Study of Some Microscopic Regularities of Electrical Breakdown in Lead Azide

O. N. Sukhushin, Yu. A. Zakharov, G. A. Rappoport

(Presented at the scientific seminar of the Department of Radiation Chemistry)

The study of electrical breakdown and excitation by means of initiating explosives is of interest from the point of view of elucidating the elementary acts of chemical reactions, excitation, and the development of the rapidly occurring processes in solids \[1–3\]. However, in solving the problem of studying the micromechanism of these processes, it is necessary to take into account a number of macroscopic factors, especially if the experiment is carried out on polycrystalline pressed specimens. One such process is the occurrence of microdischarges in the pores of such specimens \[4–6\], which can cause a decrease in the electrical strength of the material and, during the breakdown of initiating explosives, can cause ignition of the composition if the dimensions of the source exceed the critical ones. Another process that reduces the electrical strength and leads to ignition of the composition is corona discharge on the electrodes \[7, 8\]. An experimental criterion for elucidating the presence of these macroscopic factors is the direct detection of micro- and edge discharges by various methods based on the registration of nonstationary current processes \[9, 10, 11\]. However, even in homogeneous dielectrics and semiconductors, phenomena are observed that are accompanied by the appearance of a high-frequency component of the current, associated with the discrete development of electron avalanches \[12, 13\], which

complicates the detection of corona and sparking phenomena by oscillography as well. Another criterion for the presence of nonstationary discharges that alter the electrical strength is the dependence of the breakdown voltage on the thickness of the specimen, which may serve as a criterion for one mechanism or another [7, 8, 14].

The dependence of the breakdown voltage, in the presence of microdischarges, on the thickness should apparently also be determined by the porosity (density) of the specimen. Let us consider these regularities on the basis of the simplest model of a polycrystalline dielectric and an elementary equivalent circuit for it (Fig. 1).

The voltage applied to this system is distributed according to the law

\[ U = n\left(E_1 a + E_2 b\right) . \tag{1} \]

For large \(n\) (the number of elements in the equivalent circuit), if the electrical strength is determined by the first discharge in a pore, the breakdown voltage of the specimen will be:

\[ U_{\mathrm{br}} = n E_{2\mathrm{br}}\left[\frac{\varepsilon_2}{\varepsilon_1}a + b\right], \tag{2} \]

where \(E_{2\mathrm{br}}\) is the electrical strength of the air gap.

The quantities \(n\), \(a\), and \(b\) can be expressed through the densities of the single crystal \(\gamma_1\), air \(\gamma_2\), and the specimen \(\gamma\), if the dimensions of the single crystals composing the specimen are known:

\[ b = a\left(\frac{\gamma_1-\gamma}{\gamma-\gamma_2}\right); \qquad n = \frac{d}{a}\left(\frac{\gamma-\gamma_2}{\gamma_1-\gamma_2}\right). \tag{3} \]

After this, expression (2) takes the form:

\[ E_{\mathrm{br}} = E_{\mathrm{br}.2} \left(\frac{\gamma-\gamma_2}{\gamma_1-\gamma_2}\right) \left[ \frac{\varepsilon_2}{\varepsilon_1} + \left(\frac{\gamma_1-\gamma}{\gamma-\gamma_2}\right) \right]. \tag{4} \]

In accordance with (4), in the case where the breakdown mechanism is associated with microdischarges in the pores, the electrical strength does not depend on the thickness of the specimen and is determined by its porosity and by the pore size \((E_{\mathrm{br}.2})\). The dependence of the breakdown vol—

the effect of interelectrode distance at small thicknesses has at present been studied only poorly; however, a few works contain results [6, 15] that can be extrapolated to the region of small thicknesses.

An analogous calculation for the mechanism of microdischarge in an individual single crystal gives the following expression for the electrical strength:

\[ E'_{\mathrm{br}}=E_{\mathrm{br}1}\, \frac{\gamma-\gamma_2}{\gamma_1-\gamma_2} \left[ \left(\frac{\gamma_1-\gamma}{\gamma-\gamma_2}\right) \frac{\varepsilon_1}{\varepsilon_2}+1 \right]. \tag{5} \]

If the gas density is neglected in comparison with the density of the substance, then (4) and (5) take the following simplified form:

\[ E_{\mathrm{br}}=E_{\mathrm{br}2}\, \frac{\gamma}{\gamma_1} \left[ \frac{\varepsilon_2}{\varepsilon_1} +\frac{\gamma_1-\gamma}{\gamma} \right], \tag{6} \]

\[ E'_{\mathrm{br}}=E_{\mathrm{br}}\, \frac{\gamma}{\gamma_1} \left[ \left(\frac{\gamma_1-\gamma}{\gamma}\right) \frac{\varepsilon_1}{\varepsilon_2}+1 \right]. \tag{7} \]

Figure 1 presents the results of calculations, by formulas (6) and (7), of the dependence of \(E_{\mathrm{br}}\) and \(E'_{\mathrm{br}}\) on density at \(a = 10^{-5}\,\text{cm}\) and \(\varepsilon_1 = 10\). The formal calculation shows that for polycrystalline materials there is no dependence of electrical strength on thickness; however, there is a characteristic dependence of electrical strength on density (a curve with a maximum for breakdown by the mechanism of microdischarges in pores, and a straight line for breakdown by the mechanism of microdischarge in individual crystallites). From the calculated model there follows yet another way of experimentally testing the macromechanism of electrical breakdown: if the breakdown mechanism is not connected with ionization in the pores, then an increase in the dielectric permittivity of the medium \(\varepsilon_2\) (for example, upon impregnation with dielectric media) should lead to a decrease in the electrical strength of the specimen; conversely, if the breakdown mechanism is determined by mic-

by discharges in the pores, then an increase in the dielectric permittivity of the medium entails an increase in the electrical strength of the specimen; moreover, an increase in electrical strength should also be observed because of the higher, compared with air, electrical strength of the medium.

The electrical strength of the specimens was determined experimentally on the front of a standard voltage pulse (1.5 μsec/40 μsec). The specimens were tablets pressed on a polished steel roller from hardened steel into a polychlorovinyl sheath. The contact diameter was 16 mm. The external electrode was a ball 10 mm in diameter, which was pressed in a special device against the outer surface of the specimen. A study of the dependence of the breakdown voltage of a specimen in such a system on thickness showed that it is well described by the formula:

\[ E_{\mathrm{pr}} = \frac{A}{\sqrt{d}} + B \tag{6} \]

which indicates the leading role of sliding discharges in breakdown in such a system, and the need to protect the upper electrode.

Glycerin was chosen as the protective medium, as a liquid with sufficiently high conductivity, which helps equalize the field and practically does not wet the surface of the specimen. All subsequent experiments were carried out with protection of the upper electrode.

The results of studying the influence of the density and thickness of the layer being broken down on the electrical strength of lead azide are shown in Fig. 2 in the coordinates: breakdown voltage (V) — density (g/cm³), for different specimen thicknesses and polarities of the ball electrode (solid lines—negative, dash-dotted lines—positive polarity). The experiments were carried out on no fewer than 20 specimens for each polarity. The limits of the probable arithmetic-mean deviation are shown at each experimental point by a vertical line. The curves of the dependence of the breakdown voltage

of density have a maximum at a density \(\rho = 3\ \text{g}/\text{cm}^3\), and the increase in breakdown voltage toward higher density is more sharply expressed. The character of the dependences for the different polarities of the spherical electrode is qualitatively similar; only the breakdown voltage at positive potential of the sphere is lower. From the mean values of \(\overline{U}_{pr}\), the dependences \(\overline{U}_{pr}(h)\) and \(E_{pr}(h)=\overline{U}_{pr}(h)/h\) were plotted. It turned out that \(\overline{U}_{pr}\) increases with increasing thickness practically linearly:

\[ \overline{U}_{pr}=A+Bh \tag{9} \]

The values of \(A\) and \(B\) for different sample densities and polarities of the spherical electrode are presented in the following table:

\(^*\) Results of extrapolation to the density of a lead azide single crystal.

The electric strength, with increasing thickness, decreases for samples with density greater than \(\text{g}/\text{cm}^3\), and this dependence is the more strongly expressed the higher the density (see Fig. 3).

Fig. 1. Model (a), equivalent circuit (b), and the result of a calculation of breakdown in a layered-porous dielectric.

The obtained dependences of the breakdown voltage of lead azide on density agree qualitatively with the results of a calculation based on an approximate model of microdischarges in the pores of a complex dielectric. Moreover, in the region of low densities the electrical strength of lead azide practically does not depend on thickness, which also agrees with the calculation results. However, as the density of the specimen approaches the density of the single crystal, a dependence of the mean breakdown gradient on thickness is observed and becomes stronger; this is not consistent with the assumption that microdischarges in pores play the predominant role in the breakdown of polycrystalline specimens. Moreover, if the decrease in electrical strength with increasing thickness is attributed to an increase in the probability of the presence of weak spots in the specimen, then this dependence should become stronger with increasing thickness, which likewise is not consistent with the results obtained. It is natural to suppose that, at high density, the breakdown mechanism of a pressed polycrystalline specimen may be similar to the breakdown mechanism of continuous dielectrics. By analogy with the processes of gas breakdown, an increase in density is equiva-

Fig. 3. Dependence of the breakdown voltage of lead azide on the density and thickness of the layer being broken down, at the same polarity of the plane electrode.

[[unclear: beginning of line]] decrease in pressure. In both cases this leads to a decrease in the path length between acts of impact ionization, \(l_i\), and, consequently, to an increase in \(U_{pr}\). In order to clarify the validity of this hypothesis, the dependence of \(U_{pr}\) on the product \(\rho h\) was constructed (\(\rho h\) is the analogue of the \(ph\) complex in a gas gap—the Paschen law [4]), which is presented in Fig. 4. It turned out that, in the region \(\rho \geq 3\ \text{g/cm}^3\), the values of the breakdown voltage are grouped in a relatively narrow region; that is, they are determined by the product \(\rho h\), independently of thickness and density separately.

A group of experiments was also carried out on the effect of impregnation with liquids having different dielectric properties on the breakdown voltage of pressed polycrystalline lead azide specimens. Impregnation with glycerin, cresol, and carbon tetrachloride changes the character of the dependence \(U_{pr}(\gamma)\) only slightly; even the maximum of the breakdown voltage occurs at the same density, \(\gamma = 3.0 \div 3.5\ \text{g/cm}^3\). Impregnation with transformer oil, however, qualitatively changes the course of the dependence: as the density decreases, the breakdown voltage increases monotonically. Apparently, for specimens impregnated with glycerin, \(CCl_4\), and cresol, the discharge process in air pores is partially or completely replaced by discharge in the liquid; transformer oil, however, has high electrical strength, and breakdown occurs exclusively in the microcrystals of lead azide. The calculation model is also supported by the fact that the electrical strength of impregnated compositions of low density increases in the sequence of liquids in which the dielectric permittivity increases. At higher density the order is opposite. It should be noted that extrapolation of the curves \(U_{pr}(\gamma)\) to the density of a single crystal does not bring them to a single point, which indicates interference of the liquid interlayers in the electronic stages of breakdown.

Thus, the results of the investigation make it possible to assume that, during breakdown of specimens with a density close to

Fig. 3. Dependence of the average breakdown gradient of lead azide on density and thickness.

Fig. 4. Dependence of the average breakdown voltage of lead azide on the complex \(\gamma h\).

and in the single-crystal one, the breakdown mechanism is associated with the development of electron avalanches, as was previously assumed [1]; for specimens with a density of $<3\ \mathrm{g/cm^3}$ the process is definitely caused by microdischarges in the pores.

In studying the breakdown of pressed impregnated specimens of lead azide, we drew attention to the fact that in specimens of low density impregnated with glycerin and creosote, detonation is not initiated upon breakdown, while in specimens of high density the detonation is local in character and does not propagate through the entire charge. The literature describes experiments by Ubellohde and Woodward [16] on the ignition of lead azide single crystals suspended in a liquid. Bircomshaw and Taylor [16] believe that a high-boiling liquid reduces self-heating of the particles and thereby suppresses thermal ignition. Thus, the phenomenon of suppression of detonation initiation in specimens of low density may be purely thermal in nature. The occurrence of thermal detonation upon breakdown of dense impregnated specimens may have two causes:

1). at high densities the contact between particles improves and conditions arise for self-heating of the system;

2). the initiation of detonation upon breakdown is not thermal in nature, whereas its propagation is thermal.

In order to establish the true cause, experiments were carried out on the initiation of detonation in impregnated specimens of density $4.5\ \mathrm{g/cm^3}$ by other actions—heat and impact. In these cases, too, detonation could not be initiated. It should be noted that impregnation with glycerin is not associated with chemical interaction between glycerin and azide: washing out the glycerin with water followed by drying of the preparation completely restores the sensitivity of lead azide to a thermal impulse and to impact.

The phenomena described make it possible to suggest that if electrical breakdown occurs by the mechanism of microdischarges in pores or hollow defects, then initiation of detonation is purely thermal in nature; in the electron-avalanche mechanism of breakdown of lead azide, the mechanism of initiation of de-

...phonations may also have a nonthermal nature. The latter may be associated with the development of a chemical reaction between the products of impact ionization, as we indicated earlier [1].

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