STABILITY OF SOLID SOLUTIONS OF ALKALI HALIDES AND THEIR ELECTRIC STRENGTH

T. K. KOCHERBAEV

(Presented by Professor Doctor E. K. Zavadovskii)

This paper presents experimental results on the study of the impulse electric strength of solid solutions of the systems KBr—KJ and NaCl—KCl, and of the magnitude of the electric strength of equimolar solid solutions of certain alkali-halide systems relative to the electric strength of their components with the greater lattice energy and relative to the value \(E_{\text{br}}\) of these solid solutions corresponding to its additive variation as a function of their composition. The compositions of the solid solutions of these systems having the greatest electric strength are also considered, and these compositions are compared with the compositions corresponding to the critical point of mutual solubility of the components in the solid state. Results are given for a study of the effect of annealing on the electric strength of solid solutions of the NaCl—KCl system.

Stability of Solid Solutions of Alkali Halides

It is known [1] that solid solutions of binary systems of alkali halides are formed with the absorption of a certain amount of energy, which is called their heat of formation.

The heat of formation of solid solutions of binary systems of alkali halides, depending on their composition, varies along a curve with a maximum at an equimolar or nearly equimolar composition [2—4].

The magnitude of the heat of formation of solid solutions is, to a known extent, an indicator of their stability. The magnitude of the heat of formation of equimolar solid solutions, regardless of whether halogen or metal ions are substituted, is associated with the difference in the parameters of the crystal lattices of their components. The more the lattice parameters of the components differ, the greater the magnitude of the heat of formation of the corresponding equimolar solid solution. For the formation of continuous solid solutions it is very important that the lattice parameters of the components, and consequently the radii of the substituting and substituted ions, should not differ very greatly.

X-ray studies of solid solutions of alkali halides have shown [5, 6] that if the lattice parameters of the components in a binary system differ by no more than 6%, then such

components form continuous solid solutions at all compositions at room temperature. If this difference is more than 6%, then the corresponding components are incompletely mutually soluble at room temperature or form eutectics. In the latter case the solid solutions obtained by quenching from a high temperature (during their growth) are unstable at room temperature and, when favorable conditions are created for diffusion of ions in the crystal lattice—for example, upon heating in the temperature range below the solubility curve of the components—depending on the heating time at the given temperature, partially or completely decompose into equilibrium phases.

Components of the systems KCl—PbCl and KCl—KBr form continuous solid solutions at room temperature [6, 8—10].

Fig. 1. Dependence of the electric strength of solid solutions of the KBr—KJ system on their composition.

The components of the NaCl—KCl system do not form homogeneous solid solutions at room temperature [6, 7, 11], and the coordinates of the critical point of mutual dissolution of the components on the phase diagram of this system [11] are 502 ± 2°C and 36 mol% KCl.

For the KBr—KJ system the critical point of mutual dissolution of its components in the solid state is unknown. The results of X-ray studies [6, 12] show that at room temperature the components of this system form continuous solid solutions only at small contents of one component in the other.

According to [6], at room temperature KBr up to 20 mol% is completely soluble in the crystal lattice of KJ. According to the results of [12], in solid solutions of the KBr—KJ system with compositions between 34 and 93 mol% KBr, in the equilibrium state corresponding to room temperature, there are regions of their stratification, i.e., decomposition. The difference in the lattice parameters of the components of the above systems is given in [6].

In [7] it was shown that, in order to obtain solid solutions from slightly isomorphous components such as KCl and NaCl, one should use the method of quenching during their growth from a high temperature.

Fig. 2. Dependence of the electric strength of solid solutions obtained by adding NaCl to KCl on their composition: curve 1—for quenched solid solutions; curve 2—for solid solutions annealed at 240°C for 10 hours.

Below we compare the electric strength of solid solutions of the KBr—KJ and NaCl—KCl systems, grown with subsequent quenching in air from a temperature of 520—530°C, with the electric strength of solid solutions of the KCl—KBr and KCl—PbCl systems.

Electrical Strength of Solid Solutions of Alkali Halides

The electrical strength of solid solutions of the KCl—PbCl system [13] and KCl—KBr [14], as a function of their composition, changes, like their heat of formation, along a curve with a maximum at compositions close to equimolar.

Below we present the results of a study of the dependence of the electrical strength ($E_{\mathrm{br}}$) of solid solutions of the KBr—KJ and NaCl—KCl systems on their composition, and compare the relative values of $E_{\mathrm{br}}$ obtained for equimolar solid solutions of the KBr—KJ and NaCl—KCl systems with the same quantities obtained for equimolar solid solutions of the KCl—KBr and KCl—PbCl systems.

In the solid solutions of the KBr—KJ and NaCl—KCl systems that we investigated, the starting materials were KBr of “ChDA” grade and NaCl, KCl, and KJ of “KhCh” grade. The solid solutions were grown by the Kyropoulos method, followed by quenching in air from 520–530°C to room temperature over 5–6 minutes. The composition of the solid solutions of the KBr—KJ system was determined by potentiometric titration according to the halide content in the crystal, with an accuracy of 1–2%. The composition of the solid solutions of the NaCl—KCl system was determined by flame photometry using a UM-2 monochromator and an FEU-22 photoelectron multiplier, with an accuracy of $\pm 2\%$. The electrical strength of the solid solutions was determined by the method described in [14]. The thickness of the samples was 100 μ. Graphite electrodes were used, and the electrode diameter was 0.8 mm.

The study of the electrical strength of solid solutions of the KBr—KJ system showed that additions of KBr to KJ up to 20–25 mol % increase $E_{\mathrm{br}}$, while additions of KJ to KBr up to 10 mol % decrease it. The results obtained are shown in Fig. 1.

An analogous dependence of $E_{\mathrm{br}}$ on the composition of solid solutions was also obtained for the NaCl—KCl system. The results of the study are shown in Figs. 2 and 3.

Additions of NaCl to KCl up to 10 mol % increase the electrical strength. With a further increase in the NaCl content in KCl, the electrical strength gradually decreases. The electrical strength of the 10 mol % NaCl—KCl solid solution is higher, in comparison with $E_{\mathrm{br}}$ of a quenched KCl crystal, by 36.5%, and this difference is 43.3% relative to the electrical strength of a KCl crystal grown with subsequent slow cooling. Additions of KCl to NaCl, beginning with a composition of 2.5 mol %, lower the electrical strength. An addition of 12 mol % KCl to NaCl lowers the mean value of $E_{\mathrm{br}}$ by 21.8%.

Fig. 3. Dependence of the electrical strength of solid solutions obtained by adding KCl to NaCl on their composition: curve 1—for quenched solid solutions; curve 2—for solid solutions annealed at 240°C for 10 hours.

The obtained dependences of $E_{\mathrm{br}}$ for solid solutions of the KBr—KJ and NaCl—KCl systems on their composition show that additions of the component having the greater lattice energy and, correspondingly, the greater ionization-

potential of the substituting ion increase the electric strength of the components with the lower crystal-lattice energy, and vice versa. These results confirm the supposition [15] that the electric strength of alkali-halide salts should increase, for a fixed halide, when metal ions are replaced by ions having a higher ionization potential; they also agree with the assertion [15] that weakening of the crystal lattice upon the introduction of impurities with large ionic radii lowers the electric strength. The components of solid solutions that are unstable at room temperature differ from the components of a stable solid solution not only by a large difference in the parameters of their crystal lattices, but also by a comparatively large difference in the ionization potentials of the ions being replaced and replacing them. Comparison of the results obtained for quenched and annealed (Figs. 2 and 3) samples at a temperature of \(240^\circ\mathrm{C}\) (lying below the solubility curve of the components) for 10 hours shows that \(E_{\mathrm{br}}\) of solid solutions unstable at room temperature is also connected with the degree of mutual solubility of their components in the solid state.

Table 1 gives the differences in the lattice parameters of the components \(\Delta a\) for the above-mentioned systems according to the results of [6]; the differences in ionization energy \(\Delta U\) of the replaced and replacing ions [16]; the heats of formation of equimolar solid solutions \(Q\); the concentration of Schottky-type defects \(n_0\) in equimolar solid solutions of the corresponding systems; and also the magnitudes of the increase in electric strength of equimolar solid solutions relative to \(E_{\mathrm{br}}\) of their components with the higher lattice energy, \(\Delta E_1\), and relative to the value of \(E_{\mathrm{br}}\) corresponding to its value under additive variation as a function of their composition, \(\Delta E_2\), in percent. It is seen from this table that, as the stability of the systems increases, the magnitude of the positive deviation of \(E_{\mathrm{br}}\) of equimolar solid solutions from its value under additive variation as a function of composition increases.

Table 1

We did not determine the electric strength of the equimolar solid solution of the NaCl—KCl system, since, owing to the existence of large internal stresses in them, we were unable to prepare specimens. The mean value of \(E_{\mathrm{br}}\) of a solid solution of 30 mol % NaCl in KCl, which was the limiting composition with respect to obtaining specimens, is only 4.4% higher than the mean value of \(E_{\mathrm{br}}\) of NaCl crystals.

Table 2 gives the critical points of mutual dissolution of components in the solid state for the systems KCl—RbCl, KCl—KBr, and NaCl—KCl, and the compositions to which the greatest mean

value of \(E_{\mathrm{br}}\) and the magnitude of the increase \(\Delta E_m\) of the mean value of \(E_{\mathrm{br}}\) for these compositions (in percent) in comparison with the mean value of \(E_{\mathrm{br}}\) of the component possessing the greater lattice energy. From this table it is evident that, for the systems KCl—PbCl and KCl—KBr, the compositions having the largest mean value of \(E_{\mathrm{br}}\) are closer to the compositions corresponding to the critical point of mutual dissolution of their components; whereas for the NaCl—KCl system the largest mean value of \(E_{\mathrm{br}}\) corresponds to a composition rich in KCl, while the critical point of mutual dissolution of its components corresponds to a composition of 36 mol % KCl.

In the variation of \(E_{\mathrm{br}}\) as a function of the composition of solid solutions of the KBr—KJ system, its largest value corresponds (approximately) to the limiting composition indicated in [6], in which KBr dissolves completely in the KJ lattice at room temperature.

Table 2

Thus, from the results presented in Tables 1 and 2 it follows that the electric strength of solid solutions of alkali halides is connected with the mutual dissolution of their components in the solid state. From Table 2 it is evident that the value of \(\Delta E_m\) is larger in the case of solid solutions with a substituted metal, which may be connected with the greater difference between the ionization potentials of the alkali-metal ion and the halogen ion. For impact ionization of alkali-metal ions by electrons, a comparatively greater energy is required than for detaching electrons from halogen ions.

From Table 1 it is evident that the concentration of Schottky-type defects in equimolar solid solutions of alkali halides differs almost not at all.

Apparently, in equimolar solid solutions stable at room temperature, the influence of point defects of the crystal lattice on their electric strength is manifested; by scattering and capturing electrons, these defects hinder the development of the electron avalanche that leads to breakdown. The relative value of \(E_{\mathrm{br}}\) for the equimolar solid solution of the KBr—KJ system is smaller than for the equimolar solid solutions of the KCl—KBr and KCl—PbCl systems. It is known [7] that an equimolar solid solution obtained by quenching from slightly isomorphous components, such as KCl and NaCl, is isotropic in the macrovolume and anisotropic in microvolumes.

Consequently, it may be assumed that in solid solutions of intermediate compositions of the KBr—KJ and NaCl—KCl systems, their electric strength is influenced to a greater extent by microinhomogeneities of the crystal. Inhomogeneities of the solid solution should lead to a decrease—

... to a decrease in their electric strength, since in this case the electric field inside the dielectric is also nonuniform.

Conclusions

1. In solid solutions of the KBr—KJ and NaCl—KCl systems, the electric strength is influenced by the relative magnitude of the ionization energy of the substituting ion of the added component. When a component with a high ionization energy of the substituting ion is added, an increase in the electric strength of the resulting solid solution is observed, and conversely.

2. Quenching solid solutions of the NaCl—KCl system at a temperature of 240°C, which lies below the curve of mutual solubility of the components on its phase diagram, leads to a decrease in their electric strength.

3. The electric strength of equimolar solid solutions of alkali halides is associated with the mutual dissolution of their components in the solid state and, consequently, with their stability.

4. In going from a more stable system (at room temperature) to less stable systems, the electric strength of the equimolar solid solution approaches, from the maximum positive deviation from the law of additivity, the value corresponding to an additive change with composition.

5. The electric strength of equimolar solid solutions formed from weakly isomorphous components is affected to a greater extent by microinhomogeneities of the crystal, associated with the limited mutual solubility of the components when solid solutions are obtained by the quenching method with a finite cooling rate. Such inhomogeneities of the solid solution may lead to a decrease in their electric strength, since in this case the electric field inside the dielectric has local inhomogeneities that create favorable conditions for the development of discharge.

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