Electrical Strength and Chemical Resistance of Compounds

A. A. Vorob'ev and E. K. Zavadovskaya

The electrical strength of crystals of alkali-halide compounds increases with increasing lattice energy \(U\) [1], the ionization energy of the alkali-metal atom \(W_i\) [2], and the electron affinity energy of the halogen atom \(W_{\mathrm{cp}}\).

As is known, these quantities determine the heat of formation. The heat of formation of a chemical compound from free elements can be calculated by means of cyclic processes.

The equation of the energy balance for a cyclic process leading to the formation of a solid chemical compound from a metal and a gaseous halide [3] is written in the form:

\[ Q_{mm}=-\left(S_{\mathrm{met}}+\frac{1}{2}D_{\mathrm{gal}}+W_i\right)+W_{\mathrm{cp}}+Q_m+S_{\mathrm{comp}}, \tag{1} \]

where \(Q_{mm}\) is the heat of formation of the solid body,
\(S_{\mathrm{met}}\) is the heat of sublimation of the metal,
\(D_{\mathrm{gal}}\) is the heat of dissociation of the halide molecules,
\(Q_m\) is the heat of formation of the vapor molecule from free ions.

The quantities \(W_i\), \(U\), and \(Q_m\) considerably exceed all the others entering into formula (1). Thus, the magnitude and sign of the heat of formation are determined mainly by the quantities \(W_i\), \(U\), and \(Q_m\).

The magnitude of the lattice energy \(U\) and of the heat of formation of the molecule \(Q_m\) for compounds of different elements with one and the same valence differ little from one another. Therefore, the magnitude and sign of the heat of formation of the solid body \(Q_{mm}\) are determined primarily by the ionization energy \(W_i\).

Table 1 gives experimentally determined data for the magnitude of electrical strength in MV/cm, the heats of formation of the vapor molecule and of the solid compound, and the molecular heat of sublimation of the solid chemical compounds under consideration at \(18^\circ\). All data are given in kcal/mole.

Figure 1 shows the dependence of electrical strength on the heat of formation of the molecule.

Figure 2 shows the dependence of electrical strength on the heat of sublimation of solid solutions.

Figure 3 shows the dependence of electrical strength on the heat of formation of the solid compound.

An increasing dependence has been obtained between the quantities considered. The families of curves presented in Figs. 1, 2, and 3 make it possible to draw the following conclusions. The electrical strength of a compound increases with increasing heat of formation and heat of sublimation, that is, with its chemical resistance.

Table 1

Electrical strength of crystals of alkali-halide salts, heat of formation of solid compounds \(Q_{mt}\) at \(25^\circ\mathrm{C}\) and \(760\ \mathrm{mm}\ Hg\), with the corresponding states of the initial atoms; heat of formation of the vapor molecule and molecular heat of sublimation of solid chemical compounds at \(18^\circ\), in kcal/mole.

With the alkali metal unchanged, and when the halide is replaced by another with greater electron affinity, an increase in the electrical strength of the compound is observed. For a given value of the heat of formation, replacing the alkali-metal atom by another, with a lower ionization potential, gives a compound with lower electrical strength. The increasing dependence of electrical strength on the heat of formation of the compound may also be extended to other dielectrics.

Fig. 1. Electrical strength and heat of formation of chemical compounds in the gaseous state \(Q_m\)

It has already been pointed out that the oxides of many elements of the Mendeleev table form materials with high electrical strength [4]. These compounds also have a high value of the heat of formation, indicated—

Fig. 2. Electrical strength and heat of sublimation of solid compounds at 18°C

—in parentheses in kcal/mole, for example, the compounds: Nb₂O₅ (442), BeO (135), MgO (146), SrO (140), BaO (133), etc.

Fig. 3. Electrical strength and heat of formation of a solid compound

Glasses have a high value of the heat of formation, for example: CaOAl₂O₃ (620), 2CaOAl₂O₃ (857), 3CaOAl₂O₃ (1098), SrSO₃ (364), etc. It is known that glasses also have a high value of electrical strength. The considerations expressed in the present case explain the exis—

the existence of materials with a high value of electrical strength and indicate the direction for preparing these materials.

The data presented show that the electrical strength of a dielectric is related to its chemical composition and to the strength of the chemical compound.

The heat of formation \(Q_m\) of vapor molecules can be calculated if polarization is neglected and known assumptions are made concerning the spatial arrangement of the atoms in the molecule. The formula for calculating the energy \(Q_m\) is analogous to the formula for calculating lattice energy by means of the Madelung constant \(a\).

For a molecule of composition \(AX_n\), where \(X\) has valence \(Z\), the formula for determining the energy of formation has the form:

\[ Q_m = \frac{Z^2 e^2 A \cdot \beta}{R_1 + R_2}, \tag{2} \]

where \(R_1\) and \(R_2\) are the radii of the ions,
\(A\) is Avogadro’s number,
\(\beta\) is a factor analogous to the Madelung factor, which also takes into account the mutual arrangement of the atoms in the molecule and is given in tables.

The factor \(\beta\) is always smaller than the factor \(a\). This follows from the fact that the arrangement of ions in a crystal lattice, where each ion is surrounded by other ions of opposite sign, can give a higher energy than the one-sided bond in a vapor molecule. When polarization is taken into account, the magnitude of the energy of formation of vapor molecules increases by 10–15% in comparison with formula (1).

It follows from formula (2) that, other conditions being equal, as the radii of the ions entering into the compound increase, the heat of formation of the molecule of the compound decreases. In this case, an increase is observed in the solubility of the compounds, a decrease in the mechanical strength of the solid, and a lowering of the melting or boiling temperature [5]. To this it should also be added that, with an increase in the radii of the ions, the electrical strength of the dielectric will also decrease (Fig. 1).

The lattice constant is defined as the sum of the ionic radii. Thus, the electrical strength of the compound will decrease with an increase in the lattice constant. This agrees with the results of theory and experiment [6].

CITED LITERATURE

1. A. A. Vorob’ev and E. K. Zavadovskaya. DAN, 81, 375, 1951.
2. A. A. Vorob’ev. Izvestiya Tomskogo politekhnicheskogo instituta, 63, 3, 1944.
3. E. Rabinovich and E. Thilo. Periodic System of the Elements. Moscow, GTTI, p. 343, 1933.
4. E. K. Zavadovskaya. DAN, 82, 709, 1952.
5. A. E. Fersman. Geochemistry, III, ONTI, p. 77, 1937.
6. E. K. Zavadovskaya. DAN, 82, 565, 1952.