On the Question of Thermal Breakdown of Rock Salt

G. A. Andreev

(Submitted by Professor, Doctor A. A. Vorob'ev)

Numerous investigations [1—4] have established that at temperatures from 40 to 80°C there occurs a sharp change in the course of the temperature dependence of the electric strength \((E_{pr})\) of rock salt. Walter and Inge indicate that this change occurs in the temperature interval 3—5°C, after which, as the temperature rises, a thermal breakdown mechanism comes into effect, different from the electrical one that takes place in the region of lower temperatures. In the region of thermal breakdown, a dependence of \(E_{pr}\) on the time of application of the voltage is observed; as this time increases, \(E_{pr}\) decreases [5]. In electrical breakdown, and for a long time of voltage application (of the order of several seconds), this dependence is absent or very weakly expressed [6]. The sharp decrease of \(E_{pr}\) of rock salt with increasing temperature was for a long time explained on the basis of the thermal theory of breakdown developed by Wagner and Fock.

Wagner’s theory [7], explaining breakdown of solid dielectrics by the presence of inhomogeneities in them, gives only a qualitative picture of the course of the decrease of \(E_{pr}\). Fock’s theory [8], taking into account the properties of a real dielectric, expresses the dependence of \(E_{pr}\) on temperature not only qualitatively but also quantitatively.

The temperature dependence of \(E_{pr}\) for a number of solid dielectrics, including rock salt [2, 6, 9], was investigated by Walter and Inge. Their investigations showed good agreement of the experimental data with the conclusions of Fock’s theory. The experimental results of Walter and Inge were criticized by Hippel [10], according to whose assumption the decrease of \(E_{pr}\) at high temperatures occurs because of the creation in rock salt of a positive space charge and an increase in emission by the electric field from the cathode [3]. However, Hippel does not give a quantitative calculation of \(E_{pr}\) for the region of high temperatures.

In 1947 Fröhlich [11] proposed a theory explaining the decrease of \(E_{pr}\) with increasing temperature by a disturbance of equilibrium in the exchange of energy between the field and the electrons and between the electrons and the lattice of an amorphous dielectric. But this theory also explains the change in electric strength only qualitatively and cannot be tested quantitatively. In 1956 Fröhlich proposed a new theory, according to which the temperature dependence of \(E_{pr}\), in contrast to the 1947 theory, is explained by an enhancement of the interaction of electrons with one another. According to this theory, developed for real crystals, \(E_{pr}\) is expressed in terms of quantities that can be determined practically. However, the correctness of Fröhlich’s new theory has not yet been verified.

Investigations have established [5, 12, 13] that the current flowing through a rock-salt specimen increases with increasing voltage and specimen temperature.

The literature contains no data on the temperature dependence of the prebreakdown electrical characteristics, and the question of the amount of electrical energy required for the destruction of rock salt at different temperatures has not been covered. The only work in this direction [14] was carried out under pulsed voltage at room temperatures of the specimen.

The present work was begun with the aim of obtaining the temperature dependence of the prebreakdown characteristics of rock salt and estimating the energy released in the specimen from the moment the voltage begins to rise up to the moment of breakdown.

For this purpose, a method was developed for recording volt-ampere-second characteristics for rock-salt specimens under conditions of a uniform field and high temperatures, at a steadily increasing voltage.

METHOD

A. Description of the apparatus

A number of authors [2, 3, 13] have shown that, when the temperature is varied from 0 to \(500^\circ\mathrm{C}\), \(E_{pr}\) of rock salt lies within the range from \(1.5\ \mathrm{mv/cm}\) to \(2500\ \mathrm{v/cm}\), and the current from \(10^{-8}\)—\(10^{-9}\ \mathrm{a}\) to several tenths of an ampere. For specimens \(100\)—\(200\ \mu\) thick, \(U_{pr}\) will vary within the range from

Fig. 1. Schematic diagram of the apparatus.
\(1\) — specimen; \(2\) — electric furnace; \(3\) — screen of the electronic oscillograph.

\(200\)—\(300\ \mathrm{v}\) to \(35\ \mathrm{kv}\), and the current from \(10^{-9}\ \mathrm{a}\) to several tenths of an ampere.

From this follow the following requirements for the measuring apparatus:

1. The possibility of measuring voltage from several hundred volts to \(30\)—\(40\ \mathrm{kv}\).
2. The possibility of measuring currents within the range from \(10^{-1}\) to \(10^{-9}\ \mathrm{a}\).
3. The possibility of recording processes with an accuracy not lower than \(\pm 10\%\) and of simply comparing them in time.

These requirements are met by the apparatus developed by us, the schematic diagram of which is shown in Fig. 1.

To one pair of vertical plates \(P_1\) of a two-beam oscillograph of type 1551 “Orion,” from a resistance \(R_{izm}\), a voltage was applied proportional to the current flowing through the specimen when high voltage was applied to it. The value of \(R_{izm}\) was chosen deliberately smaller than the co-

resistance of the specimen \(R_o\). The basis for choosing the required value \(R_{\text{meas}}\) was the maximum possible deflection of the beam on the oscilloscope screen immediately before breakdown of the specimen. In this case the voltage across \(R_{\text{meas}}\) should be of the order of \(150\ \text{V}\), whereas the voltage across the specimen \(U_o\) amounts to several kilovolts. It follows from the circuit that in this case \(R_o \gg R_{\text{meas}}\).

Special attention was paid to the stability of the measuring resistances. As follows from Fig. 2, the values of the resistances used do not depend on voltage to within \(\pm 2\%\).

A high dc voltage of up to \(40\ \text{kV}\), obtained by means of a simple rectifier circuit through an ohmic divider \((R_2, R_3, R_4)\),

Fig. 2. Dependence of the value of the measuring resistances used on voltage.

was applied to the second pair of vertical plates \(P_2\). Calibration of the plates \(P_2\) was carried out with an electrostatic kilovoltmeter of type S-96, accuracy class 1.5. The plates \(P_1\) were calibrated with an ELB voltmeter of accuracy class 0.2.

A special photographic attachment, consisting of motor \(M_2\), a reducer, and a camera, ensured uniform motion of the film in front of the objective, whereby the time sweep was performed.

With the aid of electric motor \(M_1\), variation of the high voltage was obtained at a practically uniform rate equal to \(0.63\ \text{kV/sec}\).

Fig. 3. Section of the electric furnace with the electrode system installed in it.

1 — measuring electrode; 2 — guard ring; 3 — high-voltage electrode, diameter \(10\ \text{mm}\); 4 — steel bushing; 5 — feedthrough insulator; 6 — stand; 7 — grounding conductor; 8 — clamp; 9 — quartz tube; 10 — lead from the measuring electrode; 11 — spring; 12 — clamp; 13 — fastening ring; 14 — screen; 15 — furnace body; 16 — furnace cover; 17 — thermal insulation; 18 — cover; 19 — furnace casing; 20 — cable.

Heating and breakdown of the specimens were carried out in an electric furnace of the design of A. M. Trubitsyn [15], into which electrodes made of steel EYa-1-T were placed. A drawing and photograph of the electrode system and its arrangement in the electric furnace are given in Figs. 3 and 4.

The specimens, having a flat shape with dimensions \(40 \times 40 \times 3\ \text{mm}\), were prepared from crystals of natural rock salt. A spherical depression \(10\ \text{mm}\) in diameter was drilled in the specimens. The thickness of the specimens at the thin place was taken as 100 and \(200\ \mu\), and deviations in thickness did not exceed \(\pm 5\%\). After measuring the thickness, the specimens were rejected under a microscope at 68-fold magnification.

Electrodes were applied to the specimen by depositing graphite from a colloidal solution of soot in toluene.

The temperature was measured with a mercury thermometer with a scale up to \(800^\circ\mathrm{C}\), with an accuracy of \(1^\circ\mathrm{C}\).

The influence of the value of \(R_{\text{meas}}\) on the magnitude of the current passing through the specimen was investigated. Using the reversibility property of processes in rock salt, discovered by Walter and Inge [2, 10] and consisting in the fact that the current through rock salt does not change upon repeated application of voltage, oscillographic recording of the current through a specimen of thickness \(100\,\mu\) at \(256^\circ\mathrm{C}\) and at various \(R_{\text{meas}}\) was carried out. In processing the oscillograms, the results shown in Fig. 5 were obtained in the form of the dependence of current on voltage.

Fig. 4. Furnace with installed electrodes (the numbers correspond to the parts in Fig. 3).

It follows from Fig. 5 that, for \(R_{\text{meas}}\) from \(1\cdot10^6\) to \(1\cdot10^7\,\Omega\), the current through the specimen remains constant within the accuracy of the measurements. At larger resistances a decrease in current is observed, explained by the approach of the value \(R_{\text{meas}}\) to the resistance of the specimen \(R_o\), which under the given voltages varies from \(6\cdot10^8\) to \(2\cdot10^8\,\Omega\).

It should be noted that, when selecting \(R_{\text{meas}}\) for this temperature, full deflection of the beam on the oscilloscope screen is obtained at \(R_{\text{meas}}=0.96\cdot10^6\,\Omega\).

Thus, with such a choice of the measuring resistance, its value will be considerably smaller than \(R_o\), and the influence of \(R_{\text{meas}}\) on the magnitude of the current through the specimen will likewise be insignificant.

The accuracy of the current measurement was checked by comparing the current values calculated from the oscillograms with the readings of a mirror galvanometer of type 167301 (Goerz—Wien), accuracy class 2. A galvanometer with an internal resistance of \(355\,\Omega\), through a shunt with a resistance of \(1\cdot10^4\,\Omega\), was connected in series with the specimen, heated to \(252^\circ\mathrm{C}\), at \(R_{\text{meas}}=4.1\cdot10^6\,\Omega\). The voltage was increased in steps with a 30-second hold at each step. Recording on film and measurements with the galvanometer were carried out simultaneously.

The measurement results are presented in the table.

It follows from the table that the current values measured with the oscilloscope and the galvanometer agree well.

Fig. 5. Dependence of the current through the specimen on the voltage across it at various measuring resistances.
Specimen No. 606, \(d = 100\ \mu\), \(t = 256^\circ\mathrm{C}\).
\(1 — R_{\text{meas}} = 0.96 \cdot 10^6\ \Omega;\quad 2 — R_{\text{meas}} = 4.1 \cdot 10^6\ \Omega;\quad 3 — R_{\text{meas}} = 1.16 \cdot 10^7\ \Omega;\)
\(4 — R_{\text{meas}} = 5.2 \cdot 10^7\ \Omega;\quad 5 — R_{\text{meas}} = 0.96 \cdot 10^8\ \Omega.\)

B. Processing of the Oscillographic Results

Figure 6 shows a typical oscillogram of breakdown obtained with the setup described above. The change in voltage across the specimen and \(R_{\text{meas}}(U_n)\) is recorded by the upper trace; the lower trace \((U_i)\) corresponds to the voltage across \(R_{\text{meas}}\).

Fig. 6. Oscillogram of thermal breakdown.

The quantities \(U_n\) and \(U_i\) were determined from the oscillogram at fivefold magnification.

The calculation of the electrical characteristics of the specimen (current, resistance, power) was carried out from the known \(R_{\text{meas}}\), on the basis of Ohm’s law and the magnitude of the voltage drop across the specimen \(U_o = U_n - U_i\). The energy \(P\) released in the specimen during the time from the moment of voltage increase to breakdown was determined by geometrical integration of the area bounded by the power curve in time coordinates.

A drawback of the method is the limited measurement range, determined by the maximum deflection of the beam on the oscilloscope screen.

RESULTS OF THE EXPERIMENTS

According to Fock’s thermal theory, \(U_{\text{br}}\) should vary proportionally to the square root of the resistivity, whose temperature dependence for rock salt may be expressed as:

\[ \rho = \rho_o e^{-aT}. \]

Then the breakdown voltage is given by the expression

\[ U_{\text{br}} = \mathrm{const}\cdot e^{-\frac{a}{2}T}. \]

Thus, \(\lg U_{pr}=f(T)\) must be a straight line with slope coefficient \(\dfrac{a}{2}\).

The high-temperature qualitative theory of Fröhlich [11], developed for inhomogeneous dielectrics, gives the dependence of electrical strength on temperature in the form:

\[ \ln E_{pr}=C+\frac{\Delta v}{2k}\cdot \frac{1}{T}, \]

where \(C\), \(\Delta v\), \(k\) are constants independent of temperature.

Figure 7 gives the values of electrical strength, averaged over 10–15 points, as a function of temperature for specimens of thickness

Fig. 7. Dependence of electrical strength on temperature.
\(\circ\) — \(100\,\mu\); \(\times\) — \(d=200\,\mu\).

Fig. 8. Dependence
\(\lg U_{pr}=f(T)\).
1 — \(d=100\,\mu\); 2 — \(d=200\,\mu\);
3 — \(d=4\,\mathrm{mm}\) (after Walter and Inge).

100 and \(200\,\mu\). From Fig. 7 it follows that, in the region from \(110^\circ\) to \(440^\circ\mathrm{C}\), a sharp decrease in the electrical strength of rock salt is observed.

Figure 8 shows the dependence \(\lg U_{pr}=f(T)\). For comparison, the results of Walter and Inge [2], obtained at constant voltage with electrodes in the form of two points and with rock-salt specimens of thickness \(d=4\,\mathrm{mm}\), under a prolonged time of voltage application, are also given here.

It follows from Fig. 8 that the results obtained agree well with Fock’s theory, and the coincidence of the slopes of the straight lines with the results of Walter and Inge shows that the coefficient \(a\) is approximately the same in both cases.

The check carried out by us shows (Fig. 9) that the dependence

\[ \lg E_{pr}=f\left(\frac{1}{T}\right) \]

is justified for temperatures above \(200^\circ\mathrm{C}\). From \(110^\circ\mathrm{C}\) to \(200^\circ\mathrm{C}\), a rectilinear dependence of \(\lg E_{pr}\) was not obtained.

The observed decrease in \(E_{pr}\) for specimens of greater thickness is consistent with Fock’s thermal theory and is explained by the worsening of heat-transfer conditions as the thickness increases.

Figure 10 gives the temperature dependence of the prebreakdown current. From Fig. 10 it follows that, despite the sharp decrease in the voltage on the specimen, the current has an increasing character as the temperature increases.

The results obtained show that increasing the specimen thickness by a factor of 2 has little effect on the magnitude of the prebreakdown current. This fact is evidently connected with the circumstance that the increase in current due to the external field is compensated by its decrease owing to the increase in the resistance of the specimen.

Figure 11 shows that the dependences of current on electric-field strength for different specimen thicknesses also coincide.

Figure 12 shows the temperature dependence of the energy \(P\) released in the specimen from the moment voltage is applied up to breakdown. As follows from Fig. 12, up to \(200^\circ\)C an increase in energy is observed, and after \(200^\circ\)C, a decrease. The presence of a temperature maximum of the energy indicates that, at this temperature, processes associated with large energy losses occur in the specimen.

Thermal theories explaining breakdown by heating of the specimen when an electric current passes through it provide for an additional loss of heat due to heat removal from the place of heating in the radial (Wagner) and axial (Fock) directions. From the thermal theories it follows that, with increasing heating of the specimen,

Fig. 9. Dependence \(\lg E_{np}=f\left(\dfrac{1}{T}\right)\).

\(\circ\) — \(d=100\,\mu\); \(\times\) — \(d=200\,\mu\); \(T\) — in °K.

Fig. 10. Temperature dependence of the pre-breakdown current.

\(\bullet\) — \(d=100\,\mu\); \(\circ\) — mean value for \(d=100\,\mu\); \(\times\) — \(d=200\,\mu\); \(\times\times\) — mean value for \(d=200\,\mu\).

less energy is required for its melting. The thermal theories do not explain the presence of an energy maximum.

A possible explanation of the energy maximum follows from consideration of the temperature dependence of current and voltage. Owing to the steeper increase of the current observed in the range from \(110^\circ\)C to \(200^\circ\)C,

Fig. 11. Dependence of current on the electric-field strength in the specimen.

\(\circ\) — \(d=100\,\mu\); \(\times\) — \(d=200\,\mu\).

Fig. 12. Dependence of the energy released in the specimen on temperature for specimens of thickness

\(\circ\) — \(100\,\mu\) and \(\times\) — \(200\,\mu\).

(Fig. 10), the energy has an increasing character. Above \(200^\circ\)C, as the temperature rises, the increase in current slows down, and, with an approximately identical character of the change in voltage, the dependence of the energy on temperature decreases.

It follows from Fig. 12 that the energy released in the specimen increases almost proportionally to the thickness. Some nonproportionality in the course of the curves is evidently explained by different heat-removal conditions.

We note that the study of the question of which processes in the specimen consume the energy is of considerable practical and theoretical interest.

Conclusion

With the aid of the developed oscillographic method, volt-ampere-second characteristics of natural rock salt were obtained at a steadily increasing voltage in the range from 110 to \(440^\circ\)C.

The results obtained make it possible to determine the prebreakdown electrical characteristics, examination of which has shown that:

1) the dependence of the electric strength over the entire temperature interval from 110 to \(440^\circ\)C qualitatively satisfies well Fock’s thermal theory and only partially the “high-temperature” theory of Fröhlich;

2) the temperature dependence of the prebreakdown current has an increasing character, despite the sharp decrease in the electric-field intensity in the specimen with increasing temperature;

3) the temperature dependence of the energy has a maximum near \(200^\circ\)C; the decrease of the energy with temperature (after \(200^\circ\)C) is confirmed by Fock’s thermal theory.

In conclusion I express my gratitude to Professor, Doctor of Technical Sciences A. A. Vorob'ev for his attentive guidance of the work, and also to Candidate of Technical Sciences G. A. Vorob'ev and V. S. Dmitrevsky for checking and discussing the article.

References

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4. Kuchin V. D., Temperature dependence of the electric strength of ionic crystals (present collection).

5. Physics of Dielectrics, edited by Walter A. F., p. 364, GTTI, 1932.

6. Walter A. F., Breakdown of Solid Dielectrics, p. 12, GTTI, 1933.

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