Electric Strength of Dielectrics and Their Dielectric Permittivity

E. K. Zavadovskaya

In the formulas we have obtained for determining the electric strength of dielectrics, the dielectric permittivity enters into the expression for electric strength.

The magnitude of the electric strength obtained by us from the condition of a minimum of electron mobility turns out to be proportional to the dielectric permittivity \(\varepsilon\).

\[ E_{np}=\frac{\varepsilon W}{ea}, \tag{1} \]

where
\(\varepsilon\) is the dielectric permittivity,
\(W\) is the energy of the electrons,
\(e\) is the electron charge,
\(a\) is the lattice constant.

Figure 1 presents the dependence between the electric strength of crystals of alkali-halide salts and their dielectric permittivity, constructed by us from experimental data. From Fig. 1 it follows that the dielectrics possessing greater electric strength are those which have a larger dielectric permittivity. This is in agreement with (1). However, the linear dependence between the magnitude of the electric strength and the dielectric permittivity for crystals of alkali-halide salts, as follows from (1), is not observed.

Fig. 1. Dependence between the electric strength of crystals of alkali-halide salts and their dielectric permittivity \(\varepsilon\).

Possibly this is explained by the fact that some of the quantities entering into (1) are, in turn, connected with the dielectric permittivity. In this case the dependence of the electric strength on the dielectric permittivity will be more complicated.

We arrive at the dependence of electric strength on dielectric permittivity from other considerations as well. It is known that in dielectrics placed in an electric field, mechanical stresses arise, the magnitude of which is determined by the expression:

\[ F=\frac{\varepsilon_0 E^2}{8\pi}, \tag{2} \]

where \(\varepsilon_0\) is the fraction of the dielectric permittivity due to the displacement of electrons \((\varepsilon_0=n^2)\), where \(n\) is the refractive index of light.

It follows from formula (2) that large mechanical stresses arise in dielectrics with greater dielectric permittivity. They can cause cracking in crystals and thereby promote breakdown. The electric strength of such dielectrics will be lower.

Fig. 2. Dependence between the electric strength of crystals of alkali-halide salts and their optical dielectric permittivity \(\varepsilon_0\).

Formula (2) shows that the dependence of electric strength on the fraction of dielectric permittivity due to the displacement of electrons must be of the opposite character to the dependence of electric strength on the total dielectric permittivity.

Figure 2 presents the dependence between electric strength and \(\varepsilon_0\). It follows from Fig. 2 that the dielectrics having the smaller dielectric permittivity \(\varepsilon_0\) will possess the greater electric strength. Thus, the experimental data agree with the basic physical propositions that lead us to the dependence of electric strength on dielectric permittivity. It is also of interest to compare electric strength with another component of dielectric permittivity \((\varepsilon-\varepsilon_0)\), due to the displacement of the ions of the dielectric in an electric field.

Figure 3 presents the dependence between electric strength and \((\varepsilon-\varepsilon_0)\). It follows from Fig. 3 that the dielectrics possessing the greater dielectric permittivity have the greater electric strength.

The different character of the dependence of electric strength on \(\varepsilon_0\) and \((\varepsilon-\varepsilon_0)\) can be explained from the point of view we have developed.

It was shown that dielectrics with lower polarizability should possess greater electric strength, and, consequently, their dielectric permittivity due to ion polarization should be smaller. In dielectrics with greater dielectric permittivity \((\varepsilon-\varepsilon_0)\), the ions have a greater possibility of being elastically displaced from the equilibrium position and returning to it again. Such dielectrics may have a higher electric strength.

A number of Soviet researchers (Vorob’ev, Prikhod’ko, Vul, and Gorelik) studied the dependence of the electric strength of ferroelectrics on the magnitude of the dielectric permittivity. For the ferroelectrics investigated, no dependence between the magnitude of the strength and the dielectric permittivity was obtained.

Fig. 3. Dependence between the electric strength of crystals of alkali-halide salts and the ionic component of their dielectric permittivity \((\varepsilon-\varepsilon_0)\).

It is known that the dielectric permittivity in ferroelectrics is associated with the rotation of domains. Therefore the question considered here, concerning the relation between electronic and ionic polarization in a dielectric and its electric strength, was not resolved by the experiments of the aforementioned researchers.

It would be of interest to carry out systematic investigations of the dependence of electric strength on dielectric permittivity for dielectrics and, in particular, for solid solutions of alkali-halide salts.

I express my gratitude to Prof. A. A. Vorob’ev for discussion of the questions raised in the article.