Dielectric Losses in Oxides and Halide Compounds of Group II Elements

A. A. Vorob’ev, A. P. Nakhodnova

As the lattice energy of alkali-halide salt crystals increases, their electric strength, melting temperature, hardness, and other properties increase, while dielectric losses decrease [1, 2, 3, 4]. A connection has been established among other physicochemical properties.

A study was carried out of the temperature-frequency dependence of \(\operatorname{tg}\delta\) for oxides and fluoride and chloride compounds of Group II elements.

Measurements of the dependence \(\operatorname{tg}\delta = f(T)\) were performed in vacuum \((P = 10^{-5}\ \text{mm Hg})\) by means of a Q-meter on sintered polycrystalline specimens whose density was 65–70 and 95% of the density of a single crystal. The specimens had the form of disks 14–17 mm in diameter and 0.5–0.8 mm thick, onto which silver electrodes were deposited by evaporation.

The temperature dependence of \(\operatorname{tg}\delta\) for oxides was investigated in the range 25–480°C, and for halide compounds, 25–260°C.

The measurement results show that the dielectric losses of oxides of Group II metals having a cubic lattice are small. For BeO, MgO, and CaO at 155°C and \(f = 900\ \text{kHz}\), \(\operatorname{tg}\delta\) does not exceed \(5 \times 10^{-4}\); for SrO and BaO the losses are somewhat greater, but even here at \(T = 25^\circ\text{C}\) and \(f = 900\ \text{kHz}\), \(\operatorname{tg}\delta\) does not exceed \(8 \cdot 10^{-4}\).

For all oxides, a relatively rapid increase of \(\operatorname{tg}\delta\) with increasing temperature is observed (Fig. 1).

The replacement of \( \mathrm{Be}^{++}\) and \( \mathrm{M}^{++}\) ions by ions of metals having a larger radius is accompanied by loosening of the crystal lattice and an increase in \(\operatorname{tg}\delta\). The dielectric losses of oxides in the series BeO—BaO are the greater, the smaller the crystal-lattice energy of the substance (Fig. 1).

The dependence of \(\operatorname{tg}\delta\) on temperature for \(\mathrm{CaF_2}\), \(\mathrm{SrF_2}\), and \(\mathrm{BaF_2}\) was studied on specimens whose density was 65–70% and 95% of that of a single crystal. An increase of \(\operatorname{tg}\delta\) with temperature was observed (Fig. 2). For specimens of higher density, a weak maximum of \(\operatorname{tg}\delta\) appears in the interval 60–120°C (Fig. 3).

The presence of a temperature maximum of \(\operatorname{tg}\delta\) for specimens of relatively high density gives grounds to suppose that, in sintered polycrystalline specimens, in addition to losses caused by conductivity, there are relaxation losses caused by weakly bound ions.

Fig. 1. Temperature dependence of \(\lg \tan \delta\) for oxides of Group II metals at \(f = 900\ \text{kHz}\).

I—BeO
II—MgO
III—CaO
IV—SrO
V—BaO

Fig. 2. Temperature dependence of \(\lg \tan \delta\) for \(\mathrm{CaF_2}\), \(\mathrm{SrF_2}\), \(\mathrm{BaF_2}\) at \(f = 900\ \text{kHz}\).
The density of the specimens is 65–70% of the specific weight of the substance.

I—\(\mathrm{CaF_2}\), II—\(\mathrm{SrF_2}\), III—\(\mathrm{BaF_2}\)

In the group of fluoride compounds of Ca, Sr, and Ba, both for porous specimens and for dense ones, the greatest value of $\operatorname{tg}\delta$ is exhibited by BaF$_2$, and the smallest by CaF$_2$.

In the group of chloride compounds of Ca, Sr, and Ba, the greatest losses are observed for SrCl$_2$ (Fig. 4).

The variation of $\operatorname{tg}\delta$ for CaCl$_2$ and BaCl$_2$ is in agreement with the principal physicochemical properties of these compounds and with the energy of the crystal lattice. The observed deviations from the general regularity in the value of $\operatorname{tg}\delta$ for SrCl$_2$ are evidently connected with the crystalline structure of strontium chloride. The type of crystal lattice and the crystallographic system of SrCl$_2$ differ from the crystal lattice of BaCl$_2$ and CaCl$_2$.

Figures 5 and 6 present the dependences $\operatorname{tg}\delta = f(T)$ for Ba compounds, in which a successive replacement of the oxygen ion by F$'$ and Cl$'$ ions takes place. The value of the dielectric loss angle for SrO, SrF$_2$, SrCl$_2$ and BaO, BaF$_2$, BaCl$_2$ increases as the binding energy of the ions in the crystal lattice decreases.

The frequency dependence of $\operatorname{tg}\delta$ for the compounds under consideration is presented in Figs. 7, 8, and 9.

For specimens whose relative density is 65–70% of the specific gravity of single crystals, $\operatorname{tg}\delta$ of the oxides and halide compounds of group II elements in the range 450–900 kc decreases with increasing frequency. For denser specimens of CaF$_2$, SrF$_2$, and BaF$_2$, in the range 500–2000 kc, it likewise decreases with increasing frequency. The temperature maximum of $\operatorname{tg}\delta$ for a given substance is thereby shifted toward higher temperatures (Fig. 9).

It should be noted that the dielectric losses of porous polycrystalline specimens of compounds of group II elements depend on the conditions under which the experiment is carried out.

In air, the dielectric losses are considerably higher than in vacuum (Fig. 10). The value of $\operatorname{tg}\delta$ in air for BaO at $T = 25^\circ$C and $f = 450$–900 kc is almost two orders of magnitude higher than in vacuum; for SrO, it is more than one order of magnitude higher. The main reason for the increased value of $\operatorname{tg}\delta$ in air is apparently the presence of open pores in which adsorption of water vapor occurs.

Conclusions

1. The dielectric loss angle of oxides and halide compounds of group II elements in vacuum at 25°C and $f = 450$–900 kc has a relatively small value and, with the exception of ZnO and SrCl$_2$, does not exceed $4 \cdot 10^{-3}$.

2. The dielectric losses for polycrystalline specimens of the compounds in air are considerably higher than in vacuum.

3. The tangent of the dielectric loss angle in the range 450–900 kc varies inversely with frequency.

4. With increasing temperature, the dielectric losses for specimens whose relative density is 65–70% of the specific gravity of a single crystal increase. For specimens having a relatively high density, a temperature maximum is observed.

For a given temperature, $\operatorname{tg}\delta$ of polycrystalline sintered specimens of compounds of metals of the second group increases with decreasing energy of the crystal lattice of the substance. The regularity noted occurs both for compounds having a common cation and for compounds with a variable cation.

Fig. 3. Temperature dependence of $\lg \tan \delta$ for $\mathrm{CaF_2}$, $\mathrm{SrF_2}$, and $\mathrm{BaF_2}$ at $f = 900$ kc/s. The relative density of the specimens is 95% of the theoretical value.
I — $\mathrm{CaF_2}$, II — $\mathrm{SrF_2}$, III — $\mathrm{BaF_2}$

Fig. 4. Temperature dependence of $\lg \tan \delta$ for $\mathrm{CaCl_2}$, $\mathrm{SrCl_2}$, and $\mathrm{BaCl_2}$ at $f = 900$ kc/s.
I — $\mathrm{CaCl_2}$, II — $\mathrm{SrCl_2}$, III — $\mathrm{BaCl_2}$

Fig. 5. Temperature dependence of \(\lg \tg \delta\) for \(\mathrm{SrO}\), \(\mathrm{SrF_2}\), \(\mathrm{SrCl_2}\), at \(f = 900\ \mathrm{kc/s}\).
I — \(\mathrm{SrO}\), II — \(\mathrm{SrF_2}\), III — \(\mathrm{SrCl_2}\).

Fig. 6. Temperature dependence of \(\lg \tg \delta\) for \(\mathrm{BaO}\), \(\mathrm{BaF_2}\), \(\mathrm{BaCl_2}\), at \(f = 900\ \mathrm{kc/s}\).
I — \(\mathrm{BaO}\), II — \(\mathrm{BaF_2}\), III — \(\mathrm{BaCl_2}\).

Fig. 7. Dependence of \(\lg \tan\delta\) on frequency for BeO, MgO, CaO, SrO, BaO at \(T = 310^\circ\mathrm{C}\)

I—BeO, II—MgO, III—CaO, IV—SrO, V—BaO

Fig. 8. Dependence of \(\lg \tan\delta\) on frequency for CaF\(_2\), SrF\(_2\), BaF\(_2\) at \(T = 20^\circ\mathrm{C}\).

The density of the specimens is 65–70% of the specific gravity of the substance.

I—CaF\(_2\), II—SrF\(_2\), III—BaF\(_2\)

Fig. 9. Temperature–frequency dependence of \(\lg \tan \delta\) for \(\mathrm{CaF_2}\). The density of the specimens is 95% of the specific weight of the substance.
I — \(f = 500\) kHz, II — \(f = 900\) kHz, III — \(f = 2000\) kHz.

Fig. 10. Dependence of \(\lg \tan \delta\) on frequency in air and in vacuum for \(\mathrm{SrO}\), \(\mathrm{BaO}\), and \(\mathrm{ZnO}\) at \(T = 25^\circ\mathrm{C}\):
a) in air, b) in vacuum.

References

1. A. A. Vorob’ev and E. K. Zavadovskaya, Proceedings of the Tomsk Polytechnic Institute, 71, 3, 1953.

2. A. A. Vorob’ev and E. K. Zavadovskaya, Electrical Strength of Solid Dielectrics, Gostekhizdat, 1956.

3. K. A. Vodop’yanov and T. I. Galibina, Proceedings of the Tomsk Polytechnic Institute, 91, 269, 1955.

4. G. I. Skanavi and V. I. Sarafanov, ZhETF 27, 735, 1954.

5. G. I. Skanavi and V. V. Maslov, ZhETF 27, 1954.

6. R. S. Bever and R. L. Sproull, Phys. Rev. 83, 804, 1951.

Errata

Izv. TPI, vol. 95.