$\gamma$-Conductivity in Lead Azide and Some Solid Solutions Based on It

D. A. Zakharov, S. M. Ryabykh, N. M. Kharchenko

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

The dark electrical conductivity and photoconductivity of heavy-metal azides have been studied in a number of works [1, 2, 3]. Measurements of these characteristics in pure azides and in solid solutions based on them have been used to discuss questions concerning the nature of lattice defects in azide-type solid solutions in the systems $\mathrm{AgN_3—PbN_6—CuN_6}$ and the reasons for the observed influence of impurities on the rate of decomposition of azides under the action of heat and light.

In the context of general work on the thermal, photo-, and radiation stability of solid solutions, it was shown in [3, 4, 5] that the introduction of impurity ions $\mathrm{Ag^+}$ and $\mathrm{Cu^{++}}$ into the $\mathrm{PbN_6}$ lattice leads to noticeable changes in the rate of radiolysis of lead azide in fields of X-ray, $\gamma$-, and proton irradiation. The observed effects were tentatively associated with the donor–acceptor properties of the introduced impurities. A direct measurement of $\gamma$-currents caused by “slow electrons” in azide compositions is necessary here as a correct confirmation of the validity of this assumption.

Materials and Apparatus

The work used $\mathrm{PbN_6}$ prepared by a precipitation reaction from 0.2 N solutions of chemically pure $\mathrm{Pb(NO_3)_2}$ and twice-recrystallized $\mathrm{NaN_3}$.

When introducing $\mathrm{Ag^+}$ and $\mathrm{Cu^{++}}$ impurities, the corresponding amount of silver or copper nitrate was added to the initial $\mathrm{Pb(NO_3)_2}$ solution. Polarographic analysis showed that, with this method of preparing a solid solution, $\mathrm{Ag^+}$ enters the $\mathrm{PbN_6}$ crystal lattice in amounts close to the calculated values, whereas the amount of incorporated $\mathrm{Cu^{++}}$ is an order of magnitude smaller. According to the polarographic analysis, the concentration of impurities introduced into $\mathrm{PbN_6}$ was: for $\mathrm{Ag^+}$—0.5%; 1%; 2.2%; 4.7%, and for $\mathrm{Cu^{++}}$—0.5%; 0.1%; 0.7%.

In studying $\gamma$-conductivity we used tablets pressed under a pressure of 4 t/cm². The weight of the tablets was 300 mg, the diameter 10 mm, and the tablet thickness was $0.92 \pm 0.02$ mm.

The measurements were carried out in a vacuum of $10^{-4}$ mm Hg, using the circuit described in [6]. The radiation source was an X-ray tube ZBDM-200; the radiation dose rate was determined with a Fricke dosimeter.

Results

As shown in Fig. 1, the dark conductivity of PbN₆, both pure and with additives, increases with increasing temperature. The addition of Ag⁺

Fig. 1. Dependence of the dark and γ-conductivity on temperature.
1 — pure PbN₆; 2 — PbN₆ + 1% Ag⁺; 3 — PbN₆ + 2.2% Ag⁺; 4 — PbN₆ + 0.05% Cu²⁺; 5 — PbN₆ + 0.5% Cu²⁺. Curves with the index “a” are the dark conductivities of the corresponding compositions.

increases the dark conductivity. With increasing concentration of the additive, the dark conductivity within the investigated limits rises, but not strictly in proportion to the concentration. The addition of Cu²⁺ somewhat decreases the dark conductivity.

During irradiation the conductivity increases (Fig. 1). The addition of Ag⁺ increases the γ-conductivity; however, the degree of increase in γ-conductivity is not proportional to the concentration of the additive. The addition of Cu²⁺ decreases the γ-conductivity, likewise not entirely in proportion to the concentration. The isotherms of γ-conductivity are presented in Fig. 2. The activation energy of γ-conductivity was in all cases about 0.01 eV/mol (Fig. 4).

The γ-conductivity in all preparations is proportional to the dose rate, as shown in Fig. 3.

Discussion of the Results

According to the data of work [7], the dark conductivity in PbN₆ is predominantly ionic. In view of the considerable sizes of the ions in PbN₆, Frenkel disordering of lead azide crystals is unlikely; therefore, the dark conductivity is hardly due to interstitial ions. It is more probable that anion vacancies are responsible for the conductivity in PbN₆.

In view of the fact that the ionic radius of Ag⁺ (1.26 Å) is rather large and close to the magnitude of the ionic radius of Pb²⁺ (1.32 Å), it may be assumed that AgN₃, when coprecipitated with PbN₆, forms a substitutional solid solution. Replacement of a divalent cation by a monovalent one should lead to an increase in the number of anion vacancies and, ultimately, to an increase in the dark conductivity of PbN₆. Additional arguments in favor of this assumption are contained in [10].

The decrease in dark conductivity caused by the addition of Cu²⁺ is difficult to explain—

Fig. 2. Dependence of the γ-conductivity of lead azide on the concentration of additives.
The dashed line shows the curve of the dependence of the nitrogen gas-evolution rate on the concentration of additives.

Fig. 3. Dependence of the γ-conductivity of lead azide on dose rate.

Fig. 4. Dependence of \(\lg \delta\) on \(1/T\).
1 — \(\mathrm{PbN_6}+5\%\ \mathrm{Cu}^{+2}\); 2 — \(\mathrm{PbN_6}+1.5\%\ \mathrm{Cu}^{+2}\); 3 — \(\mathrm{PbN_6}+0.5\%\ \mathrm{Cu}^{+2}\); 4 — pure \(\mathrm{Pb_6N}\); 5 — \(\mathrm{Pb_6N}+10\%\ \mathrm{Ag}^{+}\); 6 — \(\mathrm{Pb_6N}+0.5\%\ \mathrm{Ag}^{+}\); 7 — \(\mathrm{Pb_6N}+5\%\ \mathrm{Ag}^{+}\); 8 — \(\mathrm{Pb_6N}+1.5\%\ \mathrm{Ag}^{+}\).

This can be explained if it is assumed that \(\mathrm{Cu}^{+2}\) in \(\mathrm{PbN_6}\) forms a substitutional solid solution. It is more probable that \(\mathrm{Cu}^{+2}\) enters the interstices, which is also favored by the small ionic radius of the \(\mathrm{Cu}^{+2}\) ion \((0.96\,\text{Å})\). When the \(\mathrm{Cu}^{+2}\) ion is introduced into an interstice, the number of anion vacancies in the crystal lattice will decrease, since the lattice must remain electrically neutral. The decrease in the number of anion vacancies, which are current carriers, evidently leads to the decrease in dark conductivity observed by us.

The carriers responsible for \(\gamma\)-conductivity in azide compositions are electrons or holes formed when electrons pass from the valence band to the conduction band under the action of a radiation quantum.

\[ N_3^- \;-\!\!\sim\!\!\sim\!\!\sim\!\!\sim\!\!\to N_3^0 + l \tag{1} \]

Apparently, in our case the electron passes directly into the conduction band, bypassing exciton levels. This assumption is confirmed both by the linear dependence of \(\gamma\)-conductivity on dose rate and by the small activation energy of \(\gamma\)-conductivity \((\simeq 0.01\,\text{eV/mol})\), approximately equal to the activation energy for the mobility of current carriers in classical semiconductors.

Electrons that have passed into the conduction band may subsequently either recombine,

\[ N_3^0 + e \to N_3^-, \tag{2} \]

or are captured by traps. Anion vacancies may act as traps; when they capture electrons, F-centers are formed,

\[ e+\square^{-}\to \square-e . \tag{3} \]

No studies have been carried out that would make it possible to determine unambiguously the sign of the current carriers in the \(\gamma\)-conductivity of \(\mathrm{PbN_6}\). However, in [8] it was shown that the photoconductivity of \(\mathrm{PbN_6}\) is hole-type. It is logical to assume that, on going to harder radiation, the character of the conductivity does not change, especially since the external picture of the phenomena in photo- and \(\gamma\)-conductivity is qualitatively similar. A similar point of view was also expressed in [9] in a study of photo- and \(\gamma\)-currents in semiconductors.

Assuming that the \(\gamma\)-conductivity of \(\mathrm{PbN_6}\) is hole-type and that anion vacancies serve as electron traps, it is easy to give a model explanation of the effect of \(\mathrm{Ag}^{+}\) and \(\mathrm{Cu}^{++}\) additions on the magnitude of the \(\gamma\)-conductivity. The addition of \(\mathrm{Ag}^{+}\), as was stated above, increases the concentration of anion vacancies in \(\mathrm{PbN_6}\) and, consequently, increases the probability of electron capture at traps according to reaction [3]. This leads to a decrease in the probability of recombination of electrons and holes and to an increase in the concentration of holes—carriers of the \(\gamma\)-current.

Within the framework of the concepts set forth, the decrease observed by us in the \(\gamma\)-conductivity of \(\mathrm{PbN_6}\) upon introducing impurity \(\mathrm{Cu}^{++}\) ions into the azide can also be explained in model terms.

The decrease in the \(\gamma\)-current upon addition of \(\mathrm{Ag}^{+}\) in amounts greater than 1% is apparently associated with the precipitation of \(\mathrm{AgN_3}\) into a separate phase.

Comparison of the isotherms of nitrogen gas evolution during radiolysis and of \(\gamma\)-conductivity (Fig. 2) shows that they are qualitatively similar. This makes it possible to assert that the elementary radiolysis reactions involving current carriers are determinative in the radiolysis of \(\mathrm{PbN_6}\). Since the arguments given above make it possible to assert that the carriers of the \(\gamma\)-current are holes, it is logical to suppose that the radical recombination reaction

\[ 2\mathrm{N}_3^{0}\to 3\mathrm{N}_2 \uparrow \tag{4} \]

is the rate-limiting one in the process of radiation decomposition of \(\mathrm{PbN_6}\).

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Noted Misprints