Some Electrical Properties of Fused Quartz at High Frequencies, Elevated Voltages, and High Temperatures

B. I. Vorozhtsov

Introduction

The development of radio engineering and electrical engineering often places electrical insulating materials under very severe operating conditions, which even such a high-quality insulating material as fused quartz does not always withstand. The latter, being in strong high-frequency electric fields and at elevated temperature, undergoes intense heating, which leads to the destruction of expensive equipment.

This intense heating of quartz is naturally associated with a sharp increase in the dielectric losses in it. However, the nature of high-frequency dielectric losses in fused quartz at high temperatures, owing to the absence of reliable methods for measuring the dielectric loss angle, has until now remained unknown. The available data on dielectric losses in fused quartz, relating to the temperature range 20–400°C, do not make it possible to see the causes of its sharp heating at higher temperatures.

The aim of the present work was to investigate the mechanism of dielectric losses in fused quartz at high frequencies and high temperatures.

A parallel task was the development of a method for measuring the dielectric loss angle in comparatively strong high-frequency fields, suitable at high temperatures, since the existing methods, for a number of reasons, do not permit investigations at temperatures exceeding 400°C. These reasons consist mainly in the fact that most existing methods for measuring the dielectric loss angle are very sensitive to all kinds of parasitic couplings, whose influence is very difficult to eliminate.

Free from this shortcoming is the calorimetric method, which was taken as the basis in developing our procedure.

Method for Measuring the Dielectric Loss Angle

The calculation of the dielectric loss angle in the proposed method is made by comparing the amount of heat liberated as a result of dielectric losses with the amount of heat measured from the rise in temperature of the dielectric; in deriving the formula, the heat losses resulting from heat exchange of the specimen with the surrounding medium are taken into account.

Thus one may write:

\[ 0.24 C V_{\mathrm{eff}}^{2}\omega \operatorname{tg}\delta\, dt = \lambda m\, dT + h(T - T_0)dT, \tag{1} \]

where \(C\) is the capacitance of the specimen,
\(V_{\mathrm{eff}}\) is the applied voltage,
\(\omega\) is the angular frequency at which the measurement is made,
\(\lambda\) is the specific heat capacity of the specimen,
\(h\) is the heat-transfer coefficient.

The solution of this equation is written in the form:

\[ T - T_0 = \Delta T = \frac{A}{h}\left(1 - e^{-\frac{h}{\lambda m}t}\right), \tag{2} \]

where

\[ A = 0.24\, C V_{\mathrm{eff}}^{2}\omega\, \operatorname{tg}\delta . \tag{3} \]

If

\[ \frac{h}{\lambda m}t \ll 1, \]

then, expanding \(e^{-\frac{h}{\lambda m}t}\) in a series and retaining only the first term of the expansion, we obtain

\[ \Delta T = \frac{A}{\lambda m}\,t, \tag{4} \]

i.e., under certain conditions it is possible to disregard the heat exchange of the specimen with the surrounding medium.

The experimental estimate of the dependence of \(\Delta T\) on the time \(t\), shown in Fig. 1, indicates that the simple dependence (4) is practically quite attainable. The linear dependence of the heating \(\Delta T\) on time is maintained for 5–6 minutes, while the magnitude of the heating of the specimen is approximately \(5\text{–}10^\circ\mathrm{C}\), i.e., it can be measured with high accuracy.

Fig. 1

It should be noted that, along with simplifying the calculation formulas, operation in the nonstationary heating regime considerably accelerates the measurement process (minutes instead of hours). This was pointed out at the time by Rice and Leonard [1], the authors of a nonstationary method for measuring the dielectric loss angle by the substitution method.

As is not difficult to see, equation (1) describes the heating process of the entire volume of the dielectric and is therefore valid only when the measured body temperature is equal to the mean (integral) temperature [2], i.e.,

\[ T = \overline{T} = \frac{1}{\Omega}\int_{\Omega} T\,d\Omega . \tag{5} \]

Since the heating of the specimen is measured by us from the increase in temperature of its outer surface, depending on the distribution of the field in the specimen we shall measure different temperatures. In the case of a homogeneous field, the temperature of the outer surface of the specimen is equal to the mean (integral) temperature, since the same amount of heat is released at all points of the specimen. In inhomogeneous fields, where different amounts of heat are released at different points, the measured temperature will differ from the mean (integral) temperature. The process of heat conduction will be ...

equalize the temperature in the specimen, bringing it closer to the mean (integral) temperature. In this case the heating of the dielectric will be described by the nonhomogeneous heat-conduction equation. For our case (the specimens are tubes of fused quartz with radii \(R_1\) and \(R_2\) and of great length, \((l>2R_2)\)) this equation is written in the form:

\[ K\left(\frac{\partial^2 T}{\partial r^2}+\frac{1}{r}\frac{\partial T}{\partial r}\right)+F(r)=\lambda \rho \frac{\partial T}{\partial t}, \tag{6} \]

where \(K\) is the coefficient of thermal conductivity,

\[ F(r)=\frac{M}{r^2} \]

is the density of the sources,

\[ M=0.24\,\frac{\omega \varepsilon}{4\pi}\,\operatorname{tg}\delta\, \frac{V_{\mathrm{eff}}^2}{\ln^2 R_2/R_1}. \tag{7} \]

For simplicity we take the initial and boundary conditions to be:

\[ T(r,0)=0. \]

\[ \left.\frac{\partial T}{\partial r}\right|_{R_1,R_2}=0. \]

The solution of this equation is written in the form:

\[ T(r,t)= \frac{2M\ln \dfrac{R_2}{R_1}}{(R_2^2-R_1^2)\rho\lambda}\,t + \sum_{n=1}^{\infty} \frac{ \displaystyle \int_{R_1}^{R_2}\frac{M}{\rho\lambda r}\, I_0\!\left(n\pi\frac{r}{d}\right)\,dr }{ \displaystyle \int_{R_1}^{R_2} r\left[I_0\!\left(n\pi\frac{r}{d}\right)\right]^2\,dr } \times \]

\[ \times \frac{ I_0\!\left(n\pi\frac{r}{d}\right)d^2 }{ (n\pi)^2 a^2 } \cdot \left(1-e^{-\left(\frac{n\pi}{d}\right)^2 a^2 t}\right). \tag{8} \]

The quantity

\[ \frac{2M\ln \dfrac{R_2}{R_1}}{(R_2^2-R_1^2)\rho\lambda}\,t \]

is the mean (integral) temperature.

An estimate of the sum entering expression (8), which distinguishes the temperature at a given point of the body from the mean (integral) temperature, carried out for the initial period of heating, leads to the following relation:

\[ \sum_{n=1}^{\infty} \frac{ \displaystyle \int_{R_1}^{R_2}\frac{M}{\rho\lambda r}\, I_0\!\left(n\pi\frac{r}{d}\right)\,dr }{ \displaystyle \int_{R_1}^{R_2} r\left[I_0\!\left(n\pi\frac{r}{d}\right)\right]^2\,dr } \cdot \frac{ I_0\!\left(n\pi\frac{r}{d}\right)d^2 }{ (n\pi)^2 a^2 } < \frac{2M\ln \dfrac{R_2}{R_1}}{(R_2^2-R_1^2)\rho\lambda} \times \]

\[ \times \frac{d^2}{a^2\tau^2} \left( \frac{R_2^2-R_1^2}{2r^2\ln \dfrac{R_2}{R_1}} -1 \right),\ldots, \tag{9} \]

where \(d\) is the thickness of the specimen,

\[ a^2=\frac{K}{\lambda\rho}. \]

Expression (8), therefore, can be represented in the form:

\[ T(r,t)\le \frac{2M\ln\dfrac{R_2}{R_1}}{(R_2^2-R_1^2)\rho\lambda} \left\{ t-\frac{d^2}{\pi^2 a^2} \left( 1-\frac{R_2^2-R_1^2}{2r^2\ln\dfrac{R_2}{R_1}} \right) \right\}. \tag{10} \]

Substituting into (10) the mean dimensions of the specimens \((R_2=0.9\ \mathrm{cm},\ R_1=0.6\ \mathrm{cm})\), we obtain the following value for the temperature of the outer surface:

\[ T(R_2,t)< \frac{2M\ln\dfrac{R_2}{R_1}}{(R_2^2-R_1^2)\rho\lambda}\cdot(t-0.4) \approx \frac{2M\ln\dfrac{R_2}{R_1}}{(R_2^2-R_1^2)\rho\lambda}. \tag{11} \]

Thus, the temperature measured on the outer surface of the specimen is close to its mean (integral) temperature. Consequently, equation (1) and all conclusions drawn from it are valid. That is, formula (4) is valid if \(t=4\text{--}5\) min. Formulas (4) and (11) bound the heating time from two sides, namely:

\[ 0.4\ \mathrm{sec}<t<240\ \mathrm{sec}. \tag{12} \]

As experiments have shown, such a time is quite sufficient for appreciable heating of the specimen.

Let us take into account one more circumstance. In all the preceding reasoning we have not touched upon the fact that the dielectric loss angle does not remain constant during the measurement but, owing to heating of the specimen, changes according to the law:

\[ \tg\delta=\tg\delta_0\cdot e^{B\frac{T-T_0}{TT_0}}. \tag{13} \]

Here \(T_0\) is the temperature at which the measurement is made, i.e., the ambient temperature,

\(\tg\delta_0\) is the tangent of the dielectric loss angle at \(T_0\),

\(T\) is the temperature to which the quartz has been heated as a result of dielectric losses,

\(B=10^4\) (determined from our measurements of the temperature dependence of the dielectric loss angle).

Choosing the heating time so that heat exchange with the surrounding medium may be neglected, and taking condition (13) into account, we write equation (1) in the form:

\[ \frac{dT}{dt}=-\frac{A_0}{\lambda m}\cdot e^{B\frac{T-T_0}{TT_0}}, \tag{14} \]

where

\[ A_0=0.24\,\omega C V_{\mathrm{eff}}^2 \tg\delta_0. \]

The maximum heating at \(900^\circ\mathrm{C}\) was about \(20^\circ\mathrm{C}\) over a time \(t=30\ \mathrm{sec}\). Hence

\[ B\frac{T-T_0}{TT_0} = 10^4\frac{1193-1173}{1193\cdot1173} = 0.14. \]

This permits the problem to be simplified. After simple calculations, the solution of equation (14) takes the form:

\[ \Delta T\left(1-\frac{B}{T_0}+\frac{2B}{T_0+T}\right) = \frac{A_0}{\lambda m}\cdot t. \tag{15} \]

Substituting their values in place of \(B, T\), and \(T_0\), we obtain:

\[ 0.928\Delta T=\frac{A_0}{\lambda\cdot m}\cdot t. \tag{16} \]

This expression makes it possible to assume that, with a sufficient degree of accuracy, the change in the dielectric-loss angle of fused quartz due to the increase in the temperature of the specimen during an individual measurement need not be taken into account.

Substituting in (4) the value of \(A\) from (3), we obtain the basic calculation formula for the dielectric-loss angle in the form:

\[ \operatorname{tg}\delta=\frac{\lambda m\Delta T}{0.24\omega C V_{\mathrm{eff}}^{2}t}. \tag{17} \]

This formula is valid both for the case of a homogeneous field and for an inhomogeneous one, provided that the specimen has a sufficiently small thickness.

In the proposed method the quantities of heat capacity \((\lambda)\), mass \((m)\), and capacitance \((C)\) of the specimen must be determined either by separate measurements or, when the density \((\rho)\) and dielectric permittivity \((\varepsilon)\) are known, analytically (for a cylindrical capacitor

\[ m=\rho\pi(R_2^2-R_1^2)l,\quad C=\frac{\varepsilon l}{2\ln \dfrac{R_2}{R_1}}). \]

This is a substantial drawback of calorimetric methods in general.

The determination of the other quantities entering formula (17) is carried out as follows: \(t\)—with a stopwatch, \(\omega\)—with a wavemeter, \(\Delta T\) and \(V_{\mathrm{eff}}\) by means of the apparatus described below.

Before describing the apparatus, let us dwell on an important question in measuring the dielectric-loss angle—the question of electrodes.

Investigation of the suitability of various electrodes for measuring dielectric losses in fused quartz at high temperatures

The question of electrodes becomes especially acute in high-temperature measurements of the dielectric-loss angle, where the electrodes must be stable over the entire temperature range and must not react with the specimen. High frequency and elevated voltage impose their own requirements on the electrode material.

We investigated a number of electrodes: nickel cylinders applied to the specimen from outside and inside, powder electrodes, silver electrodes deposited on the specimen by firing a paste, and, finally, “air” electrodes.

The first two types of electrodes proved unsuitable, since it is practically impossible to avoid the presence of air gaps between the specimen and the electrode, the ionization of which significantly distorts the measurement results.

Silver and “air” electrodes proved more suitable. Investigation of the suitability of silver electrodes showed that with their aid measurements of the dielectric-loss angle of fused quartz can be made only up to \(600^\circ\mathrm{C}\). The repeatability of the results in this case is very good.

Measurements at temperatures above \(600^\circ\mathrm{C}\) cannot be carried out because of the high evaporation of the electrodes and the interaction of silver with the specimen. Here repeated measurements give different results.

Air electrodes have the following design (Fig. 2). Here, as is seen from the figure, which shows a section of a cylindrical capacitor with the specimen being measured, the possible inter-

Fig. 2. 1—Metal electrodes.
2—Specimen. 3—Quartz spacers.
4—Air layer.

action between the metal electrode and the specimen at high temperatures has been eliminated, since the metal electrode is separated from the specimen by an air layer. If a specimen of sufficient length is taken and the thermocouple junction is placed on the specimen at the same distance from the quartz spacers located at the edges of the electrodes, then, owing to the considerable length of the specimen and the low thermal conductivity of quartz, heating of the specimen edges under the spacers will not affect the heating of the thermocouple. The results of measuring the dependence of the thermocouple heating on the position of the junction on the specimen are presented in Fig. 3.

Fig. 3. Dependence of thermocouple heating on the position of the junction on the specimen.

Fig. 4

Let us denote the total voltage on the capacitor by \(V\), and that on the specimen by \(V_2\). We shall find the dependence of \(V_2\) on \(V\) and on the losses in the specimen. To do this, let us consider the equivalent circuit of the air–quartz–air system, shown in Fig. 4. From this circuit one may write:

\[ V_2=\frac{V}{1+C_2\left(\frac{1}{C_1}+\frac{1}{C_3}\right)(1-j\tg\delta)} \tag{18} \]

under the condition that \(\tg\delta_1=\tg\delta_3=0\), as \(\tg\delta\) of air. This condition is valid only when the air in the air gaps is not ionized. Hence it is necessary to select the optimum operating voltage. Calculations by for-

Pike’s formula [3] for our case (radius of the inner electrode \(R_0 = 0.45\ \mathrm{cm}\), radii of the specimen: \(R_1 = 0.6\), \(R_2 = 0.9\ \mathrm{cm}\), and radius of the outer electrode \(R_3 = 1.25\ \mathrm{cm}\)) gives the following value for the initial (corona) field strength at the inner electrode: \(E_n = 13.7\ \mathrm{kV_m/cm}\). The maximum field strength at the inner electrode at \(V_{\mathrm{eff}} = 1200\ \mathrm{V}\) is \(E_m = 6\ \mathrm{kV_m/cm}\). Thus, the operating voltage, equal to \(1200\ \mathrm{V}\), is entirely suitable.

Let us turn to expression (18). It can be verified that the first derivatives of \(V_2\) with respect to frequency and temperature are not zero unless the corresponding derivatives of \(\tg\delta\) are zero. If \(\tg\delta\) has a temperature or frequency maximum, then at this temperature or frequency \(V_2\) is minimal.

Solving equations (17) and (18) simultaneously, we obtain the following formula for calculating the dielectric loss angle when measuring with “air” electrodes:

\[ \tg\delta = \frac{V_{\mathrm{eff}}^{2}}{2Bb^{2}} \left( 1 - \sqrt{ 1 - \frac{4B^{2}b^{2}(1+b)^{2}}{V_{\mathrm{eff}}^{4}} } \right), \tag{19} \]

where

\[ B = \frac{\lambda m \Delta T}{0.24\omega C_2 t}. \]

For \(\tg^{2}\delta \ll 1\), the root in formula (19) may be represented approximately. Then formula (19) is replaced by the simpler one:

\[ \tg\delta = \frac{\lambda m \Delta T}{0.24\,\omega C_2 V_{\mathrm{eff}}^{2}\,t}(1+b)^{2}. \tag{20} \]

Formulas (19) and (20) are the desired formulas for calculating the dielectric loss angle of fused quartz with air electrodes. Investigation of the temperature dependence of the dielectric loss angle of fused quartz showed that, in measurements with “air” electrodes, complete coincidence is observed between the points of the direct and reverse runs, as well as in repeated measurements, although these measurements were carried out up to temperatures exceeding \(1000^\circ\mathrm{C}\). None of the electrodes considered earlier could provide this. Thus, the use of “air” electrodes, by preventing diffusion of impurity from the metal into the specimen, makes it possible to determine dielectric losses in a “pure” dielectric over a wide temperature range, up to \(1000^\circ\mathrm{C}\). In addition, such an electrode arrangement corresponds to the conditions under which quartz operates in practical installations.

The sensitivity of the method (with respect to \(\tg\delta\)) when using “air” electrodes is of the order of \(5 \cdot 10^{-4}\) (with silver electrodes, \(5 \cdot 10^{-5}\)). The maximum error in measuring the dielectric loss angle at high temperatures (\(600\text{--}1000^\circ\mathrm{C}\)) is \(30\text{--}40\%\); with silver electrodes it is \(20\text{--}30\%\). The error decreases with increasing temperature.

Thus, despite a certain decrease in the sensitivity and accuracy of the method, the use of “air” electrodes is fully justified.

Block Diagram of the Apparatus

The apparatus consists of a high-frequency generator, a measuring circuit with instruments for measuring the voltage and heating of the specimen by high-frequency currents, and a crucible electric furnace. The general diagram of the apparatus is shown in Fig. 5.

The high-frequency oscillation generator, assembled with a GU-500 tube, delivered an output power of up to 0.5 kW in the frequency range 10–40 MHz.

The measuring circuit, inductively coupled to the self-oscillator circuit, consists of a self-inductance coil \(L\), a trimming capacitor \(C^0\), and a capacitor \(C\) with the dielectric.

A thermocouple \(T\), pressed tightly against the specimen, serves to determine the high-frequency heating and to measure the temperature of the specimen (the furnace temperature). These two operations are carried out by alternately connecting it either to an instrument graduated in degrees of the centigrade scale (when determining the furnace temperature), or to a differential galvanometer (when measuring the high-frequency heating of the specimen).

Fig. 5

When determining high-frequency heating at elevated temperatures, the thermoelectromotive force developed by the thermocouple as a result of heating of the specimen in the furnace is compensated by means of a special circuit connected to the second coil of the galvanometer¹.

The heating is determined by extrapolating the curve for measuring the furnace temperature and the cooling curve of the specimen to the instant at which the field is switched off.

To determine the voltage on the specimen, an oscillographic tube is connected in parallel with it through a capacitive voltage divider. The voltage is determined from the magnitude of the blurring of the spot on the screen of the oscillographic tube; for this purpose this device is calibrated beforehand.

Investigation of the electrical properties of fused quartz at high frequencies and high temperatures

Three kinds of fused quartz were investigated: Leningrad, Moscow, and quartz from rock crystal.

The Leningrad and Moscow quartz, so named according to the place of manufacture, had the form of tubes of various diameters and of standard length (100 cm). A section of such a tube 8–10 cm long served as the specimen investigated. All specimens (50 specimens of Leningrad and Moscow quartz were investigated) contain a small amount of gaseous inclusions in the form of thin capillaries directed along the tube.

These specimens contain, as impurities, magnesium (0.03–0.1%), copper (0.03–0.1%), and iron (0.01%). The chemical composition was determined by semi-quantitative spectral analysis.

Quartz from rock crystal, prepared by melting crystals of smoky quartz, had the form of disks and contained a large number of gas bubbles.

An investigation of the temperature–frequency dependence of the dielectric-loss angle of fused quartz led to the following. As Fig. 6 shows, where a typical dependence of the dielectric-loss angle of fused quartz on temperature is presented, the dielectric losses in fused quartz can be divided into two parts: a low-temperature part (up to \(450\text{--}500^\circ\mathrm{C}\)), where the dielectric-loss angle is almost independent of temperature and is small in absolute magnitude, and a high-temperature part, with a sharp increase of dielectric losses with temperature. As is known, such a temperature behavior of the dielectric-loss angle is characteristic of glasses. Only in glasses does the increase in the dielectric-loss angle, determined by the amount and character of the impurities present in them, occur at lower temperatures.

Fig. 6. Temperature dependence of the dielectric-loss angle for quartz MA, \(f = 25\) MHz.

Fig. 7. Frequency dependence of \(\operatorname{tg}\delta\) for quartz LD.
\(\times\)—calculated from the point \(f = 25\) MHz.

Let us turn to the previously uninvestigated high-temperature part of the dielectric losses in fused quartz. The temperature–frequency dependence of the dielectric-loss angle is presented in Fig. 7, from which it follows that the dielectric-loss angle is inversely proportional to frequency. This, as is known, is the principal characteristic of ohmic losses.

In addition, at high temperature there is equality between the measured dielectric-loss angle and that calculated from the bulk conductivity of the specimen, as well as identical heating of the specimen by high-frequency current and by direct current at the same voltage (Figs. 8 and 9).

All these facts make it possible to conclude that the high-temperature part of the dielectric losses in fused quartz is determined by through conductivity.

An investigation of the temperature–frequency dependence of the dielectric constant also confirms this conclusion (the dielectric constant depends neither on temperature nor on frequency). The measurement of \(\varepsilon\) was carried out on a Q-meter KV-1.

In the course of investigating the dielectric-loss angle of fused quartz at high temperatures, a very interesting fact became clear—po

reduction of the dielectric loss angle as a result of heat treatment of the specimen at high temperatures (1100–1300°C) for several hours.

A detailed study of the influence of high-temperature heat treatment shows that the reduction in the dielectric loss angle of fused quartz in this case amounts to 40–50% (Fig. 10). As can be seen from the figure, grinding off the altered surface layer (white deposit—cristobalite) and a second firing do not lead to any further change in the dielectric loss angle of the specimen subjected to heat treatment.

Fig. 8. ×—\(\operatorname{tg}\delta\) measured at 25 MHz.
○—\(\operatorname{tg}\delta\), calculated from (6);
quartz PE 50.

Fig. 9. ×—heating at 25 MHz;
○—heating by direct current;
quartz PE 50.

The study of the influence of the duration of temperature treatment on the magnitude of the dielectric loss angle shows that the process causing the decrease in dielectric losses is fully completed in 2–3 hours: a thirty-hour firing has the same effect as a three-hour firing.

To determine whether the surrounding atmosphere affects this effect, firing was carried out in vacuum. It turned out that in this case as well the reduction of the dielectric loss angle is the same as in the preceding cases, i.e., 40%.

A study of the influence of firing on the dielectric loss angle of fused quartz as a function of temperature showed that a noticeable effect begins only at \(1000^\circ\mathrm{C}\).

All these facts indicate that the decrease in the dielectric loss angle as a result of high-temperature heat treatment occurs at the expense of internal changes in the specimen. We believe that, as a result of heat treatment, part of the impurity ions is immobilized through complex formation, formation of a chemical compound, etc., and thus does not participate in the process of current passage through the specimen.

A number of authors [4], [5], [6] have shown the possibility of reducing the conductivity of solid dielectrics, including fused quartz, after

passing a direct current through them, which removes the excess of impurity ions caused by the high temperature. It is of interest

Fig. 10. ○ — unannealed specimen; Δ — electrocleaning after annealing;

lower curve — after annealing;

× — grinding of the surface. Quartz PS 17.

to determine the effect of electrocleaning on the magnitude of high-temperature dielectric losses in fused quartz.

Fig. 11. Quartz PS 23 \((l = 0.19\ \text{cm})\).

● — untreated specimen; ○ — electrocleaning;

× — heating at \(500^\circ\text{C}\); ◐ — annealing at \(1200^\circ\text{C}\), 3 hours.

Electrocleaning was carried out at a temperature of 500°C for 5–8 hours. The magnitude of the constant voltage applied to the specimen in this process was 600 V.

We studied the influence of electrocleaning on the dielectric-loss angle of quartz at a frequency of 25 MHz. The results of these investigations, presented in Fig. 11, show that the high-temperature dielectric losses in fused quartz decrease after electrocleaning. This decrease is the same for all the types of fused quartz studied and amounts to approximately 30%.

A second electrocleaning does not cause any further change in the dielectric-loss angle.

Clarification of the influence of the combined action of high-temperature heat treatment and electrocleaning on the value of the dielectric-loss angle of fused quartz shows that:

1) electrocleaning after firing (Fig. 10) has no noticeable effect on the value of the dielectric-loss angle;

2) heat treatment after electrocleaning additionally lowers the value of the dielectric-loss angle to a level determined by heat treatment alone, which evidently indicates that they act on one and the same type of ions.

Fig. 12. Specimen VIII
1 — \(E = 1.03\ \mathrm{kV/cm}\); 2 — \(E = 0.43\ \mathrm{kV/cm}\).

Fig. 13. Specimen VIII (1) \(T = 510^\circ\mathrm{C}\).

Thus, the fixation of some impurity ions during firing, or their removal during electrocleaning, leads to an improvement in the electrical-insulating properties of fused quartz.

Experiments with quartz specimens made from rocks containing a considerable number of gas inclusions are of great interest. Measurement of the temperature dependence of the dielectric-loss angle of these specimens showed (Fig. 12) that, at a certain temperature characteristic of the given specimen, the dielectric-loss angle begins to increase sharply. Measurement at a lower voltage showed the disappearance of this phenomenon in the temperature range studied.

In this connection, a study was carried out of the dependence of the dielectric-loss angle on voltage at a temperature close to the onset of the sharp increase in the temperature dependence. Fig. 13, representing this dependence, reproduces the familiar picture of ionization losses.

This is also indicated by the discharges occurring in the pores, observed in the form of flashes within the body of the specimen.

Thus, the presence of gas inclusions in fused quartz has an unfavorable effect on the magnitude of the dielectric-loss angle. Along with conduction losses, ionization losses arise, leading to sharp heating of the dielectric in a high-frequency field.

Conclusion

The work carried out permits the following conclusions.

1. A calorimetric method for measuring the dielectric-loss angle has been improved; it makes it possible to investigate fused quartz at high temperatures and elevated voltages in the frequency range of 10–40 MHz, with a sufficient degree of accuracy.

2. As a result of the investigation of dielectric losses in fused quartz, it has been established that:

a) the high-temperature dielectric losses in transparent fused quartz are conduction losses, the magnitude of which is determined by the amount and degree of fixation of the impurity present in the specimen;

b) removal of part of the impurity ions during electrocleaning, or their fixation during annealing, leads to a decrease in the dielectric-loss angle;

c) dielectric losses in specimens containing gas inclusions consist of conduction losses and ionization losses. The latter account for the high value of the dielectric-loss angle of these specimens, the dependence of the magnitude of the dielectric-loss angle on voltage, and its sharper increase with temperature.

In conclusion, I express my gratitude to K. A. Vodolyanov for supervising the work. I also consider it my duty to note the great assistance in the work given by the first supervisor, A. M. Venderovich.

LITERATURE

1. H. H. Race, C. Leonard.—Trans. Amer. Inst. El. Eng. 55, 1936.
2. A. V. Lykov.—Heat Conductivity of Nonstationary Processes, Gosenergoizdat, 1952.
3. A. P. Aleksandrov, A. F. Walter et al.—Physics of Dielectrics, GTTI, 1932.
4. A. A. Shaposhnikov.—ZhRFKhO, Phys. 42, 8, 1910.
5. L. G. Shentsova and N. E. Vedeneeva.—DAN SSSR, vol. LXVIII, No. 2, 1949.
6. N. g. Rahimi—j. Phys. Rad, vol. 9, No. 7 (291), 1938.

Siberian Physico-Technical Institute

QUESTIONS AND ANSWERS

M. S. Metsik—Were heat losses by radiation taken into account?

B. I. Vorozhtsov—It was shown that, for up to 5 minutes, the losses may be disregarded.

G. I. Skanavi—How was the distribution of potential between the air and the quartz determined?

B. P. Vorozhtsov—From the equivalent circuit, taking the dielectric losses into account.

G. I. Skanavi—What is the dielectric heating of the specimens?

B. P. Vorozhtsov—Approximately \(3^\circ\), possibly more. At elevated temperatures it is always greater.

G. I. Skanavi—When do ionization losses begin?

B. P. Vorozhtsov—At a temperature of \(300^\circ\) and a field strength \(E = 1\ \text{kV/cm}\).

R. L. Müller—Are you aware that at a temperature of \(300\text{–}400^\circ\) the dissociation energy of sodium ions decreases sharply?

B. P. Vorozhtsov—Yes; however, spectroscopic investigations have shown that sodium ions are either absent or amount to less than 0.001.

R. L. Müller—He points out that the purest boric anhydride contains a certain amount of sodium—from 0.01 to 0.001%.

According to his calculations, at a temperature of about 500, excitation of valence bonds is observed, i.e., liberation of sodium ions. He is convinced that the rise of \(\operatorname{tg}\delta\) with temperature in quartz is caused by sodium ions.

G. I. Skanavi—Vorozhtsov’s work represents a major step forward. Until now the calorimetric method has not yielded accurate results. It is important that the work was carried out on quartz, which has broad application. Vorozhtsov’s report is one of the best that have been heard at the conference.

1. The possibility of using a compensation device for determining the magnitude of dielectric heating \(\Delta T\) at elevated temperatures was tested by A. M. Venderovich and A. P. Vyatkin. ↩