Experimental Studies of the Relationship Between the Properties of Ionic Dielectrics and Their Composition

A. A. Vorob’ev

A general theory of the properties of ionic dielectrics that has found broad practical application does not exist. One of the most general characteristics of a substance, connected with all its properties, is the energy of interaction between particles. Experimental data show that all the other characteristics of ionic dielectrics are determined by the lattice energy, the magnitude of which, for dielectrics of a single series, characterizes their properties.

The lattice energy is related to the polarizability of ions and to the properties of the dielectric determined by polarization phenomena. With an increase in the polarizability of the ions forming compounds of metals of the first and second groups of Mendeleev’s table, the energy of the crystal lattice decreases (Figs. 1, 2), the refractive index increases (Figs. 3, 4), and the dielectric constant increases. As the lattice energy decreases, the boundary of intrinsic absorption in the ultraviolet and infrared parts of the spectrum shifts toward longer wavelengths. The maximum of the $F$ absorption band also shifts toward the longer-wavelength part of the spectrum when the energy of interaction between ions decreases.

According to the data of Lefeld, B. M. Gokhberg, K. A. Vodop’yanov, A. P. Nakhodnova, V. I. Sarafanova, and others, with increasing lattice energy the activation energy increases and the ionic electrical conductivity decreases (Figs. 5, 6), as do the dielectric losses in ionic dielectrics (Fig. 7, Fig. 8a and Fig. 8b).

These regularities were observed for compounds of metals of the first and second groups, taken in the form of single crystals and sintered powders.

The electrical strength of ionic crystals increases with increasing lattice energy (Fig. 9).

According to measurements by A. F. Kalganov, the energy expended in the breakdown of solid dielectrics increases with increasing lattice energy.

According to measurements by V. D. Kuchin, the electrical strength of NaCl and KCl in the low-temperature region, under constant voltage and pulses down to $10^{-7}$ sec, increases with increasing temperature. For pulses of $(2 \div 3)\,10^{-8}$ sec, $E_{\mathrm{br}}$ does not depend on temperature and exceeds the value of $E_{\mathrm{br}}$ at an exposure of $10^{-6}$ sec by a factor of 3. The volt-time characteristics of the indicated ionic crystals at positive tempera-

Fig. 1. Change in the crystal-lattice energy of alkali-halide compounds with composition

Fig. 2. Change in the crystal-lattice energy of halide compounds of metals of the second group of Mendeleev’s table as a function of composition

Fig. 3. Dependence of the refractive index \(n_D\) (at \(\lambda_D = 5893\,\text{Å}\)) on the lattice energy for single crystals of halide compounds of metals of the first and second groups (according to measurements by Gessmann, Kahn, and Shockley).

— lattice structure of the NaCl type,
– – – lattice structure of the CsCl type.

Fig. 4. Dependence of the refractive index on the lattice energy for oxides of metals of the second group of the Mendeleev periodic table.

Fig. 5. Dependence of the logarithm of electrical conductivity at \(t^\circ = 400^\circ\mathrm{C}\) (xxx) and \(t^\circ = 600^\circ\mathrm{C}\) (ooo) on lattice energy for crystals of alkali-halide salts.

Fig. 6. Dependence of the logarithm of the specific electrical conductivity of oxides of Group II metals on

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

Fig. 7. Dependence of \(\tg\delta\) on lattice energy

Fig. 8a. Dependence of \(\tg\delta\) on temperature for oxides of metals of the second group, at
\(f = 900\ \mathrm{kHz}\)

Fig. 8b. Dependence of \(\tg\delta\) on frequency for CaF\(_2\), SrF\(_2\), BaF\(_2\), at \(t^\circ = 100^\circ\mathrm{C}\)

…temperatures have a minimum in the region of exposures of \(10^{-6}\) sec. At negative temperatures \(E_{\mathrm{br}}\), down to \(10^{-7}\) sec, does not depend on the time of application of the voltage. This circumstance confirms the assumption of the ionic nature of the space charge in ionic crystals for voltage-action times of \(10^{-5}\div 10^{-6}\) sec.

According to oscillographic measurements by G. A. Andreev, in the region of high temperatures an exponential decrease of the electric strength is observed for rock salt. The magnitude of the damping resistance in the specimen circuit does not affect the electric strength at high temperatures. In the temperature region where a rapid decrease of the electric strength is observed (\(125\)—\(175^\circ\)C for NaCl), a maximum of the current and of the energy of breakdown formation is observed.

Fig. 9. Dependence between the value of the electric strength of alkali-halide salts and the energy of the crystal lattice

K. K. Sonchik determined that, in a uniform field, the duration of the processes leading to breakdown of a crystal reaches \(10^{-8}\) sec, decreasing with increasing electric strength.

E. K. Zavadovskaya established a relation between the magnitude of the electric strength and many physicochemical properties of dielectrics and external conditions. The electric strength increases with increasing stability of the chemical compound (Fig. 10), hard-

Fig. 10. Electric strength and heat of formation of chemical compounds in the gaseous state \(Q\)

ness, melting point (Fig. 11), increasing binding energy of the most weakly bound electrons in dielectrics, decreasing electron mobility, etc. Space charge increases the breakdown voltage of crystals.

According to data of G. A. Vorob’ev, the electric strength of single crystals of alkali-halide salts in uniform and nonuniform fields, with increasing duration of voltage action from \(10^{-8}\) sec, was—

… decreases (Fig. 2, [5]). At an exposure of \(10^{-7}—10^{-6}\) sec \(E_{\mathrm{pr}}\) reaches a minimum. Then, probably owing to the action of the space charge, the electric strength of the single crystals increases somewhat.

The volt-time dependence for organic glass decreases monotonically with increasing exposure and contains no region of minimum values.

Fig. 11. Dependence of Mohs hardness (H), electric strength (\(E_{\mathrm{pr}}\)), and melting temperature (\(T_{\mathrm{pl}}\), °C) on the lattice energy of crystals of alkali-halide salts

The volt-time dependence for rock-salt crystals containing color centers lies lower than for uncolored salt. Photoconductivity lowers the volt-time characteristic of the crystals still more than do color centers. The average velocity of propagation of the discharge in single crystals is \(10^6\) cm/sec (Fig. 12). It increases with increasing electric strength, overvoltage, and lattice energy, and decreases with the thickness of the specimen.

At small exposures in single crystals of NaCl, KCl, KBr, KI and in organic glass, G. A. Vorob'ev observed one and the same polarity effect: a lowering of \(U_{\mathrm{pr}}\) for positive polarity of the point. The same phenomenon is observed in the breakdown of air. This circumstance, as well as the proportionality of the rate of discharge development to the lattice constant, indicates the predominant role of impact ionization in the process of breakdown of solid dielectrics.

The electric strength of crystals over a wide range of exposures increases with increasing lattice energy.

A. D. Shchelokov found that irradiation with a dose of X-rays causes an increase in the conductivity of rock salt. The electrical conductivity of the irradiated crystal increases with time and reaches a certain steady value.

The relative increase in the electrical conductivity of crystals under irradiation with X-rays, with increasing temperature,

decreases, disappearing altogether at \(100\)—\(150^\circ\)C. The activation energy for the conductivity added by irradiation is of the order of hundredths of an electron-volt, whereas without irradiation it is of the order of \(0.8\)—\(1\) eV.

With increasing lattice energy of alkali-halide salt crystals, the coefficient of absorption of X-rays, and the intensity and duration of phosphorescence in visible light of crystals under irradiation by X-rays, decrease. Lithium fluoride crystals do not fluoresce under X-ray irradiation.

When determining the coefficient of X-ray absorption in two-component systems (single crystals) KCl—RbCl, KCl—KBr, NaCl—NaBr as a function of composition, positive nonadditivity was found (the absorption coefficients of the system are greater than the sum of the absorption coefficients of the components), whereas for the lattice constant (according to measurements by A. N. Kislina) negative nonadditivity is observed. Both facts are in qualitative agreement.

Fig. 12. Dependence of the discharge formation time \((t_{\phi})\) and the average discharge-development rate \((V_{\mathrm{av}})\) on the lattice energy of NaCl (oo), KCl (··), KBr (xx), and KJ (△△) crystals.

A. A. Vorob’ev, N. A. Prikhod’ko, K. M. Kevroleva, and A. V. Astafurov measured the electrical strength under different exposures for ice in thick and thin layers.

The electrical strength of ice under short pulses is comparable with the strength of rock salt. According to A. V. Astafurov, the volt-second characteristics for ice at different thicknesses have the usual course. With increasing thickness, the electrical strength of ice decreases. The polarity effect in a nonuniform field is also manifested at large thicknesses: the electrical strength for negative pulse polarity is always higher than for positive polarity.

In a strong electric field, ice luminesces. Figure 13 presents a photograph of a piece of ice glowing in an electric field (pulse \(100\) kV, field—point against plane, distance between electrodes \(7\) cm).

K. M. Kevroleva showed that the electrical strength of crystal hydrates (gypsum, copper sulfate, talc, and other crystals and pressed powders) depends on the number of water molecules entering the crystal lattice. The electrical strength of crystal hydrates increases with increasing lattice energy and with decreasing number of water molecules.

According to data of A. M. Trubitsyn and E. K. Zavadovskaya, and A. N. Kislina, the electrical strength and hardness of single crystals of solid solutions increase with increasing stability of the chemical compound and with decreasing amount of heat absorbed during formation of the solid solution. Measurements by M. S. Ivankina showed that the greatest amount of heat is absorbed in the formation of an equimolar solid solution, which, thus, will be

the least strong of all the compounds of this system. As the solution is stored, it ages, accompanied by a decrease in the amount of heat absorbed during formation of the solid solution.

In the studies of A. N. Kislina and N. V. Beinarovich, a change was shown in the lattice constant and in the refractive index as a function of the composition of the solid solution and the time of storage. If, after the preparation of single crystals of solid solutions of certain systems, the value of the refractive index of light differs from those calculated by the additivity rule, then over the course of storage of the crystals it changes and reaches the values obtained by the mixing rule.

Fig. 13. Photograph of ice in an electric field

Measurements of the electrical conductivity of single crystals of solid solutions and mechanical mixtures for alkali-halide compounds, carried out by E. K. Zavadovskaya, Burgraev, and A. P. Borovikova; measurements of dielectric losses, carried out by K. A. Vodopyanov, M. A. Krivov, and G. I. Galibina; data on electric strength obtained by Hippel, Hippel and Lee, A. M. Trubitsyn, L. G. Koretskii, A. N. Kislina, and others for single crystals of alkali-halide compounds, made it possible to establish the rules according to which the properties of solid solutions change, and their aging, as a function of composition.

The physical properties of solid solutions are related to the heat absorbed during their formation, which varies with chemical composition either along a curve with a minimum, or along a curve with a maximum in the region of approximately equal composition of the components. With a decrease in the heat absorbed during formation of the solid solution, its melting temperature and electric strength increase (Fig. 14), while electrical conductivity and dielectric losses decrease (Fig. 6 [6]).

N. P. Bogoroditskii, A. I. Avgustinik, N. S. Antselevich, G. I. Skanavi, and V. I. Sarafanov studied the electrical properties of alloys of metal oxides forming complex multiphase systems.

Zirconium dioxide forms solid solutions with calcium oxide at a temperature of about 1700°C.

In Figs. 15 and 16, according to the measurements of A. I. Avgustinik and N. S. Antselevich, the variation with temperature of the resistance at constant voltage and of the dielectric losses at a frequency of \(10^6\) Hz is presented as a function of composition for the system CaO—ZrO\(_2\). The character of the temperature dependence indicates the ionic nature of the processes considered. With increasing concentration of calcium oxide in the specimens, their resistance increases and the dielectric losses of the compositions decrease. The minimum value of losses and electrical conductivity corresponds

Fig. 14. Dependence of the electric strength and the difference of the heats of dissolution in water of a mechanical mixture and a solid solution \((Q)\) on composition for single crystals of the KCl—RbCl system.

Fig. 15. Dependence of the logarithm of the specific resistance of the CaO—ZrO₂ system on temperature. CaO content in the system: curve 1—10%; 2—20%; 3—30%; 4—40%; 5—50%; 6—5%.

composition with equal content of the components (curve 5), when the chemical compound \(\mathrm{CaZrO_2}\) is formed.

In Fig. 17 the dependence of dielectric losses at a frequency of \(10^6\) Hz and a temperature of \(100^\circ\mathrm{C}\) is presented for the \(\mathrm{TiO_2}—\mathrm{SiO_2}\) system, according to N. P. Bogoroditskii.

In the region of equal content of the components, a maximum of dielectric losses is observed, associated with the formation of solid solutions of the components in this region and with loosening of the lattice.

Fig. 16. Dependence of \(\operatorname{tg}\delta\) of the \(\mathrm{CaO}—\mathrm{ZrO_2}\) system on temperature. CaO content in the system: 1—10%; 2—20%; 3—30%; 4—40%; 5—50%; 6—60%; 7—80%.

Concentration dependence of \(\operatorname{tg}\delta\) at \(t = 100^\circ\mathrm{C}\) for the \(\mathrm{TiO}—\mathrm{SiO_2}\) system at \(f = 1 \cdot 10^6\) Hz.

Fig. 17. Dependence of \(\operatorname{tg}\delta\) of the \(\mathrm{TiO_2}—\mathrm{SiO_2}\) system on chemical composition. \(t^\circ = 100^\circ\mathrm{C}\), \(f = 10^6\) Hz (according to N. P. Bogoroditskii).

For complex alloys of metal oxides and mechanical mixtures of components, the same simple regularities are observed as for systems formed from compounds of metals of the first group. Electri-

properties of mechanical mixtures change additively with composition. The properties of solid solutions change depending on the binding energy of the ions. With equal component content and the greatest weakening of the ion bond energy, a maximum of the dielectric constant, dielectric losses, and electrical conductivity is observed.

Dielectric losses are caused by physical processes associated with polarization of the dielectric, structural inhomogeneity, the presence of conducting and semiconducting inclusions, through conductivity, etc.

N. P. Bogoroditskii believes that, among the possible mechanisms of dielectric losses in ceramic materials at high frequencies, the greatest attention should be given to dielectric losses caused by displacement of the structure’s ions in a high-frequency electric field—polarization losses (ionic relaxation losses). The latter is due to the fact that losses due to through conductivity in most ceramic materials are small, while losses due to inclusions can be eliminated by proper technology.

Ionic relaxation losses are caused by displacements of ions under the influence of an alternating electric field in connection with their thermal motion, and must depend on the structure of the material and on the character of the packing of ions in the lattice. At present, dielectric losses associated with ion displacement, owing to the high sensitivity of measurement methods, are observed for almost all ionic compounds, including ionic crystals.

Impurities in ionic crystals, by weakening the ion bond energy, cause an increase in dielectric losses.

N. P. Bogoroditskii, V. A. Ioffe, and others showed that in glasses the role of dielectric losses caused by ion displacement (relaxation losses) is so significant that even in the region of low temperatures a clearly expressed dependence of dielectric losses on temperature is observed.

The regularities of dielectric losses associated with ion displacement in glasses and crystals must be taken into account when selecting the components of ceramic materials, metal oxides and their compounds.

Changes in the physical properties of single crystals and sintered powders with composition under various external conditions make it possible to understand the regularities for complex technical dielectrics and to recommend directions in the search for dielectrics with the required properties.

Ionic dielectrics with a large value of lattice energy, and mixtures formed with less heat absorption, possess a high melting point, low thermal conductivity, high mechanical and electrical strength, low electrical conductivity, low losses, and a small dielectric constant.

P. A. Savintsev established a relation between the physicochemical properties of crystals and the ionic concentration $\alpha$:

\[ \alpha = \frac{D}{M}\cdot 10^3, \]

(where $D$ is the density, $M$ is the molecular weight of the crystal). For ionic crystals it has been established that, with increasing ionic concentration, the electrical strength, volume resistivity of the crystals, activation energy, heat of fusion, heat of sublimation, and heat of formation of the solid compound increase.

With increasing ionic concentration, the refractive index of light, the coefficient of linear expansion, and dielectric losses decrease. The mechanical properties of crystals are also associated with ionic concentration.

With increasing ionic concentration, the hardness of crystals, determined by scratching, drilling, damped-oscillation, and grinding methods, increases.

With increasing ionic concentration, the shear modulus, Young’s modulus, and flow pressure increase.

It has been established that with increasing ionic concentration the heat capacity of crystals, entropy, and heat of hydration decrease.

Ionic concentration is associated with the properties of liquid dielectrics. With increasing ionic concentration, the electrical strength of a homologous series of liquid dielectrics decreases.

The use of ionic concentration for determining the properties of crystals with impurities has proved successful. A relationship has been established between ionic concentration and electrical strength, dielectric losses, electrical conductivity, dielectric permittivity, and the heat of formation of a solid solution.

Ionic concentration is associated with the melting temperature of binary and ternary eutectics and with the temperature coefficient of hardness of alloys.

Using the experimental data of A. I. Avgustinik and N. S. Antselevich, P. A. Savintsev showed that in solid solutions of the systems $\mathrm{ZrO_2—MgO}$ and $\mathrm{ZrO_2—CaO}$, with increasing ionic concentration, dielectric permittivity increases, while dielectric losses and conductivity decrease.

The relationships found confirm the considerable influence of the principal crystal structure on the properties of crystals. Ionic concentration may be regarded as an aggregate characteristic of many properties of crystals.

REFERENCES

1. Vorob’ev A. A. Physical properties of ionic crystalline dielectrics (in press).

2. Belyankin D. S., Lapin V. V., Toropov N. A. Physicochemical systems of silicate technology. Promstroiizdat, 1954.

3. Bogoroditskii N. P. Dielectric losses in radio ceramics. Proceedings of a scientific-technical conference on radio ceramics. Leningrad, 1955.

4. Skanavi G. I. Physics of dielectrics. GITTL, 1949.

5. Vorob’ev A. A., Vorob’ev G. A. Pulse breakdown of solid dielectrics (present collection).

6. Potakhova G. I. Dielectric losses in solid solutions of alkali-halide crystals at high frequency (present collection).