Relaxation Dielectric Losses in Some Silicate Glasses

V. I. Odelevskii and N. M. Verebeichik

The significant role of glass in technology, in particular in electrical engineering and radio engineering, is well known. In this connection, glasses have long been the object of numerous investigations. Nevertheless, the important question of the mechanism of dielectric losses in glasses still cannot be considered sufficiently clear.

Our work pursues two aims: on the one hand, it is an attempt to develop a theory of high-temperature relaxation dielectric losses in alkali glasses; on the other, it brings to the attention of practicing technologists a number of glass compositions with high electrical properties.

Alkali Aluminosilicate Glasses.

Dependence of Properties on Composition

Potassium aluminosilicate high-silica glasses of molecular composition

\[ \mathrm{K_2O}\cdot x\,\mathrm{Al_2O_3}(17-2x)\,\mathrm{SiO_2} \tag{1} \]

have high dielectric losses in comparison with ordinary alkali-silicate glasses. The magnitude of the dielectric losses, as the content of \(\mathrm{Al_2O_3}\) is varied, passes through maxima at values \(x = 1 \pm 0.2\) (Fig. 1).

It has been suggested [1] that the glass network at \(x = 1\) is denser than at the points \(x = 1 \pm 0.2\) and to a certain extent approaches the structure of quartz glass.

In view of the exceptional difficulty of obtaining homogeneous specimens from the very viscous potassium glasses, in subsequent investigations they were replaced by analogous sodium glasses

\[ \mathrm{Na_2O}\cdot x\,\mathrm{Al_2O_3}\cdot(17-2x)\,\mathrm{SiO_2}. \tag{2} \]

The technology for preparing the specimens is described in [1].

Figure 2 presents the dependence of the specific volume, thermal linear expansion, dielectric losses, and electrical conductivity on the atomic ratio

\[ x=\frac{\mathrm{Al}}{\mathrm{Na}}. \]

From a comparison of Figs. 1 and 2 it is seen that the positions of the maxima of \(\operatorname{tg}\delta\) in sodium and potassium glasses coincide.

Simultaneously with the dielectric losses, the electrical conductivity, specific volume, and thermal expansion pass through maxima; thus, the existence of regions has been experimentally confirmed where…

Fig. 1. Dependence of the dielectric losses of potassium aluminosilicate glasses on the content of aluminum oxide.

a) \(f = 10^3\) Hz; 1 — \(t = 20^\circ\mathrm{C}\); 2 — \(t = 100^\circ\mathrm{C}\).

b) \(f = 10^6\) Hz; 1 — \(t = 100^\circ\mathrm{C}\); 2 — \(t = 20^\circ\mathrm{C}\).

Fig. 2. Dependence of the electrical and physical properties of sodium aluminosilicate glasses on the content of aluminum oxide:

1 — \(\tg\delta\) at \(f = 10^3\) Hz and \(t = 20^\circ\mathrm{C}\); 2 — \(\tg\delta\) at \(f = 10^6\) Hz and \(t = 20^\circ\mathrm{C}\); 3 — specific electrical conductivity at \(100^\circ\mathrm{C}\); 4 — specific volume; 5 — thermal linear expansion.

softening near the compositions corresponding to the points \(x = 1 \pm 0.2\), and also the effect of very small changes in the oxygen number

\[ b=\frac{O}{\mathrm{Si}+\mathrm{Al}} \tag{3} \]

of the order of hundredths of a unit, on the structure and properties of certain glasses.

Dielectric losses in sodium aluminosilicate glasses are higher than in the corresponding potassium glasses; at room temperature \(\operatorname{tg}\delta\) for sodium glasses is \(10\)–\(20\%\) at a frequency of \(1\ \mathrm{kHz}\), and \(3\)–\(4\%\) at a frequency of \(1\ \mathrm{MHz}\). The simplest calculation shows that these losses at room temperature are several times greater than the conduction losses, for which

\[ \operatorname{tg}\delta_{\mathrm{p}}=\frac{1.8\cdot 10^{12}}{\rho \varepsilon f}. \tag{4} \]

Three types of dielectric losses in glasses are known: conduction, relaxation, and resonance losses. Since there is no need to speak of ionic resonance at frequencies of \(10^2\)–\(10^6\ \mathrm{Hz}\), we arrive at the conclusion that, near room temperature, in the glasses studied the predominant mechanism of dissipation of electrical energy is the relaxation mechanism.

Review of Existing Theories of Relaxation High-Temperature Dielectric Losses in Glasses

We shall consider the theory of Skanavi [2, 3] and Weyl [4]. The works of Jevons [5] and Stevels [6], in their theoretical part, concern low-temperature relaxation, with a different physical mechanism, and therefore are not discussed.

a) Theory of relaxation in pores.
Skanavi proposed that the principal mechanism of relaxation consists of jumps of alkali ions inside micropores, these “active” ions being bound only by polarization forces and, consequently, torn from their anchoring sites, or dislocated ions.

The model of the relaxator, according to Skanavi, is presented in Fig. 3; the author postulates the impossibility of motion of the ion along the wall and along small chords, and calculates the height of the barrier from the motion of the ion along the diameter of the spherical cavity.

The theory under consideration was an interesting attempt that attracted the attention of researchers to theoretical problems connected with the advance calculation of the electrical properties of glasses; therein lies its undoubted positive role. However, both the model and the calculated results raise serious objections.

Fig. 3. Diagram of a cationic relaxator according to Skanavi.

The author introduced into the model an unjustified prohibition of ion motion along the circumference and along small chords; when this prohibition is removed, it turns out that the model in general does not make it possible to calculate the transition energy (it gives \(U = 0\)), that is, it is too primitive.

The existence in annealed glass of a significant number of extensive voids, with volumes of the order of 100–1000 ion volumes (radius \(R \cong 10 r_1\)), has likewise not been proved.

It is possible that Skanavi’s theory is applicable to some extent to tempered glasses, with a loosened structure; it should be noted that in this case the calculation of the height of the energy barrier and, correspondingly, of the value of the time constant must be carried out anew, proceeding from the discrete structure of the glass, which is a very complex problem.

b) Theory of pseudodipole relaxation.

Weyl considers the process of “formation and disappearance of dipoles” during thermal dislocation of alkali ions in glass. He assumes that in the ground state, corresponding to the absolute minimum of the potential energy, an alkali ion, together with a group of charge-balancing charges, does not form a dipole and that, consequently, the distribution of charges around the alkali ion is sufficiently symmetric.

According to Weyl, the relaxation of such pseudodipoles upon application of a field, in the form of a certain mean-statistical displacement of semi-bound ions that have passed through the first stage of thermal dissociation, is the principal relaxation mechanism responsible for dielectric losses in glasses at ordinary (not too low) temperatures.

It is quite obvious that in the region of intermediate concentrations of alkalis, of the order of 5–15% by weight, the activation energy of a pseudodipole is very close to the dissociation energy corresponding to the conduction process; thus, the dielectric losses associated with Weyl’s pseudodipole relaxation acquire an appreciable magnitude only in the region of large conduction losses, being at first approximately proportional to them and then decreasing to zero with a further rise in temperature; by virtue of this, the mechanism of pseudodipole relaxation has no practical significance and cannot explain the existence of appreciable dielectric losses in the region of small conduction losses. Let us note in passing that, with increasing concentration of alkali ions, the relative effectiveness of the pseudodipole relaxation mechanism should decrease, since when the mean distances are reduced below a certain limit, the distinction between the states of predissociation and complete dissociation, which determines the existence of pseudodipoles, is erased.

Below is set forth a theory of relaxation polarization based on the idea of the existence, at least in some varieties of glasses, of typical permanent, mobile dipoles.

Structural model of a high-silica alkali aluminosilicate glass

According to modern views, the structure of glasses is to a considerable extent similar to the structure of crystalline solids, despite the absence of “long-range order” in the arrangement of atoms; for example, quartz glass resembles the crystalline modifications of \(\mathrm{SiO_2}\)—cristobalite and tridymite [7, 8, 9].

Let us suppose that the glass which is basic for us,

\[ \mathrm{R_2O}\cdot \mathrm{Al_2O_3}\cdot 15\,\mathrm{SiO_2} \tag{5} \]

is, in its structure, similar to quartz glass and also, to a certain extent, to cristobalite.

By idealizing the structure, it may be reduced to a cristobalite network of \(\mathrm{SiO_2}\) with partial substitution of \(\mathrm{Si}^{n+}\) ions according to the scheme

\[ \mathrm{Si}^{n+} \longrightarrow \mathrm{Al}^{(n-1)+} + \mathrm{R}^{+}. \tag{6} \]

The structure of cristobalite is characterized by an open anionic network that includes a series of pseudocavities with tetrahedral symmetry. Each pseudocavity is bounded by four oxygen triangles and communicates directly with four neighboring pseudocavities through openings formed by four oxygen six-membered rings.

Figure 4 shows the structure of cristobalite; the ions located inside the oxygen tetrahedra are not shown. The six-membered ring and the through channel are clearly visible.

Fig. 4. Structure of cristobalite. Only oxygen ions within one unit cell are shown.

Fig. 5. Idealized structural model of an alkali high-silica aluminosilicate glass. The dark oxygen tetrahedron contains an $\mathrm{Al}^{3+}$ ion, the light one—$\mathrm{Si}^{4+}$ ions. Inside the pseudocavity an $\mathrm{R}^{+}$ ion is visible, adjacent to the dark $\mathrm{A}^{-}$ tetrahedron. The match heads show the other three possible positions of the alkali ion.

In substitutions of type (6), aluminum ions take the place of silicon ions, producing charged tetrahedra $[\mathrm{Al}(\mathrm{O}_{1/2})_4]^{-}$ (we shall hereafter call them, for brevity, “$\mathrm{A}^{-}$ tetrahedra”). Alkali ions $\mathrm{R}^{+}$ are located in the pseudocavities at a minimum distance from the $\mathrm{A}^{-}$ tetrahedra, forming with them certain permanent dipoles $\mathrm{A}^{-}\mathrm{R}^{+}$.

An alkali ion, passing from one cavity to another, can occupy any of four energetically equivalent positions near the center of the faces of the $\mathrm{A}^{-}$ tetrahedron and, thus, the dipole is not fixed but mobile (Fig. 5).

A rough geometrical estimate gives the following expression for the dipole arm:

\[ a \simeq r_0\left(0.48+\sqrt{\frac{r_1^2}{r_0^2}+2\frac{r_1}{r_0}-\frac{1}{3}}\right), \tag{7} \]

where $r_0$ is the radius of the oxygen ion, and $r_1$ is the radius of the alkali ion. Substituting the values of the ionic radii according to Zachariasen, we obtain the data of Table 1.

Thus, the magnitudes of the dipole moments in the glasses under investigation are substantially higher than in ordinary dipolar liquids $(1\text{–}2D)$ and even exceed the moments of nitriles and of all disubstituted benzene derivatives $(3\text{–}5D)$.

Table 1

Approximate calculated characteristics of permanent dipoles in alkali aluminosilicate glasses

With respect to the height of the potential barrier corresponding to the transition from one pseudocavity to another, in the present communication we shall confine ourselves to purely qualitative considerations.

Let us denote by $\Delta U$ the height of the potential barrier overcome in the process of the dipole relaxation under consideration; neglecting the change in the London dispersion forces, we have:

\[ \Delta U = \Delta U_k + \Delta U_{om} - |\Delta U_p|, \tag{8} \]

where the subscript “$k$” denotes the ordinary Coulomb interaction, “$om$” the repulsive forces of the electron shells of the ions, and “$p$” the interaction between the ion and the induced dipoles surrounding it.

When the ion R$^+$ moves “onto the barrier,” the Coulomb energy undoubtedly increases, since the positive ion moves away from the center of the A$^-$ tetrahedron. The value of $\Delta U_k$ is greatest in the case of the small ion Li$^+$; it decreases on passing to the large ions K$^+$, Rb$^+$, Cs$^+$.

Consideration of the model shows quite clearly that the energy of repulsion of the electron shells increases substantially when large alkali ions are transferred “onto the barrier,” inside the six-membered oxygen ring; thus, in contrast to the Coulomb energy, small ions are characterized by an insignificant value of the change in energy $\Delta U_{om}$, whereas for large ions it is large.

The third component—the change in the energy of interaction of the ion with the induced dipoles, $\Delta U_p$—must be a negative quantity because of the increase in the electric moment of the dipole when the ion R$^+$ is displaced into the oxygen ring; this circumstance is reflected in formula (8).

The principal features of the model with mobile dipoles are also retained in the case of a tridymite-like structure, including the number of possible dipole positions (four).

To verify the correctness of the theory of permanent mobile dipoles, dielectric losses in glasses were investigated in the region of high values of $\operatorname{tg}\delta$.

Investigation of dielectric losses in sodium aluminosilicate glasses at high values of $\operatorname{tg}\delta$

Measurements of $\operatorname{tg}\delta$ and capacitance in the audio-frequency range were carried out on an MLE bridge using a highly sensitive electronic indicator. A variable capacitor was connected in parallel with the specimen.

with low losses—air, with a maximum capacitance of 1000 pF, or a styroflex decade capacitor—from 0.001 to 1 μF.

The additional capacitance introduced was selected in such a way that the \(\operatorname{tg}\delta\) of the system did not exceed 15%, since otherwise the accuracy decreased owing to the need to introduce additional corrections to the value of \(\operatorname{tg}\delta\) of the system.

Fig. 6. Temperature dependences of \(\operatorname{tg}\delta\) and \(\varepsilon\) (dashed curves) of sodium aluminosilicate glasses with values of the parameter \(x=\dfrac{\mathrm{Al}_2\mathrm{O}_3}{\mathrm{Na}_2\mathrm{O}}\):
\(a\)—\(x=0.8\); \(b\)—\(x=1.0\); \(v\)—\(x=1.2\); \(g\)—\(x=1.4\).
1—\(f=10^2\) Hz; 2—\(f=4\cdot10^3\) Hz; 3—\(f=10^2\) Hz.

In Fig. 6 are presented the temperature dependences of \(\operatorname{tg}\delta\) and \(\varepsilon\) for four glasses. The characteristics of the intermediate glasses are analogous. In all glasses with a value of the parameter \(x \leqslant 1.1\), distinct maxima were found in the temperature dependence of \(\operatorname{tg}\delta\) at audio frequencies.

For one of the glasses, the frequency dependence of \(\operatorname{tg}\delta\) was also taken at elevated temperatures; it likewise revealed characteristic maxima (Fig. 7).

For separating the relaxation component of \(\tg\delta\) by the formula

\[ \tg\delta_{\mathrm{rel}}=\tg\delta-\frac{1.8\cdot 10^{12}}{\rho\varepsilon f}, \tag{9} \]

it is necessary to know, in addition to \(\varepsilon\), also the value of the specific resistance. The temperature dependence of the specific resistance of the four glasses of interest to us is given in Fig. 8.

Fig. 7. Frequency dependence of \(\tg\delta\) for sodium glass with parameter \(x=1.0\) at various temperatures:
1—\(t=110^\circ\mathrm{C}\); 2—\(t=133^\circ\mathrm{C}\); 3—\(t=162^\circ\mathrm{C}\).

The measurements were carried out on an electrometric setup, using the compensation version of Bronson’s circuit [10].

Figure 9 gives the results of the calculation by formula (9). The temperature maxima of \(\tg\delta_{\mathrm{rel}}\) for glasses with the ratio

\[ x=\frac{\mathrm{Al}}{\mathrm{Na}}<1.1 \]

are manifested quite clearly.

It may be assumed that in cases в, г, the maxima were not detected because measurements could not be made at sufficiently high temperatures (\(\tg\delta\) is too large, which requires the use of very large parallel capacitances; in this case the error in determining the capacitance and \(\tg\delta\) of the specimen increases sharply owing to the transition to the last capacitance range of the bridge). Table 2 gives the coefficients \(B_{\mathrm{rel}}\) and

Table 2

Values of the conditional “activation energies” for the processes of relaxation and electrical conductivity

the corresponding values of the energies \(U_{\mathrm{rel}}\), calculated from the frequency shift of the temperature maxima \(\operatorname{tg}\delta_{\mathrm{rel}}\), and also, for comparison, analogous quantities characterizing the through conductivity (\(B_{\sigma}\) and \(U_{\sigma}\)).

The static dielectric constant \(\varepsilon_0\) could not be determined directly because of the excessive increase of losses in the specimen at high temperatures (see above). As a rough approximation, \(\varepsilon_0\) can be calculated, knowing the height of the dipole maximum, from the formula

\[ \varepsilon_0=\varepsilon_\infty\left(1+2\operatorname{tg}^2\delta_m+ 2\operatorname{tg}\delta_m\sqrt{1+\operatorname{tg}^2\delta_m}\right). \tag{10} \]

For the glasses investigated, \(\varepsilon_\infty \simeq 8\). The frequency of the natural oscillations of the ion (angular) is

\[ \nu'=\frac{f_m}{2}\sqrt{\frac{\varepsilon_\infty}{\varepsilon_0}}\cdot e^{\frac{u_{\mathrm{rel}}}{kT_m}}, \tag{11} \]

where \(f_m\) is the frequency of the applied electric field,

\(T_m\) is the absolute temperature corresponding to the maximum of \(\operatorname{tg}\delta_{\mathrm{rel}}\) at the frequency \(f_m\).

Fig. 8. Temperature dependence of the specific resistance of sodium glasses with the parameter

\[ x=\frac{\mathrm{Al}_2\mathrm{O}_3}{\mathrm{Na}_2\mathrm{O}}: \]

No. 4—0.8; No. 7—1.0; No. 11—1.2; No. 15—1.4.

Fig. 9. Temperature maxima of relaxation dielectric losses in sodium glasses with values of the parameter

\[ x=\frac{\mathrm{Al}_2\mathrm{O}_3}{\mathrm{Na}_2\mathrm{O}}: \quad \text{a—0.8; б—1.0; в—1.2; г—1.4;} \]

1—\(f=10^2\) Hz; 2—\(f=4\cdot10^2\) Hz; 3—\(f=10^3\) Hz.

Calculation by formulas (10) and (11), using averaged values of \(B_{\mathrm{rel}}\) and \(\operatorname{tg}\delta_m\), gives:

\[ \varepsilon_0 \simeq 200;\qquad \nu' \simeq 10^{10}\ \text{Hz}, \]

A high value of the dielectric permittivity indicates a sharply expressed association of dipoles, connected with the large magnitude of the electric moment of the dipole and with its great length.

Relaxation dielectric losses in lime–soda (window) glass

The discovery of “high-temperature” relaxation maxima in alkaline aluminosilicate glasses prompted a more thorough investigation of other types of alkaline glasses, first of all the long-known window glass.

Fig. 10. Temperature dependence of $\operatorname{tg}\delta$ and $\varepsilon$ (dashed curves) of window glass; 1, 2, 3, 4, 5—respectively frequencies $10^2$, $4 \cdot 10^2$, $10^3$, $10^5$, and $10^6$ Hz.

We have not yet set ourselves the goal of constructing a structural model of lime–soda glass; however, it could be said in advance that the mobility of dipoles in this glass (if they exist) must be strongly limited by the presence of a large number of strongly bound $\mathrm{Ca}^{2+}$ ions, which fill part of the pseudovoids in the anionic network.

The comparatively small magnitude of the relaxation dielectric losses made it necessary to take special measures to eliminate errors associated with possible inaccuracy in determining the temperature of the sample: measurement of the value of the direct-current resistance and of $\operatorname{tg}\delta$ with alternating current

…of different frequencies was carried out practically simultaneously, on one and the same specimen, in one and the same furnace, using the corresponding switch.

The results of the measurements are given in Figs. 10 and 11.

On the curve of the temperature dependence of $\operatorname{tg}\delta$, the bends are almost imperceptible, even at the lowest frequency—100 cps.

Fig. 11. Temperature dependence of the specific volume resistivity of window glass.

Fig. 12. Temperature dependence of relaxation dielectric losses in window glass: 1, 2, 3, 4, 5—respectively, frequencies $10^2$, 400, $10^3$, $10^5$, and $10^6$ cps.

Isolation of the relaxation component, according to (9), made it possible to detect at low frequencies relaxation maxima that shift regularly with a change in frequency (Fig. 12).

Calculation directly from the positions of the temperature maxima of $\operatorname{tg}\delta_{\text{rel}}$ gave overestimated values of the activation energy. After plotting curves in the coordinates “$\log \operatorname{tg}\delta - \dfrac{10^4}{T}$” (Fig. 13), a correction for the shift was made (the magnitude of the shift was taken from the displacement of the asymptote). The corrected value of the constant $B_{\text{rel}} \simeq 8300$ is smaller than $B_{\sigma}=10500$, as it should be.

The static dielectric permittivity, calculated by formula (10), exceeds the value $\varepsilon_{\infty}$ by only $1 \tfrac{1}{2}$ times; even if one assumes that the height of the maximum of $\operatorname{tg}\delta_{\text{rel}}$ is underestimated by 50%, the static dielectric permittivity will not be greater than $1.8\varepsilon_{\infty}=12$.

Let us return to the consideration of the temperature–frequency dependence of $\operatorname{tg}\delta_{\text{rel}}$ for window glass (Fig. 12). At low frequencies, beyond the maximum of $\operatorname{tg}\delta_{\text{rel}}$ there follows a clearly pronounced minimum, with a further rise of the curve; such a form of the temperature dependence indicates the existence of a second relaxation mechanism with an activation energy very close to the energy characteristic of the conduction process. It may be supposed that such a mechanism is the relaxation of Weyl pseudodipoles.

A simple calculation shows that, as the frequency is increased, the maxima of \(\operatorname{tg}\delta\) corresponding to both relaxation processes must converge; this effect explains the disappearance of the minimum on the \(\operatorname{tg}\delta_{\mathrm{rel}}\) curve at a frequency of \(1\) Mc/s.

Fig. 13. Same as in Fig. 12, but in coordinates \(\log \operatorname{tg}\delta_{\mathrm{r}} — \dfrac{10^4}{T}\).

Investigation of the Electrical Properties of Annealed Alkali-Free Aluminosilicate Glasses

Alkali-free glasses with good electrical properties are known; however, they all contain boric anhydride—a relatively scarce raw material (Tables 3, 4, glass TK-6); alkali-free boron-free glasses, as a rule, have too high a melting temperature and an unsatisfactory temperature dependence of dielectric losses (glass No. 40, glass II—Table 4).

Table 3

Compositions of alkali-free glasses

Note. The compositions and properties of glasses marked with an asterisk are given according to literature data.

Properties of alkali-free glasses
Table 4

In developing new formulations of alkali-free glasses, the method of gradual change of composition is usually used in order to obtain the required properties. Sometimes it is possible to obtain good glasses even with a sharp change in composition; however, such results are accidental in character. A striking example is the interesting work [11]; the author made the following bold substitutions in Jena glass (by weight!):

\[ 12\%\, \mathrm{BaO} \longrightarrow 12\%\, \mathrm{CaO} \]

\[ 15\%\, \mathrm{B_2O_3} \longrightarrow 15\%\, \mathrm{Al_2O_3} \]

\[ 4{,}2\%\, \mathrm{ZnO} \longrightarrow 4{,}2\%\, \mathrm{MgO} \]

Comparing the molecular formulas of the original and “derived” glasses:

\[ \begin{array}{rcl|rcl|l} \text{Jena} & 0{,}40\,\mathrm{ZnO} && 1{,}66\,\mathrm{B_2O_3} &&& \\ & 0{,}60\,\mathrm{BaO} && 0{,}26\,\mathrm{Al_2O_3} &&& 8{,}5\,\mathrm{SiO_2} \end{array} \]

\[ \begin{array}{rcl|l} \text{glass “P”} & 0{,}33\,\mathrm{MgO} && \\ & 0{,}67\,\mathrm{CaO} && 0{,}57\,\mathrm{Al_2O_3}\cdot 3{,}4\,\mathrm{SiO_2} \end{array} \]

we become convinced that they are completely different; the method of “substitution by weight” is of a purely formal character.

Much more effective is the use of diagrams of heterogeneous equilibria, with the inclusion of a number of additional considerations that make it possible to estimate in advance, approximately, the crystallization tendency and viscosity of fusible compositions indicated on the diagrams.

On the basis of equilibrium diagrams [12], the compositions of three glasses were selected: calcium K (a eutectic with a melting temperature of 1170°), barium B with equiatomic substitution of calcium by barium in the composition K (checking the liquidus temperature on the diagram shows that such a composition has a temperature of complete melting below 1300°), and magnesia-calcium MK (temperature of complete melting 1260°).

In view of the observed increased tendency of glass K to crystallize, glasses derived from K were also studied, into which a comparatively small amount of magnesium oxide was introduced (KM-1 and KM-2, Table 3).

Figure 14 presents the temperature dependence of the dielectric losses of the alkali-free glasses studied.

At high frequency, for all the glasses the temperature dependence of \(\operatorname{tg}\delta\) is small; at \(300^\circ\mathrm{C}\) the losses only double. Glass B is distinguished by an especially small temperature dependence; in it, doubling of \(\operatorname{tg}\delta\) is reached only upon heating to \(400^\circ\mathrm{C}\).

Fig. 14. Temperature dependence of \(\operatorname{tg}\delta\) of alkali-free glasses.

The temperature dependence of the specific resistance is shown in Fig. 15.

Fig. 15. Temperature dependence of the specific volume resistance of alkali-free glasses.

Glass with a high magnesium content has the greatest conductivity; barium glass has the least; calcium glass occupies an intermediate position.

At low temperatures the slope of the characteristics \(\lg \rho_v = f\left(\dfrac{10^4}{T}\right)\) decreases sharply, which is apparently connected with the existence of a small amount of alkaline impurities.

Table 4 compares the main technical characteristics of alkali-free glasses.

It may be considered that, in terms of the magnitude of the dielectric losses and the temperature dependence of \(\operatorname{tg}\delta\), the colorless alkali-free glasses KM-1, B, and MK proposed by us are close to the boron-containing glass TK-6 and substantially surpass the boron-free glasses No. 40 and “P.”

The melting properties of our glasses are somewhat better than those of the “P” glasses (not to mention glass No. 40, with its exceptionally difficult technology); in this respect they are also entirely acceptable.

Effect of Heat Treatment on the Electrical Properties of Some Alkali-Free Aluminosilicate Glasses

In studying the electrical properties of unannealed samples of magnesium–calcium glass KM-2, poor reproducibility of the properties from sample to sample was found, and in some cases maxima appeared in the temperature dependence of \(\operatorname{tg}\delta\), as did a divergence between the temperature dependences of \(\operatorname{tg}\delta\) upon heating and cooling in the temperature range \(20\text{–}300^\circ\mathrm{C}\), etc.

The effect of heat treatment on the electrical properties of alkali-free glasses was investigated.

The following were studied:

a) the effect of quenching unannealed glass (brief heating at \(700\text{–}750^\circ\mathrm{C}\) and rapid cooling in air);

b) the effect of annealing at \(700\text{–}750^\circ\mathrm{C}\) (holding for 2 hours) on quenching effects;

c) the change in \(\operatorname{tg}\delta\) and electrical conductivity during “low-temperature annealing” (holding the sample at temperatures of the order of \(200\text{–}400^\circ\mathrm{C}\));

d) the effect of prolonged storage of the glass at room temperature.

Glass KM-2, which gives a sharply pronounced quenching effect, was studied in greatest detail.

When a quenched sample is heated, the dielectric constant and \(\operatorname{tg}\delta\) pass simultaneously through maxima at a temperature of \(\sim 200^\circ\mathrm{C}\), independently of frequency (Fig. 16).

At a temperature of \(240^\circ\mathrm{C}\), a rapid decrease in dielectric losses and capacitance with time is readily observed.

It is quite obvious that the maxima mentioned are not normal relaxation maxima. Upon cooling a quenched glass that has been held at \(240^\circ\mathrm{C}\), relaxation maxima are found in the temperature region \(50\text{–}80^\circ\mathrm{C}\) (audio frequencies).

Figure 17 shows the effect of quenching and low-temperature annealing on the electrical conductivity of glass KM-2.

The electrical conductivity of the quenched glass is at least three orders of magnitude higher than that of the annealed glass. The constant “\(B\)” in the case of the quenched glass is substantially smaller (\(\sim 8000^\circ\) for the quenched glass and \(\sim 14000^\circ\) for the annealed glass).

The change in \(\operatorname{tg}\delta\) with time during low-temperature annealing is shown in Fig. 18.

Fig. 16. Temperature dependence of \(\operatorname{tg}\delta\) and \(\varepsilon\) of KM-2 glass, quenched (at \(700^\circ\mathrm{C}\), holding time 30 min.): 1—\(\operatorname{tg}\delta\) at \(f = 10^2\) cps; 2—\(\operatorname{tg}\delta\) at \(f = 10^3\) cps; 3—\(\varepsilon\) at \(f = 10^2\) cps.

Fig. 17. Effect of quenching and low-temperature annealing on the specific volume resistance of KM-2 glass: 1—annealed glass; 2—quenched glass.

![Graph: change of \(\operatorname{tg}\delta \cdot 10^4\) with time \(t\), min, for glass KM-2 during low-temperature annealing.]

Fig. 18. Change of \(\operatorname{tg}\delta\) with time during low-temperature annealing—glass KM-2.

![Graph: \(\operatorname{tg}\delta \cdot 10^4\) versus \(t,{}^\circ\mathrm{C}\), showing the influence of high-temperature annealing on the quenching effect for glass KM-2; curves 1, 2, and 3.]

Fig. 19. Influence of high-temperature annealing on the quenching effect—glass KM-2: 1—700°C, holding for 30 min; 2—700°C, holding for 2 hours; 3—700°C, holding at 20°C for 60 days.

The change in properties upon quenching and low-temperature annealing is reversible; approximately the same properties can be obtained in a series of successive quenchings and annealings.

Further investigations established the appearance of irreversible changes in the properties of glass during prolonged holding near the point \(T_g\) (700–740°C), i.e., during “high-temperature annealing.” Fig. 19 shows that two-hour high-temperature annealing sharply reduces the quenching effect.

Fig. 20. Temperature dependence of \(\tan\delta\) of annealed (solid curves) and glass KM-1 quenched at 700°C (dashed curves).

Prolonged holding of the glass (60 days) at room temperature completely eliminates the possibility of the occurrence of quenching anomalies (Fig. 19, curve 3).

Considerable quenching effects were found in barium glass B, and also, to a lesser extent, in calcium glass K.

In MK glass and especially in KM-1 glass, the influence of heat treatment is very slight (Figs. 20 and 21).

On the basis of the experimental data obtained, it is possible to put forward a working hypothesis concerning the nature of quenching anomalies.

Freshly prepared unannealed glass is in a nonstationary state. It is characterized by the existence of a number of loosened sites, which create additional energy levels intermediate between the levels of fixation and dislocation (Fig. 22).

In the nonstationary state, owing to the existence of “loosening levels,” the properties of the glass depend on quenching and low-temperature annealing.

At 700°C a considerable fraction of the ions is fixed at the “loosening levels” (levels 2, Fig. 22a). If the glass is cooled slowly, at a rate of about 50° per hour, redistribution has time to occur, and the excess ions from level “2” pass to the main level “1.” Such a transition at a quite noticeable rate is possible even at temperatures of 200–250°C (KM-2 glass).

At temperatures below 200° the dispersal of the excess ions proceeds slowly; both the electrical conductivity and the dielectric losses have elevated values: the former because of the gradual filling of the dislocation zone (Fig. 22a, 3) by ions from level 2, the latter in connection with the relaxation of residual ions at levels 2.

Fig. 21. Temperature dependence of the specific volume resistivity of annealed and quenched (dashed curve) KM-1 glass.

Annealing at a temperature of 700°C for several hours leads to the elimination of “rupture levels” 3. Prolonged holding of the glass at room temperature leads to the same result.

Fig. 22. Scheme of energy levels in alkali-free glass:

a) unannealed glass, b) annealed glass.

Let us note that the phenomenon of the “zero depression” of thermometers, connected with a change in the density of glasses at low temperatures, has long been known; deformation of glass tubes at room temperature has also been observed. Thus, the fact that the electrical properties of certain glasses change, evidently coupled with certain structural changes already at a temperature of 20°C, should not seem altogether improbable.

Conclusion

In the present work:

1. An analysis is given of existing theories of “high-temperature” dielectric losses in alkali glasses; their inadequacy is shown.

2. A structural model of alkali aluminosilicate glass with mobile dipoles is considered.

3. The temperature dependence of dielectric losses in sodium high-silica aluminosilicate glasses in the region of high values of $\operatorname{tg}\delta$ has been investigated; it is shown that, in such glasses, in agreement with theory, sharply expressed relaxation temperature maxima of $\operatorname{tg}\delta$ and high values of the dielectric constant exist at temperatures of the order of $100$—$150^\circ\mathrm{C}$.

4. The temperature dependence of $\operatorname{tg}\delta$ of alkali window glass at various frequencies has been investigated; the existence in it of relaxation maxima of $\operatorname{tg}\delta$ is shown (taking conductivity losses into account).

5. On the basis of diagrams of heterogeneous equilibria, a number of recipes for alkali-free boron-free glasses using nondeficit raw materials and possessing high electrical properties has been developed.

6. The effect of quenching and annealing on the electrical properties of alkali-free glasses has been investigated. The existence of the phenomenon of relaxation dielectric losses in some alkali-free glasses has been demonstrated.

A change in the properties of glass with time at room temperature has been established.

Literature

1. N. M. Verebeichik, A. E. Kamenchik, V. I. Odelevskii, ZhTF, 22, 12, 1952.

2. G. I. Skanavi, ZhTF, 9, 612, 1939.

3. G. I. Skanavi, Physics of Dielectrics (Region of Weak Fields), GITTL, Moscow–Leningrad, 1949.

4. W. A. Weyl, J. Soc. Glass Techn., 33, 220—38 T, 1949; Ph. Abs., 53 (629), 3144, 1950.

5. M. Gevers, Philips, Res. Rep., 1, 279, 1946.

6. J. M. Stevels, J. Soc. Glass Techn., 34, 80, 1950.

7. J. T. Randall, H. P. Rooksby, B. S. Coopr. J. Soc. Glass Techn., 14, 219, 1930.

8. F. Matossi, Z.S.f. techn. Phys, 18, 585, 1937.

9. V. A. Florinskaya, DAN SSSR, 90 (6), 1953.

10. M. M. Mikhailov, “Testing of Electroinsulating Materials,” ONTI, NKTP USSR, 1936.

11. N. M. Pavlushkin, Glass and Ceramics, No. 3, 1954.

12. D. S. Belyankin, V. V. Lapin, N. A. Toropov. Physicochemical Systems of Silicate Technology, pp. 169, 174, 325, 1954.

Questions and Answers

K. A. Vodopyanov—Were the measurements carried out at frequencies of \(10^2\)—\(10^3\) cycles? Was space charge taken into account?

V. I. Odelevskii—No traces of space charge were observed for times from half a second and longer; at shorter times they were not determined.

M. P. Tonkonogov points out that although the motion of the anion in the cavity, as follows from the report, is more likely along the “chord” of the cavity and not along its “diameter,” the latter will give a larger component of the dipole moment, and therefore the effect of this displacement will be greater.

V. I. Odelevskii replies that motion along the “chord” is physically more understandable and possible, all the more so because motion along the line of the small barrier is more probable.

B. N. Matsonashvili—How were the relaxation losses calculated, and what is the error in measuring the relaxation losses?

V. I. Odelevskii replies that the error is the greater, the smaller the relaxation losses, but the accuracy was sufficient. Errors due to temperature were avoided by measuring \(\sigma\) and \(\operatorname{tg}\delta\) simultaneously.

A. A. Vorob’ev points out that the given model of an ion in a pore is schematic. The speaker indicated that another model can be given which makes it possible to calculate the relaxation; this possible model should be explained.

V. I. Odelevskii—It is assumed that the bonds are partly ionic in character and that ionic radii can be used in the calculations. The voids in the glass structure are such that ions with a small ionic radius pass easily through them.

In this case it is necessary to take into account the considerable repulsive forces that will hinder the displacement of the ions. The relaxation energy will be composed of the Coulomb and polarization repulsion energies.

Errata