ELECTRICAL STRENGTH OF SOLID SOLUTIONS OF THE NaCl—KCl SYSTEM

M. S. IVANKINA and A. F. GORODETSKII

The influence of impurities on the magnitude of the electrical strength of solid dielectric crystals is treated differently by theories of electrical breakdown in solid dielectrics.

Hippel [1], considering impact ionization by electrons as the principal process leading to breakdown, comes to the conclusion that impurities must increase the electrical strength of dielectrics by disturbing, through the impurities, the regular course of the potential function in the crystal. This latter circumstance increases the probability of electron capture.

Fröhlich’s calculations [2] lead to the conclusion that the electrical strength of solid dielectrics is inversely dependent on the mean free path of electrons. The introduction of impurities leads to a decrease in the mean free path of electrons as a result of their additional scattering by the field of foreign atoms. The result of this is an increase in electrical strength.

Quantum theories of electrical breakdown in solid dielectrics take into account the effect of impurities in changing the energy spectrum of the lattice—namely, in the appearance of allowed energy levels in the forbidden band. As a consequence of the facilitated transition of electrons into the conduction band, a decrease in electrical strength should be expected.

Experiments performed by Hippel [3] with solid solutions KCl—RbCl and KCl—KBr showed that the dependence of the breakdown voltage on composition for the KCl—RbCl system is expressed by a curve with a maximum, while for the KCl—KBr system the curve shows an increase in breakdown voltage up to the region of decomposition of the solid solution. The greatest increase in electrical strength (about 30% in comparison with the pure components) corresponds to approximately equal percentage contents of both components (Figs. 1 and 2).

In the NaCl—AgCl system, Hippel and Lee [4] likewise obtained an increase in electrical strength of almost twofold upon adding up to 15 mol.% AgCl to NaCl (Fig. 3).

However, the results obtained by N. B. Bogdanova [5] for the KJ—NaJ and KBr—KJ systems showed that, in the named systems, the electrical strength of mixed crystals decreases relative to its values for the pure components (Figs. 4 and 5).

This contradiction between Bogdanova’s results and the theoretical conclusions of Fröhlich and Hippel was explained by one of us [6] by the fact that the decrease in electrical strength in the case of the KJ—NaJ and KBr—KJ systems is due to the decomposition of the unstable solid solutions which these systems represent.

In order to test this supposition, an investigation was undertaken of the NaCl—KCl system, which is characterized by low thermodynamic stability, since the formation of solid solutions of this system proceeds with very large absorption of heat [7, 8].

Fig. 1—Dependence of electrical strength on the percentage composition of the components of the KCl–RbCl system (after Hippel).

In addition, it should be noted that there is a considerable difference in the ionic radii of the particles entering into this system \((R_{\mathrm{Cl}} = 1.81\ \text{Å};\ R_{\mathrm{Na}} = 0.98\ \text{Å};\ R_{\mathrm{K}} = 1.33\ \text{Å})\), as well as in the lattice constants \((d_{\mathrm{KCl}} = 3.137\ \text{Å};\ d_{\mathrm{NaCl}} = 2.812\ \text{Å})\).

Fig. 2—Dependence of electrical strength on the percentage composition of the components of the KCl–KBr system (after Hippel).

It could therefore have been expected that there would be an unconditional decrease in electrical strength for crystals of a composition lying in the region of intermediate concentrations, but in the region of low concentrations the authors expected behavior analogous to Fig. 2, for the KCl—KBr system.

Fig. 3—Dependence of electrical strength on the percentage composition of the components of the NaCl—AgCl system (according to Hippel and Lee).

Fig. 4—Dependence of electrical strength on the percentage composition of the components of the KJ—NaJ system (according to N. B. Bogdanova).

For the investigation, single crystals of solid solutions KCl—NaCl of various concentrations were grown from the melt by the Kyropoulos method [9]. In addition, pure single crystals of KCl and NaCl were grown.

Fig. 5—Dependence of electrical strength on the percentage composition of the components of the KJ—KBr system (according to N. B. Bogdanova).

From the single crystals, specimens were prepared with a hemispherical depression, 8–10 mm in diameter, opposite the plane.

By grinding, the specimens were brought to an average thickness of about 200 μm, and then tin electrodes were deposited by evaporation in vacuum.

The experiments were carried out under pulsed voltage in the laboratory of Prof. A. A. Vorob’ev.

Fig. 6—Dependence of the electrical strength and of the difference in heats of dissolution of the mechanical mixture and the solid solution on the percentage composition of the KCl—NaCl system.

The oscillogram of the voltage pulse at the moment of breakdown was photographed. From the form of the oscillograms it was possible to judge the quality of the specimens and to reject defective ones. The experiments were carried out at room temperature. The specimens were broken down in transformer oil.

From the data of Table 1 and Fig. 6 it follows that the dependence of the electrical strength on composition for the KCl—NaCl system is characterized by a curve with a minimum.

Table 1

Using the data of Zhemchuzhnyi and Rambakh [10], as well as of Kurnakov and Zhemchuzhnyi [8] on the energy absorbed in the formation of a solid solution, we plotted in Fig. 6 the dependence of the absorbed energy on composition (dashed line) in the form of a curve with a maximum.

Fig. 7—Dependence of microhardness on the percentage composition of the components of the KCl—NaCl system.

Thus, the relationship established in [6] between the absorbed heat, i.e., the measure of the instability of the system, and the electrical strength is also confirmed in the case under consideration. The decomposition of the solid solution and the structural inhomogeneity arising as a result probably play a significant role in the second stage of the electrical pro—

Fig. 8—Dependence of surface energy on the percentage composition of the components of the KCl—NaCl system (according to P. A. Savintsev and V. V. Kutepalenko).

breakdown, culminating in the disruption of bonds between the particles of the dielectric and, as a consequence, its destruction.

Analogous phenomena also occur in mechanical fracture. Therefore such characteristics as microhardness and surface energy must be related in a definite way to electrical strength.

Measurement of the microhardness of our specimens on the PMT-3 instrument [11] showed (Fig. 7) that the relation between microhardness and composition in the KCl—NaCl system is expressed by a curve with a maximum. The measurements were carried out on specimens that had undergone breakdown. On each specimen, 3–4 measurements were made at different, arbitrarily selected sites. For each point of the curve, 4–5 specimens were taken.

The course of the microhardness—composition curve is analogous to the course of the absorbed heat—composition curve. Thus, in the system studied, the decrease in electrical strength is accompanied by an increase in microhardness.

A study of the relative surface energy of single crystals of the KCl—NaCl system, carried out by P. A. Savintsev and V. V. Kutsepalenko [12], showed that the surface energy of single crystals of solid solutions decreases with increasing percentage content of the second component (Fig. 8). The authors explain this effect by a weakening of the bonds in the crystal lattice.

It should be supposed that in this case as well the instability of the system and its tendency toward spontaneous decomposition make themselves felt.

Conclusions

1. The electrical strength of single crystals of solid solutions of alkali-halide salts decreases with increasing heat absorbed in the formation of the system, i.e., with decreasing stability of the system.

2. The mechanical characteristics (microhardness and surface energy) are in a regular relationship with the electrical strength.

The authors thank A. A. Vorob’ev for useful discussions and A. M. Trubitsyn for assistance in the breakdown of specimens on his apparatus.

Literature

1. Hippel A. v. J. Appl. Phys. 8, 815, 1937.

2. Fröhlich, H. Proc. Roy. Soc. Av. 172, 94, 1939.

3. Hippel A. v. ZS. f. Physik, 88, 358, 1934.

4. Hippel A. v. and G. M. Lee—Phys. Rev. 59, 824, 1941.

5. Bogdanova N. B. ZhETF. 14, 30, 1944.

6. Gorodetskii A. F. Izvestiya TPI, vol. 71, 21, 1952.

7. Kurnakov N. S. Collected Selected Works, vol. I, p. 369, 1938.

8. Kurnakov N. S. and Zhemchuzhnyi S. F. Isomorphism of potassium and sodium compounds. Kurnakov, Collected Selected Works, vol. I, p. 186, 1938.

9. Kublitskii A. M. and Toporets A. S. Artificial Single Crystals. Publishing House of the Academy of Sciences of the USSR, 1935.

10. Zhemchuzhnyi S. F. and Rambakh F. Izvestiya SPbPI, 12, 349, 1909.

11. Khrushchev M. M. and Berkovich E. S. PMT-2 and PMT-3 instruments for microhardness testing. Publishing House of the Academy of Sciences of the USSR, 1950.

12. Savintsev P. A. and Kutsepalenko V. V. Proceedings of SFTI, issue 4, 1955.

Tomsk Polytechnic Institute.