DIELECTRIC LOSSES IN CRYSTALS WITH NONISOMORPHOUS IMPURITIES IN THE HIGH-FREQUENCY RANGE

G. I. POTAKHOVA

(Presented by Corresponding Member of the Academy of Sciences of the USSR V. D. Kuznetsov)

It is known that when small amounts of impurity are introduced into alkali-halide crystals, their mechanical characteristics change [1]. With the introduction of impurities, the electrical conductivity of crystals changes significantly [2, 3]. Hippel [4] notes the great influence of small impurities on the electric strength of crystals. Yu. A. Sikorsky points to an increase in the dielectric constant of rock-salt crystals containing colloidal color centers [5]. A whole series of works report results of studies of the influence of impurities on dielectric losses in alkali-halide crystals. But these studies were carried out mainly in the low-frequency range \((10^1—10^5\ \text{c/s})\) [6—10].

The present work, being a continuation of studies of the dielectric properties of simple and complex crystals carried out in the electrophysics laboratory of the SFTI, considers the influence of nonisomorphous impurities on the dielectric losses of alkali-halide crystals in the high-frequency range.

Crystals of NaCl and KCl with impurities of \(\mathrm{CaCl_2}\), \(\mathrm{BaCl_2}\), and \(\mathrm{MgCl_2}\) were considered.

The impurities were introduced into the melt from which the crystal was grown by the Kyropoulos method [1]. The concentration of impurity in the crystals studied was determined by the method of quantitative chemical analysis [11]. The impurity concentration in the crystals was much lower than the concentration of impurity in the melt from which the crystal was grown, which is in agreement with data of other authors [12].

In addition to chemical analysis, spectral analysis was performed on crystals both containing impurities and without them. As a result of the spectral analysis, traces of copper impurity were found in NaCl crystals and calcium in KCl crystals. In crystals with impurities, apart from those impurities that had been specially introduced into the melt, only the same impurities were found as in the corresponding “pure” NaCl and KCl crystals.

In order to clarify the influence of impurities on the structure of the crystals studied, X-ray and optical investigations of them were carried out.

The lattice constants of the crystals under investigation were determined radiographically, and no change was found in the parameters of the crystal lattice of the crystals with impurities as compared with the lattice parameters of crystals containing no impurities.

The values of the lattice constants of the crystals containing the largest amount of impurities differed from the lattice constants of the corresponding impurity-free crystals by no more than \(0.002\ \text{\AA}\), which lies within the accuracy of the method used. These results agree with the data of Glover [13], who measured the lattice parameters of KCl crystals, both containing impurities and impurity-free, in the temperature range \(20\div 600^\circ\text{C}\).

In studying NaCl crystals with the highest concentration of the CaCl\(_2\) impurity by the Laue method, a Laue pattern typical of a single crystal was obtained.

An X-ray study of NaCl—CaCl\(_2\) alloys by the rotating-crystal method, carried out by Miyake and Suzuki [14], enabled them to detect a change in the diffraction pattern due to the introduction of the CaCl\(_2\) impurity into NaCl. Taking into account the results of various authors who investigated the structure of NaCl—CaCl\(_2\) alloys, we may draw the following conclusion concerning the structure of the NaCl crystals containing CaCl\(_2\) impurity that we investigated: the NaCl—CaCl\(_2\) crystals studied are single crystals with the NaCl structure, in whose [111] and [310] planes there are impurity thin platelets with a structure similar to that of CaCl\(_2\), consisting of Ca\(^{++}\), Cl\(^{-}\), and vacant Na\(^{+}\) sites.

There are no data in the literature on the structure of KCl alloys with CaCl\(_2\), BaCl\(_2\), and MgCl\(_2\) impurities in the region of low concentrations of these impurities. Our X-ray studies do not reveal the presence of impurities in the crystals under consideration. Therefore additional studies of the crystals with impurities were carried out by the immersion method.

As a result of the immersion-method study of KCl crystals containing CaCl\(_2\) impurity, the existence of two phases was discovered, the refractive index of one of which is equal to the refractive index of KCl; the refractive index of the second phase differs from the refractive indices of KCl and CaCl\(_2\). Similar results were also obtained in the investigation of KCl—MgCl\(_2\) alloys.

Taking these results into account, as well as the data of other authors [15] who studied the structure of KCl—CaCl\(_2\) and KCl—MgCl\(_2\) alloys in regions richer in CaCl\(_2\) and MgCl\(_2\), we may suppose that the KCl crystals with CaCl\(_2\) and MgCl\(_2\) impurities that we investigated are KCl single crystals (as indicated by the X-ray patterns of all KCl crystals with the corresponding impurities), into which a second phase, different from the phases of the introduced impurities, enters as an impurity. The formation of solid solutions, which could be this second phase, is rejected by the literature data and is unlikely because of the large difference in the ionic radii of potassium, calcium, and magnesium.

The dielectric losses of the crystals with impurities were measured in the frequency range \(3\cdot 10^5\)—\(10^8\) cps at various temperatures by the resonance method of resistance variation.

The composition of the specimens studied and the value of the loss angle in them at room temperature and a frequency of \(10^6\) cps are given in Table 1.

Table 1

The concentration of impurity in the crystals was determined with an accuracy of up to 0.01 mol %. The composition of crystals containing only thousandths and hundredths of a molecular percent of impurity is given according to the synthesis data; the impurity concentration in them was not determined by chemical analysis. As is clear from the data given in the table, the greatest change in the loss angle among all the impurities considered is caused by the CaCl$_2$ impurity. It is also seen that the relative change in the loss angle increases as the impurity concentration increases.

The frequency dependences of the loss angle in crystals with impurities are shown in Figs. 1, 2, 3.

Fig. 1. Frequency dependences of the loss angle in NaCl crystals with a CaCl$_2$ impurity.
1. NaCl. 2. NaCl + 0.11 mol % CaCl$_2$, 3. NaCl + 1.6 mol % CaCl$_2$

As is seen from the figures, when the frequency is decreased an increase in the loss angle is observed in all the crystals. This increase is the more considerable, the higher the impurity concentration. From Figs. 1–3 it is seen that impurities have a more substantial effect on the magnitude of the loss angle in the low-frequency region: in NaCl crystals with a CaCl$_2$ impurity, for all the concentrations studied, the loss angles at frequencies $3 \cdot 10^6$–$10^7$ Hz differ only very slightly (by a factor of 1.5–2), whereas at frequencies of $10^6$ and $3 \cdot 10^5$ Hz the loss angle in NaCl + 1.6 mol % CaCl$_2$ is already approximately 4 times larger than the loss angle in NaCl.

As at the frequency of the external electric field $10^6$ Hz, over the entire investigated frequency interval the strongest change in the angle

losses is observed upon introducing the impurity CaCl\(_2\). Comparing the change in the loss angle upon introducing CaCl\(_2\) impurities into NaCl and KCl, it may be noted that the loss angle increases much more substantially when CaCl\(_2\) is introduced into KCl than into NaCl. This is especially evident at the highest concentrations of the CaCl\(_2\) impurity. The introduction of the CaCl\(_2\) impurity—0.10 mol %—causes approximately the same change in the loss angle in NaCl and in KCl, whereas upon introducing an impurity of the order of one percent the loss angle in NaCl—CaCl\(_2\) increases by approximately a factor of 5 in comparison with the loss angle in NaCl, and in KCl—CaCl\(_2\)—by almost a factor of 30 in comparison with KCl (at a frequency of \(3 \cdot 10^5\) cps).

Fig. 2. Frequency dependences of the loss angle in KCl crystals with CaCl\(_2\) impurities of various concentrations.
1. KCl. 2. KCl + 0.11 M% CaCl\(_2\).
3. KCl + 0.40 M% CaCl\(_2\).

Fig. 3. Frequency dependences of the loss angle in KCl crystals with MgCl\(_2\) impurities.
1. KCl and KCl + 0.03 M% MgCl\(_2\). 2. KCl + 0.13 M% MgCl\(_2\). 3. KCl + 0.55 M% MgCl\(_2\).

Upon introducing BaCl\(_2\) and MgCl\(_2\) impurities into KCl, a noticeable increase in the angle is observed only at impurity concentrations of the order of several tenths of a molecular percent. BaCl\(_2\) and MgCl\(_2\) impurities in amounts of approximately one tenth of a molecular percent at room temperature practically do not change the loss angle over the entire frequency interval studied.

With increasing temperature, the influence of small impurities on the magnitude of the loss angle becomes noticeable. In Fig. 4 typical temperature dependences are given for KCl crystals with impurities of various concentrations. If the loss angle in crystals of KCl + 0.12 mol % BaCl₂ and in KCl at room temperature is approximately the same, then as the temperature is raised above 160°C the loss angle in KCl + 0.12 mol % BaCl₂ becomes noticeably greater than the loss angle in KCl at these temperatures. The higher the temperature, the more significantly the loss angle in the crystal with BaCl₂ exceeds the loss angle in KCl. Similar regularities also occur for KCl crystals with other impurities (CaCl₂ and MgCl₂). If hundredths and thousandths of a molecular percent of impurity do not change the loss angle in crystals at room temperatures, they nevertheless change the temperature dependences of the loss angle in these crystals, being distinguished by an earlier and sharper increase in the loss angle with increasing temperature than the corresponding dependences for simple crystals (Fig. 5).

Fig. 4. Temperature dependences of the loss angle in KCl crystals containing different amounts of BaCl₂ impurity at a frequency of \(10^5\) Hz.

1. KCl.
2. KCl + 0.12 M% BaCl₂.
3. KCl + 0.40 M% BaCl₂.

The temperature dependences of the loss angle in crystals with impurities of CaCl₂, BaCl₂, and MgCl₂ are similar to the temperature dependences of the loss angle in simple crystals and in crystals with an isomorphous impurity: over a certain temperature interval the loss angle depends little on temperature, and then rises sharply. The temperature above which a sharp increase of the loss angle is observed with further—

Fig. 5. Temperature dependences of the loss angle in KCl crystals with a small content of CaCl₂ impurity at a frequency of \(10^5\) Hz.

1. KCl.
2. KCl + 0.12 M% BaCl₂.
3. KCl + 0.40 M% BaCl₂.

... upon further increase in temperature depends both on the impurity concentration and on the frequency of the external electric field. The greater the impurity concentration and the lower the frequency of the electric field, the lower the temperature at which a sharp increase in the loss angle is observed (Fig. 6).

To clarify the role of conductivity in the process of energy losses in crystals with impurities, the conductivity of several crystals with impurities was measured.

Fig. 6. Temperature dependences of the loss angle in KCl + 0.03M% MgCl$_2$ crystals, obtained at different frequencies.
1. $f = 10^6$ Hz, 2. $f = 3 \cdot 10^5$ Hz (o—points for the forward run, x—points for the reverse run)

crystals with impurities. Table 2 gives the values of the loss angle measured directly and calculated from the conductivity measurements of these same crystals.

Table 2

As is seen from consideration of Table 2, the loss angle in the crystals studied only at temperatures of 180–200°C becomes equal, in order of magnitude, to the loss angle calculated from the conductivity.

All dependences of the loss angle in the investigated crystals with impurities are analogous to similar dependences of the loss angle in simple ...

in crystals, differing only in a sharper increase of the loss angle when the frequency is decreased and in an earlier significant increase of $\operatorname{tg}\delta$ when the temperature is raised. From this one may conclude that the loss mechanism in pure crystals, into which no impurity was specially introduced, and in crystals with impurity is the same. The increase of the loss angle in crystals upon the introduction of impurities into them is explained by the fact that the impurity distorts the crystal lattice, facilitating the dissociation of ions and increasing the number of free and weakly bound ions. The sharper increase of the loss angle in crystals with impurities when the frequency is decreased and the temperature increased indicates a greater role of conductivity in crystals with impurities as compared with crystals into which impurity was not specially introduced. If one takes into account studies on the influence of impurities on the electrical conductivity of crystals [2—3], this is entirely understandable.

The liberation energy of ions in a crystal lattice decreases in the presence of impurities in it. As Frenkel indicates [16], the more strongly the impurity ions differ from the ions of the parent substance, the more strongly the loosening energy of the crystal decreases. Of the crystals considered, KCl and NaCl with CaCl$_2$ impurity, the greatest change in the loss angle under the influence of introducing the impurity is observed for KCl crystals. Evidently, the CaCl$_2$ impurity destroys the KCl lattice more than the NaCl lattice. This is in agreement with Frenkel’s statement on the influence of the size of the impurity ion on the decrease in the loosening energy of the crystal lattice: the ionic radii of Ca$^{++}$ [1.06–0.99 Å] and Na$^+$ [0.98–0.95 Å] are closer than the radii of Ca$^{++}$ (1.06 Å) and K$^+$ [1.22–1.35 Å]; therefore it is understandable that Ca$^{++}$ destroys the KCl lattice more strongly.

Structural studies also confirm the assumption that the CaCl$_2$ impurity destroys the KCl lattice more than the NaCl lattice. As noted in the literature [15], KCl with CaCl$_2$ impurity does not form solid solutions; NaCl at small concentrations of CaCl$_2$ forms solid solutions with this impurity, while the second phase formed at large concentrations of CaCl$_2$ in NaCl has much in common with the structure of NaCl, and therefore distorts it less.

The greater change in the loss angle in KCl upon introduction of CaCl$_2$ than of BaCl$_2$ can also be explained by the greater decrease in the loosening energy of KCl by impurity ions Ca$^{++}$ than by ions Ba$^{++}$. The ionic radii Ba$^{++}$ [1.43–1.35 Å] and K$^+$ [1.33–1.35 Å] are close, which promotes the formation, in a certain concentration range of BaCl$_2$, of solid solutions KCl—BaCl$_2$ with an excess of the KCl component; therefore the distortion of the KCl lattice by the BaCl$_2$ impurity will be smaller than by the CaCl$_2$ impurity.

The MgCl$_2$ impurity introduced into KCl has only a small influence on the change in the loss angle. The ionic radius Mg$^{++}$ [0.78–0.65 Å] differs considerably from the radius of K$^+$, which should promote a significant change in the loosening energy of the KCl lattice, in accordance with Frenkel’s statement. But this is not observed. Possibly the small influence of MgCl$_2$ impurity on the change in the loss angle in KCl is connected with the fact that the radius of Mg$^{++}$ ions is very small, and they are distributed in the KCl lattice without causing large distortions in it.

The literature gives results of studies of dielectric losses in crystals with impurities, but the loss measurements were carried out in the region of low frequencies [$10^1$—$10^5$ Hz]. The temperature dependences of the loss angle of crystals with impurities, obtained by Breckenridg-

...and Wilke, at a frequency of \(\sim 10^3\) cps, are curves with maxima [6, 8].

The frequency dependences of the loss angle of NaCl crystals with a CaCl\(_2\) impurity at various temperatures also have maxima, which shift, with increasing temperature, toward higher frequencies. The same regularities in the change of the loss angle with changes in frequency and temperature have also been found in the study of additively colored KBr crystals [9].

In the investigation of the loss angle of the KCl and NaCl crystals with CaCl\(_2\) and MgCl\(_2\) impurities considered in the present work, in the studied frequency range \([3 \cdot 10^5 \div 10^8\ \text{cps}]\) and temperature range \([20 \div 200^\circ\text{C}]\), no maxima of the loss angle were found either in the frequency or in the temperature dependences. This is probably connected with the fact that the maxima of \(\tg \delta\), observed in the low-frequency region in the temperature dependences of the loss angle of crystals with impurities, will appear in the high-frequency region at higher temperatures, where the investigation was not carried out. Indeed, in the work of Sutta [10], who made measurements at 3 Mcps, a maximum of \(\tg \delta\) was found in its dependence on temperature at temperatures above \(300^\circ\text{C}\). But Sutta’s work raises doubts because, even at a temperature of \(100^\circ\text{C}\), the loss angle in NaCl crystals obtained by him is much greater than according to the data of other authors [6, 7].

Conclusion

On the basis of the investigations carried out, the following conclusions may be drawn:

1. The temperature and frequency dependences of the loss angle in crystals containing impurities are similar to the analogous dependences of the loss angle in simple crystals, which makes it possible to assume a common mechanism of losses in simple crystals and in crystals containing impurities.

2. The increase in the loss angle in crystals with impurities is connected with the loosening of the crystal lattice by the impurity, with a lowering of the activation energy and dissociation of the ions of the crystal lattice, which contributes to an increase in the number of free and weakly bound ions.

In this work on elucidating the influence of impurities on dielectric losses and on the structure of crystals, the student G. F. Yarushevskaya [17] took part.

LITERATURE

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