ON THE RELATIONSHIP BETWEEN CERTAIN PROPERTIES OF SINGLE CRYSTALS OF SOLID SOLUTIONS OF ALKALI-HALIDE SALTS WITH A SUBSTITUTED HALIDE

A. A. VOROB'EV and A. M. TRUBITSYN

Investigations in recent years have established the existence of a relationship between electrical strength and a number of physicochemical characteristics of a substance and its chemical composition.

A. A. Vorob'ev [1] showed that the electrical strength of single crystals of alkali-halide salts increases with increasing crystal-lattice energy. This proposition is confirmed by the results of our experiments (Fig. 1). The maximum and average values of the impulse electrical strength of single crystals of KJ, KBr, KCl, NaBr, and NaCl increase regularly with increasing crystal-lattice energy. Owing to the absence of reliable data concerning the change in crystal-lattice energy with change in the chemical composition of solid solutions of alkali-halide salts, it is not possible to compare directly the values of electrical strength and lattice energy of these solid solutions.

One of the quantities connected with the energy of the crystal lattice is the heat of formation of a compound. If, in forming a solid, a considerable amount of energy must be expended, i.e., the process of formation proceeds with absorption of heat, then the stability of the chemical compound will be small and the interrelations of the particles may be destroyed by the action of relatively small external forces. Compounds of this type spontaneously decompose with time, as was demonstrated by the school of Academician N. S. Kurnakov [2]. If, however, heat is evolved in the formation of a solid, then the more heat is evolved during formation, the more energy will be required for its destruction.

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

According to the data of E. K. Zavadovskaya [3], for single crystals of pure alkali-halide salts, with the alkali metal unchanged and the halide substituted, the electrical strength increases with increasing heat evolved in the formation of the solid compound. We made use of the works of N. S. Kurnakov, S. F. Zhemchuzhnyi, and others [2, 4, 5] and compared

the results of our measurements of the impulse electric strength of solid solutions with the difference between the heats of solution in water of a mechanical mixture and of a solid solution of the same weight and composition (the quantity \(Q\)). Since the formation of these solid solutions occurs with the absorption of a certain excess amount of heat in comparison with the mechanical mixture, the quantity \(Q\) is a measure of the instability of the solid solution.

Fig. 2. Dependence of the electric strength \((E_{\mathrm{pr}})\), microhardness \((H)\), and the heat absorbed in the formation of the solid solution \((Q)\) on the composition of single crystals. System NaCl—NaBr.

Fig. 3. Dependence of the electric strength \((E_{\mathrm{pr}})\), microhardness \((H)\), and the heat absorbed in the formation of the solid solution \((Q)\) on the composition of single crystals. System KCl—KBr.

It may be expected that the character of the change in electric strength as a function of the composition of the solid solution will be inverse to the change in the quantity \(Q\) with composition. The graphs presented in Figs. 2, 3, and 4 show that the considerations expressed are in good agreement with the experimental data. An analogous relation between electric strength and the quantity \(Q\) was established by A. F. Gorodetskii [6], using data of other authors for the systems KCl—RbCl, KI—KBr, and KI—NaI. In all cases, an increase in the quantity \(Q\) corresponds to a decrease in the electric strength of the solid solutions and, conversely, an increase in the electric strength of the solid solutions coincides with a decrease in the quantity \(Q\).

It should also be noted that, for the systems of solid solutions investigated by us, the courses of the dependences of electric strength and melting temperature on chemical composition coincide. As an illustration, Fig. 5 gives graphs of the indicated dependences for the KCl—KBr system. Thus, with a decrease in the stability of solid solutions of alkali-halide salts, as also with a decrease in the stability of pure salts, a lowering of electric strength is observed.

Another quantity connected with the energy of the crystal lattice is the surface energy of the crystal. The physical meaning and methods of determining the surface energy of crystals have been considered in detail in the works of V. D. Kuznetsov [7, 8]. V. V. Efremov and P. A. Savintsev [9], using different measurement methods, obtained a decrease in surface energy with an increase in the amount of impurity salt in the systems of solid solutions KCl—NaCl and came to the conclusion that:

1) with an increase in impurity content, the dispersion energy of the crystal decreases, which is evidently connected with a weakening of the interaction forces in the lattice;

2) since the surface energy characterizes the measure of the strength of a crystal, one should expect a decrease in the strength of the crystal with an increase in the amount of impurities.

Fig. 4. Dependence of the electrical strength \((E_{\mathrm{pr}})\), microhardness \((H)\), and heat released during formation of a solid solution \((Q)\), on the composition of single crystals. System KJ—KBr.

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

Subsequent studies by P. A. Savintsev and V. V. Kuchepalenko [10] showed that the dependence of the surface energy on the composition of single crystals of the KCl—KBr system is expressed by a curve with a minimum (Fig. 6).

Fig. 6. Dependence of the electrical strength and surface energy on composition for single crystals of the KCl—KBr system.

The change in electrical strength [11] and surface energy with composition of the solid solutions of this system has the same character. The increase in brittleness during the formation of solid solutions of other systems was clearly demonstrated by N. S. Kurnakov and S. F. Zhemchuzhnyi [2] and was qualitatively observed in our experiments. This gives grounds

one may suppose that in the other systems we investigated the dependence of the surface energy on composition will also be determined by a curve with a minimum. Consequently, the changes in electrical strength and in surface energy as functions of the composition of the solid solutions must coincide.

We measured, with a PMT-3 instrument, the microhardness of single crystals of NaCl, NaBr, KCl, KBr, KI, and some of their solid solutions. The choice of the PMT-3 instrument was determined by the following considerations. The processes leading to electrical breakdown develop in microvolumes of the crystals. It is practically impossible to obtain a perfectly homogeneous crystal. Therefore it is desirable that the measurements whose results are compared with electrical strength be made on the smallest possible volumes of the crystals. When measuring microhardness with the PMT-3 instrument, the diagonal of the indentation on KCl single crystals did not exceed 57 microns. The diameter of the breakdown channel in these crystals reached 80–100 microns. Thus the measurements were made on comparable volumes.

Experiments showed that the microhardness values measured before and after breakdown of the specimen coincide. The microhardness values we give were measured near the breakdown channel after the electrical tests.

A. A. Vorob’ev [12] showed that, with increasing lattice energy of alkali-halide crystals, the electrical strength and the hardness determined on the Mohs scale increase linearly. This proposition is confirmed by the results of our measurements (Fig. 1). The increase in electrical strength coincides with the increase in microhardness. A comparison of the electrical strength and microhardness measured by us for single crystals of the systems NaCl—NaBr (Fig. 2), KCl—KBr (Fig. 3), and KI—KBr (Fig. 4) shows that, for these solid solutions, another relation is observed: a decrease in electrical strength coincides with an increase in microhardness.

To explain this phenomenon, one may probably make use of the known principles of the theory of hardening metallic alloys. The increase in hardness upon quenching of steel is due to the appearance of internal stresses in the steel, which are connected with the latent energy absorbed during formation of the compound. With an increase in this energy, the hardness of the compound must increase, as is observed for the systems investigated by us (Figs. 2, 3, and 4). Consequently, the increase in the microhardness of single crystals of solid solutions is caused by internal stresses arising because of deformation of the lattice by impurities. The increase in the latent energy absorbed during formation of the compound leads to a decrease in the binding energy of the particles. The consequence of this, as indicated above, must be a lowering of the electrical strength.

On the basis of the foregoing, we arrived at the following conclusion:

1. The electrical strength of single crystals of solid solutions of alkali-halide salts decreases with increasing energy absorbed during formation of the solid solution, i.e., with decreasing stability of the latter.

2. The character of the dependence of electrical strength and surface energy on the composition of single crystals of solid solutions of alkali-halide salts with a substituted halide is the same and is expressed by a curve with a minimum at intermediate molecular-percent contents.

3. In contrast to single crystals of alkali-halide salts, for which the electrical strength increases with increasing microhardness, in single crystals of solid solutions with a substituted halide there is a decrease in electrical strength with increasing microhardness.

References

1. Vorob'ev A. A. DAN SSSR, vol. 27, 934, 1940.
2. Collected Selected Works of N. S. Kurnakov, vol. 1, ONTI, 1938.
3. Zavadovskaya E. K. Dissertation, Tomsk, 1954.
4. Zhemchuzhnyi S. F. and Rombakh F., Izvestiya SPB PI, 12, 349, 1909.
5. M. A. Fineman and W. E. Wallace, J. Amer. Chem. Soc. 70, 4165, 1948.
6. Gorodetskii A. F. Izvestiya TPI, vol. 71, 21, 1952.
7. Kuznetsov V. D. Physics of the Solid State, vol. 1, Tomsk, 1937.
8. Kuznetsov V. D. Surface Energy of Solids, 1954.
9. Efremova V. V. and Savintsev P. A. Work report, Tomsk Polytechnic Institute, 1952.
10. Savintsev P. A., Kutsevalenko V. V. Proceedings of SFTI, issue 34, 1955.
11. Trubitsyn A. M. Dissertation, Tomsk, 1955.
12. Vorob'ev A. A. Izvestiya TPI, vol. 83, pp. 27–29, 1956.

Tomsk Polytechnic
Institute