must be a lag of polarization.

A. A. Vorob’ev—G. I. Skanavi expressed the thought that there is no theory of dielectric losses independent of temperature, which were discovered by Vodop’yanov. These losses are due to oscillations of the lattice itself. As for errors due to moisture, this influence would be noticeable—\(\operatorname{tg}\delta\) would decrease with temperature. Since this is not the case, there is no reason to speak of the influ-

moisture does not occur. The results were obtained on the same apparatus under the same conditions. As for the physics of the process, there is no less of it here than in the theory of relaxation processes. Qualitatively the phenomenon has been predicted, and more cannot be demanded of the theory. The physics here is that, as the coupling between particles decreases, the losses increase. The theory of relaxation losses contains very little physics. At present there are enough data to develop a more detailed molecular theory.

S. F. Ryaboshenko—says that he measured \(\operatorname{tg}\delta\) for NaCl, using mercury electrodes (whereas Breckenridge carried out measurements with silver electrodes), and obtained, without temperature treatment, a curve with maxima the same as Breckenridge’s. If the specimen is heated at a temperature of \(150^\circ\) (3–4 hours) and the heated specimen is tested under a stream of hot air, then no maxima are observed; only occasionally does a second maximum of \(\operatorname{tg}\delta\) appear at \(110\text{–}120^\circ\mathrm{C}\). The same effect can also be obtained with graphite electrodes. The activation energy is determined from

\[ \operatorname{tg}\delta = C e^{\pm \frac{U_1}{kT}} \quad \text{and} \quad f_{\max} = a e^{-\frac{U_2}{kT}}. \]

Which of these energies is the activation energy?

Measurements give: \(\dfrac{U_1}{U_2} = 3\) for Ca; 3 for Sr; 2 for Mg.

R. I. Müller.—In my calculation the repulsive forces were not taken into account. It was assumed that these forces cancel out in obtaining the difference of energies in the potential well and on the potential barrier. Evidently, V. I. Odelevskii is right in his assertion. But in the published article I noted that the calculation does not claim to be rigorous. At the same time, it seems to me that Odelevskii’s calculation also is not rigorous. It should be noted that Odelevskii and I think in the same direction, and the discrepancy is that Odelevskii proceeds from the crystal-chemical ionic concepts of Goldschmidt–Zachariasen, whereas I base myself on my ion–atom–valence concept.

V. I. Odelevskii.—1) Because of the counting set of relaxators, the maximum of \(\operatorname{tg}\delta\) is broadened, and the calculation of \(U\) (the activation energy) is made difficult. Therefore a more accurate method is the calculation of the energy from the displacement of the maximum.

2) Why must \(\operatorname{tg}\delta\) and \(E_{\mathrm{pr}}\) necessarily depend directly on the lattice energy? It is more reasonable to suppose that the influence of the lattice energy is not direct but indirect. It would be more correct to find those intermediate links which determine the connection between \(\operatorname{tg}\delta\), \(E_{\mathrm{pr}}\), and the lattice energy. According to Vodop’yanov’s data, dielectric losses are caused by relaxation. But a relaxation process is necessarily connected with the presence of defects, and the connection with the lattice energy is necessarily indirect.

3) Remarks on the growth of crystals.—Crystals grown from the melt have an electrical conductivity 10–100 times greater than those grown from solution. This is due to the “capture” of holes. It would be interesting to investigate crystals grown from solution.

T. N. Verbitskaya.—The appearance of the independence of \(\operatorname{tg}\delta\) from temperature is incomprehensible. Perhaps K. A. Vodop’yanov will give an explanation of this phenomenon. There is no basis for speaking of inaccuracy of measurement. It would be interesting to know whether losses were measured in the region of negative temperatures and whether an increase of \(\operatorname{tg}\delta\) is observed with decreasing temperature.

G. I. Skanavi.—In the absence of a maximum, \(\operatorname{tg}\delta\) can be used to calculate the activation energy also from the rise of the \(\operatorname{tg}\delta\) curve with temperature.

It is necessary to take into account the set of relaxation times; this is of great importance.

In my report there is a more accurate calculation of the quantity \(U\) (the activation energy). As for the independence of \(\operatorname{tg}\delta\) from temperature, what is needed here is not guesswork but detailed study. In the report I wanted to show, using SrBiTiO\(_2\) as an example, that, starting from the relaxation mechanism, we predicted and obtained what we had predicted; i.e., the molecular theory of relaxation losses can not only explain but also predict.

It may be that the increase in losses upon heating is determined by the properties of the crystal, while the decrease of the loss angle occurs at the expense of the evaporation of moisture.

K. A. Vodop’yanov.—There are no data in the literature on the absolute value of \(\operatorname{tg}\delta\) for simple alkali-halide crystals. In his latest work, Hippel indicates that \(\operatorname{tg}\delta\) for simple crystals is less than \(2\cdot 10^{-4}\).

We have made measurements of \(\operatorname{tg}\delta\) of the order of \(10^{-5}\) by a more precise method developed in our laboratory, and we are able to relate \(\operatorname{tg}\delta\) to the physicochemical properties of the crystal. We have shown that the \(\operatorname{tg}\delta\) of a crystal depends on the energy of the crystal lattice.

Measuring the temperature dependence (direct and reverse) of \(\operatorname{tg}\delta\), we did not detect maxima in unannealed crystal specimens. These maxima are obtained only for annealed crystals.

According to our experimental data, it follows that dielectric losses in simple crystals are due to weakly bound ions, which, depending on external conditions (frequency and temperature), can give losses of an ohmic and a relaxation character.

There is reason to believe that the lower the energy of the crystal lattice, the greater the number of weakly bound ions; hence a quite reasonable connection is obtained between \(\operatorname{tg}\delta\) and the lattice energy. The existence of this connection makes it possible to judge the quality of technical dielectrics both during their operation and during manufacture.