ELECTRICAL STRENGTH OF CRYSTALS, THEIR MECHANICAL AND THERMAL STABILITY, AND LATTICE ENERGY

A. A. VOROB’EV

The bonds between the particles of a solid dielectric can be broken by electrical breakdown, mechanical fracture, or melting. The various processes of destruction of a solid dielectric have, in their final stage, a common nature, namely: the breaking of the bonds between the particles composing it. Consequently, one should expect an interrelation between the quantities that characterize melting, mechanical fracture, and electrical breakdown.

The investigations of Academician A. E. Fersman, A. F. Kapustinskii, and others [1] have shown that many properties of materials are regularly related to the lattice energy, its type, and its geometrical features. It must be assumed that the electrical properties of materials should not be an exception to this rule. If the type of lattice and its geometrical features are excluded from consideration by taking a lattice of a single type, then the properties of the material will be unambiguously related to the energy of the crystal lattice.

Fig. 1. Dependence of Mohs hardness \(H\), electrical strength \(E_{\mathrm{pr}}\), and melting temperature \(t^\circ_{\mathrm{pl}}\) C on the lattice energy of crystals of alkali-halide compounds

Figure 1 shows the dependence of the electrical strength, Mohs hardness, and melting temperature on the magnitude of the lattice energy for crystals of alkali-halide salts.

Electrical strength, hardness as determined on the Mohs scale, and the melting temperature of crystals increase with increasing lattice energy and, consequently, with the stability of compounds. As a result, a simple relation is obtained between the magnitude of electrical strength and hardness. With an increase in the mechanical stability of a crystal, characterized by the magnitude of its hardness, its electrical strength also increases. With an increase in the melting temperature of compounds, their electrical strength also increases.

Fig. 2. Dependence of Mohs hardness and melting temperature on lattice energy for oxides crystallizing in a rock-salt-type lattice.

Figure 2 shows the dependence of Mohs hardness and melting temperature on lattice energy for oxides of metals of the second group of the Mendeleev table, crystallizing in a rock-salt-type lattice. With increasing lattice energy, the thermal stability and hardness of the crystal increase.

The investigations of V. D. Kuznetsov and M. A. Bolshanina [2] showed that the laws governing the change in the resistance of materials to various kinds of deformation under the action of various factors are common to different kinds of deformation. Therefore it should be considered that the resistance of crystals to any kind of mechanical destruction will increase with increasing energy of the crystal lattice. Consequently, the increase in Mohs hardness of the crystals gypsum, rock salt, calcite, fluorite, and quartz corresponds to an increase in their electrical strength and lattice energy in the same order. With increasing hardness in this series of crystals, the dielectric losses will decrease.

The magnitude of hardness is a relative measure of the electrical strength of ionic crystals. In this case we approach the problem of nondestructive testing of materials. Without testing the material for breakdown, its electrical strength can be measured by determining its hardness. Such a measurement is carried out without destroying the specimen. The electrical strength is then determined from the corresponding conversion tables.

Figure 3 shows the dependence of electrical strength and of the compression coefficient on lattice energy. The largest compression coefficient is possessed by compounds with lower lattice energy, greater polarizability, and the smallest concentration of ions per unit volume. Crystals possessing the largest compression coefficient have the lowest electrical strength.

Academician N. S. Kurnakov and his school showed that the mechanical properties and characteristics of alloys (for example, the pressure of flow of a material through an orifice, hardness, and other mechanical characteristics) depend on composition and are sensitive to physicochemical transformations of the substance.

Corresponding Member of the Academy of Sciences of the USSR V. D. Kuznetsov and K. V. Savitskii [6] studied the drilling method for investigating alloys. The drilling method gives relative values of surface energy, connected with lattice energy. They showed that the diameter of the drilled recess changes regularly with a change in the composition of the alloy and in dependence on the melting diagram—

Thus, for a mechanical mixture of two components, the diameter of the pit changes additively with composition. If, upon fusion of two components, a continuous series of solid solutions is formed, then the diameter of the pit changes along a curve corresponding to the melting diagram.

Fig. 3. Dependence of the compressibility coefficient H and the electrical strength \(E_{\mathrm{pr}}\) on the lattice energy for crystals of alkali-halide salts according to Moos.

Studies by Hippel, N. B. Bogdanova, and others have shown that the electrical strength of crystals of alkali-halide salts varies regularly with their composition. The dependence of the mechanical properties of alloys and of the electrical strength of mixed crystals on composition is probably the result of a change in lattice energy with the composition of the compound.

The connection between the electrical strength and the thermal and mechanical stability of ionic crystals appears to be a particular case of the existence of an interrelation among the physical properties of dielectrics, determined by the magnitude of the lattice energy. The connection between the various physical characteristics of a dielectric and the lattice energy, established experimentally, must be taken into account in constructing a general theory of dielectrics.

REFERENCES

1. A. F. Kapustinskii, ZhOKh, 13, 497—503, 1943. S. A. Barzhov, ZhOKh, 19, 991—494, 1949. Acad. A. E. Fersman, Geochemistry, vol. 3, ONTI, 1937.

2. V. D. Kuznetsov, Physics of the Solid Body, vol. 2, p. 732. Tomsk, 1941. A. A. Vorob’ev and E. K. Zavadovskaya, DAN, 81, 3, 375—377, 1951.

3. A. A. Vorob’ev and K. A. Vodop’yanov, DAN, 94, 3, 429—432, 1954.

4. N. S. Kurnakov and I. V. Vrzhesnevskii, ZhRFKhO, Chemical Section, 43, 1932—1936, 1911.

5. N. S. Kurnakov and S. F. Zhemchuzhnyi, ZhRFKhO, Chemical Section, 38, 49—53, 1906.

6. V. I. Kuznetsov and K. V. Savitskii, Transactions of the Siberian Physicotechnical Institute, 5, 175—194, 1939.