ON THE PROPERTIES OF IONIC DIELECTRICS

A. A. VOROB'EV

For a long time, natural materials were used as dielectrics, selected mainly on the basis of their high mechanical strength and low electrical conductivity. With the increase in the operating voltage of installations and the use of alternating current, it became necessary to take into account the electric strength and dielectric losses of insulation. In electrical-current installations, transformer oil came into wide use for insulation and heat removal. Then phenol-formaldehyde resins and bakelite were discovered. Varnished paper and fabrics, and molded articles, became widespread. Ebonite enjoyed great success.

At the present time, notable successes have been achieved in the development of insulation made from plastics, ceramic materials, and others.

The complex service conditions of electrical insulation in electrical-engineering and radio-engineering installations require dielectrics to possess, simultaneously, high mechanical, thermal, and electrical strength, small dielectric losses, and so forth.

Insufficiently high physical properties of solid dielectrics force one to allow large safety margins in designs, making products more expensive. To reduce the heating of dielectrics, special cooling devices have to be installed. All this complicates and increases the cost of the apparatus. Improvement of the properties of solid dielectrics will lead to a reduction in the dimensions of products, to their lower cost, and to higher quality. The development of new types of dielectrics must be carried out on the basis of advances in chemistry, physics, and the technology of materials manufacture.

The classical theory of ionic lattices has, in practice, satisfactorily solved the question of certain properties of crystals, correctly indicating the basic regularities and, in individual cases, also determining the numerical values characterizing the properties.

Among such properties, the theory of which was given by Born, Karman, and others, one may include the value of the coefficient of hydrostatic compression, the velocity of sound, polarizability and the dielectric constant, the spectrum of natural vibrations of ions, and certain others. An exposition of the classical theory of perfect ionic lattices is presented in the well-known monographs of Born and Gepppert-Mayer, Ya. I. Frenkel, and others.

Quantum theory explained the nature of the homopolar bond, refined the formulas of the theory of ionic lattices, made it possible to improve the theory of the heat capacity of ionic structures, and so forth.

Despite the well-known successes in the theoretical description of certain properties of ionic crystals, there is as yet no unified theory explaining the thermal, mechanical, optical, and electrical properties of a solid body.

The properties of a solid body that are not connected with the violation of its continuity are explained more or less satisfactorily theoretically. At present there is no accepted theory that satisfactorily explains the mechanical destruction of a crystal and makes it possible to calculate its stren-

...strength, there is no theory of melting and no theory of electrical breakdown of solid dielectrics. The large number of known theories of mechanical strength, melting, or theories of electrical breakdown indicates that none of them can claim to provide a satisfactory explanation of the phenomenon considered in this theory.

In recent decades the attention of researchers has been drawn to the study of disturbed structures and alloys. In this field very great successes have been achieved, and new materials have been obtained that possess properties necessary for practice. Let us note the advances in the field of semiconductors and devices employing them, magnetic alloys, heat-resistant materials, ferroelectrics, etc. Successes in the study of disturbed structures have led to a weakening of work on the study of the original undisturbed structure. The last recognized theoretical achievement is still the band theory of electrical and optical properties, proposed more than twenty years ago.

Without lessening attention to the development of questions in the theory of disturbed structures, one should undertake the development of a unified theory of the properties of undisturbed structures.

A significant shortcoming in theoretical investigations of the preceding period in the field of the solid state was the development of theories of individual properties without connection with one another. Such properties of a solid as electronic and ionic electrical conductivity, dielectric losses, breakdown, diffusion and self-diffusion, etc., generally occupied a separate position and lay outside the circle of questions that belonged to solid-state theory. There was not, and is not, the necessary connection among scientists developing questions of the mechanical and electrical strength of solids. Ignorance of achievements in one field of science by those working in another delays the development of science.

The considerable materials accumulated in the study of various properties of solids have not been compared with one another. In the books of Prof. V. D. Kuznetsov on solid-state physics, extensive material is collected only on the mechanical properties of crystals.

The comparison of various properties of dielectrics and the establishment among them of regular relations, on the basis of experimental and theoretical data, is a necessary stage for the further development and elaboration of dielectrics with specified properties.

In the present work an attempt is made to consider the connection among the various properties of ionic crystals. As a characteristic connected with all the properties of ionic crystals, the value of the energy of the crystal lattice is chosen.

The theory of the crystal lattice establishes a regular connection between the lattice energy and certain mechanical, optical, and thermal characteristics of dielectrics. In Born’s theory the phenomena of electronic and ionic electrical conductivity and diffusion in dielectrics, dielectric losses, electrical and thermal breakdown, and other properties of crystals are not considered. These electrical properties of dielectrics were studied separately from the mechanical, optical, thermal, and chemical properties and without connection with other properties of dielectrics. Theories explaining the electrical properties of dielectrics, the processes of electrical conductivity and especially breakdown, were developed in weak connection with the general theory of the crystal lattice. Meanwhile, it is obvious that whatever properties of a crystal are considered, they, as properties of a single whole, must be connected with one another.

A change in some properties of solids entails a change in others; for example, heating a body causes an increase in ionic electrical conductivity, dielectric losses, etc.

Other properties of a solid, without directly determining one another, change simultaneously because the cause affecting both properties changes. The properties of a solid are determined by the energy of interaction between its particles and by the properties of the particles composing it. Using experimental data, we have traced how the properties of a solid change when its composition changes. Impurities of foreign particles and disturbances of the crystal structure change its properties and bring about the appearance of new properties not inherent in a pure, undisturbed crystal, for example, luminescence, the property of crystals with F-centers, etc.

For the theory of solids and for practice, it is of interest to establish the regular variation of properties as a function of the composition and structure of a solid. Under the complex modern conditions of use of solid dielectrics, it is of practical interest how many properties of a dielectric change simultaneously if the conditions in which it is found are changed. It is of practical interest, by monitoring the change of one or several characteristics of a dielectric, to know how the others change as well. In this connection, comparisons have been made of the changes in different properties of dielectrics under the action of certain factors.

The construction of a unified theory of the solid in general, and of dielectrics in particular, is possible if simple general properties of these bodies are taken as a basis. Several simple fundamental properties of dielectrics, laid at the foundation of their general theory, must reflect the essence of the phenomena. It is obvious that the thermodynamic properties of bodies are the most general.

The physical structure of real crystals and their composition practically always deviate more or less from the ideal. Practical dielectrics are often complex chemical compounds or solid solutions of two or several components. In this connection, attention has been drawn to the study of disturbed structures, and to the influence of impurities and lattice defects on the properties of crystals. We have considered the properties of crystals with impurities and lattice defects, as well as of two-component solid solutions, in connection with the binding energy of the particles in these crystals. This made it possible to establish definite relationships between the properties of disturbed structures and solid solutions and the binding energy between particles.

The absence of a theory of dielectric alloys, and the insufficient study of the properties of solid solutions, is an obstacle to the development of dielectrics consisting of many components, and to the selection of these components. Certain relations between the properties of crystals of solid solutions and of their mechanical mixtures, described in this work, will suggest directions in the development of new dielectrics.

To describe electronic processes in crystals, quantum mechanics has provided the band theory of the solid. At present the limits of applicability of this theory and its fundamental shortcomings have been established. One of the fundamental shortcomings of band theory is the replacement of the problem of the behavior of many electrons in a crystal by the problem of the behavior of a single electron. In band theory, the behavior of one electron in a periodic potential field is considered. The interaction of each individual electron with all the others is taken into account approximately by introducing an external effective field. In this so-called “self-consistent field,” the electron moves independently of the others. The “self-consistent” field must express the interaction of the electron under consideration with the total charge of all the other electrons, including its own charge.

Band theory takes defects and impurities in real crystals into account by introducing additional discrete levels of inhomogeneities in

energy spectrum of crystals. Local levels of inhomogeneities account for all the special features of semiconductors and dielectric crystals.

F. F. Volkenshtein believes that the one-electron description given by band theory may be acceptable in a number of cases with respect to electrons transferred into the conduction band. In exactly the same way, and within the same limits, the behavior of holes in the normal band can be described. Thus, band theory can describe the excited states of a system, but within its framework one cannot describe the normal state, characterized by the absence of electrons in the conduction band and the absence of holes in the normal band.

In band theory the interaction of conduction electrons with lattice vibrations is treated as a small perturbation. This is another fundamental shortcoming of the theory, since in reality, for most crystals, the interaction turns out to be large.

Electrons moving in the lattice are accompanied by the dielectric polarization of the ionic crystal created by the electrons themselves. The local polarization that arises in this process is connected with the displacement of ions and possesses inertia. It cannot follow a comparatively rapidly moving electron and forms a potential well for the electron. The depth of this potential well for most crystals is of the order of 0.5–1 eV. Discrete energy levels of the electron will exist in it. Such states of an electron in a crystal with a polarization potential well in which the electron is localized were called polarons by S. I. Pekar.

S. V. Tyablikov believes that the spectrum of polarons has a band character, irrespective of whether the coupling with the polarization vibrations of the lattice is strong or weak. In general, the polaron spectrum represents a series of narrow bands located at some distance from one another. It is possible that, beginning at some point, the bands will overlap one another.

With the aid of polaron theory, as well as band theory, electronic phenomena in crystalline dielectrics and semiconductors—electrical conductivity, photoconductivity, luminescence, breakdown, etc.—are described with a certain accuracy. These theories do not consider ionic processes or the interrelation between electronic and ionic processes.

Modern quantum theories describe electronic and ionic processes in crystals separately. In this connection difficulties arise in describing processes which may begin as electronic processes and end as predominantly ionic processes. Let us point to the phenomenon of electrical breakdown of solid dielectrics, which in the first stage is associated with high-voltage electronic conductivity and ends with the destruction of the ionic structure of the dielectric, with the rupture of bonds between ions. Separate consideration of the initial electronic stage of breakdown and the final stage of breakdown, the rupture of bonds between ions, does not make it possible to describe the phenomenon of electrical breakdown completely, or to establish theoretically the connection between electric strength and the composition and structure of the dielectric.

The study of the properties of ionic crystals and of their dependence on composition and structure is of practical interest for describing inorganic dielectrics in general, and ceramic dielectrics in particular. By regulating the composition of the ceramic body and the processing, it is possible to obtain materials of different physical structure. Electroceramic materials, depending on their composition and structure, have different mechanical, thermal, and electrical properties. The regularities determining the connection between the composition, structure, and properties of ceramic materials have not been studied.

Electroceramic materials constitute a multiphase system that includes crystalline, amorphous, and gaseous (pores) phases. The composition, structure, and quantitative ratios of the phases determine in a complex way the properties of electroceramic materials.

The crystalline phase largely determines the physical properties of electroceramic materials. This gives rise to great practical interest in studying the properties of ionic crystals. The crystalline phase consists of chemical compounds or solid solutions of the components that make up electroceramic materials.

Exceptionally high dielectric properties have been found in ceramic materials produced on the basis of noble spinel \((\mathrm{MgOAl_2O_3})\), forsterite \((2\mathrm{MgOSiO_2})\), periclase \((\mathrm{MgO})\), perovskite \((\mathrm{CaOTiO_2})\), clinoenstatite \((\mathrm{MgOSiO_2})\), and others.

The study of the properties of ionic crystals should help in understanding the basic properties of electroceramic dielectrics, the relationship between the composition and properties of ionic insulating materials, and should provide scientific grounds for choosing their composition and processing.

A solid is a quantum-mechanical system of many particles strongly interacting with one another. For this reason, particles in a solid largely lose their individual properties, while at the same time the system of particles acquires new collective properties characterizing the solid. At the same time, the principal properties of a solid are determined by its chemical composition, physical structure, and external conditions.

The energy of interaction between the particles forming a solid, on which its physical properties depend, is determined by the position of the constituent elements entering into the compound in the table of D. I. Mendeleev.

It is of interest to investigate the dependence of the physical properties of the simplest ionic dielectrics on the position of the components in the table of D. I. Mendeleev, on their atomic weight and number. The bond between particles in crystals is most fully expressed by the magnitude of the energy that must be expended in order to separate the ions to an infinitely large distance from one another. This quantity is called the energy of the crystal lattice.

Theoretical and experimental studies show that the basic properties of crystals of ionic compounds are related to the magnitude of the lattice energy.

With a decrease in the volume and polarizability of molecules, the lattice energy of ionic compounds crystallizing in lattices of the rock-salt, fluorite, cesium chloride, wurtzite, and zinc blende types increases (Figs. 1, 2). Molecular refraction decreases with increasing lattice energy (Fig. 3).

For alkali-halide crystals, with the metal unchanged, the electronic component of the dielectric constant increases with increasing polarizability of the halide and with decreasing lattice energy (Figs. 4, 5).

According to V. I. Sarafanov, the substitution of magnesium by calcium, strontium, etc., in titanates is accompanied by an increase in the dielectric constant. This substitution of second-group metals is accompanied by a decrease in the energy of binding of particles in the lattice (Fig. 6).

Physical phenomena in crystals determined by elastic vibrations of ions are connected with the lattice energy. The heat capacity, calculated per gram-atom, for compounds of metals of the first and second groups decreases with increasing lattice energy (Figs. 7, 8). The melting temperature of crystals of alkali-halide salts increases with increasing lattice energy...

Fig. 1. Dependence of molecular volume on lattice energy for compounds crystallizing in a lattice of the type:

○ — rock salt,
△ — fluorite,
◊ — cesium chloride,
△ — wurtzite,
× — zinc blende.

Fig. 2. Relation between molecular polarizability and lattice energy for compounds crystallizing in a lattice of the type:

○ — rock salt,
△ — fluorite,
◇ — cesium chloride,
△ — wurtzite,
× — zinc blende.

increases (Figs. 9, 10). Experimental data show that, with increasing lattice energy of compounds of metals of the first and second groups, the frequency of the natural vibrations of the lattice ions increases (Fig. 11).

For compounds of metals of the first and second groups crystallizing in a rock-salt-type lattice, the absorption of light in the infrared, visible,

Fig. 3. Dependence between the sum of the refraction of the anion \(R_a\) and the refraction of the cation \(R_k\), and the lattice energy for crystals of alkali-halide salts.

and ultraviolet parts of the spectrum is regularly related to the energy of the crystal lattice. The onset, edge, and maxima of the absorption bands shift into the short-wavelength part of the spectrum with increasing lattice energy (Figs. 12, 13).

Fig. 4. Dependence of the electronic component \(\varepsilon_\infty\) on the polarizability of the halide \(\alpha_m\) at \(\lambda = 5893\) Å.

Surface energy substantially affects the course of many processes occurring at the contact of two bodies, in particular the phenomena of formation and destruction of surfaces, diffusion, etc. (Fig. 14).

By its physicochemical nature, surface energy represents a manifestation of the forces of interaction between particles and of the chemical bond

between them. Therefore, the crystal-lattice energy and the surface energy of a body in vacuum are connected with each other. An increase in the specific surface energy occurs simultaneously with an increase in the lattice energy (Fig. 15).

Fig. 5. Dependence of \(\varepsilon_\infty\) on the lattice energy for compounds of metals of the first group of Mendeleev’s table with a NaCl-type lattice.

Fig. 6. Change in \(\lg \varepsilon\) upon substitution of the cation in titanates of metals of the second group of Mendeleev’s table. Plotted according to data of V. I. Sarafanov.

A. V. Tolvinskaya made a successful attempt to relate the surface resistance of solid dielectrics to the magnitude of the surface energy.

The high value of the lattice energy and surface energy of ionic compounds determine wettability and a significant increase in their

Fig. 7. Dependence of the molecular heat capacity \(C_p\) on the lattice energy for compounds of metals of the first group of Mendeleev’s table with a NaCl-type lattice.

surface conductivity. Thus, the generally high electrical properties of dielectrics are lowered. Alumina and fused quartz—substances having a structure intermediate between substances with ionic and atomic bonding—possess high surface resistance.

Fig. 8. Dependence of heat capacity on lattice energy for compounds of elements of Group 2 of the Mendeleev table.

The theory of the crystal lattice establishes a connection between the coefficients and moduli characterizing the elastic properties of crystals. According to theoretical and experimental data, the coefficient of volume

Fig. 9. Dependence of the melting temperature in °C on the lattice energy for alkali-halide compounds with a NaCl-type lattice.

compression increases with increasing lattice energy (Fig. 16). The hardness of crystals increases with lattice energy (Figs. 17, 18). With increasing lattice energy, the elastic properties of crystals increase, and their

compressibility (Fig. 19). Resistance to flow, to forcing through an orifice, etc., increases.

According to the experimental data of B. M. Gokhberg, Lefeld, K. A. Vodopyanov, G. I. Skanavi, N. P. Bogoroditskii, A. P. Nakhodnova, V. I. Sarafanova, and others, it follows that, with increasing binding energy of the ions in the lattice, the electrical conductivity of ionic crystals decreases (Fig. 20), as do the dielectric losses; the electric strength of ionic crystals increases with increasing lattice energy (Figs. 21, 22, 23).

Fig. 10. Dependence of the melting temperature on the lattice energy for compounds crystallizing in a CsCl-type lattice.

Fig. 11. Dependence of the frequency of natural vibrations of lattice ions on the lattice energy of alkali-halide compounds.

With increasing energy of the crystal lattice, the heat of formation of the compound in the solid state increases (Fig. 24). The heat of formation

of a chemical compound in the solid state, reduced to the given temperature (25°C) and pressure of 760 mm, for the corresponding initial states of the atoms, represents a certain measure of the stability of the compound. Comparison of the stability of compounds by the heat of formation is indicative when compounds of identical types are compared.

Fig. 12. Energy of a quantum of light absorption in crystals of alkali-halide salts and lattice energy.

I — Edge of intrinsic absorption.

II — Maximum of the \(F\)-band.

III — Intrinsic absorption in the infrared region of the spectrum.

Fig. 13. Dependence of the quantum energy of the edge of intrinsic absorption and the quantum energy of intrinsic lattice vibrations on the lattice energy for oxides of metals of group 2.

The existence of various ionic compounds and the explanation of their greater or lesser stability are associated with the magnitude and sign of the heat of formation from the free elements.

Fig. 14. Relationship between the surface energy of minerals and the Mohs scale number.

Experimental data show that, with an increase in the heat of formation, the electrical strength of crystals of alkali-halide salts increases (Fig. 25), while their electrical conductivity and dielectric losses decrease (Figs. 26, 27). The experimental characteristics of ionic compounds obtained from various measurements are in a regular dependence

Fig. 15. Relationship between the specific surface energy and the lattice energy for alkali-halide crystals.

Fig. 16. Dependence of the coefficient of uniform compression on the lattice energy of crystals of alkali-halide compounds.

![Graph: coefficient of uniform compression vs. lattice energy for alkali-halide crystals. Vertical axis: coefficient of uniform compression, \(10^{7}\) dyne/cm\(^2\) (approx.); horizontal axis: lattice energy, eV/ion pair. Points labeled KJ, KBr, NaBr, KF, LiBr, NaCl, LiCl, LiF.]

![Graph: Mohs hardness vs. lattice energy for alkali-halide crystals. Vertical axis: Mohs hardness; horizontal axis: lattice energy, eV/ion pair. Points labeled KJ, KBr, KCl, NaBr, NaCl, LiBr, LiCl, NaF, LiF.]

Fig. 17. Dependence of Mohs hardness on lattice energy for crystals of alkali-halide compounds.

Fig. 18. Dependence between the magnitude of Mohs hardness and lattice energy for crystals of the NaCl type.

![Graph: Mohs hardness vs. lattice energy for crystals of the NaCl type. Vertical axis: Mohs hardness; horizontal axis: lattice energy, eV/ion pair. Points labeled BaS, SrS, BaO, SrO, CaS, MgS, CaO, MgO.]

Fig. 19. Dependence of the compressibility \(\beta\) of alkali-halide compounds on the lattice energy \(\left(\beta=\frac{1}{x}\right)\).

Fig. 20. Conductivity of NaCl (Smekal)

\(\triangle\), \(\bullet\), \(\times\) — for single crystals
\(\circ\) — for polycrystalline material.

from one another, as determined by the theory of the crystal lattice. The experimental establishment of correspondences among the various characteristics of ionic dielectrics is a useful refinement of the theory and is necessary for its more detailed development in the future.

Fig. 21. Dependence of the logarithm of electrical conductivity at \(t=600^\circ\mathrm{C}\) on lattice energy for alkali-halide compounds.

A certain amount of material has been accumulated on the properties of ionic solid solutions and isomorphic mixtures, material that is of scientific and practical interest for the theory of dielectrics and provides a basis for further scientific investigations.

Fig. 22. Dependence of electrical conductivity \((\lg \gamma)\) at a temperature of \(500^\circ\mathrm{C}\) on lattice energy for single crystals of alkali-halide salts. (Plotted from B. M. Gokhberg’s measurements of electrical conductivity.)

The investigations of Academician N. S. Kurnakov and his collaborators make it possible to conclude that the mechanical properties of solid ionic solutions are characterized by the heat absorbed in the formation of the solid solution. The less heat is absorbed in the formation of a solid compound, the more stable and mechanically stronger it is. Unstable solid solutions ...

disintegrate with time. The rate of their decomposition depends on external conditions and, above all, on temperature. During the decomposition of solid solutions and their approach to the state of a mechanical mixture, part of the heat stored in the alloy is released.

Fig. 23. Change in the logarithm of the electrical conductivity of titanates of the metals of the second group of the periodic table upon substitution of metals (according to data of V. I. Sarafanov).

The crystals of solid solutions are characterized by the frequencies of residual rays inherent in the compound of the given chemical composition, by definite absorption bands in the ultraviolet and infrared regions of the spectrum, and, in the presence of color centers, by a definite absorption band in the visible region of the spectrum and by the absorption coefficient.

All this shows that in a solid solution there exists a single lattice of the solid solution.

Fig. 24. Dependence of the heat of formation on the lattice energy of alkali-halide compounds in the solid state at \(t = 25^\circ\mathrm{C}\) and \(p = 760\) mm Hg.

The magnitude of the energy quantum corresponding to the position of the maximum of the absorption band in the visible, infrared, and ultraviolet parts of the spectrum varies linearly as a function of the chemical composition of the crystal.

Fig. 25. Dependence of electric strength on the heat of formation of alkali-halide compound crystals.

E. K. Zavadovskaya, A. M. Trubitsyn, and others showed that the electric strength of solid solutions increases with a decrease in the amount of heat absorbed during their formation and with an increase in stability.

Fig. 26. Dependence of the logarithm of electrical conductivity \((\lg \gamma)\) at \(t = 600^\circ\mathrm{C}\) on the heat of formation of the chemical compound in the solid state.

(Fig. 28). A. N. Kislina showed that the electric strength and hardness of solid solutions increase as they age.

According to measurements by K. A. Vodopyanov, M. A. Krivov, G. I. Galibina, A. P. Borovikova, B. N. Burgaev, and L. G. Koretskii, with a decrease in the stability of the solid solution, dielectric losses and electrical conductivity increase.

Fig. 27. Dependence of the dielectric coefficient on the heat of formation of alkali-halide salt crystals in the solid state.

Fig. 28. Dependence of the electrical strength \((E_{\mathrm{pr}})\), microhardness \((H)\), and heat absorbed in the formation of the solid solution \((Q)\) on the composition of single crystals of the KJ—KBr system.
(Constructed by the authors from data of A. M. Trubitsyn, N. S. Kurnakov, S. F. Zhemchuzhny, and Rombakh.)

The properties of ionic solid solutions of substitution are determined by the heat absorbed during formation, with which the mechanical, thermal, optical, and electrical properties of crystals are simply connected. With a decrease in the energy absorbed during the formation of a solid solution, its stability against decomposition increases, the electrical strength and melting temperature increase, the hardness decreases, etc.

At present, despite the considerable development of the classical and band theories of the solid state and the exhaustion of their resources, the most important properties of crystals of the simplest physical structure still do not have a satisfactory physical description. Numerous theories of plastic deformation and mechanical fracture, melting, and electrical breakdown do not explain the basic regularities of these phenomena, and do not give detailed indications as to the direction of searches for materials with better properties.

The study of some properties of crystals without connection with others has sometimes led to the explanation of one phenomenon by means of another, the nature of which was likewise unclear, as was observed in the example of the explanation of electrical breakdown.

There are two directions in the explanation of physical processes in the breakdown of dielectrics. Supporters of one direction try to understand and explain breakdown as a melting phenomenon; supporters of the other direction explain breakdown as a phenomenon of mechanical fracture. Meanwhile, neither the former nor the latter have raised the question of how clear the physical picture of melting and mechanical fracture is. The disputing scientists tacitly proceeded from the notion that the phenomena of melting and mechanical fracture, long studied by physics and long known to mankind, should be understood and known to science in detail. Meanwhile, it turns out that the phenomena of melting and mechanical fracture of crystals are no less, if not more, physically unstudied than breakdown.

It is quite possible that the phenomenon of breakdown, which can be studied with the aid of more advanced apparatus and methods, will provide the necessary materials for understanding the atomistic picture of the processes during melting and mechanical fracture of solids.

Theoretical consideration of plastic deformation and mechanical fracture, melting, or electrical strength may be carried out in three different ways. One of them consists in constructing a phenomenological theory of the phenomenon on the basis of a generalization of the experimental laws for the course of processes in the simplest cases. These laws are formulated mathematically, and then attempts are made to solve the resulting equations, which make it possible under various conditions to analyze the behavior of solids in more complex cases. The second way, which brings us closer to solving the problems of the properties of solids, has as its aim the creation of a theory of the mechanism, of atomic motions accompanying plastic deformation, melting, or breakdown. The description of molecular motions during plastic deformation and breakdown is still at an early stage of its development. The third direction in the development of the processes of fracture of crystals is thermodynamic. There exists a thermodynamic theory of melting (Ya. I. Frenkel), of mechanical fracture (Fers), and of breakdown (Geller).

When considering the properties of dielectrics separately, knowing, for example, the value of the electrical strength, one can say nothing about other most important characteristics of the substance, the melting temperature or electrical conductivity. In modern technology, solid dielectrics bear a combined load. It is often necessary to evaluate several properties of a dielectric simultaneously. The comparisons of the properties of crystalline dielectrics carried out in this communication, and the establishment of their dependence on one

characteristic—the lattice energy—is also of definite interest for constructing a unified theory of the properties of ionic crystals.

The high electrical properties of crystals with a large lattice energy may find broader practical application.

Modern technology makes it possible to grow large crystals from solutions and melts. The technology has been mastered for producing large single crystals of Rochelle salt and vitriols from solutions. Crystals of alkali-halide salts, as well as MgO, SrO, BaO, Al₂O₃, SiO₂, etc., are grown from the melt.

It is possible to organize industrial production of single crystals. There are successful experiments in producing, by hot pressing in vacuum, ceramic materials of very high homogeneity and with a density approaching that of single crystals.

Taking into account the high dielectric properties of single crystals, it is time to develop an industrial technology for obtaining them and introducing them into practical products as homogeneous dielectrics.

Violation of the regularity of the structure of the crystal lattice of ionic dielectrics of the rock-salt type by monovalent and divalent ions is accompanied by an increase in electrical conductivity, dielectric losses, hardness, mechanical strength, and by a decrease in melting point, electric strength, and plasticity—that is, by a deterioration of the dielectric. It is possible that in lattices of a more complex type, for example rutile, by analogy with metals, the situation will be different.

It is necessary to introduce impurities that would increase the bond between ions, reduce the reserve of free energy, and, for alloys, increase the internal energy and the entropy of the system.

Alloys of ionic dielectrics and their solid solutions can yield insulating materials with good properties.

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Tomsk Polytechnic Institute