DIELECTRIC RELAXATION IN POLYCRYSTALLINE SOLID DIELECTRICS AT HIGH FREQUENCY

M. P. Tonkonogov

General Regularities of Dielectric Relaxation in Liquids and Solids

In orientational phenomena, the deep connection existing between the solid (crystalline) and liquid states is manifested especially clearly. The works of Fowler and Bernal [1], Holtsman [2], Vuks [3], and others show that the liquid state may be characterized by short-range order in the orientations of molecules, and in some cases by a certain degree of long-range orientational order. On the other hand, the large magnitude of the internal field cannot serve as an obstacle to the orientation of crystal molecules in an external electric field [4]. Thus, with respect to orientational phenomena, the properties of the solid and liquid states may overlap. This suggests that in crystals with polar molecules, as in liquids, relaxation dielectric losses may occur. Whereas the regularities of dielectric relaxation in liquids and amorphous bodies have been well studied [5], the nature of dielectric losses in ionic crystals has been clarified only recently in the works of Vodopyanov [6], [7], [8] and his collaborators.

Analysis of the experimental data shows that dielectric losses in ionic crystals with polar molecules are characterized by the fact that, depending on the frequency (or temperature), there is one or several maxima of the loss angle, shifting with increasing temperature toward higher frequencies.

The features of the process of dielectric relaxation—the positions of the frequency and temperature maxima of \(\operatorname{tg}\delta\), the number of maxima, and their absolute magnitude—are determined by the structure of the crystal, on which the specific type of mechanism for the formation of weakly bound dipoles depends.

Thus, for example, in the dependence of the loss angle in phlogopite mica on temperature there is one relaxation maximum, whereas gypsum is characterized by two [7], and copper sulfate by three relaxation maxima of the loss angle [9].

Structural formulas make it possible to understand the differences in the conditions of fixation of molecules of crystallization water in the lattice.

The positions of the frequency and temperature maxima of \(\operatorname{tg}\delta\) are determined by the magnitude of the activation energy of weakly bound dipoles. If the latter, owing to structural features, are fixed differently in the crystal lattice, then there are several values of the activation energy and, correspondingly, in the dependence of the loss angle on temperature and frequency there are several maxima. Thus, for example, the change in the structure of talc as a function of the calcination temperature directly determines the magnitude of the ener-

activation energies of weakly bound dipoles, as well as the number of different values of the activation energy [9].

The magnitude of the maxima of \(\operatorname{tg}\delta\) is determined primarily by the number of weakly bound dipoles participating in the process of dielectric relaxation. Thus, for example, in copper vitriol [9] and in gypsum [8] the value of \(\operatorname{tg}\delta\) after annealing the crystal may increase, which is apparently connected with an increase in the number of weakly bound dipoles.

It is of interest to determine to what extent the regularities of dielectric losses set forth above are preserved in the case of complex polycrystalline aggregates. For the investigation a ceramic body was chosen, prepared on the basis of Onega talc (more than 90%) by the technology proposed by Novodvorskii [10]. It also contains Elin kaolin and boracite, containing boric acid, magnesium oxide, and calcium oxide. The nature of the dielectric losses should depend on the firing temperature of the specimen. According to Belyankin and Lapin [11], sintering of such bodies, containing on the order of 90% talc, gives clinoenstatite ceramics. As a result of sintering, mainly clinoenstatite is formed, as well as cristobalite, mullite, and glass.

During firing, dehydration of the specimen occurs, i.e., the concentration of polar molecules in the composition of the crystalline phase changes. It is of interest to investigate specimens at different degrees of sintering, which gives a whole set of different polycrystalline aggregates. The crystalline phase of the finished ceramic no longer contains polar groups; therefore the losses in the ceramic are due, first of all, to the presence of glassy interlayers.

However, the dielectric properties of the crystalline phase are of very great importance, since the volume accounted for by glassy interlayers in talc ceramics is very small [12].

Results of Measurements

The specimens used for the investigation were disks 30 mm in diameter and 2 mm thick, made by pressing the ceramic body. Firing was carried out in accordance with the ceramic manufacturing technology [10].

The firing process was interrupted at \(230^\circ\mathrm{C}\), \(500^\circ\mathrm{C}\), and \(960^\circ\mathrm{C}\); the specimen was removed from the furnace and enclosed in a special capacitor mounted in a quartz beaker, at the bottom of which \(CaCl_2\) was placed in order to prevent possible absorption of moisture by the specimen, after which \(\operatorname{tg}\delta\) was measured; then the firing process was continued, beginning from the temperature point at which it had been interrupted. The ceramic obtained in this way was also investigated. The measurements were performed by the method developed by Karandeev and Volopyanov [7].

In the frequency dependence of \(\operatorname{tg}\delta\) for specimens fired at \(230^\circ\mathrm{C}\), there are two maxima—at \(f = 3 \cdot 10^5\) cps and \(f = 4 \cdot 10^9\) cps (Fig. 1). Subsequent firing leads to a shift of the low-frequency maximum toward higher frequencies (Figs. 2 and 3).

A firing temperature of \(500^\circ\mathrm{C}\) corresponds to the position of the low-frequency maximum at \(4 \cdot 10^5\) cps, and a temperature of \(960^\circ\mathrm{C}\) to \(6 \cdot 10^5\) cps. At the same time, the high-frequency maximum does not change its position. The frequency dependence for specimens fired at \(960^\circ\mathrm{C}\) differs in that an increase of \(\operatorname{tg}\delta\) is observed in the region of short waves (compare Figs. 2 and 3).

The dielectric permittivity, in general, changes little with frequency. As firing proceeds, a decrease in the value of \(\operatorname{tg}\delta\) is observed. In the finished ceramic, fired at a temperature of \(1300^\circ\mathrm{C}\), the losses are small, especially at short waves (Fig. 4),—\(\operatorname{tg}\delta\) changes from 10

Fig. 1. Dependence of \(\operatorname{tg}\delta\) on frequency for samples of ceramic bodies fired at \(230^\circ\text{C}\).

Fig. 2. Dependence of \(\operatorname{tg}\delta\) on frequency for samples of ceramic bodies fired at \(500^\circ\text{C}\).

Fig. 3. Dependence of \(\operatorname{tg}\delta\) on frequency for samples of ceramic bodies fired at \(960^\circ\text{C}\).

at \(f = 1.2 \cdot 10^5\) cps, which agrees fairly well with the measurements of Vodol’yanov and Vyatkin for ceramics of this type [13].

In order to clarify the relaxation character of the dielectric losses, the temperature dependence of \(\operatorname{tg}\delta\) was studied at frequencies \(1.2 \cdot 10^7\) cps and \(6 \cdot 10^5\) cps at a firing temperature of the specimens of \(700^\circ\)C. The curves shown in Fig. 5

Fig. 4. Dependence of \(\operatorname{tg}\delta\) and \(\varepsilon\) on frequency for specimens of ceramic fired at \(1300^\circ\)C.

1 and 2 correspond to the frequency characteristics of \(\operatorname{tg}\delta\) already considered. There are three temperature maxima of the loss angle, shifting with decreasing frequency toward lower temperatures.

Fig. 5. Temperature dependence of \(\operatorname{tg}\delta\) for specimens of ceramic masses fired at \(700^\circ\)C.

Curve 1—for a frequency of \(1.2 \cdot 10^5\) cps; curve 2—for a frequency of \(6 \cdot 10^5\) cps.

Discussion of Results

The observed shift of the maxima in the dependence of the loss angle on temperature with change in frequency indicates the relaxation character of the process, apparently caused by the orientation of \((\mathrm{OH})^{-}\) dipoles in an external field with different values of the activation energy. In favor of the latter assumption is the absence of relaxation maxima of \(\operatorname{tg}\delta\) in the finished ceramic (Fig. 4).

The position of the frequency maxima of the loss angle for the ceramic mass fired at \(230^\circ\) is the same as for Onega talc [9]. They should apparently be attributed to the talc component of the ceramic. Pos-

The appearance of a third maximum in the frequency dependence of the loss angle in specimens calcined at temperatures above 500°C reflects changes occurring in the talc lattice during sintering. Studies by Avgustinnik [14], [15], Belyankin [11], and other authors indicate that firing Onot talc at 700–1000°C causes a change in its structure, leading to loosening and alteration of the crystal lattice.

A similar increase in the loss angle in the high-frequency region is also observed in the case of Onot talc calcined at temperatures above 700°C [9].

The shift of the low-frequency maximum toward higher frequencies with increasing firing temperature of the specimen (Figs. 1, 2, 3) is characteristic only of ceramic bodies and is not observed for pure Onot talc.

Apparently, in the process of sintering the ceramic, even at relatively low temperatures (500–1000°C), talc and kaolin (which also contains dipoles \((\mathrm{OH})^{-}\)) interact with one another to some extent; the body obtained as a result of sintering may have a very loose structure, and consequently less activation energy is required for orientation of the corresponding polar groups, so that their relaxation time

\[ \tau=\frac{1}{2\nu_0} e^{\frac{U}{kT}} \]

decreases for higher firing temperatures. (Here \(\nu_0\) is the natural vibration frequency of the dipoles, \(T\) is the absolute temperature, \(U\) is the activation energy, and \(k\) is Boltzmann’s constant.)

Thus, according to the condition \((\omega\tau)_m \simeq 1\), the maximum in the frequency dependence of \(\operatorname{tg}\delta\) shifts, with increasing firing temperature, toward higher frequencies.

Using the example of a complex polycrystalline aggregate, such as ceramic bodies fired at different temperatures, Kobeko’s proposition [5], advanced by him in the analysis of relaxation processes in polymers, is confirmed: if weakly bound dipoles are present in a dielectric, then, independently of the aggregate state and the strengths of the bonds, their orientation in an alternating electric field is governed by general laws.

At the same time, the structure of a polycrystalline body, as in the case of amorphous substances, has a most essential influence on the features of the dielectric relaxation process.

It is this structure that determines the magnitude of the activation energy, as well as how many different values of activation energy a dipole may have. Thus, in specimens of ceramic bodies fired at 230°C and 500°C, the dipoles are oriented with two different values of activation energy, whereas in specimens calcined at 960°C they are oriented with three values of activation energy.

The absolute value of the activation energy of the dipoles also depends on the change in structure during firing. In the case under consideration, the activation energy of the dipoles responsible for the low-frequency maximum of \(\operatorname{tg}\delta\) decreases with increasing firing temperature, as is seen from the shift of this maximum toward higher frequencies.

Thus, the change in the structure of the specimen during firing affects both the number of possible values of the activation energy and its absolute magnitude.

In the finished ceramic, fired at a final temperature of 1300°C (Fig. 5), conductivity losses appear at low frequencies; at frequencies greater than \(6\cdot10^{5}\) c/s, \(\operatorname{tg}\delta\) does not depend on frequency; the losses are apparently due to thermal polarization of weakly bound ions of the glassy phase. At a temperature of 1300°C, clinoenstatite [11] is formed, the crystals of which contain no polar groups and are characterized by a very small loss angle [16].

The addition of boracite to talc, which contains magnesium oxide, according to Lapin and Frid [11], should promote an increase in the amount of clinoenstatite in the specimen and its more perfect crystallization, which apparently has a positive effect on the dielectric properties of the ceramic.

Conclusions

1. In ceramic bodies fired at temperatures of 230°C, 500°C, and 960°C, the dielectric losses are relaxation losses and are caused by the orientation of hydroxyl groups in an external field with different values of the activation energy. The number of possible values of the activation energy and its absolute magnitude are determined by the change in the structure of the specimen during firing.

2. In ceramics fired at a temperature of 1300°C, the dielectric losses are small and are caused chiefly by the glassy phase. There are no relaxation maxima in the frequency dependence of the loss angle.

3. The high dielectric properties of the ceramic studied are due to the transformation of talc during firing into clinoenstatite and to the perfection of its crystallization.

Students of Tomsk University, Zabolotskaya and Arshibasova, took part in the experimental portion of the work.

The work was carried out under the supervision of K. A. Vodopyanov, whom I take this opportunity to thank.

References

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Karaganda, Mining Institute.

Errata