DIELECTRIC LOSSES IN ALKALI METAL HALIDES IN RELATION TO THEIR CHEMICAL COMPOSITION

Yu. M. Annenkov, E. K. Zavadovskaya

Brickenridge showed that, in alkali-halide crystals, lattice defects cause dielectric absorption in the region of audio frequencies [1]. Ionic-relaxation processes depend to the greatest extent on the physicochemical properties of the substance, increasing dielectric losses the more “loose” the crystal structure is. Vorob’ev and Vodop’yanov expressed the idea of a connection between the dielectric-loss angle in alkali-halide crystals and the lattice energy [2]. This assumption was experimentally confirmed in the high-frequency region by Potakhova’s investigations [3]. However, some authors [4] consider the observed dependence of dielectric losses on chemical composition doubtful, arguing their objections by the influence of the hygroscopicity of the crystals, since Potakhova carried out measurements under atmospheric conditions. Partly for this reason, we again turned to clarification of this question.

Single crystals of KI, KBr, KCl, and NaCl were grown by the Kyropoulos method from salts of chemically pure grade. The specimens had the form of plates with an area of 7–10 cm² and a thickness of 0.7–1.0 mm. Platinum, deposited on the specimens by cathodic sputtering, was used as the electrodes. Measurements of dielectric losses were carried out in the audio-frequency range (100–10000) Hz on an unbalanced bridge [5] at temperatures from room temperature to 250°C. During the measurements a vacuum of \(10^{-3}\)–\(10^{-4}\) mm Hg was maintained in the cell. The rate of heating of the specimens did not exceed 1°C per minute, which excludes a noticeable gradient of the thermal field inside the crystal. Figure 1 presents the temperature variations of \(\operatorname{tg}\delta\) for the compounds studied. Comparison of the magnitude of the loss angle in the crystals of the investigated series shows that the temperature interval from 20°C to 200°C is divided into two regions, within which different dependences of the dielectric losses on the lattice energy are observed:

1. In the low-temperature interval (20–120)°C, a maximum of \(\operatorname{tg}\delta\) is observed for NaCl single crystals. Increasing the field frequency shifts the position of the peak toward higher temperatures, which indicates the Debye character of the relaxation phenomenon. If the Debye absorption is subtracted graphically, then in the interval under consideration

temperatures a decrease in $\operatorname{tg}\delta$ is observed with increasing lattice energy of the crystals studied.

1. At temperatures above 120°C, for all compounds $\operatorname{tg}\delta$ increases exponentially with increasing temperature, and the values of the dielectric-loss angle are greater in crystals with a stronger ionic bond.

Fig. 1. Dependence of $\operatorname{tg}\delta$ on temperature at a frequency of 1000 Hz for: 1—NaCl, 2—KCl, 3—KBr, 4—KI.

To determine the contribution of migration of free vacant sites to the magnitude of energy losses, the temperature dependences of the electrical conductivity of alkali-metal halides were measured. From the values of the electrical resistance of the specimens, the value of the loss angle due to electrical conductivity was calculated. Comparing the measured values of $\operatorname{tg}\delta$ and those calculated from the dc resistance, we came to the conclusion that in the temperature range above 100–120°C the dielectric losses are caused by ionic conductivity. Moreover, as the lattice energy of the crystals increases, the electrical conductivity of the compounds increases.

In view of the fact that the structure-sensitive conductivity of alkali-halide crystals changes noticeably from specimen to specimen, a large body of statistical material was accumulated on measurements of resistance and $\operatorname{tg}\delta$.

The observed dependence of the ionic electrical conductivity on the lattice energy of the crystals in the temperature interval 120–250°C cannot be explained by scatter of the experimental points, but has a causal connection with definite processes in the crystals.

From the temperature variation of the electrical conductivity for all the compounds studied, the activation energy for the displacement of current carriers was calculated; the results are summarized in Table 1.

Table 1

$U$ is the activation energy for vacancy migration in the region of structure-sensitive conductivity.

It follows from Table 1 that, with increasing lattice energy of alkali-halide crystals, the activation energy for migration of current carriers increases. Consequently, the increase in electrical resistance on going to more “loose” crystals (from NaCl to KJ) is connected only with the pre-exponential term in the formula for the temperature dependence of electrical conductivity:

\[ \sigma = A \cdot \exp(-U/KT) \]

If it is assumed that all equilibrium cation vacancies are in a free state, then the coefficient $A$ for NaCl, KCl, KBr, and KJ crystals should differ much less than the experimentally obtained dependence of electrical conductivity on chemical composition.

In alkali-halide crystals, oppositely charged vacancies readily combine into neutral pairs. There is a series of direct and indirect proofs that point defects can also assemble into more complex groups [6, 7, 8] owing to the interaction of their charges.

Probably, as the lattice energy decreases, the possibility of formation of complex vacancy aggregates increases. Such groupings of anion and cation vacancies are electrically neutral and do not contribute to ionic conductivity. Consequently, despite the greater defectiveness of crystals with lower lattice energy, owing to the aggregation of vacancies into dipoles, quadrupoles, and so on, their electrical conductivity decreases, and the more so the more “loose” the structure of the substance.

Another reason is also possible for the experimentally observed dependence of electrical conductivity on the chemical composition of alkali-metal halides. Spectral analysis of the crystals studied indicates a considerable “contamination” of the compounds by $Ca^{++}$ ions. The unequal isomorphism of $Ca^{++}$ ions and alkali-halide crystals of different chemical composition changes the concentration of current carriers in the region of structure-sensitive conductivity. Thus, in order to determine the cause of the observed dependence of crystal conductivity on the bond energy between ions, the compounds under study must be normalized with respect to the content of $Ca^{++}$ ions dissolved in the lattice.

In addition, dielectric relaxation in sodium chloride may be caused either by complexes of the type “divalent metallic impurity—cation vacancy,” or by associated oppositely charged vacancies. The introduction of controlled additions of divalent ions into NaCl crystals makes it possible to determine unambiguously the structure of the relaxing defects.

For this purpose we studied dielectric losses in NaCl, KCl, and KBr crystals containing various concentrations of $Ca^{++}$.

In the temperature dependences of $\tg \delta$ for the KCl—$Ca^{++}$ and KBr—$Ca^{++}$ systems, one relaxation maximum appears in each case. The concentration dependences of the amplitude of the maxima are expressed by a function close to parabolic.

The magnitude of the temperature peak of $\operatorname{tg}\delta$ observed for “pure” sodium chloride increases upon the introduction of $\mathrm{Ca}^{++}$. The activation energy of the relaxation process remains equal to 0.68 eV (Fig. 3). The results of the investigations performed suggest that neutral complexes “$\mathrm{Ca}^{++}$—cation vacancy” are responsible for the relaxation in “pure” NaCl

Fig. 2. Dependence of $\operatorname{tg}\delta$ on temperature at a frequency of 1000 Hz for:
1 — $\mathrm{NaCl}+1.5\cdot10^{-2}\,\mathrm{M}\%$,
2 — $\mathrm{KCl}+2.1\cdot10^{-2}\,\mathrm{M}\%$,
3 — $\mathrm{KBr}+2.6\cdot10^{-2}\,\mathrm{M}\%$.

Fig. 3. Dependence of $\operatorname{tg}\delta$ on temperature at a frequency of 1000 Hz for:
1 — $\mathrm{NaCl}$,
2 — $\mathrm{NaCl}+10^{-2}\,\mathrm{M}\%\,\mathrm{Ca}^{++}$,
3 — $\mathrm{NaCl}+2.1\cdot10^{-2}\,\mathrm{M}\%\,\mathrm{Ca}^{++}$,
4 — $\mathrm{NaCl}+3\cdot10^{-2}\,\mathrm{M}\%\,\mathrm{Ca}^{++}$,
5 — $\mathrm{NaCl}+5\cdot10^{-2}\,\mathrm{M}\%\,\mathrm{Ca}^{++}$,
6 — $\mathrm{NaCl}+6.3\cdot10^{-2}\,\mathrm{M}\%\,\mathrm{Ca}^{++}$.

vacancies,” and not associated Schottky defects, as we had assumed earlier [9].

We compared the values of the dielectric-loss angle in NaCl, KCl, and KBr crystals containing the same number of \(Ca^{++}\) ions occupying regular sites of the crystal lattice. The concentration of the latter was determined from the amplitude of the relaxation maxima using the Clausius–Mossotti–Debye theory [10], under the assumption of an insignificant difference in the degree of association of \(Ca^{++}\) ions and cation vacancies in crystals of different chemical composition [11]. The data shown in Fig. 2 indicate that, even when the different solubility of \(Ca^{++}\) ions in the NaCl, KCl, and KBr lattices is taken into account, the structure-sensitive electrical conductivity decreases as the bond strength between the ions weakens.

Thus, we may conclude that, in going from alkali-halide crystals with a higher degree of ionicity of the chemical bond (NaCl) to more “loose” ionic structures (KI), the process of vacancy aggregation is enhanced.

If Debye relaxation is not observed in the crystals, then \(\operatorname{tg}\delta\) in the temperature range below \(120^\circ\mathrm{C}\) varies only slightly with field frequency and temperature. The energy losses in the temperature interval considered are probably caused by the accumulation of current carriers (cation vacancies) at the boundaries of mosaic blocks, which is equivalent to thermal ionic polarization [12].

In view of the fact that this process is described by a very large set of relaxation times, no sharply expressed maxima are observed; instead, there is a “plateau.” Dielectric losses determined by such polarization effects should decrease with increasing interaction energy between the ions, which is indeed observed experimentally.

LITERATURE

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