Electrical Properties of Ionic Compounds of Group II Elements in Relation to the Ion Interaction Energy in the Crystal Lattice

A. P. Nakhodnova

The electrical properties of alkali-halide compounds [1, 2, 3] are determined by the position of the elements forming the compound in D. I. Mendeleev’s table and by external conditions.

In compounds of the elements of Group I, in passing from Na to K and further, a regular change is observed in the crystal-lattice energy for oxides, sulfides, and halides.

A decrease in the binding energy in compounds of the elements of Group I is accompanied by an increase in specific electrical conductivity and dielectric losses, and by a decrease in electric strength.

In this connection the question arises whether the principal thermochemical and electrical properties of a substance are not determined by the energy of interaction of the ions in the lattice. To resolve this question, it is of interest to trace the regularities in the change of electrical properties for ionic compounds of the elements of Group II.

Known studies [5, 6, 7, 8, 9, 10] of the temperature dependence of the electrical conductivity of oxides of Group II metals under conditions of disturbed stoichiometric composition, the presence of impurities of foreign atoms, etc., lack systematic measurements under identical conditions and therefore do not make it possible to draw conclusions about the dependence of the specific electrical conductivity of oxides of Group II metals on the energy of liberation of ions in the lattice (Table 1). On

Table 1

on this basis we undertook measurements of the temperature dependence of the electrical conductivity, dielectric permittivity, and \(\operatorname{tg}\delta\) of oxides of Group II metals and halide compounds of the alkaline-earth metals, and also made comparisons with the energy of the crystal lattice.

Experimental Method

The study of the specific electrical conductivity, \(\varepsilon\), and \(\operatorname{tg}\delta\) was carried out on sintered polycrystalline specimens prepared from chemically pure materials. The specimens were in the form of disks 10–16 mm in diameter and 0.35–0.8 mm thick. The specimens were calcined in a silite furnace for 2 hours at the same, for a given class of chemical compounds, relative sintering temperature. For oxides,

\[ \frac{T^\circ\mathrm{C}\ \text{of sintering}}{T^\circ\mathrm{C}\ \text{of melting}} \simeq 0.46; \]

for the halide compounds of Ca, Sr, and Ba, it was 0.65.

The density of the polycrystalline specimens obtained (relative to the specific gravity of the substance) was 65–75%. Platinum electrodes were applied by thermal spraying to the specimens intended for the study of electrical conductivity. In studying \(\varepsilon\) and \(\operatorname{tg}\delta\), silver electrodes were applied.

Fig. 1

All measurements were carried out in vacuum at a pressure of \(10^{-5}\) mm Hg. To study the temperature dependence of the electrical conductivity, the specimen was placed between two plane-parallel electrodes provided with heating elements and a guard ring.

The measurement of electrical conductivity was carried out with direct current according to the circuit shown in Fig. 1. The potential difference applied to the specimens was varied from 0.2 to 6 V. The temperature was measured with a Mo—Ni thermocouple welded to one of the electrodes.

Fig. 2. Dependence of the logarithm of the specific electrical conductivity of Group II metal oxides on

\[ \frac{10^3}{T}. \]

The temperature dependence of \(\varepsilon\) and \(\tg \delta\) was studied with the aid of a Q-meter and an experimental parallel-plate capacitor in the frequency range 450–900 kHz.

The dielectric constant was determined as the ratio of the capacitance of a capacitor filled with the dielectric to the capacitance of a vacuum capacitor of the same dimensions. Measurements of $\varepsilon$ and $\operatorname{tg}\delta$ were carried out for the oxides in the interval 155–480°C, and for the halide compounds of Ca, Sr, and Ba in the interval 25–255°C.

Dependence of Electrical Conductivity on Temperature

The results of measuring the temperature dependence of electrical conductivity are presented in Figs. 2, 3, and 4.

In all the compounds studied, the usual increase in electrical conductivity with temperature, characteristic of ionic conductivity, is observed.

Fig. 3. Dependence of $\operatorname{tg}\delta$ on $\dfrac{10^3}{T}$ for fluoride compounds of alkaline-earth metals.
I—CaF$_2$, II—SrF$_2$, III—BaF$_2$.

For a given temperature, the electrical conductivity of the oxides, other conditions being equal, increases in going from BeO to BaO (Fig. 2).

A similar character of the change in electrical conductivity is also observed in the group of halide compounds. As an exception, we note SrCl$_2$, for which the value of the specific electrical conductivity is somewhat greater,

than in BaCl₂. In this connection it should be noted that the type of crystal lattice and the crystallographic system of SrCl₂ differ from those of BaCl₂ and CaCl₂. Apparently, this factor accounts for the observed deviations in the value of the specific electrical conductivity.

Fig. 4. Dependence of $\operatorname{tg}\delta$ on $\dfrac{10^3}{T}$ for chloride compounds of alkaline-earth metals.
I — CaCl₂, II — SrCl₂, III — BaCl₂.

From the curves presented in Figs. 2, 3, 4 it is evident that the linear dependence $\ln \sigma = f\left(\dfrac{1}{T}\right)$ has a break, which indicates the presence of two types of current carriers, one of which predominates at lower temperature, the other at higher temperature.

The values of the activation energy, calculated from the slope of the curves
$\ln \sigma = f\left(\dfrac{1}{T}\right)$, are given in Table 2.

Table 2

The magnitude of the activation energy of the current carriers was calculated from the equation:

\[ \sigma = \sigma_1 e^{-\frac{\Phi_1}{kT}} + \sigma_2 e^{-\frac{\Phi_2}{kT}} . \]

In the high-temperature region the activation energy $\Phi_1$ changes in accordance with the crystal-lattice energy. In the low-temperature region the activation energy $\Phi_2$ for all compounds is considerably smaller than $\Phi_1$ and lies within the range 0.15–0.58 eV.

We had previously investigated the dependence $\sigma = f(E)$. Experiments on measuring electrical conductivity as a function of the applied electric field showed that, in the region of weak fields, the specific electrical conductivity of the compounds under consideration increases with increasing field strength (Fig. 5).

Electrical-conductivity measurements were carried out in fields where relatively small deviations from Ohm’s law were observed.

Dependence of $\varepsilon$ and $\operatorname{tg}\delta$ on temperature

The results of measuring the temperature dependence of $\varepsilon$ and $\operatorname{tg}\delta$ are presented in Figs. 6, 7, 8, 9, 10.

Consideration of the measurement results shows that $\varepsilon$ and $\operatorname{tg}\delta$ increase with increasing temperature.

For a given temperature, $\varepsilon$ is the greater, the smaller the crystal-lattice energy of the substance; moreover, with increasing temperature this dependence assumes the most clearly expressed character (Fig. 7). As an exception, the previously mentioned SrCl$_2$ should be noted, for which an increased value of $\varepsilon$ is observed. The dielectric constant of BeO, MgO, CaO, SrO, and CaF$_2$ increases almost linearly with rising temperature. For BaO, SrF$_2$, BaF$_2$, CaCl$_2$, SrCl$_2$, and BaCl$_2$, the change of $\varepsilon$ with temperature does not follow a linear dependence.

Fig. 5. Dependence of specific electrical conductivity on field strength.

I—BeO, II—MgO, III—CaO, IV—SrO.

Fig. 6. Dependence of dielectric permittivity on temperature for BeO, MgO, CaO, SrO, BaO.

\(f = 450 \div 900\ \text{kHz}\).

I—BeO, II—MgO, III—CaO, IV—SrO, V—BeO.

The dielectric losses of the oxides of Group II metals crystallizing in the cubic lattice are relatively small. For BeO, MgO, and CaO at \(155^\circ\mathrm{C}\) and \(f = 900\ \mathrm{kHz}\), \(\tg \delta \simeq 5 \cdot 10^{-4}\); for SrO and BaO the losses are somewhat higher, but even here at \(f = 900\ \mathrm{kHz}\) and \(t = 25^\circ\mathrm{C}\), \(\tg \delta\) does not exceed \(8 \cdot 10^{-4}\).

Fig. 7. Dependence of the dielectric permittivity \(\varepsilon\) on temperature for
\(\mathrm{CaCl_2}\), \(\mathrm{SrCl_2}\), \(\mathrm{BaCl_2}\).

I — \(\mathrm{CaCl_2}\), II — \(\mathrm{SrCl_2}\), III — \(\mathrm{BaCl_2}\).

The dielectric losses of the halide compounds of Ca, Sr, and Ba at \(25^\circ\mathrm{C}\) are approximately of the same order as those of BaO.

The curves of the dependence \(\tg \delta = f(T)\) for all compounds indicate a relatively large temperature coefficient of \(\tg \delta\) (Figs. 8, 9, 10). At a given temperature, \(\tg \delta\) increases regularly on passing from

Fig. 8. Dependence of \(\tg \delta\) on temperature
for oxides of Group II metals

at \(f = 900\ \mathrm{kHz}\).

I — BeO, II — MgO, III — CaO, IV — SrO,
V — BaO, VI — ZnO.

from compounds with higher crystal-lattice energy to compounds with lower crystal-lattice energy, i.e., the character of the change in $\tg \delta$ in the group of oxides and halide compounds of Group II elements is analogous

![Fig. 9 graph]

Fig. 9. Dependence of $\tg \delta$ on temperature for fluoride compounds of the alkaline-earth metals.

I — CaF$_2$, II — SrF$_2$, III — BaF$_2$.

to the change in specific electrical conductivity and dielectric permittivity, and is in agreement with the change in the principal physicochemical properties of the substance.

![Fig. 10 graph]

Fig. 10. Dependence of $\tg \delta$ on temperature for chloride compounds of the alkaline-earth metals.

I — CaCl$_2$, II — SrCl$_2$, III — BaCl$_2$.

Conclusions

1. The temperature dependence of the electrical conductivity of oxides and halide compounds of Group II elements increases according to an exponential law characteristic of ionic conduction.

2. Electrical conductivity increases with decreasing crystal-lattice energy of the substance.

3. The values of the activation energy calculated from the slope of the straight lines $\ln \sigma = f\left(\dfrac{1}{T}\right)$

...of activation of current carriers decrease regularly as the energy of the crystal lattice decreases.

1. The dielectric constant and $\operatorname{tg}\delta$ of ionic compounds of Group II elements, like the electrical conductivity, increase with temperature.

2. At a given temperature, $\varepsilon$ and $\operatorname{tg}\delta$ increase correspondingly with a decrease in the energy of the crystal lattice.

3. The electrical properties of compounds of Group II elements—electrical conductivity, activation energy of current carriers, $\varepsilon$, and $\operatorname{tg}\delta$—are closely related to the physical properties of the substance and are determined by the energy of the crystal lattice.

In conclusion, I consider it my pleasant duty to express my deep gratitude to A. A. Vorob'ev, under whose supervision the present work was carried out, and to G. V. Krivoshchekov for valuable advice.

REFERENCES

1. A. A. Vorob'ev and E. K. Zavadovskaya. Izv. Tomskogo politekhnicheskogo instituta, vol. 71, 1952.
2. E. K. Zavadovskaya. Izv. Tomskogo politekhnicheskogo instituta, vol. 73, 1952.
3. B. Flexig. Electrical Conductivity of Nonmetallic Crystals.
4. S. A. Shchukarev. Vest. Leningrad. Univ., 1954.
5. T. Stöckmann. Zs. f. Phys., 127, 1950.
6. A. Lempieki. Proc. Phys. Soc., 66, 19[[unclear: digit]].
7. Hauffe and L. Tränckler. Zs. f. Phys., 136, 1953.
8. D. Yhng. J. Appl. Phys., 23, 1129—1138, 1952.
9. E. Tell. Phys. Rev., 87, 1952.
10. C. M. Brentano and L. Loldberg. Phy. Rev., 94, 1954.

Novosibirsk,
West Siberian Branch
of the Academy of Sciences of the USSR