RELATIONSHIP BETWEEN THE ELECTRIC STRENGTH OF SINGLE CRYSTALS OF SOLID SOLUTIONS OF ALKALI-HALIDE SALTS AND CERTAIN PHYSICOCHEMICAL PROPERTIES

A. N. KISLINA

Introduction

Real dielectrics, as is known, are either complex chemical compounds, or solid solutions of two or several components, or heterogeneous mixtures.

According to Chappel’s data [1], the dependence of the electric strength under constant voltage on the chemical composition of single crystals of solid solutions of the systems KCl—KBr and KCl—RbCl has the form of curves with maxima. The maxima correspond to approximately the same molecular content of the components in the solid solution. The noted results are in agreement with the theories of Hippel [2] and Fröhlich [3] on the influence of impurities on the electric strength of crystals. Further study of the dependence of electric strength on the chemical composition of solid solutions was carried out under constant voltage by Hippel and Li [4] for the system NaCl—AgCl, by N. B. Bogdanova [5] for the systems KJ—NaJ and KJ—KBr, and under impulse voltage by A. M. Trubitsyn for the systems KCl—KBr, KJ—KBr, NaCl—NaBr. Hippel found that, when up to 15 mol % AgCl was introduced into NaCl, the electric strength of the mixed crystals increased by approximately a factor of two. The results of N. B. Bogdanova and A. M. Trubitsyn show that, when impurities are introduced into a pure crystal, the electric strength, as a rule, decreases, and in the course of the dependence of electric strength on the chemical composition of the solid solutions there is a minimum corresponding to approximately the same molecular composition of both components. Thus, the results of N. B. Bogdanova and A. M. Trubitsyn differ substantially from Hippel’s results.

A. M. Trubitsyn determined the electric strength on a single impulse with a short front. In such tests, secondary phenomena in dielectrics caused by the prolonged action of the voltage were eliminated, or their influence was considerably weakened. Since the available experimental data are contradictory, and data obtained by a more refined method were obtained by A. M. Trubitsyn only for three systems of solid solutions with a substituted halide, we set as the aim of our work to determine certain physicochemical properties of solid solutions of alkali-halide salts with a substituted halide and to use the literature data in order to compare the electric strength with other physicochemical properties of the solid solutions.

X-ray Study of the Structure of Solid Solutions and Measurement of the Lattice Constant

All measurements were carried out on single crystals of solid solutions grown by the Kyropoulos method in a porcelain crucible from a melt of a mixture of analytically pure salts. The difficulty in growing single crystals of solid solutions was that these crystals have large internal stresses. To partially relieve these stresses, the grown crystals were cooled to room temperature over approximately 24 hours.

In determining the structure of systems consisting of more than one component, the following cases may occur:

1) chemical compounds of the components;
2) eutectic mixtures of the components; and
3) solid solutions.

X-ray studies of the structure make it possible to distinguish these three cases. On the basis of X-ray studies, Vegard [7] concluded that the lattice constant of solid solutions changes approximately according to a linear law with change in chemical composition. In his works [8, 9] concerning the physical properties of solid solutions, N. N. Sirota shows that the lattice parameters of binary systems will deviate from the additivity rule, and the more so the greater their heat of formation. Pines [10] draws attention to

Fig. 1. Change in the lattice constant of single crystals of solid solutions of the KCl—KBr system as a function of chemical composition.

a significant deviation of the lattice constant for certain systems of solid solutions from Vegard’s law. Thus, for example, Zaks showed that in the Au—Ag system, where there is a continuous series of solid solutions, the lattice constant changes not according to Vegard’s law, but along a curve with an inflection point.

We carried out an X-ray study of single crystals of solid solutions of the systems KCl—KBr, KBr—NaBr, and KJ—NaJ, which have a face-centered cubic lattice. X-ray photographs were taken in a Debye camera, on polycrystalline cylindrical specimens prepared by grinding single crystals into powder and filling a celluloid pouch with the powder. From 10 to 15 symmetric lines appeared on the X-ray photograph. The X-ray photographs were measured using a transparent celluloid ruler with a division value of 0.5 mm. The lattice constant was calculated as the mean value from measurements of all lines of the X-ray photograph, with allowance for the error due to the thickness of the specimen. Figures 1, 2, and 3 show the dependences obtained by us of the lattice constant of solid solutions KCl—KBr, KBr—NaBr, and KJ—NaJ on chemical composition. The change in the lattice constants for all three systems does not correspond to the law

Vegard. For the systems KJ—NaJ and KBr—NaBr, the deviation from Vegard’s law is observed both in the direction of an increase and in the direction of a decrease of the lattice constants—curves with an inflection point. For the KCl—KBr system this deviation from Vegard’s additivity law occurs in the direction of decreasing lattice constants. It must be noted, however, that the X-ray patterns were not always taken from fresh specimens. At this stage of our investigations, due attention was not paid to questions of aging. It is possible that such facts as the presence, in X-ray patterns of specimens of composition

Fig. 2. Change in the lattice constant of single crystals of solid solutions of the KBr—NaBr system as a function of chemical composition.

40 mol% KBr + 60 mol% NaBr, 40 mol% KJ + 60 mol% NaJ, and 20 mol% KJ + 80 mol% NaJ, of lines characteristic of the individual components, are explained by the phenomenon of aging and decomposition of solid solutions. The decomposition of supersaturated solid solutions was checked by us on a single crystal of KBr—NaBr of composition 50/50 mol%. For a specimen made from a freshly grown crystal, the lines of the X-ray pattern corresponded to the solid solution, whereas for a specimen made from a crystal after a month’s storage in dried transformer oil, the lines of the X-ray pattern corresponded to the lines of the components KBr and NaBr. The latter is in agreement with the work of A. Tobolsky [1], who notes, on the basis of an X-ray study, that the indicated systems have complete solubility at the melting temperature, while at a temperature of 15°C the solid solutions of these systems have complete solubility only for small impurity concentrations. At intermediate concentrations the solid solutions are supersaturated and decompose with time (the presence of 2 phases is noted).

Fig. 3. Change in the lattice constant of single crystals of solid solutions of the KJ—NaJ system as a function of chemical composition.

Determination of Electric Strength

The electric strength of single crystals of solid solutions was tested on plates approximately \(25 \times 25 \times 7\) mm in size, in which a spherical recess 10 mm in diameter was drilled. The recess was polished with a wooden ball wrapped in slightly damp cotton wool. The lower flat surface of the specimen was polished on moistened cloth. The thicknesses of the specimens at the thinnest point were brought to \(100 \div 200\) microns. Thickness was measured on a vertical optical length gauge “IZV-1” with an accuracy of up to 1 micron.

From each crystal, 40 to 50 specimens were broken out, but only 15–30 specimens were tested; the rest were rejected during preparation (appearance of cracks during drilling and measurement). The spherical recess and the lower plane of the specimen were coated with tin evaporated in vacuum.

Fig. 4. Change in impulse electric strength of single crystals of solid solutions of the KBr—NaBr system as a function of chemical composition.

Breakdown of the specimens was carried out in transformer oil on the straight-line portion of the front of a single high-voltage impulse with a front duration of about 5 μsec. An electronic impulse oscilloscope with an accelerating voltage up to 21 kV was used to record the breakdown voltages. We measured the electric strength of single crystals of solid solutions of the systems: KBr—NaBr, KJ—NaJ, and partly KCl—RbCl. A particular difficulty in measuring electric strength arose when working with KBr—NaBr crystals with a high NaBr content, since on the surface of these crystals in air a hard enamel-like layer forms. The electric strength of such specimens is found to be overestimated. To avoid this, the specimens were treated and stored until breakdown in dried transformer oil. For all three systems the electric strength changes with change in chemical composition (Figs. 4, 5, 6). In this case, the curves drawn through the maximum values of electric strength and through the points corresponding to the arithmetic mean values run approximately parallel to one another. For the KJ—NaJ system the curve of the change in electric strength with composition

decreases with increasing NaJ concentration up to 40 mol% in KJ, and then begins to increase.

An analogous decrease in electric strength was obtained by N. B. Bogdanova under constant voltage when NaJ was introduced into KJ up to 40% NaJ. However, for the pure NaJ crystal the electric strength in our experiments proved to be lower than the strength of the single crystal of the solid solution of composition 80 mol% NaJ and 20 mol% KJ. These crystals were insufficiently transparent and cleaved poorly along the cleavage planes.

Fig. 5. Change in the impulse electric strength of single crystals of solid solutions of the KJ—NaJ system as a function of chemical composition.

For the KBr—NaBr system, the electric-strength curve likewise passes through a minimum corresponding to the equimolecular composition. But for small concentrations of the dissolved substance, especially if

Fig. 6. Change in the impulse electric strength of single crystals of solid solutions of the KCl—RbCl system as a function of chemical composition.

the solvent is NaBr, there is also an increase in electric strength in comparison with the pure crystal. The latter is more noticeable at the maximum values of electric strength than at the arithmetic mean-

...typical. A similar increase in electric strength was observed by A. M. Trubitsyn for small admixtures in the KJ—KBr system (up to 10 mol% KBr in KJ).

For the KCl—RbCl system, electric strength was measured only on single crystals of composition 50 mol% KCl—50 mol% RbCl and 60 mol% KCl—40 mol% RbCl. Moreover, for the indicated solid solutions the electric strength proved to be considerably higher than for pure KCl. It may be expected that the plot of electric strength as a function of composition for this system will pass through a maximum, analogously to the plot obtained for this system by Hippel at constant voltage.

Determination of microhardness

Microhardness was determined with a PMT-3 instrument. Under the action of a constant load, a diamond pyramid with an apex angle of 136°8′ and a square base was pressed into the surface of the specimen. The hardness number in kg/mm² was determined as the quotient obtained by dividing the force pressing in the pyramid by the area of the resulting impression. The diagonal of the impression under a load of 20 g was of the order of 60–80 microns.

Fig. 7. Change in microhardness, heat of formation, and electric strength of single crystals of solid solutions of the KJ—NaJ system as a function of chemical composition. (The heat-of-formation curve is plotted from literature data).

Microhardness was measured for 3–5 specimens taken from a single crystal on which the lattice constant and electric strength were determined. On each specimen, 5 measurements were made at different places and the mean value of the microhardness was determined. The mean values were plotted on graphs of the dependence of microhardness on chemical composition for solid solutions of the KJ—NaJ system (Fig. 7) and partly for the KCl—RbCl system (Fig. 8). The microhardness for intermediate concentrations of solid solutions of the KJ—NaJ systems could not be measured, since crystals of intermediate concentrations disintegrate very rapidly. The change in microhardness of single crystals of solid solutions of the above-mentioned systems with change in chemical composition was found to be the same as in the experiments of N. S. Kurnakov and S. F. Zhemchuzhnyi [12] and V. D. Kuznetsov and K. V. Savitskii [13] for

hardness determined by other methods and for other systems, and also that determined by A. M. Trubitsyn [6] by an analogous method for the systems KCl—KBr, KJ—KBr, and NaCl—NaBr.

Fig. 8. Change in microhardness, heat of formation, and electric strength of single crystals of solid solutions of the KCl—RbCl system as a function of chemical composition. (The heat-of-formation curve was constructed from literature data.)

Relationship of the electric strength of single crystals of solid solutions to melting point, heat of formation, and surface energy

Figures 9, 10, and 11 show the dependences of the melting point or the temperature of the onset of crystallization and the electric strength on the chemical composition of solid solutions of the systems KBr—NaBr, KJ—NaJ, and KCl—RbCl.

For the systems KBr—NaBr and KJ—NaJ, the temperatures of the onset of crystallization were taken from the data of N. S. Kurnakov and S. F. Zhemchuzhny [12], and for the KCl—RbCl system the melting points were taken from the data of S. F. Zhemchuzhny and F. Rambach [14].

It is evident from the graphs that, for solid solutions of the KJ—NaJ and KBr—NaBr systems, the melting-point curves have the same trend as the electric-strength curves. The minimum value of the melting point of the solid solutions corresponds approximately to the minimum value of the electric strength. For solid solutions of the KCl—RbCl system, no such analogy is observed in the variation of melting point and electric strength with chemical composition. Consequently, it is not yet possible to draw an unambiguous conclusion about the relationship between the electric strength and the melting point of solid solutions.

N. S. Kurnakov and his collaborators established that the physicochemical properties of solid solutions depend on the heat absorbed during their formation [12]. As the heat of formation of a solid solution they took the difference between the heats absorbed upon dissolution in water of a mechanical mixture of salts and of a solid solution of the same composition. The heat of formation characterizes the internal energy of the system. The smaller the internal energy, the more stable the system. For most solid solutions,

for those possessing complete solubility, the heat of formation changes with change in chemical composition according to a parabolic law [17]. The maximum value of the heat of formation corresponds approximately to the equimolar solid solution.

Fig. 9. Change in the temperature of the onset of crystallization and in the electric strength of single crystals of solid solutions of the KBr—NaBr system as a function of chemical composition. (The curve of the temperature of the onset of crystallization was taken from literature data.)

For solid solutions of the systems investigated by us with respect to electric strength, the heat of formation was determined by S. Zhemchuzhnyi and F. Rambach [14]. For the KBr—NaBr and KJ—NaJ systems, the heat of formation changes

Fig. 10. Change in the temperature of the onset of crystallization and in the electric strength of single crystals of solid solutions of the KJ—NaJ system as a function of chemical composition. (The curve of the temperature of the onset of crystallization was taken from literature data.)

along a curve with a maximum, and for the KCl—RbCl system—along a curve with a minimum (Figs. 12, 7, 8). The pulsed electric strength of solid solu-

solutions (Figs. 12, 7, 8) formed with absorption of heat, the greater the less heat was expended on the formation of the solid solution. Such a conclusion was made earlier by A. A. Vorob’ev, E. K. Zavadovskaya, and A. M. Trubitsyn when comparing the electric strength of single crystals of solid solutions of alkali-halide salts with a substituted halide.

Fig. 11. Change in the melting temperature and electric strength of single crystals of solid solutions of the KCl—RbCl system as a function of chemical composition. (The melting-temperature curve is taken from literature data).

The electric strength of solid dielectrics is determined by the bonding energy between the particles composing the dielectric [15]. The latter, in turn, is determined by the lattice energy. For pure crystals it has been observed that the electric strength increases with increasing energy of the crystal lattice. For solid solutions of alkali-halide salts at the present time there are still no reliable formulas for calculating the lattice energy. The change in the coefficient of repulsive forces upon introduction of impurities into the crystal is unknown; this could introduce certain corrections into the formula for determining the lattice energy of solid solutions of alkali-halide salts. Surface energy is closely connected with the energy of the crystal lattice, since in its physicochemical nature surface

Fig. 12. Change in the electric strength and heat of formation of single crystals of solid solutions of the KBr—NaBr system as a function of chemical composition. (The heat-of-formation curve is constructed from literature data).

energy is a manifestation of the forces of interaction between the particles and of the chemical bond between them. Consequently, one may expect that with an increase in the specific surface energy the electric strength will also increase. In Fig. 13 the change in electric strength (mean values) and in surface energy is compared with the change in the chemical composition of single crystals of solid solutions of the KBr—NaBr system. It is seen from Fig. 13 that the electric strength and the surface

Fig. 13. Change in the electric strength and surface energy of single crystals of solid solutions of the KBr—NaBr system as a function of chemical composition. (The surface-energy curve is given according to the data of V. V. Kutsepalenko and P. A. Savintsev.)

energy vary with chemical composition according to approximately the same law. The surface energy was determined by the method of mutual grinding by V. V. Kutsepalenko and P. A. Savintsev on the very same crystals on which we measured the electric strength.

An analogous relation between electric strength and surface energy was noted by A. M. Trubitsyn for single crystals of the KCl—KBr system [16].

Conclusions

1. The change in the lattice constant of single crystals of solid solutions of the KCl—KBr, KBr—NaBr, and KJ—NaJ systems with change in chemical composition does not obey Vegard’s law.

Thus, for the KCl—KBr system the deviation from Vegard’s law occurs in the direction of a decrease in the lattice constants, while for solid solutions of the KJ—NaJ and KBr—NaBr systems it occurs both in the direction of decrease and in the direction of increase (curves with an inflection point).

1. The dependence of the microhardness of solid solutions KJ—NaJ and KCl—RbCl on chemical composition is expressed by a curve with a maximum.

2. The electric strength under pulses of single crystals of solid solutions KJ—NaJ and KBr—NaBr varies with chemical composition along a curve with a minimum, while for single crystals KCl—RbCl it varies along a curve with a maximum.

3. The electric strength of solid solutions KBr—NaBr, KJ—NaJ,

and KCl–RbCl decreases with increasing heat absorbed in their formation and increases with decreasing heat of formation.

1. The changes in surface energy and electrical strength with changes in the chemical composition of solid solutions of the KBr–NaBr system follow the same course.

In conclusion, I consider it my duty to express my gratitude to A. A. Vorob’ev for proposing the topic and for scientific guidance of the work, and to A. M. Trubitsyn for useful advice and for the use of the oscillograph he assembled.

REFERENCES

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Tomsk Polytechnic Institute

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