On the Thirtieth Anniversary of Soviet Physics

Physics of Dielectrics in the Soviet Union

G. I. Skanavi

Technical physics as a whole arose and took shape in our country only after the Great October Socialist Revolution, when the rapidly growing socialist industry required the search for new and independent paths of development. This applies fully also to the young branch of physics closely connected with the technology of electrical insulation—the physics of dielectrics.

In tsarist Russia, electrical-insulation technology was at a very low level. Electrical-industry plants worked entirely according to foreign instructions and with insulating materials imported from abroad.

Naturally, the theory of the electrical properties of dielectrics, having had before the Revolution no practical stimuli for its development, did not attract serious attention, especially since electrical engineering at that time did not impose particularly stringent requirements on electrical insulation. Insulating materials were selected by a crudely empirical method, without any attempts at calculation. At best, the working voltages of one or another type of insulation were determined on the basis of measurements of breakdown voltages by introducing a more or less arbitrary safety margin.

It is to the credit of Soviet physicists that they were the first to begin an in-depth study of the processes occurring in dielectrics under the action of an electric field. Such study is not only of purely scientific interest, but is also absolutely necessary for the conscious selection and synthesis of electrically insulating materials.

At the present time, the results of the work of Soviet scientists in the field of the physics of dielectrics make it possible, first, in a number of cases to understand the mechanism of the complex processes occurring in a dielectric placed in an electric field; second, to calculate some of the most important constants of a dielectric from its other constants, linking the basic electrical properties of dielectrics with their molecular structure; and, third, often to guide the work of chemists and technologists in creating new high-quality dielectrics possessing the required special properties.

The achievements of Soviet physics of dielectrics have considerably facilitated the development of insulation technology, both with respect to the selection and synthesis of insulating materials and with respect to the design and calculation of technical insulation and capacitors, and have made it possible to find new independent ways of solving practical problems.

1. IONIC ELECTRICAL CONDUCTIVITY OF DIELECTRICS

By 1922–1923—the beginning of the work of Soviet scientists in the field of the physics of dielectrics—only a few studies relating to it had been published in the world literature. Questions of dielectric polarization, electrical conductivity, and breakdown of gaseous dielectrics, dielectric polarization and dielectric losses of polar liquids, and some others had been clarified. The electrical properties of solid dielectrics, the most important from the standpoint of insulation technology, had been studied extremely little. Only isolated experimental facts were known, dealing mainly with the so-called “dielectric anomaly”—the decrease of current in a solid dielectric with the passage of time at constant voltage and, in connection with this, the apparent nonfulfillment of Ohm’s law.

Soviet physicists, under the direction of A. F. Ioffe, who initiated this work, first of all undertook the study of the electrical conductivity of solid dielectrics. A number of new experimental facts and regularities were established, which made it possible to clarify in general terms the nature of the electrical conductivity of solid dielectrics and the causes of the apparent nonfulfillment of Ohm’s law. Subsequently these works developed intensively, and at the present time the nature of the electrical conductivity of dielectrics has become considerably clearer.

The electrical conductivity of the overwhelming majority of dielectrics in the region not close to breakdown is predominantly ionic in character. This is convincingly proved by a number of studies devoted to the verification of Faraday’s law. For ionic crystals, glasses, varnish films, etc., it was shown (Pruzhinina) that Faraday’s law is well justified. At the same time, the classical method for verifying Faraday’s law, established by Tubandt for crystals, was developed and modified for application to technical insulating materials (glasses, varnish films, mica). Owing to the work of Ioffe, Frenkel, and others, the mechanism of ionic electrical conductivity of non-gaseous dielectrics can now be interpreted from a single general point of view.

Weakly bound ions present in a dielectric (in a crystal, for example, ions in the interstitial space; in glass, ions located in places of loose structural packing, etc.), participating in thermal motion, can move progressively from one “potential well” to another. In each such displacement an ion overcomes a certain potential barrier determined by the structure of the dielectric. In this process the kinetic energy of the ion

is expended in the work of overcoming this barrier—the work of activation. Even in a liquid dielectric an analogous mechanism of the thermal motion of ions may occur. An ion adheres to a molecule, enters into a complex common with it, and thereby becomes fixed, being in a “potential well.” However, participating in thermal motion, the ion has some probability of detaching itself from the molecule. Upon detachment the kinetic energy of the ion is expended in work against the forces of adhesion to the molecule—the work of activation. Thus activation energy is inherent in an ion located not only in a solid body, but also in a liquid body. After traversing a certain “free” path, the ion again falls into a “potential well.” When an external electric field is applied, the “activated” ions drift in the direction of the field. The average velocity of an ion in the direction of the field, at small fields, is directly proportional to the field strength.

Therefore the electrical conductivity of any non-gaseous dielectric is readily related, by means of the expression for mobility, to constants characterizing the molecular structure of the dielectric, and may be expressed as follows:

\[ \gamma = nq\kappa=\frac{nq^{2}\delta^{2}\nu}{6kT}e^{-\frac{U}{kT}}, \]

where \(n\) is the number of current-carrying ions per \(\mathrm{cm}^{3}\), \(q\) is the charge of the ion, \(\kappa\) is the mobility of the ion, \(\delta\) is the length of the “free” path, \(\nu\) is the frequency of the ion’s natural vibrations at the site of fixation, \(U\) is the activation energy, and \(kT\) is the energy of thermal motion. For liquid dielectrics, using the interpretation set forth above, it is easy to relate electrical conductivity to a macroscopic characteristic of the liquid—viscosity. The internal friction in a liquid is due to the motion of the molecules of the liquid, which may be interpreted in the same way as the motion of ions. In flow—the motion of layers of a liquid—the molecules are subjected to the action of a certain force. The ordered motion of the molecules under the action of this force is what gives rise to the internal friction of the liquid. This analogy makes it possible to establish a relation between the electrical conductivity and the viscosity of a liquid, i.e. to explain the long-known experimental Walden law, according to which the product of the electrical conductivity and the viscosity is constant for a given liquid dielectric and does not depend on temperature. According to the foregoing, the temperature dependence of the ionic electrical conductivity of a non-gaseous dielectric must have the following general form:

\[ \gamma = Ae^{-B/T}. \]

The quantity \(A\) depends comparatively little on temperature. If different ions can move in the dielectric, or the same ions but fixed to different degrees, then

\[ \gamma=\sum_{i=1}^{i=N} A_i e^{-B_i/T}. \]

This dependence was established experimentally (work by Kobenko, Kuvshinskii, Shishkin, Lazarev, and others) for very many non-gaseous dielectrics (the right-hand side of the equality sometimes consists of two terms, and sometimes of one).

Thus, the mechanism of ionic electrical conductivity of a non-gaseous dielectric is, in general outline, sufficiently clear.

The question of precisely which ions move in the dielectric when current passes through it has also been the subject of investigations by Soviet physicists. It has been established that in liquid nonpolar dielectrics used for insulation purposes (transformer oil, vegetable oil, solvents for insulating varnishes—benzene, toluene, xylol, etc.), the principal current carriers are the ions of impurities—contaminants. In crystalline dielectrics, what move first of all are the light and relatively weakly bound ions of alkali metals. The break in the curve \(\lg \gamma = f\!\left(\frac{1}{T}\right)\), observed for the simplest ionic crystals (of the NaCl type), long served as the subject of lively discussion. The school headed by Smekal advanced the view that the electrical conductivity of these crystals can be divided into two parts: defect conductivity, dominant at low temperatures, and intrinsic conductivity, occurring only at high temperatures. Defect conductivity is caused by the motion of ions in defective sites—distortions of the crystal lattice—which, apparently, must exist in every crystal. At the same time, Smekal assigned the decisive role to defect conductivity.

However, Soviet physicists (Gokhberg and others) experimentally demonstrated that, in work devoted to elucidating the mechanism of the electrical conductivity of crystals, the decisive influence had been attributed to lattice defects only because the crystals were poorly purified and their electrical conductivity was caused by impurity ions.

Frenkel’s work in 1926 laid the foundation for the theoretical study of the intrinsic electrical conductivity of crystals.

At the present time it may be considered established that two principal mechanisms of ion displacement in a crystal are possible, namely: the transition of an ion into an interstitial site with its subsequent motion in the interlattice space, and the transfer of an ion from one lattice site to a neighboring, unoccupied site (the motion of “holes”).

The predominance of one or the other type of motion is clarified on the basis of approximate calculations of the corresponding energy differences. For alkali-halide crystals it has been established that the “hole” mechanism of electrical conductivity is the most probable.

The electrical conductivity of crystals at low temperatures depends to a very large extent on the presence and character of impurities. Impurity ions are usually bound more weakly than the principal ions of the lattice, since they are located chiefly either in the interlattice space-

ve, or in defective places. Only in the case of a “hole” character of conductivity can a small number of impurity ions be placed in unoccupied lattice sites and (owing to the high degree of fixation) fail to cause a noticeable increase in electrical conductivity.

It is very difficult experimentally to separate the motion of impurity ions from the motion of the principal ions of the lattice in its defective places. In this connection, the mechanism of electrical conductivity proposed by Smekal, although it may occur, is far from being the only possible one.

Much has also been done by Soviet physicists in the field of the study of the electrical conductivity of glasses (Shukarev, Müller, Markin, and others). In pure glasses containing only one glass-forming oxide, there are no ions whose displacement would determine the electrical conductivity. And indeed, the electrical conductivity of such pure glasses is vanishingly small. Technical glasses have a complex composition: in addition to the glass-forming oxide, they also contain oxides of alkali and alkaline-earth metals, whose presence determines the necessary physicochemical and technological properties of the glass. The electrical conductivity of technical glasses is determined primarily by the presence of alkali metals in them.

If an oxide of a monovalent metal ($\mathrm{Na_2O}$, $\mathrm{K_2O}$) is introduced into the glass batch, then, during the formation of the glass, the oxygen atom of the oxide binds with a silicon or boron atom and occupies one of the vertices of the elementary cell. The alkali-metal atom, having one valence bond, binds only with one oxygen atom. As a result, at the place where the atom of the monovalent metal is situated, a loosening of the structure is formed, since it has no possibility of binding with another oxygen atom and continuing the network. The loosening of the structure is expressed in the fact that, around the atom of the monovalent metal, a region of increased potential energy is formed. Thus, the introduction of an oxide of a monovalent metal, first, creates a loosening of the glass structure and, second, leads to the presence of weakly bound atoms (or ions) of the monovalent metal. Both these factors greatly increase the electrical conductivity of glass.

The introduction of oxides of divalent metals, for example $\mathrm{CaO}$, $\mathrm{BaO}$, etc., not only does not increase, but may even decrease the electrical conductivity of glass. The atom of a divalent metal, by means of its second bond, can bind simultaneously with two oxygen atoms. Therefore no rupture will occur in the structural network of the glass. It may even happen that the atom of the divalent metal will bind the ends of the ruptured network, eliminating the looseness of the structure of the pure glass. A systematic investigation of the influence of glass composition on its electrical conductivity was begun and carried out by Soviet physicists. As a result of their work, not only were the above-stated points of view established, but a number of interesting experimental data were also obtained—

...which make it possible to approach consciously the choice of formulations for electrotechnical glasses.

The special attention of Soviet physicists, even in the first years after the October Revolution, was attracted by those secondary phenomena which are connected with the passage of current through a solid dielectric at low temperatures and which for a long time seemed especially mysterious. The question is of the decrease with time of the current passing through a dielectric under a constant applied voltage, and of deviations from Ohm’s law. This phenomenon was discovered more than 50 years ago by Pierre Curie; the work of Soviet physicists helped, to a considerable extent, to clarify its nature.

As early as 25 years ago A. F. Ioffe, by his investigation of quartz, initiated work on the physics of dielectrics, in particular in the field of studying the decrease of current with time in solid dielectrics and the phenomena connected with it. In this investigation he first introduced the concept of high-voltage polarization of solid dielectrics and brought in, for its explanation, the possibility of accumulation of a volume charge in a solid body.

At the present time, thanks to the work of Hochberg, V. A. Ioffe, Sinelnikov, Venderovich, and others, it is possible to divide solid dielectrics according to the character of the decrease of current with time into a number of types.

The first type consists of crystals with a high degree of symmetry: in pure crystals, in the absence of defects in the crystal lattice, there is no decrease of current with time; the potential distribution is rectilinear.

The second type consists of crystals of the calcite and selenite type: a sharp decrease of current with time; the volume charge is distributed concentratedly in a thin layer at the cathode.

The third type consists of crystals with a low degree of symmetry (quartz, mica): a considerable decrease of current with time with a very complex distribution of the volume charge; forming is possible.

The fourth type consists of amorphous and ceramic dielectrics: a decrease of current occurs at very short times (establishment of dielectric polarization), and also at high temperatures (forming); the potential drop is concentrated mainly in the formed layer.

The fifth type consists of inhomogeneous dielectrics (technical layered insulating materials): the decrease of current is connected with the accumulation of charge at the surfaces of separation of the inhomogeneities (the classical, Maxwellian case).

The works of Ioffe showed that, if one takes into account the electromotive force of polarization arising as a consequence of the accumulation of volume charge, then the resistance of a dielectric in the region of weak fields proves not to depend on the voltage.

Actual deviations from Ohm’s law in solid dielectrics begin in very strong fields.

Applying the reasoning about the mechanism of motion of ions in a dielectric that was given above, it is not difficult to obtain an expression for the current density in a non-gaseous dielectric in strong fields, i.e., in those cases when the work of the field along the path of the “free” run of an ion is comparable with the energy of thermal motion:

\[ j=\frac{n}{6kT}\,\nu q^{2}\delta^{2}e^{-U/kT}\left(E+\frac{q^{2}\delta^{2}E^{3}}{24k^{2}T^{2}}+\ldots\right) \]

(the notation is the same as above).

The current density is no longer proportional to the field strength, but depends on it according to a complex law; the electrical conductivity, however, increases with increasing field strength, which is in qualitative agreement with the well-known experimental law of Poole.

In strong fields (for glass, for example, above \(2\cdot 10^{6}\ \frac{\text{volts}}{\text{cm}}\)) an electronic component is superposed on the ionic electrical conductivity; in small fields, for most dielectrics, this is vanishingly small.

The temperature coefficient of electrical conductivity in strong fields changes. This follows first of all from the expression for the ionic electrical conductivity

\[ \gamma=j/E=\frac{n}{6kT}\,\nu q^{2}\delta^{2}e^{-U/kT}\left(1+\frac{q^{2}\delta^{2}E}{24k^{2}T^{2}}+\ldots\right); \]

as is evident from this expression, the electrical conductivity, as the field strength increases, begins to depend more weakly on temperature.

In addition, the electronic electrical conductivity that appears in strong fields has a different temperature coefficient than the ionic one.

The question of the electronic electrical conductivity of dielectrics in strong fields is closely connected with the electrical breakdown of dielectrics (see below).

The dependence of electronic electrical conductivity on field strength was first analyzed in the theoretical work of Ya. I. Frenkel.

2. DIELECTRIC POLARIZATION AND DIELECTRIC LOSSES

The extensive series of works by Soviet physicists in the field of dielectric polarization and dielectric losses may be divided into: a) studies of the anomalous polarization of Rochelle salt and ferroelectrics; b) studies of dielectric polarization and losses of polycrystalline dielectrics; the discovery of a new type of polarization of barium titanate; c) studies of dielectric polarization and dielectric losses of amorphous dielectrics and high-molecular compounds, which subsequently developed into a very large complex of works devoted to the study of the amorphous state; d) studies of dielectric losses and dielectric

polarization of glasses and ceramic materials with a practical outcome in the form of the production of new high-quality insulating materials; closely adjoining these works are the works of Soviet chemists, technologists, and engineers on the study of the dielectric losses of many technical insulating materials (oils, varnishes, compounds, fibrous materials, plastics), which made it possible both to develop new materials and to improve the insulating properties of already known materials; d) the study of the dielectric properties of a new class of insulating materials consisting of silicon-organic compounds, and the creation of insulating materials with increased heat resistance.

a) The fundamental works of Kurchatov, Kobeko, and others, devoted to a detailed study of Rochelle salt, made it possible to establish a number of regularities that, to a considerable extent, clarify the nature of its anomalous polarization, and to discover a group of dielectrics—isomorphous crystals containing Rochelle salt—which possess, like Rochelle salt, the property of spontaneous polarization and dielectric hysteresis. These substances were named ferroelectrics.

Kurchatov was the first to give a theory of the polarization of ferroelectrics, qualitatively explaining the established regularities. Theories of ferroelectricity are still not entirely satisfactory. However, the point of view of Kurchatov and others, according to which rotation of polar molecules is possible in a solid substance, proved to be very fruitful and received further development in explaining a number of regularities observed for technical dielectrics (fibrous materials, oleowax, halowax, etc.).

b) A large group of works carried out in recent years by Soviet scientists (Vul, Skanavi, Gol’dman, Barzakovskii, Bogoroditskii, and others) is devoted to the study of dielectric polarization and dielectric losses of polycrystalline dielectrics formed as a result of solid-state reactions occurring at high temperature. The most interesting of these works concern dielectrics containing in their composition titanium dioxide in the crystalline form of rutile, or titanates of metals of the second group of Mendeleev’s periodic system.

The reason for the high dielectric permittivity of rutile \((\mathrm{TiO}_2)\), known since 1902, and of perovskite \((\mathrm{CaTiO}_3)\), first established by Soviet physicists, has been clarified by their theoretical works (Skanavi).

For complex crystals such as rutile and perovskite, neither Born’s formula for calculating dielectric permittivity, based on the assumption that the local field is equal to the average macroscopic field, nor the Clausius–Mossotti formula, in the derivation of which the internal field is assumed equal to the Lorentz field \(\left(\frac{4\pi I}{3}\right.\), where \(I\) is the electric moment per unit

volume). Taking the internal field in the crystal lattice into account can be carried out in the first approximation if one is based on the so-called “point” model of an ionic crystal (point ions acquiring dipole moments under the action of the field). The method of allowing for the internal field, based on the Lorentz method, leads ultimately to the following general equation for the electronic polarization in place of the Clausius–Mossotti equation:

\[ \frac{\varepsilon-1}{\varepsilon+2}= \frac{\frac{4\pi N}{3} \left\{ \sum_{j=1}^{m} n_j\alpha_j+ \frac{1}{2}\sum_{j,k=1}^{m}\alpha_j\alpha_k \left(n_k c_{kj}+n_j c_{jk}-n_k c_{jj}-n_j c_{kk}\right)+O(\alpha^3) \right\}} {1-\sum_{j=1}^{m}\alpha_j c_j+ \frac{1}{2}\sum_{j,k=1}^{m}\alpha_j\alpha_k \left(c_{jj}c_{kk}-c_{jk}c_{kj}\right)+O(\alpha^3)} , \tag{1} \]

where \(\varepsilon\) is the square of the refractive index, \(N\) is the number of molecules in \(1\ \mathrm{cm}^3\) of crystal, \(\alpha_j\) is the electronic polarizability of the \(j\)-th ion, \(n_j\) is the number of \(j\)-th ions in the molecule, \(m\) is the number of ions of different geometrical arrangement in the lattice, and \(c_{jj}\), \(c_{jk}\), and \(c_{kj}\) are the so-called structural coefficients of the internal field, depending only on the geometry of the lattice and determining, for the given polarizability of the ions and the given external field, the addition to the Lorentz internal field created by the polarized ions surrounding the ion under consideration. By \(O(\alpha^3)\) are denoted small terms containing triple and higher products of polarizabilities. If all the structural coefficients are equal to zero, the above formula passes into the Clausius–Mossotti formula

\[ \frac{\varepsilon-1}{\varepsilon+2}=\frac{4}{3}\pi N\sum n_j\alpha_j . \tag{2} \]

Calculation of the structural coefficients for the rutile and perovskite lattices shows that formula (1), in contrast to the Clausius–Mossotti formula, gives quite satisfactory agreement with experiment. At infrared and lower frequencies it is necessary, in addition to the electronic polarization of the ions, also to take into account the displacement of the positive ions relative to the negative ones. In this case formula (1) for rutile assumes the following form, if small terms are neglected:

\[ \frac{\varepsilon-1}{\varepsilon+2}\cong \frac{4\pi N}{3}\cdot \frac{\alpha_1+2\alpha_2+\alpha_i}{1+|c_{22}|\alpha_3-c_{12}\alpha_i}, \tag{3} \]

where \(\alpha_i\) is the polarizability of the ionic displacement, referred to the titanium ion. From (3) it is seen that the introduction of even a small \(\alpha_i\) sharply increases \(\varepsilon\), since it not only increases the numerator, but also decreases

decreases the denominator. The physical nature of this effect consists in the fact that, with ionic displacement, a large additional internal field of the same direction as the external field arises, favoring polarization. Therefore even a small polarizability of ionic displacement \((\alpha_i)\) leads to high values of the dielectric constant.

It may be considered that the high dielectric constant of crystals of the rutile and perovskite type is due primarily to the large electronic polarizability of the oxygen ions, which, at high density, entails a high refractive index in combination with a large additional internal field of the “foreign environment,” directed along the direction of the external field and sharply increasing the dielectric constant in the transition from light frequencies to infrared frequencies (from 7.3 to 173 for rutile), even with small ionic displacement.

An outstanding achievement of Soviet physicists (Vul and Goldman) was the discovery of the exceptionally high dielectric constant \((\varepsilon = 1000 \div 2000)\), passing through a sharp maximum upon an increase in temperature, and of dielectric hysteresis in barium metatitanate \((\mathrm{BaTiO}_3)\). Detailed investigations of the properties of dielectrics of this kind revealed a new and very interesting type of dielectric polarization, close to ferroelectric polarization, but differing from it by the high value of \(\varepsilon\) over a very wide temperature range (from the temperature of liquid helium to \(+(250 \div 300)^\circ \mathrm{C}\)). The exceptionally high dielectric constant of barium metatitanate, as well as its sharp dependence on temperature and on the strength of the electric field, opens broad prospects for its application in various fields of electrical and radio engineering. The theoretical interpretation of the mechanism of polarization of barium metatitanate and of ferroelectrics has recently been developed by Ginzburg. He showed that a phase transition of the second kind, occurring at a certain temperature (the Curie point), can lead to the tendency of the dielectric constant to infinity at this temperature, if the spontaneous polarization disappears at this transition. X-ray investigations of the structure of barium metatitanate at temperatures below and above the Curie point, and measurement of the dependence of heat capacity on temperature, showed that in barium metatitanate at the temperature corresponding to the sharp maximum of \(\varepsilon\) (about \(80^\circ \mathrm{C}\)), a phase transition of the second kind may occur.

The investigation of materials of the \(\mathrm{TiO}_2\)—\(\mathrm{BaO}\) system (Skanavi) showed that changing the \(\mathrm{TiO}_2/\mathrm{BaO}\) ratio shifts the Curie point and lowers the dielectric constant. Barium tetratitanate \((4\mathrm{TiO}_2 \cdot \mathrm{BaO})\) has \(\varepsilon = 30\), changing very little with temperature, which makes it possible to use it for temperature-stable capacitors. A set of studies on dielectric

by the properties of rutile and titanates opened up broad practical possibilities, which were partly realized during the war and are being realized at the present time. The production of ceramic capacitors with specified characteristics was accomplished by combining titanates of different crystalline structures, possessing different dielectric constants and temperature coefficients. Regularities determining the properties of the combined polycrystalline material were established and confirmed by X-ray and other investigations (Vul, Skanavi).

Dielectric losses in polycrystalline dielectrics, which were also studied very intensively, are determined by the composition and amount of the glassy interlayer.

c) The work of Soviet physicists (Kobeko, Kuvshinskii, Zhurkov, Shishkin, G. Mikhailov, and others) in the field of the dielectric properties of amorphous bodies proved fruitful both with respect to the theoretical interpretation of the processes occurring in an amorphous body and with respect to practical results.

Investigations of the dependence of the loss angle and dielectric constant, carried out over a very large temperature interval for a whole series of supercooled liquids containing polar molecules (glycerin, phenolphthalein, isobutyl alcohol, etc.), showed that the loss angle passes through a clearly pronounced temperature maximum, while the dielectric constant changes with temperature similarly to the way it does in polar liquids. This was observed at such temperatures at which the substance was in a solid-amorphous state. An increase in frequency shifts the temperature maximum toward higher temperatures, as also occurs for polar liquids. Recently it has been shown (G. Mikhailov) that in solid-amorphous polymers containing polar groups, the loss angle also has a second, weaker temperature maximum in the region of low temperatures.

All this undoubtedly confirms the possibility of rotation of polar groups in a solid substance.

Further work showed that the chief and basic source of dielectric losses in polymers is polar molecules, polar radicals, or polar complexes. If a polymer does not contain them, then the dielectric losses in it are very, very small. A striking example of this is pure polystyrene, which possesses negligible losses. The slightest contamination of polystyrene by polar substances sharply increases the loss angle and gives the whole process the evident character of dipole losses.

Work on the study of the mechanical properties and viscosity of amorphous bodies led to the establishment of interesting regularities. It proved possible to show that the curves of the temperature dependence of electrical conductivity, viscosity, and dielectric relaxation time are similar

among themselves. (The time constant of dielectric polarization is estimated approximately as \(1/2\pi\nu\), where \(\nu\) is the frequency corresponding to the maximum of the product \(\varepsilon \tan \delta\) at the given temperature.) The correspondence between the indicated dependences suggested the existence of a profound connection between the dielectric and mechanical relaxations of an amorphous body.

The presence of this connection was confirmed by parallel measurements of dielectric permittivity and plastic deformation for amorphous bodies (Kobeko, Kuvshinskii, and others).

Thus, one may suppose that displacements and rotations of dipole groups are connected with the displacements and rotations of entire molecular complexes that determine plastic deformation.

Work on the study of the amorphous state made it possible to obtain new insulating materials of high quality. One of the first such materials was Soviet polystyrene, possessing very small dielectric losses (loss angle \(0.5—1'\) at high frequencies), very high volume resistance, and other valuable properties, in particular ease of processing.

The investigation of the dielectric and mechanical properties of rubber (Kobeko, Ponomarev) led to the development of an exceptional-quality, grainless ebonite—escapon—which is a product of the polymerization of rubber and at the same time possesses great heat resistance, easy processability, and a comparatively very small loss angle (\(1—2'\) at high frequencies). This material is in all respects superior to ordinary ebonite, which contains sulfur. Each sulfur atom is bonded to two carbon atoms and, under the action of the carbon and hydrogen atoms, is strongly polarized, forming a permanent electric moment. The mobility of the hydrocarbon chain in rubber enables the polar “sulfur bridge” formed in this way to execute rotational oscillations, taking part in thermal motion. The electric field orients the “sulfur dipoles.” The process of establishing this orientation at high frequencies leads to pronounced dipole losses. The absence of sulfur in escapon and its high degree of polymerization are the principal reason for the small dielectric losses of escapon.

In the field of the theory of dielectric losses, Soviet scientists began working long ago. Broad and systematic investigations established (Lazarev and others) that Debye’s classical theory of dipole losses is qualitatively applicable to a large number of amorphous technical dielectrics above their solidification temperature (for example, to oils, varnishes, compounds), but that this theory does not provide quantitative agreement with experimental data for the indicated dielectrics. Alongside this, a number of points of view were developed on the mechanism of dielectric losses in various classes of dielectri-

which is of great help in developing new dielectrics with low losses.

Most works concerning the theory of dielectric losses in solid dielectrics, published in the foreign literature, are of a purely phenomenological character. The author assumes one or another form of the function describing the decay of current with time and, applying the well-known principle of superposition of currents in a dielectric, by more or less exact and cumbersome calculations obtains an expression for $\varepsilon$ and $\operatorname{tg}\delta$ of the dielectric as functions of frequency.

Soviet scientists have made attempts to construct such theories of dielectric losses which are based on the specific structural features of the class of dielectrics under consideration.

d) Measurements of dielectric losses in crystalline dielectrics (Bogoroditskii and Malyshev) made it possible to establish that in crystals dielectric losses have a purely ohmic character (conductivity losses). Conversely, in a number of amorphous dielectrics containing no polar groups or molecules, at high frequencies losses were found which do not have the character of conductivity (works of Kobeko, Aleksandrov, Skanavi, Bogoroditskii, Malyshev, Fridberg). The presence of these losses is of great practical importance, since it greatly limits the use of a whole series of amorphous dielectrics (above all glasses) for high-frequency insulation purposes. The work of Soviet physicists (Kobeko, Skanavi) on the study of the mechanism of dielectric losses in glasses made it possible to discover a new group of phenomena in solid-amorphous dielectrics, analogous to the phenomena caused by the rotation of polar molecules. This new group of phenomena has a mechanism determined by the translational displacement of weakly bound ions or charged groups.

The motion of such charged particles under a constant voltage gives rise to an absorption current decreasing with time, and under an alternating voltage it gives rise to dielectric losses of the relaxation type.

The absorption current in a solid dielectric, for the indicated mechanism of ion motion, should, as calculations show, decay with time according to a simple exponential law; moreover, the time constant of the current decay is proportional to the relaxation time of weakly bound ions, equal to $\tau \simeq \dfrac{e^{U/kT}}{2\nu}$, where $U$ is the activation energy, $\nu$ is the frequency of the natural vibrations of the ions at the site of fixation, and $kT$ is the energy of thermal motion. However, for describing the experimental data a power function of the form $I = A(t+\Theta)^{-n}$ is more suitable, reflecting the process over a limited interval of time ($A$, $\Theta$, and $n$ are constants).

This discrepancy is apparently connected with the fact that in a real dielectric there are a number of groups of ions with different activation energies, i.e., with different relaxation times. In addition, pro-

there arises a series of other processes (for example, the accumulation of volume charge), whose aggregate leads to a complication of the law of decay of the absorption current.

The use of a power-law function for the decay of the current leads to cumbersome mathematical developments and does little to help elucidate the mechanism of dielectric losses. The exponential decay function reflects one of the processes (in many cases prevailing over the others) in the dielectric. A theory of losses constructed on the basis of the application of this function, although it cannot claim rigor and completeness, nevertheless, like Debye’s theory for polar liquids, connects the magnitude of the dielectric losses in a solid-amorphous dielectric with its molecular constants.

The work of Soviet physicists devoted to the application and development of the theory of losses in solid-amorphous dielectrics (first of all in glasses) helped to create new points of view on their mechanism and greatly contributed to the discovery of new ways of obtaining glasses with small dielectric losses.

A number of interesting facts have been established (the works of Kobeko, Skanavi, Martyushov, Gladkikh, and others) concerning the influence of the composition of glass on its dielectric losses. These facts include: 1) the “neutralization” effect, which consists in the fact that the harmful action of ions of one alkali metal can be neutralized by introducing an oxide of another alkali metal (the neutralization observed in this case is so great that alkali glass can have as small a loss angle as pure glass containing no extraneous ions); 2) the “crystallization” effect, which consists in the fact that crystallization of an amorphous dielectric (sugar, glass) sharply lowers its loss angle at high frequencies, and so forth.

These same works made it possible to classify the dielectric losses in glasses, which may be regarded as consisting of three parts: 1) conductivity losses, appearing at low frequencies and high temperatures, 2) relaxation losses, appearing at high frequencies, and 3) structural losses, for which the loss angle does not depend on temperature. These latter appear at high frequencies and low temperatures. Their mechanism is still insufficiently clear.

3. NEW INSULATING MATERIALS

The work of Soviet physicists, chemists, and technologists in the field of studying the dielectric properties of various kinds of materials has provided a theoretical basis for obtaining new insulating materials with high insulating properties.

This applies above all to the development of new inorganic materials (glasses and ceramics), the use of which plays

especially important role in high-frequency technology, since they possess considerably smaller dielectric losses than many organic materials, and very high heat resistance.

The conditions for research work created in our country are exceptionally favorable for carrying out comprehensive studies in which the activity of physicists is closely coordinated with that of chemists and technologists. Electrical insulation is precisely such a field of science and technology where this kind of cooperation is absolutely necessary.

Ceramic materials consist of crystalline and amorphous phases. It may be assumed that, to a first approximation, the dielectric losses in ceramic materials are additively composed of the losses in each of the phases.

As was indicated above, losses in crystalline dielectrics have the character of conductivity and therefore are very small at high frequencies. Consequently, the main source of dielectric losses in a ceramic material is the glassy interlayer.

A number of regularities established for dielectric losses in glasses made it possible to approach deliberately the choice of composition and structure of a ceramic material with small dielectric losses. The principles for obtaining such a material are as follows: 1) the material must have a fine-crystalline structure with a minimal glass interlayer; 2) the glassy interlayer, insofar as possible, must not contain alkalis in its composition, or else the action of these alkalis must be neutralized by the presence of heavy oxides.

In accordance with these general principles, a number of special high-frequency ceramic materials with small dielectric losses were developed. The first material of this group, developed in the Union and widely used, was a ceramic material based on the mineral pyrophyllite (Vaneev, Popov). A composition of pyrophyllite and clay possesses a number of very important production qualities: great plasticity before firing, making it possible to manufacture articles by all methods adopted in ceramic technology (forming on a machine, drawing through a mouthpiece, pressing), and a wide firing interval. At the same time, ceramic materials based on pyrophyllite possess, in comparison with ordinary insulating porcelain, a small loss angle at high frequencies (8–12 minutes at a frequency of \(\sim 10^6\) cycles).

By introducing heavy oxides instead of feldspar into insulating porcelain, it proved possible to “refine” it considerably and obtain the so-called radio porcelain, which in its dielectric properties is not inferior to pyrophyllite and technologically is close to ordinary porcelain (work of Bogoroditskii and Fridberg).

Work on obtaining ceramic materials with very small losses and other special properties (for example, high

dielectric permittivity and its stability under changes in temperature—capacitor ceramics) was carried out very intensively.

A number of low-loss high-frequency materials based on aluminum oxide were developed (Bogoroditskii, Odelevskii, and others). These materials possess a very small loss angle at high frequencies \((\delta = 1 \div 3')\).

Special attention was devoted to the development of ceramic materials for high-frequency capacitors. A ceramic material based on titanium dioxide and clay—ticonde—was developed (Bogoroditskii and others), possessing a high dielectric permittivity \(\varepsilon = 60 \div 70\) and a comparatively large negative temperature coefficient of its variation:

\[ \frac{1}{\varepsilon}\frac{d\varepsilon}{dT} \simeq -6 \cdot 10^{-4}\ \text{1/deg}. \]

This material is a suitable dielectric for special capacitors compensating for frequency drift under temperature changes in radio circuits, owing to the negative sign of the temperature coefficient of capacitance.

During the war, the importance of high-frequency crystalline ceramic materials increased still further, owing to the cheapness and non-scarcity of the raw materials used for their manufacture, and also owing to the possibility of regulating the dielectric permittivity and its temperature coefficient by changing the composition and structure of the crystalline phase of these materials.

On the basis of calcium titanates and magnesium titanates, a new ceramic material for compensating radio capacitors—tidol (Skanavi)—was obtained, possessing an even higher negative temperature coefficient of dielectric permittivity than ticonde

\[ \left(\frac{1}{\varepsilon}\frac{d\varepsilon}{dT} = -10 \cdot 10^{-4}\ \text{1/deg}\right), \]

and a high dielectric permittivity \((\varepsilon = 70 \div 80)\). The loss angle of tidol is \(2 \div 3'\). A number of materials based on magnesium titanates were developed (Vul, Skanavi, Barzakovskii, Bochkarev). These ceramic materials are intended for the manufacture of circuit radio capacitors of large and small reactive powers. They possess a very small loss angle \((\delta = 0.5 \div 1'\) at high frequencies), a very small dependence of it on frequency and temperature, a dielectric permittivity \(\varepsilon = 14 \div 16\), and, what is especially important, high temperature stability of the dielectric permittivity:

\[ \frac{1}{\varepsilon}\cdot \frac{d\varepsilon}{dT} = +(0.4 \div 1.3)\cdot 10^{-4}\ \text{1/deg}. \]

A material based on titanium dioxide and clay with alumina—tiglinn (Smolenskii)—was developed, also quite suitable for manu-

formation of tuned radio capacitors. Of great importance is the discovery of the possibility of regulating the dielectric constant and its temperature coefficient in titanate ceramic materials by applying Lichtenecker’s logarithmic law (Wul, Skanavi); when crystalline materials of different structure are combined, special methods can be used to avoid the formation of new structures during the sintering process. In these cases the dielectric constant of the composite material can be calculated in advance from the dielectric constants of the components:

\[ \lg \varepsilon = x \lg \varepsilon_1 + (1-x)\lg \varepsilon_2, \]

where \(\varepsilon_1\) and \(\varepsilon_2\) are the dielectric constants of the components and \(x\) is the volume concentration of the first component. Differentiating this equation with respect to temperature gives

\[ \frac{1}{\varepsilon}\frac{d\varepsilon}{dT} = x\frac{1}{\varepsilon_1}\frac{d\varepsilon_1}{dT} + (1-x)\frac{1}{\varepsilon_2}\frac{d\varepsilon_2}{dT}, \]

i.e., the temperature coefficient varies linearly with concentration.

By combining materials with negative and positive temperature coefficients of \(\varepsilon\), it is possible with a high degree of accuracy to obtain a prescribed dielectric constant and, what is especially important, a prescribed temperature coefficient of the dielectric constant.

On the basis of this method, numerous capacitor ceramic materials have been developed with various temperature coefficients of \(\varepsilon\) from \(+1\cdot10^{-4}\) to \(-12\cdot10^{-4}\), including temperature coefficients of \(\varepsilon\) close to zero (Skanavi, Stepanov, Voronkov, Bogoroditskii, Smolenskii, Odelevskii, Nekrasova, and others).

Following the discovery of the exceptionally high dielectric constant of barium metatitanate (Wul and Goldman), ceramic crystalline dielectrics based on barium metatitanate were developed with a superhigh dielectric constant: from 700 to 1500 at room temperature (Skanavi, Voronkov, Odelevskii). Work is under way on applying these materials in various areas of electrical and radio engineering. Crystalline ceramic dielectrics based on barium tetratitanate \((4TiO_2\cdot BaO)\) and related compounds (Skanavi) have been developed; they have a very small loss angle at high frequencies, a dielectric constant of about 30, a temperature coefficient close to zero, and a very high specific volume resistance \((10^{15}—10^{16}\ \mathrm{ohm/cm})\). These dielectrics made it possible to manufacture thermostable ceramic radio capacitors of increased specific capacitance.

A number of achievements have also been made in the Union in the field of using glass as an insulating material.

These include, above all, special glasses used in radio engineering (for example, for high-power radio tubes). Glasses Nos. 23,

46 possess, along with the necessary technological properties, low dielectric losses. Potash Pyrex (Bogoroditskii and Fridberg) has been developed, which, along with high heat resistance, has a very small loss angle at high frequencies.

The fundamental problem of obtaining glass fiber and glass fabric for heat-resistant electrical insulation has been solved (Chernyak, Aslanova, and others). In this field further work is still necessary, in particular on selecting a more suitable composition of glass.

Extensive investigations were carried out by Soviet scientists in the field of heat-resistant and heat-conducting insulation (Andrianov, Tareev, Chernyak, and others), as well as in the field of the hygroscopicity of dielectrics (Mikhailov, Bogoroditskii, and others). Much attention was devoted to the creation of electrically insulating varnishes.

Glyptal varnishes have gone into production and are widely used; their film has higher heat resistance than films of shellac and asphalt varnishes. At the same time, the dielectric properties of glyptal varnishes are comparatively very high. Asphalt varnishes, which have displaced scarce shellac, have been finally mastered in production and application (especially for electrical machines).

Among the new plastics, the already mentioned polystyrene and escapone deserve much attention. A major achievement is the development of fundamentally new electrical insulating materials based on organosilicon compounds (Andrianov, Gribanov). These materials (liquid and solid) combine the properties of organic compounds (plasticity, flexibility, etc.) with increased heat resistance (up to \(300^\circ\) C). The indicated materials were developed as a result of the profound study of a new branch of science—the chemistry of organosilicon compounds (Andrianov). This enumeration by no means exhausts the list of new insulating materials developed in recent years.

4. BREAKDOWN OF DIELECTRICS

Let us now turn to the consideration of the results of the work of Soviet physicists in the field of the study of dielectric breakdown. The breakdown voltage of insulation depends on the electric strength of the insulating substance and, in equal measure, on its construction, which determines the distribution of the field in the insulation and the conditions of heat transfer. Therefore the study of dielectric breakdown acquires practical significance only when the dielectric is investigated not only on specimens but also under the practical conditions of its operation.

Work on the theory of dielectric breakdown in the Union began more than 20 years ago (Semenov, Fok, Bragin, and others).

Extensive experimental investigations established a number of factors characterizing thermal and electrical breakdown of insulation, and established criteria making it possible to judge the charac-

...breakdown in each individual case was studied; the nature of the breakdown of a number of dielectrics (Bragin et al.) was investigated.

Along with this, Fock, Semenov, and others for the first time gave a rigorous theory of thermal breakdown, which has been successfully applied to a large number of various practical cases.

The study of the electrical breakdown of dielectrics also developed rather intensively.

a) Thermal breakdown

In studying the thermal breakdown of dielectrics, two groups of problems are usually considered that are of interest from the point of view of the application of this theory. The problems of the first group reduce to determining the “breakdown voltage,” which in the case of thermal breakdown may be interpreted as a certain maximum voltage (critical voltage), beginning with which a stationary state becomes impossible. When the critical voltage is reached, continuous heating of the dielectric begins, which, for a sufficiently long duration of operation, leads to thermal breakdown. The problems of the second group reduce to determining the “breakdown time,” i.e., the time after the expiration of which a dielectric under a voltage exceeding the critical one will break down. Both groups of problems are of very great technical interest for the following reasons:

1) Calculation of the critical voltage of thermal breakdown makes it possible to choose correctly the quality and design of insulation that ensure its long service under operating conditions.
2) Calculation of the “breakdown time” at voltages above the critical one makes it possible, when choosing insulation, to take into account its resistance to short-term overvoltages. The problems of the first group have been solved, and their results have already been applied for a number of years. The problems of the second group have also, in the main, been solved in recent years.

Thermal breakdown of a dielectric is caused by the fact that the liberation of heat in the dielectric due to dielectric losses (or to conductivity under constant voltage) increases as the dielectric is heated. For most dielectrics, the heat generation in a limited interval depends on temperature according to an exponential law

\[ Q = Q_0 e^{a(T - T_0)}, \]

where \(T\) and \(T_0\) are temperatures, and \(a\) is the temperature coefficient of conductivity or of the tangent of the loss angle.

The solution of the problem of thermal breakdown consists in integrating the known heat-conduction equations of the form

\[ c\rho \frac{\partial T}{\partial t} = K \Delta T + Q, \]

where \(c\) is the specific heat of the medium, \(\rho\) is the density, \(K\) is the thermal...

conductivity and \(Q=\gamma E^2\) is the specific heat generation (\(\gamma\) is the active conductivity, \(E\) the field strength), or, for the one-dimensional case frequently encountered in practice:

\[ c\rho \frac{\partial T}{\partial t}=K\frac{\partial^2T}{\partial z^2}+Q. \]

In solving the first group of problems (finding the critical breakdown voltage), the case of an equilibrium state is considered,

\[ \left(\frac{\partial T}{\partial t}=0\right), \]

and time is thereby excluded from consideration.

The differential equation

\[ K\frac{\partial^2T}{\partial z^2}+Q=0 \]

serves as the basis for calculating the critical voltage.

The transition of the dielectric, as the applied voltage is increased, from an equilibrium thermal state to a nonequilibrium one, which is the onset of thermal breakdown, is characterized by the fact that \(\frac{\partial E}{\partial T_m}=0\), where \(E\) is the field strength and \(T_m\) is the maximum heating temperature of the dielectric at the given voltage.

For \(\frac{\partial E}{\partial T_m}>0\) we have an equilibrium state; for \(\frac{\partial E}{\partial T_m}<0\), a nonequilibrium state of the dielectric. The equality \(\frac{\partial E}{\partial T_m}=0\) is therefore the condition for breakdown.

Solving the differential equation given above with allowance for the boundary conditions and applying the breakdown condition formulated above, one can find an expression for the breakdown (critical) voltage of thermal breakdown. For example, for a one-dimensional alternating field,

\[ U_{\mathrm{br}}=\sqrt{\frac{60.5K}{fa\varepsilon \tg d}}\cdot 10^6 \varphi(C), \]

where \(\varepsilon\) and \(\delta\) are the dielectric constant and loss angle of the dielectric at the ambient temperature, \(f\) is the frequency, \(\varphi(C)\) is a rather complicated function, the numerical value of which is found approximately from the value

\[ C=\frac{K_1\lambda h}{K(K+\lambda d)} \]

(\(K\) and \(K_1\) are the thermal conductivities of the dielectric and the electrode, \(h\) is the half-thickness of the dielectric, \(d\) is the thickness of the electrode, and \(\lambda\) is the coefficient of external heat conduction), \(a\)—see above.

This formula, like the others similar to it (the case of one-sided cooling, a cylindrical capacitor, etc.), has the great advantage that all the quantities entering into its right-hand side can be known exactly. Therefore its application to any

in a practical case presents no fundamental difficulties. It is only necessary to take the cooling conditions properly into account.

An extensive series of investigations made it possible to establish that, if the nature of breakdown is thermal, then with a sufficiently slow increase of voltage the experimental value of the breakdown voltage agrees well with the theoretical one. With a rapid increase of voltage, the experimental value of the breakdown voltage exceeds the theoretical one.

For most dielectrics there exists a certain region of thermal breakdown, determined by external factors, chiefly by frequency and temperature.

At high frequencies, breakdown in the overwhelming majority of dielectrics has a clearly pronounced thermal character. Only some dielectrics (quartz, the best grades of mica, special ceramic materials), possessing an exceptionally small loss angle at high frequencies, apparently have a mixed character of breakdown.

At high temperatures many dielectrics break down thermally even at low frequencies (glass, porcelain).

Finally, a whole series of dielectrics has a thermal character of breakdown even at moderate temperatures and low frequencies. These include almost all varnishes, compounds, fibrous materials, and many plastics.

Thus, the development of the theory of thermal breakdown and the derivation of practically applicable formulas for the breakdown voltage served as a strong impetus toward the deliberate choice of insulation and toward the development of technically substantiated standards for insulating materials.

A number of special works were devoted to the calculation of the insulation of large machines, antenna insulators, cable insulation, and capacitors on the basis of the theory of thermal breakdown. The results of these works made it possible to modify and refine the standards for the electrical properties of varnishes and compounds (insulation of electrical machines—Skanavi), ceramic materials (antenna insulators—Gailish), oils and paper (cable insulation—Bragin), and so forth.

In some of these works the theory of thermal breakdown underwent further development (the works of Gailish).

In all these works, however, the question of the course of thermal breakdown in time remained unresolved. All calculations were made for the case of a prolonged presence of the insulation under voltage. The safety factors of insulation, which are determined not only by the possibility of thermal breakdown during prolonged operation of the insulation under the action of the operating voltage, but also, first and foremost, by its resistance to overvoltages, cannot be justified with sufficient precision by means of the theory of thermal breakdown based on the premise that the voltage is applied for an arbitrarily long time.

In recent years Grinberg, Kantorovich, and Lebedev have developed a method for calculating thermal breakdown taking account of the time factor (the second group of problems indicated above).

The differential equations determining the process of heating of a dielectric under voltage are extremely complicated and do not admit exact integration. Even in the simplest one-dimensional case one has to integrate two coupled partial differential equations of the second order, one of which is nonlinear. At first the problem was solved by approximate numerical integration for specific cases.

However, numerical integration for each separate case takes a very long time, since it requires very cumbersome computations.

In view of this, an approximate theory was developed which, with a small expenditure of time, makes it possible to obtain the principal dependences with accuracy sufficient for practical purposes. The idea of the method is that, on the basis of certain physical considerations, a law of temperature distribution in the thickness of the dielectric and in the electrodes is prescribed. If one adopts a parabolic law of temperature distribution in the dielectric and in sufficiently massive electrodes, then the system of equations is considerably simplified in comparison with the original one (one obtains a system of ordinary coupled differential equations of the first order), the work of the computer is greatly reduced, but the integration still cannot be carried through to the end and, ultimately, one again has to resort to numerical integration. The problem is solved analytically in the case where it is assumed that in the thickness of the electrodes (external thermal insulation) the temperature is distributed not according to a parabolic but according to a linear law. One may think that the indicated law is preserved during the greater part of the process, at least if the electrodes are not too thick. The duration of the remaining part of the process is a small part of the total time required for the development of breakdown.

The calculation of the breakdown time, carried out by the indicated approximate method, leads to sufficiently good agreement with experiment. The breakdown time is found from the condition that the temperature of the dielectric is equal to infinity. This condition can be fulfilled only in the case where the applied voltage is greater than the critical voltage of thermal breakdown, i.e. the stationary state of the dielectric cannot exist.

The result of the calculation for a plane capacitor can be written in the following simple form:

\[ t_{\mathrm{br}}=\frac{C_1\rho_1}{0.24\cdot a\sigma_0 E^2}\,\varphi(b), \]

where \(C_1\) is the heat capacity and \(\rho_1\) is the density of the dielectric; and

\[ \varphi(b)=\int_0^\infty \frac{d\xi}{e^\xi-\mu \xi} =1+\frac14 b+\frac{2}{27}b^2+\frac{3}{128}b^3+\frac{24}{3125}b^4+\cdots \]

and

\[ b=\frac{6\beta}{3-\beta}\cdot \frac{1}{Bn^2} \]

\[ \left( \beta=\frac{\mu}{2+\mu} \quad \text{for} \quad \mu=\frac{\lambda n K_1}{K(K_1+K\lambda)} \quad \text{and} \quad B=\frac{0.24a\sigma_0}{K}E^2 \right). \]

\(\sigma_0\) is the conductivity of the dielectric at the ambient temperature; the remaining notation is the same as above.

b) Electrical breakdown of solid dielectrics

A large number of works by Soviet physicists are devoted to electrical breakdown.

The mechanism of electrical breakdown of dielectrics is still not completely clear. The initially expressed supposition that the development of currents in the electrical breakdown of a solid dielectric is due to impact ionization by ions proved untenable.

In the development of our subsequent ideas about the mechanism of electrical breakdown, two periods are clearly distinguished: the pre-quantum period and the quantum-mechanical period.

The old (pre-quantum) theories lead to values of the breakdown voltage exceeding the experimental data. Modern (quantum-mechanical) theories give the correct order of magnitude for the breakdown voltages, but none of them gives sufficiently good agreement with experimental data. It is therefore difficult to choose from among them the one closest to reality.

The unsatisfactory character of the old theories is explained not by the incorrectness of the ideas laid at their foundation, but, apparently, by the fact that the elaboration of these ideas was carried out classically, and not by a quantum-mechanical route.

In all theories, electrical breakdown is regarded as melting of the dielectric (in the simplest case, usually considered in theory, of a crystalline dielectric).

Thus, it may be considered that both types of breakdown—thermal and electrical—lead to one and the same result: to the thermal destruction of the dielectric. However, the processes leading to this result differ sharply.

In thermal breakdown, the dielectric is thermally destroyed as a result of an increase in current with increasing temperature, which is caused by heating of the dielectric under the action of this same current. The determining role in this process is played by the ionic current, which increases sharply with temperature and increases comparatively little with increasing field.

In electrical breakdown, the thermal destruction of the dielectric is caused by an increase in current with increasing field strength.

The decisive role in this process is played not by the ionic, but by the electronic current, which is vanishingly small at low fields and increases sharply with increasing field in strong fields. The electronic current in a dielectric depends comparatively little on temperature, and therefore the development of electrical breakdown depends only on the field strength.

The electronic current in a crystal lattice may be of three types: purely electronic, hole, and mixed. The energy spectrum of the crystal lattice of a dielectric is characterized, first, by a large width of the forbidden region separating the conduction band and the normal band, and, second, by the practically complete absence of electrons in the conduction band. Under normal conditions, therefore, the electronic current in a dielectric is vanishingly small.

Between the normal band and the conduction band in any real dielectric there are localized discrete levels, whose presence may be due to: a) foreign atoms embedded in the lattice, b) unfilled lattice sites, c) mechanical ruptures in the lattice, etc.

Electrons sitting on these levels, in contrast to electrons sitting on proper levels (merging into bands), are confined in their motion to very narrow regions in the crystal. In order to produce an electronic current in a crystalline dielectric, it is necessary: 1) to enrich the conduction band with electrons, 2) to impoverish the normal band of electrons. These conditions, in the presence of localized discrete intermediate levels in the forbidden region, may be fulfilled not only simultaneously, but also each separately. The transition of electrons from localized levels into the conduction band ensures the presence of a purely electronic current.

The transition of electrons from the normal band to localized levels of the forbidden region is a necessary condition for the occurrence of a hole current.

Finally, the transition of an electron from the normal band to the conduction band gives rise to a mixed electron–hole current.

Thus, in order to excite an electronic current in a dielectric, it is necessary to act upon it with ionizing agents that ensure at least one of the above-mentioned electronic transitions. Such agents may be high temperature and a strong field. The first of these agents—high temperature—proves effective only when the forbidden region is narrow, i.e. in the case of semiconductors. A dielectric, however, would have to be heated to a very high temperature, considerably exceeding its melting temperature, in order to obtain in it an appreciable electronic current in weak fields.

The ionizing capability of a strong field, on the contrary, is sufficiently effective for a dielectric. It is due to deformation of the energy spectrum of the lattice, which is caused by the application of a strong field and is expressed in the tilting and broadening of the bands. In the process

ionization the first effect plays the principal role. The indicated deformation of the levels makes possible vertical (with expenditure of energy) and horizontal (without expenditure of energy) transitions of electrons.

A horizontal transition is similar to the seepage of an electron through a potential barrier. A vertical transition is analogous to excitation.

In accordance with this, two mechanisms of ionization should be distinguished: 1) ionization by collisions (vertical transition), and 2) ionization by tearing out (horizontal transition).

Modern theories of electrical breakdown may be divided into two groups: 1) theories based on the mechanism of impact ionization, and 2) theories based on the tunnel effect.

Theories of impact ionization do not lead, in contrast to the older views, to an avalanche-like increase of the current with distance, since not only the process of liberation of electrons is taken into account, but also the process of their binding. In connection with this, modern theories of impact ionization in a solid dielectric do not predict strengthening in thin layers, which is not observed experimentally.

The works of Soviet physicists devoted to elucidating the mechanism of electrical breakdown have recently made it possible to reveal such experimental facts which, on the one hand, confirm the exceptional role of the electron current in the electrical breakdown of a dielectric and, on the other hand, make it possible, to a certain extent, to give preference to tunnel-effect theories as compared with theories of impact ionization (Volkenshtein).

For the “tunnel” mechanism of electrical breakdown, an almost complete independence from temperature and the suddenness of its manifestation are characteristic. These features are indirectly confirmed by experimental data of Soviet investigators.

The scheme of ideas described above concerning the nature of dielectrics and their electrical breakdown is constructed on the basis of applying to them the “band” theory, developed in detail for metals. The application of this theory to dielectrics is only a very rough approximation to reality.

In 1936–1937 Ya. I. Frenkel developed other ideas concerning the nature of dielectrics. According to these views, a crystalline dielectric is treated as a compressed gas in which each atom has its normal complement of electrons. Partial collectivization of the outer electrons can occur only when the crystal is excited. When light is absorbed by one of the atoms, not only the detachment of an electron—its collectivization—is possible, but also the excitation of the atom is possible. In a gas, the excited state can be transferred from one atom to another in collisions. In a crystal this transfer of excitation can also occur without collisions, as a result of the intense interaction between neighboring atoms. Thus, the excited state proves capable of moving through the atoms of the crystal in the same way as collectivized

electrons or “holes,” and according to the same wave laws. Consequently, the excited states may be interpreted as certain fictitious particles, which Frenkel called excitons. The absence of a clearly expressed internal photoelectric effect in many crystals can, according to this conception, be explained by the fact that, when light is absorbed, collectivized electrons and holes are not formed, but electrically neutral excitons are.

Davydov developed a theory of gas breakdown based on the idea that “ionizing” collisions of atoms with electrons are preceded by “exciting” collisions.

Developing the conception set forth concerning a dielectric as a compressed gas, Frenkel derived a formula giving the dependence of the electronic conductivity of a crystal on the field strength

\[ \sigma = \sigma_{0}\cdot e^{\frac{\sqrt{q^{3}E}}{kT}}, \]

where \(q\) is the elementary charge, \(E\) the field strength. It is possible that further development of this conception will make it possible to construct a new theory of the electrical breakdown of crystalline dielectrics.

In reality, electrical breakdown manifests itself in a number of dielectrics under appropriate conditions. The criteria of electrical breakdown (as distinct from thermal breakdown) are: 1) independence of temperature, 2) independence of the duration of application of the voltage, 3) destruction of the dielectric at the place of greatest field (most often at the edge of the electrode).

These conditions, however, are comparatively rarely fulfilled simultaneously and completely. Most dielectrics, depending on the conditions, may break down by both thermal and electrical mechanisms. Therefore, for example, under prolonged action of voltage, one and the same dielectric may undergo thermal breakdown, while under short-time action—electrical breakdown. At high temperatures and high frequencies, as indicated above, all dielectrics are characterized by thermal breakdown, etc. It is therefore very essential to establish not only the criterion of electrical breakdown, but also the conditions under which it develops in each particular dielectric. The work of Soviet physicists in this field has played a great role.

Of very great importance (both theoretically and practically) was the discovery by Soviet scientists (Vul and others) of special forms of electrical breakdown: incomplete breakdown and successive breakdown. It was shown that if a dielectric (rock salt, glass, mica, etc.) is subjected to pulses of voltage somewhat smaller than the breakdown voltage, the dielectric begins to be destroyed; however, this destruction does not proceed to the end: an incomplete breakdown of the dielectric is formed, leading to the formation of microscopic cracks, and sometimes cracks visible to the naked eye, and other traces of discharge within the bulk of the dielectric.

A consecutive series of incomplete breakdowns may lead to final breakdown at a voltage almost half as large as the normal breakdown voltage. Such consecutive breakdown was observed for cable paper, bakelite-paper boards, and micanite.

The development of consecutive breakdown is closely connected with the gradual destruction of the dielectric under the action not only of incomplete breakdowns, but also of edge discharges. In the presence of edge discharges, consecutive breakdown is possible under an alternating voltage of low frequency.

The danger of consecutive breakdown of insulation must be taken into account in the design, operation, and testing of high-voltage installations, transformers, electrical machines, cables, and transmission lines. Breakdown of insulation in all these installations, at the safety margins now accepted, has the character of a consecutive breakdown (with the exception of direct lightning strokes).

If insulation testing by impulses is set up irrationally, incomplete breakdown of the insulation may occur, which will manifest itself during operation of the installation.

c) Breakdown of Liquid Dielectrics and Gases

Soviet physicists have studied not only the breakdown of solid dielectrics, but also the breakdown of liquid dielectrics and, in particular, gases.

The work carried out in the field of studying the breakdown of liquid dielectrics, although it does not yet make it possible to resolve the question of its mechanism, has clarified a number of secondary phenomena (the role of gas, the role of water, etc.) that extraordinarily complicate the picture of liquid breakdown, has made it possible to outline a rigorous methodology for investigation, and has brought us close to solving the question of the mechanism of liquid breakdown.

Soviet physics has made great achievements in the study of gas breakdown. Here the physics of dielectrics comes into close contact with the physics of gas discharge.

At present, the requirements of the electrical industry have especially increased with regard to obtaining non-aging and heat-resistant high-voltage insulation. Compressed gas has begun to find application as such insulation (gas-filled cable, capacitor with compressed gas, etc.). It is quite understandable that work on the investigation of gas breakdown has acquired great practical significance.

The influence of various factors on the breakdown of an inert gas (in particular nitrogen) was studied in detail and systematically. The influence of pressure and temperature, electrode shape, distance between electrodes, irradiation, etc. was investigated (works of Vull, Goldman, Kovalenko, Parnas).

The electric strength of various gases was also intensively studied, in particular with the aim of finding a gas of increased electric strength whose use would not require such a large…

high pressures, such as the use of nitrogen (works of Hochberg, Sandberg, Kovalenko, and others).

It turned out that the electric strength of a gas is connected with its molecular weight. Gases with low molecular weight possess low electric strength. Conversely, heavy gases, as a rule, are characterized by high electric strength. However, there is apparently no direct dependence between molecular weight and the electric strength of a gas.

The study of the electric strength of vaporous gases made it possible, first, to establish a number of regularities, in particular, to show that the value of the first ionization coefficient \(\alpha\) (ionization by electrons), which occurs during gas breakdown, does not depend on, or depends little on, the individuality of the gas; and, second, to discover a gas with high electric strength (2.5 times greater than the electric strength of air), the use of which as insulation, for example for powerful capacitors, presents no difficulties. This gas was called elegas (works of Hochberg and others).

Recently these works have received further development (Hochberg, Sandberg). Precise investigations have established that the first ionization coefficient \(\alpha\) in various gases reaches one and the same value at sharply different field strengths. At the same time, the field strengths at which the value of \(\alpha\) reaches one and the same value in different gases are related to the field strength in air in the same way as the breakdown voltages of these gases are related to the breakdown voltage of air. Thus it has been unequivocally established that the development of gas breakdown is determined first of all and mainly by the process of impact ionization by electrons, and the value of the breakdown voltage is conditioned only by the dependence of the first ionization coefficient on the voltage.

5. AGING OF ELECTRICAL INSULATION AND MEASURES TO COMBAT IT

Of very great importance in insulation engineering is the guarantee of long-term operation of insulation under service conditions. Such a guarantee in a number of cases can be given only when special measures have been adopted to combat the aging of insulation.

The systematic study of the aging of insulating materials was initiated by the works of Vull and Goldman. The aging of insulating materials under the action of high voltage is caused by the following factors: 1) heating of the insulation as a result of increased dielectric losses—chiefly at high frequencies (or under the action of elevated temperature at which the electrical apparatus operates), leading to a slow, gradual thermal destruction of the material; 2) ionization of air gaps within the insulation and between the insulating layer and the insulated conductor, leading a) to local heating of the insulation,

b) to mechanical destruction of insulation under the action of spark discharges in air gaps, and c) to chemical destruction of insulation under the action of ozone and nitrogen oxides released in ionized air gaps.

The first factor—the gradual thermal destruction of insulation—is eliminated by selecting materials possessing the appropriate heat resistance and a sufficiently small loss angle. A large number of works by Soviet physicists and chemists in recent years have been devoted to the problem of heat-resistant insulation. As a result of these works, insulating varnishes with increased heat resistance—primarily glyptal varnishes—have been obtained and partly introduced into production. Various asbestos materials have been developed (asbestos tape, asbestos paper), which have become widely used in the insulation technology of high-voltage electrical machines. Alongside this, a number of works applying the theory of thermal breakdown have made it possible to establish and substantiate standards for the loss angle of various materials used in electrical machine building, in cable technology, and in high-frequency technology; these standards guarantee prolonged operation of these materials without internal heating. Work has begun on the use of glass fabric in cable and electrical-machine construction, which will lead to a strong increase in operating temperatures and, in connection with this, in the power of machines and cables.

Factory work on obtaining heat-conducting insulation based on bitumen and quartz, which has already found practical application, belongs to the same range of questions.

The second factor causing aging of insulation—ionization of air interlayers—has been subjected to detailed and systematic study (Skanavi, Kanonykin, Bugel). A method has been established for detecting the onset of ionization.

Aging of insulation is caused not only by ionization of internal air inclusions, but to a considerable extent also by corona on the surface of the insulation, which can occur at the edges of insulated conductors and is not eliminated by making the insulation monolithic.

A number of works by Soviet physicists (Ioffe, Vul, Gold’man, Skanavi, and others) have been devoted to combating corona. As these works have shown in practice, smoothing of the field at the edges of insulated conductors can be accomplished by very simple methods: 1) by coating the edges of the conductors and the surface of the insulation with a varnish of high dielectric constant; 2) by coating with a semiconducting varnish. The second method is used when employing soot-asphalt and soot-bakelite varnishes in large-scale electrical machine building, where the latter are usually used in combination with asbestos semiconducting tapes.