DEPENDENCE OF THE ELECTRIC STRENGTH OF CRYSTAL HYDRATES ON THE DURATION OF VOLTAGE EXPOSURE AND CRYSTALLOGRAPHIC DIRECTION

K. M. KEVROLEVA

(Presented by the Scientific Seminar on Dielectrics)

The study of the electric strength of crystal hydrates as a function of the duration of voltage exposure is of interest not only from the standpoint of revealing the breakdown process and determining its regularities, but also because of the purely structural features of crystal hydrates. As follows from the works of K. A. Vodop’yanov [1, 2] and his collaborators [3, 4], molecules of water of crystallization, becoming oriented under the action of an external field, give rise to relaxation losses in crystal hydrates. Depending on the degree to which the molecules of water of crystallization are fixed, one or another number of maxima of dielectric losses is observed in the temperature–frequency dependence of \(\operatorname{tg}\delta\). The magnitude of the maximum of \(\operatorname{tg}\delta\) is determined by a change in the structure of the crystal hydrate and in the concentration of dipoles during dehydration caused by the conditions of the investigation.

On the basis of experimental data, the authors calculated the activation energy, relaxation time, and frequencies of the natural oscillations of the molecules of water of crystallization. According to the data of K. A. Vodop’yanov [5] and M. P. Tonkonogov [4], the relaxation time of water dipoles in the lattice of the crystal hydrates of talc, copper sulfate, and gypsum is of the order of \(10^{-8}\) sec; the frequency of the natural oscillations of the molecules of water of crystallization is \(10^8\ \text{sec}^{-1}\); the activation energy of the molecules of water of crystallization is \((0.6—1.62)\) erg.

As a result of the investigation, it was necessary to determine whether the process of maximum orientational polarization of the molecules of water of crystallization manifests itself at different rates of voltage exposure in strong fields, and how this affects the magnitude of the electric strength of the crystal hydrates studied. Samples from crystals of Rochelle salt, ice, Onot talc, and pressed samples from gypsum hemihydrate were subjected to single pulses of various duration under conditions of a uniform field (Figs. 1–4). As follows from Figs. 1–4, the values of the breakdown field strength show considerable scatter; therefore the question arises of statistical processing of the measurement results [6, 7].

The values closest to the true value of the electric strength are the maximum values \(\dot{E}_{\mathrm{pr}}\), which corresponds to 100% probab-

Fig. 1. Dependence of the electric strength of Rochelle salt on the duration of voltage exposure. Uniform field. \(t=18^\circ\mathrm{C}\). Breakdown along the \(a\)-axis.

Fig. 2. Dependence of the electric strength of Onyot talc on the duration of voltage exposure. Sample thickness \(140\pm10\%\ \mu\mathrm{m}\). Uniform field. \(t=20^\circ\mathrm{C}\).

Fig. 3. Dependence of the electric strength of river ice on the duration of voltage exposure. Uniform field. Sample thickness \(180\pm3\ \mu\mathrm{m}\). Breakdown in a mixture of alcohol with carbon dioxide. \(t=-4^\circ\mathrm{C}\).

breakdown, but random maximum values may not be obtained; therefore, in order to establish the dependence we plot curves according to the values corresponding to a 90% probability of breakdown.

Fig. 4. Dependence of the electric strength of pressed gypsum ($\mathrm{CaSO_4 \cdot \tfrac{1}{2}H_2O}$). Specimen thickness $0.180 \pm 10$ μm. $t = 20^\circ\mathrm{C}$.

In a number of cases (Fig. 5) the course of the dependence of $E_{\mathrm{br}}$, plotted for breakdown probabilities of 100% and 90%, differs only very slightly. Figure 6 presents the dependence of the electric strength of crystal hydrates on the duration of voltage exposure, plotted for a breakdown probability equal to 90%.

Fig. 5. Volt–time characteristic of Rochelle salt in a uniform field at different breakdown probabilities.

The volt–time characteristics of crystal hydrates (Fig. 6) show an increase in electric strength at voltage exposure times of $10^{-7}$ sec and less, which should be attributed to the delay of the discharge, determined by the time of discharge formation under the given conditions [7].

The results for determining the maximum and minimum discharge-formation time \(\tau\), the average maximum and minimum discharge-propagation velocity at different values of the field overvoltage \(U\), are given in Table 1.

Table 1

The following regularities are observed.

1. The discharge-formation time in crystal hydrates is of the same order as in anhydrous alkali-halide crystals and is equal to \(10^{-8}\) sec [7] (the investigation was carried out under identical conditions).

Fig. 6. Dependence of the electric strength of crystal hydrates on the voltage exposure time.
1—Onot talc, 2—ice, 3—Rochelle salt, 4—pressed gypsum.

1. The discharge-propagation velocity is of the order of \(10^{-6}\) cm/sec and increases, for one and the same material, with increasing field overvoltage.

2. Pressed samples of gypsum hemihydrate, as a result of the greater inhomogeneity of their structure, have a large scatter in the discharge-propagation velocity.

Analysis of the volt-second characteristics of crystal hydrates shows that the molecules of water of crystallization do not manifest themselves at short voltage-exposure times of \(10^{-6}\) sec and less and, probably, facilitate thermal breakdown under prolonged voltage exposure (\(10^{-1}\) sec), in direct and alternating current (only Rochelle salt). The noted situation is not general for all crystal hydrates. Breakdown of mica, both at direct and at impulse voltage, is electrical in character.

The effect of maximum orientational polarization of dipoles under the action of a field of a definite frequency could not be detected, since the relaxation time of the molecules of water of crystallization, according to the data of K. A. Vodop’yanov, is of the same order as the discharge lag time in crystal hydrates according to our data, and the effect of discharge formation is more decisive for the magnitude of the electric strength.

The dependence of the electric strength of crystal hydrates on the crystallographic direction was measured on specimens of Rochelle salt and epsomite.

The crystal hydrates investigated in the present work, \(\mathrm{MgSO_4 \cdot 7H_2O}\), \(\mathrm{KNaC_4H_4O_6 \cdot 4H_2O}\), are anisotropic. Anisotropy is manifested in unequal growth rates, unequal cohesion forces in different directions, in the ability of crystals to split along planes parallel to certain plane nets of the crystal lattice, and also in different values of thermal conductivity, refractive index of light, and elasticity [8].

Figures 7 and 8 present photographs of the crystals studied, indicating the directions along which the electric strength was determined.

Fig. 7. Crystal of Rochelle salt \(\mathrm{KNaC_4H_4O_6 \cdot 4H_2O}\). The study was carried out in the plane of the axes \(a\), \(b\), and \(c\).

Whether electric strength, as a physical property, belongs to the isotropic or anisotropic type must be shown by experiment.

The electric strength of epsomite, $\mathrm{MgSO_4 \cdot 7H_2O}$, in our experiments was determined along the $m$ face, perpendicular to it, and along the cleavage plane (the direction parallel to the $b$ plane). In the first two directions the crystals were cut with a wet thread (Fig. 9); in the last, they were split. Breakdown was produced by an impulse voltage of $\sim 10^{-6}$ sec, under conditions of a uniform and nonuniform field in transformer oil. The shape of the specimens is shown in Fig. 10. As Fig. 11 shows, no dependence of the electric strength of epsomite on crystallographic direction was found.

Fig. 8. Crystals of epsomite, $\mathrm{MgSO_4 \cdot 7H_2O}$. The electric strength was determined along the $m$ face, perpendicular to it, and along the cleavage plane (the direction parallel to the $b$ plane).

The independence of the breakdown strength of crystals from crystallographic direction (according to the hypothesis of A. A. Vorob’ev and E. K. Zavadovskaya [9]) is explained by the fact that in thick dielectric layers breakdown develops in microscopically small regions in the direction in which the motion of electrons is facilitated.

In thick dielectric layers, independently of crystallographic direction, breakdown always develops in the direction along which the electric strength will be the smallest. Only for thin dielectric layers, whose thickness is comparable with the mean free path of an electron, will it be possible to detect a dependence of electric strength on crystallographic direction.

Determination of the dependence of the electric strength of Rochelle salt on crystallographic direction is of interest, since Rochelle salt possesses sharp anisotropy.

All ferroelectric properties, namely: spontaneous polarization within the temperature range $(-18)$ to $(+24)^\circ\mathrm{C}$, the piezoelectric effect, unattainable in other known substances, the jump in heat capacity, the nonlinear dependence of polarization on field strength, and other properties occur only along the crystallographic axis $a$.

Fig. 9. Machine for cutting crystals with a wet thread.
aa—hose for supplying water and for water drainage,
b—tubular heater,
c—endless thread,
d—combs for guiding the thread and securing the specimen,
e—drive roller with grooves defining the width of the specimen.

Dielectric  Metal  Metal
Metal  Dielectric  Metal

Uniform field  Nonuniform field

Fig. 10. Shape of specimens for determining the dependence of \(E_{\mathrm{br}}\) on crystallographic direction under conditions of a uniform and a nonuniform field.

Fig. 11. Electric strength of epsomite \(\mathrm{MgSO_4 \cdot 7H_2O}\) under impulse voltage \(t_\phi = 10^{-6}\ \mathrm{sec}\) along different crystallographic directions. 1—nonuniform field, 2—uniform field.

The literature contains contradictory data on the magnitude of the electric strength of Rochelle salt as a function of crystallographic direction.

According to N. A. Prikhod’ko [10], the electric strength of Rochelle salt in a nonuniform field under alternating current depends on the crystallographic direction; moreover, along the “\(a\)” axis the strength is 2 times lower than along the \(b\) and \(c\) axes. The author relates this to the high value of the dielectric permittivity along this axis.

B. V. Gorelik [11] did not observe any dependence of electric strength on crystallographic direction.

We carried out a systematic investigation of the electric strength of Rochelle salt along different crystallographic directions as a function of the duration of the applied pulses and the type of voltage [12].

In addition to the previous investigations, we determined the electric strength along the \(a\) and \(b\) axes under homogeneous-field conditions for a pulse duration of \(10^{-8}\) sec, since the structural effect should be manifested most fully at short times, and under nonuniform-field conditions at a pulse voltage of \(\tau_{\mathrm{f}} = 10^{-6}\) sec. As follows from Figs. 12 and 13, no dependence of electric strength on crystallographic direction was found under the voltage-exposure conditions considered.

Fig. 12. Electric strength of Rochelle salt for different crystallographic directions in a homogeneous field.
\(o\)—axis \(a\), \(\Delta\)—axis \(b\).

Fig. 13. Electric strength of Rochelle salt for different crystallographic directions in a nonuniform field. \((\pm)\). Breakdown under \(10^{-6}\)-sec pulses.
\(T = 20^\circ\mathrm{C}\), specimen thickness 0.200 mm.
\(o\)—axis \(a\), \(\Delta\)—axis \(b\).

Thus, experimentally no dependence of electric strength on crystallographic direction was found for

of epsomite and Rochelle-salt crystal hydrates under conditions of homogeneous and inhomogeneous fields at a pulse voltage of duration \(10^{-6}\) sec. For Rochelle salt, no dependence of \(E_{\mathrm{br}}\) on crystallographic direction was found also for pulse durations \(10^{-4}\)–\(10^{-6}\) sec and for direct current.

Conclusions

1. The molecules of water of crystallization do not manifest themselves in strong fields under the action of single pulses of duration \(10^{-6}\) sec and less. The dependence of the electric strength of the crystal hydrates Rochelle salt, Onot talc, and river ice on the time of voltage exposure has the form of gently sloping curves at exposure times \(10^{-6}\), \(10^{-5}\), \(10^{-4}\) sec, with a considerable rise at a pulse duration of \(10^{-7}\) sec and less. The electric strength of talc and Rochelle salt under direct and alternating voltage is considerably lower than under pulse voltage.

2. The formation time and the propagation velocity of the discharge in the crystal hydrates Rochelle salt and Onot talc are of the same order as in anhydrous alkali-halide crystals, and are respectively \(10^{-8}\) and \(10^{-6}\) cm/sec. The propagation velocity of the discharge in crystal hydrates increases with increasing overvoltage.

3. The effect of orientational polarization of dipoles under the action of a field of definite frequency could not be detected, since the relaxation time of molecules of water of crystallization is of the same order as the discharge formation time in crystal hydrates.

4. No dependence of the electric strength of single crystals of \(\mathrm{KNaC_4H_4O_6 \cdot 4H_2O}\) and \(\mathrm{MgSO_4 \cdot 7H_2O}\) on crystallographic direction was found under conditions of homogeneous and inhomogeneous fields. Breakdown was produced at pulse voltages of different duration and by direct current.

LITERATURE

1. Vodop’yanov K. A. ZhTF, 19, 1067, 1949.
2. Vodop’yanov K. A. DAN SSSR, 84, 919, 1952.
3. Izergin A. P. Tr. SFTI, issue 30, p. 181, 1950.
4. Tonkonogov M. P. Izv. Tomsk Polytechnic Institute, vol. 91, p. 287, 1956.
5. Vodop’yanov K. A. ZhTF, vol. XXIV, issue I, p. 216, 1954.
6. Zingerman A. S. ZhTF, 18, 1629, 1948.
7. Vorob’ev G. A. ZhTF, vol. 30, issue 2, p. 256, 1956.
8. Shubnikov A. V. Crystal Formation. Publishing House of the USSR Academy of Sciences, 1947.
9. Vorob’ev A. A., Zavadovskaya E. K. Electric Strength of Solid Dielectrics. Moscow, p. 38, 1956.
10. Prikhod’ko N. A. Trudy SFTI, vol. VI, issue 2, 1942.
11. Gorelik B. V. ZhTF, vol. X, issue 5, p. 369, 1940.
12. Kevroleva K. M. ZhTF, vol. XXVII, issue 10, p. 2243, 1956.

ERRATA