ON THE ELECTRICAL STRENGTH OF SOLID SOLUTIONS

A. F. Gorodetskii

Existing theories of the electrical breakdown of solid dielectrics take different account of the influence of impurities in a dielectric crystal.

Thus, Hippel [1] considers impact ionization by electrons to be the basic process leading to breakdown, and comes to the conclusion that impurities should increase the electrical strength of a dielectric by disturbing the regular course of the potential function in the crystal. Distortions of the potential barriers increase the probability of electron capture.

Fröhlich [2] calculates the field strength from the condition that the electron must receive from the field more energy than it gives up to the crystal lattice in the form of heat. The final expression obtained by Fröhlich is connected with the electron mean free path in the lattice in such a way that the electrical strength should increase as the mean free path decreases. Consequently, the less ordered the structure, the greater the electrical strength should be.

Experiments carried out by Hippel [3] with solid solutions

\[ \mathrm{KCl}—\mathrm{RbCl}\ \text{and}\ \mathrm{KCl}—\mathrm{KBr} \]

showed that, in the course of the dependence of electrical strength on composition, there is a maximum for the \(\mathrm{KCl}—\mathrm{RbCl}\) system and an increase in strength up to the boundaries of the decomposition region of the solid solution for the \(\mathrm{KCl}—\mathrm{KBr}\) system.

At the same time, the greatest increase in electrical strength (about 30%) corresponds to approximately equal amounts of both components (Figs. 1, 2, solid curves).

These experimental results could be interpreted both within Hippel’s theory and within Fröhlich’s theory.

Further study of the dependence of electrical strength on composition in solid solutions was carried out by Hippel and Lee [4] for the \(\mathrm{NaCl}—\mathrm{AgCl}\) system, and also by Bogdanova [5] for the \(\mathrm{KI}—\mathrm{NaI}\) and \(\mathrm{KI}—\mathrm{KBr}\) systems.

Hippel showed that the introduction of up to 15 mol.% \(\mathrm{AgCl}\) into \(\mathrm{NaCl}\) doubles the electrical strength.

However, the results obtained by Bogdanova showed that impurities can also lower the electrical strength. Thus, in the case of the \(\mathrm{KI}—\mathrm{NaI}\) system, the addition to pure \(\mathrm{KI}\) of impurities up to 40 mol.% \(\mathrm{NaI}\) leads to a decrease in the electrical strength of the mixed crystals, in comparison with pure \(\mathrm{KI}\), by approximately a factor of two. For the \(\mathrm{KI}—\mathrm{KBr}\) system, a decrease in electrical strength was observed from its value for pure \(\mathrm{KI}\) to a minimum at the composition 50 mol.% \(\mathrm{KI} + 50\) mol.% \(\mathrm{KBr}\), and then an increase to the value of the electrical strength of pure \(\mathrm{KBr}\) (Figs. 3, 4, solid lines).

Bogdanova’s results thus contradicted the predictions of the theories of Hippel and Fröhlich.

Bogdanova’s attempt to relate the electrical strength of solid solutions to the melting temperature, in our opinion, also did not lead to positive results. It was not possible to construct a single regular relationship [6].

Fig. 1

Fig. 2

Fig. 3.
Labels visible in the graph: \(E,\ \mathrm{kV/cm}\); \(\mathrm{kV}\); \(\mathrm{mol}\%\); \(\mathrm{NaJ}\); \(\mathrm{calories/mole}\).

Fig. 4.
Labels visible in the graph: \(E,\ \mathrm{kV/cm}\); \(\mathrm{kV}\); \(\mathrm{mol}\%\); \(\mathrm{KJ}\); \(\mathrm{KBr}\); \(\mathrm{calories/mole}\).

Analysis of these results, as well as the data available to us on the relatively low thermodynamic stability of solid solutions of alkali-halide salts [7, 8, 9], indicated the advisability of comparing the data on the electrical strength of solid solutions with their thermodynamic stability.

Using the data of Zhemchuzhnyi and Rambach [8], and also of Kurnakov and Zhemchuzhnyi [9], on the energy absorbed in the formation of solid solutions, we plotted these values on the diagrams of electrical strength—composition (Figs. 1–4, dotted curves).

As is readily seen, the dependence obtained is quite unambiguous: systems characterized by a decrease in electrical strength, KI—NaI, KI—KBr, absorbed a relatively large amount of energy. At the same time, for one and the same system, an increase in the energy absorbed during its formation corresponds to a decrease in electrical strength.

In the case of the KCl—KBr system there is an analogous dependence, in essence, for the composition corresponding to the region of decomposition of the solid solutions.

It is characteristic that at room temperature, after 2.5 months, a solid solution of 50 mol.% KI in the KI—NaI system decomposes by approximately \(2/3\); a solid solution of 50 mol.% KI in the KI—KBr system decomposes by approximately \(1/2\); a solid solution of 50 mol.% KCl in the KCl—KBr system decomposed by \(2/3\) at room temperature 1.5 months after its formation.

At the same time, in the case of the KCl—RbCl solid solution, under the same conditions no traces of decomposition were found.

The results presented make it possible to suggest that, in the case of the systems KI—NaI, KI—KBr and partly KCl—KBr, the process of decomposition of the solid solution leads to the lowering of electrical strength observed experimentally. In this case the strengthening effect associated with the conclusions of the theories of Hipped and Fröhlich is masked.

Conversely, in the KCl—RbCl system, where the phenomenon of decomposition practically does not occur, the effect of strengthening by impurities plays the principal role.

Thus, owing to the diffusion character of the process of decomposition of solid solutions [10], in studying electrical strength it is necessary to take diffusion phenomena in the systems into account.

The accumulation of additional experimental data, begun in our laboratory, will probably make it possible to draw further conclusions.

I take this opportunity to express my gratitude to Professor Doctor A. A. Vorob’ev for interesting discussions on the questions touched upon.

REFERENCES

1. A. v. Hippel, I. Appl. Phys., 8, 815, 1937.
2. H. Frölisсh, Proc. Roy. Soc., (A) 160, 230, 1937.
3. A. v. Hippel, Zs. f. Physik, 88, 358, 1934.
4. A. v. Hippel and G. M. Lee, Phys. Rev., 59, 824, 1941.
5. N. B. Bogdanova, ZhETF, 14, 30, 1944.
6. A. A. Vorob’ev. Bulletin of the Tomsk Polytechnic Institute, 63, 3, 1944.
7. V. A. Anosov and S. A. Pogodin. Fundamentals of Physicochemical Analysis, Publishing House of the Academy of Sciences of the USSR, 1947.
8. S. F. Zhemchuzhnyi and F. Rambach. Bulletin of the St. Petersburg Polytechnic Institute, 12, 349, 1909.
9. N. S. Kurnakov and S. F. Zhemchuzhnyi. Collected Selected Works of N. S. Kurnakov, vol. 1, p. 186, 1938.
10. Ya. S. Umanskii, B. N. Finkel’shtein, M. E. Blanter. Physical Foundations of Metallurgy, 1949.