Study of the Radiolysis of Solid Salts by Measuring the Rate of Gas Evolution When They Are Irradiated in Vacuum

V. A. Novostruev

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

To determine the amount of gaseous products of radiolysis of solid inorganic salts, the irradiated sample is dissolved in water [1], or else heated to the temperature of a modification or phase transition [2,3]. In both cases, a change in the composition and amount of the gaseous products of radiolysis is possible.

A method free from the indicated shortcomings for determining the rate of gaseous products during irradiation of solid salts is the recording of the change in gas pressure in the calibrated volume [4]. Since the main part of the gaseous products in this case remains inside the irradiated crystals, one cannot judge the rate of radiolysis directly by the amount of gas released. Moreover, because of the superposition of diffusion, the rate of gas evolution proves not to be constant in time even in those cases when the radiation-chemical yield is constant. Indeed, as is seen from the data [4–6], independently of the chemical composition of the irradiated salt, the form of the kinetic curves of gas evolution is the same; with increasing absorbed dose, the rate of gas evolution increases.

The aim of the present work was to examine the applicability of such a procedure for obtaining a quantitative characteristic of relative changes in the rate of radiolysis of solid salts.

It is not possible to find the dependence of the amount of gas evolved and of the gas concentration in the lattice on time and coordinates in a general form, since the equation is not integrable. However, the problem can be simplified by making the following assumptions.

1). Gases are released from thin near-surface (diffusion) layers \(\Delta x\), whereas in the depth of the crystal the gases are continuously accumulated. In this case, a concentration gradient \(\partial C/\partial x\) is created in the diffusion layer, while in the depth of the crystal

\[ \frac{\partial C}{\partial x}=0 . \]

Such an assumption is apparently not too crude. This is indicated by the fact that, during the radiolysis of many salts, the accumulation of gases inside the crystal is linear with dose [1] up to large percentages of decomposition, when cracking of the irradiated crystals is observed [2].

2). Let us assume that the concentration gradient, which is some function of the irradiation time, does not depend on the coordinate within \(\Delta x\), i.e., the equality is valid

\[ \frac{\partial C}{\partial x}=\frac{\Delta C}{\Delta x}=\frac{C-C_n}{\Delta x}, \]

where \(C\) is the current concentration of gases inside, and \(C_n\) is that at the surface of the crystal, mol/cm\(^3\); \(\Delta x\) is a certain layer of the crystal from which diffusion of gases into the surrounding space occurs, cm.

3). Since irradiation is carried out in vacuum, we assume that \(C \gg C_n\), and therefore \(C \approx \Delta C\). Then, using Fick’s first equation, we obtain

\[ \frac{dm}{dt}=DS\frac{\partial C}{\partial x}=DS\frac{C}{\Delta x}=\beta SC, \tag{1} \]

where \(\frac{dm}{dt}\) is the specific rate of gas evolution, mol/g·sec;
\(S\) is the specific surface area of the irradiated crystals, cm\(^2\)/g;
\(\beta\), as defined by Frank-Kamenetskii [3], is the diffusion-rate constant, cm/sec.

The dependence of \(C\) on the irradiation time \(t\) for the initial stage of radiolysis (as long as the concentration of the initial substance may be considered constant) can be written in the form

\[ C=kGJt, \tag{2} \]

where \(G\) is the radiation-chemical yield of gases, molecules/100 eV;
\(J\) is the dose rate absorbed by the irradiated salt, eV/cm\(^3\)·sec;
\(t\) is the irradiation time, sec;
\(k=\frac{1}{100N_A}\) is the dimensional coefficient, \(N_A\) is Avogadro’s number.

From equations (1) and (2), taking into account the initial condition (at \(t=0\), \(m=0\)), we obtain:

\[ m=\frac{1}{2}kGJ\beta St^2. \tag{3} \]

Dependence of the specific gas evolution under irradiation with X-rays for ammonium perchlorate (1), potassium nitrate (2) with crystal size 250 microns, ammonium nitrate (3), and sodium nitrate with crystal sizes: 90 microns (4), 170 microns (5), 250 microns (6).

Processing of the experimental results on gas evolution under irradiation of nitrates \([5,6]\) and ammonium perchlorate shown in the figure indicates that in all cases the gas evolution is proportional to \(t^2\). Thus, the slope of the straight lines in the coordinates of equation (3) is determined by two unknown parameters, \(G\) and \(\beta\) (\(S\) and \(T\) are known or can be determined experimentally). Therefore, the method under consideration cannot be used to determine the absolute values of the gas \(G\) values if the corresponding diffusion coefficients are not known. On the other hand, using known values of the gas \(G\) values, one can determine the coefficient of gas diffusion in the solid salt. Thus, an estimate from equation (3) of the value of \(\beta\) in \(KNO_3\), using \(G(O_2) = 1.0\) \([1,3]\), gives \(\beta_a \le 10^{-6}\) cm/sec. If \(\Delta x\) is taken to be the same as in the case of lead \([6]\), i.e. \(\Delta x \le 5 \cdot 10^{-4}\) cm, then the diffusion coeffi-

the diffusion of oxygen \(D\) is obtained as \(< 10^{-9}\ \text{cm}^2/\text{s}\), which is consistent with the few numerical literature data on the magnitude of \(D\) for gases in a solid [9].

In those cases where only the relative change in the rate of radiolysis of salts under various conditions is of interest (for example, when studying the effect of additives), equation (3) may be used for quantitative estimates, provided that \(A\) and \(S\) remain constant. Then the ratio of the tangents of the angle of inclination will be determined only by the ratio of the radiolysis rates.

The author considers it a pleasant duty to express gratitude to D. A. Zakharov and S. M. Rabikh for their attention to the work and for discussions.

REFERENCES

1. D. A. Zakharov, V. A. Novostruev, Uspekhi khimii, 37, 143, 1968.
2. A. S. Baberkin, M. I. Proskurnin, V. O. Orlov. In: “Action of Ionizing Radiations on Inorganic and Organic Systems,” Publishing House of the Academy of Sciences of the USSR, Moscow, 1958, p. 195.
3. J. Cunningham, J. Phys. Chem., 67, 1772, 1963.
4. N. M. Bakhmet’eva, Abstract of dissertation, Research Institute of Nuclear Physics, Academy of Sciences of the Uzbek SSR, 1963.
5. V. A. Novostruev, D. A. Zakharov, Kinetika i kataliz, 8, 210, 1967.
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8. A. A. Frank-Kamenetskii, Diffusion and Heat Transfer in Chemical Kinetics, Moscow–Leningrad, Publishing House of the Academy of Sciences of the USSR, 1947, p. 24.
9. R. Barrer, Diffusion in Solids, IL Publishing House, 1948.