ELECTRICAL STRENGTH AND HARDNESS OF SINGLE CRYSTALS OF SOLID SOLUTIONS

A. A. VOROB’EV and A. M. TRUBITSYN

The physical characteristics of crystalline dielectrics are determined by the magnitude of their lattice energy. As a consequence, there must be a relationship between the various characteristics of a substance [1].

With an increase in the lattice energy of crystals of alkali-halide salts, their electrical strength, melting point, and hardness, determined by the scratching method [2], increase.

N. S. Kurnakov and S. F. Zhemchuzhnyi [3] established that, for continuous solid solutions, the dependence of electrical conductivity and of the temperature coefficient of resistance on the chemical composition of the solid solution is expressed by a curve with a minimum. For these cases, the diagrams of the dependence of hardness and of extrusion pressure through an orifice are expressed by curves with a maximum.

Using the drilling method, V. D. Kuznetsov and K. V. Savitskii [4] established that the dependence of the diameter of the cavity on the composition for solid solutions of the KCl—NaCl system has a minimum near 50% KCl, and for KCl—KBr alloys near 60 mol.% KCl. Accordingly, the hardness of the indicated alloys as a function of composition will vary along a curve with a maximum.

A. M. Trubitsyn measured the values of electrical strength under pulses in a uniform field for single crystals of solid-solution systems: NaCl—NaBr, KCl—KBr, and KI—KBr. The electrical strength of single crystals of pure salts and of solid solutions was compared with the value of the microhardness, determined with the aid of a PMT-3 instrument.

To determine hardness under the action of a constant load, a diamond pyramid with an apex angle of 136° and a square base was pressed into the surface of the crystal. The hardness number in kg/mm² was determined as the quotient obtained by dividing the force of indentation of the pyramid by the area of the resulting impression.

For comparison of electrical strength with a mechanical characteristic, it is likewise desirable to have the latter for a small volume.

The small size of the diagonal of the impression (of the order of 60 microns at a load of 20 g) characterizes the mechanical properties of the material in a small volume. The processes leading to breakdown develop in small volumes. The diameter of the breakdown channel was 80—100 microns. Thus, measurement of the properties of the material in these experiments was carried out in comparable volumes.

The change in microhardness near the breakdown site was specially investigated. No changes in the microhardness of the single crystal after the action of high voltage or breakdown were detected.

Fig. 1 presents the dependence of electrical strength and microhardness on lattice energy for the same crystals of pure alkali-halide salts. With increasing lattice energy, and consequently the chemical stability of the compound, their microhardness increases.

This result agrees with that obtained earlier for hardness by the scratching method.

Figures 2, 3, and 4 present the variation of microhardness, electrical strength, and the heat absorbed during the formation of a solid solution, as a function of the composition of the single crystals. The microhardness measurements were carried out on 3–5 broken-down specimens. The microhardness of each specimen was measured at 5–7 points. In the figures, large circles denote the mean values of the microhardness.

Fig. 1. Dependence of electrical strength and microhardness on lattice energy for crystals of alkali-halide salts.

Fig. 2. Dependence of electrical strength \((E_{\mathrm{br}})\), microhardness \((H)\), and the heat absorbed during the formation of a solid solution \((Q)\), on the composition of single crystals of the NaCl—NaBr system.

The variation of the microhardness of single crystals of solid solutions was found to be the same as in the experiments of N. S. Kurnakov and S. F. Zhemchuzhnyi and of V. D. Kuznetsov and K. V. Savitskii for hardness determined by other methods.

Fig. 3. 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 KCl—KBr system.

Fig. 4. 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 KI—KBr system.

In contrast to the results obtained for single crystals of pure salts, for solid solutions with a substituted haloid an increase in microhardness is accompanied by a decrease in their electrical strength.

We earlier related the change in the electrical strength of single crystals of solid solutions to the amount of energy absorbed in the formation of the solid compound, to its chemical stability [5]. The electrical strength and melting temperature for the alloys considered here with a substituted anion change in the same way, decreasing or increasing as the chemical composition changes (Figs. 5, 6, 7). Consequently, with an increase in the chemical stability of the alloys, their melting temperature and electrical strength increase.

Fig. 5. Change in electrical strength \((E_{\mathrm{pr}})\) and melting temperature \((T_{\mathrm{pl}})\) as functions of the chemical composition of single crystals of NaCl—NaBr solid solutions.

Fig. 6. Change in electrical strength \((E_{\mathrm{pr}})\) and melting temperature \((T_{\mathrm{pl}})\) as functions of the chemical composition of single crystals of KCl—KBr solid solutions.

Fig. 7. Change in electrical strength \((E_{\mathrm{pr}})\) and melting temperature \((T_{\mathrm{pl}})\) as functions of the chemical composition of single crystals of KI—KBr solid solutions.

The relationship between the microhardness of single crystals of solid solutions and their electrical strength can, on the basis of alloy theory, be explained as follows.

It is considered that the change in the physical properties of a metal is due to the presence in the crystal lattice of stresses and residual microdistortions. The excess potential energy of atoms displaced from the equilibrium po-

...deposition, representing the latent energy of deformation of the lattice, quantitatively characterizes the degree of imperfection of the crystalline lattice. The properties of a deformed metal are associated with the magnitude of this energy.

It is known from the theory of alloys that the internal stresses arising during the hardening of steel increase its hardness and microhardness. Therefore, with an increase in the concentration of the energy absorbed in the formation of a solid solution, the microhardness of single crystals also increases.

As the magnitude of the absorbed energy increases, the microhardness of single crystals of solid solutions does indeed increase. Thus, the decrease in the electrical strength of single crystals of solid solutions and the simultaneous increase in their microhardness can be explained as a consequence of the degree of distortion of the crystalline lattice and the concentration of internal stresses.

The materials of experimental investigations presented in this article establish a connection between the magnitude of the electrical strength of solid dielectrics and their mechanical characteristic—microhardness—and internal stresses, the magnitude of which is determined by the energy absorbed during the formation of the solid solution.

LITERATURE

1. Fersman A. E. Geochemistry, vol. 3, 1937. Vorob’ev A. A. and Zavadovskaya E. K. Izvestiya TPI, vol. 83, 1955. DAN 81, 375, 1951. ZhFKh XXVIII, 7, 1210—1212, 1954.

2. Vorob’ev A. A. Izvestiya TPI, vol. 83, 1955.

3. Kurnakov N. S. and Zhemchuzhnyi S. F. Collected Selected Works of N. S. Kurnakov, vol. 1, 1938.

4. Kuznetsov V. D. and Savitskii K. V. Trudy SofTI, 5, 175, 1939.

5. Vorob’ev A. A., Zavadovskaya E. K. and Trubitsyn A. M. DAN.

6. Khotkevich V. I., Chaikovskii E. F. and Zashkvara V. V. DAN 96, 483, 1954.