On the Question of the Influence of Plastic Deformation on the Radiation Generation of Vacancies in Alkali-Halide Crystals

I. Ya. Medik-Gaikazyan, S. U. Gold'enberg

A number of works have shown that the formation of the most abundant radiation defects—$F$-centers—in alkali-halide crystals occurs as a result of the localization of electrons both on isolated anion vacancies that existed in the crystal before irradiation and on vacancies generated by irradiation (radiation vacancies). At considerable absorbed doses, the number of electrons localized on radiation vacancies may exceed the number of $F$-centers formed on primary vacancies by two to three orders of magnitude [1—3]. Thus, the contribution of vacancies generated by irradiation to the overall defectiveness of the crystal may be very substantial.

The question of the mechanism of the radiation formation of vacancies is one of the central questions of modern radiation physics. It has been shown that the formation of vacancies through direct displacements of ions from the sites of the crystal lattice under the action of high-energy particles and photons is unlikely [4]. In this connection, a number of mechanisms for the indirect formation of vacancies have been proposed, which may be divided into two classes:

1. Formation of anion vacancies due to multiple ionization of a halogen ion located in the regular lattice. This idea was first proposed by Varley [5] and developed in works [6, 7].

2. Mechanisms requiring the presence of dislocations in the crystal, first proposed by Seitz [8, 9] and Markham [10].

According to the generally accepted view, one way of clarifying the role of dislocations in the process of radiation formation of vacancies is to compare the rate of accumulation of $F$-centers in the second stage (the stage of slow coloration), associated with the capture of electrons by generated vacancies, in crystals with differing densities of geometric microdefects created by plastic deformation. In this case, different authors obtain directly opposite experimental results concerning the relationship between dislocation density and the rate of slow coloration.

Thus, according to Brony [11] and Novik [12], an increase in dislocation density increases the rate of vacancy generation; according to Mitchell et al. [13] it decreases it; and according to Abramson and Kaspari [14] it does not change it at all.

In the work of Davidge and Pratt [15] it is concluded that, under irradiation with soft x rays, deformation does not change the rate of radiation generation of vacancies, whereas under irradiation with hard x radiation a very noticeable increase in this parameter is observed.

In the present article an attempt is made, on the basis of an analysis of the kinetics of accumulation of \(F\)-centers, to show that, in view of the insufficient purity of the crystals used in all the works listed above, the results of experiments on the influence of deformation on the coloration of alkali-halide crystals cannot serve as an unambiguous criterion of the role of dislocations in the process of vacancy generation. At the same time an attempt is made to show that the contradictions mentioned above are in some cases only apparent and are connected merely with the difference in the intensities of the radiation fluxes used.

In fact, it is customary to judge the rate of vacancy generation from the slope of the linear part of the accumulation curve of \(F\)-centers—\(a^*\). As was shown by Mitchell and coauthors [3], the quantity \(a^*\) is determined by the following expression:

\[ a^*=\frac{a\cdot c}{c+\beta}, \tag{1} \]

where \(a^*\) is the rate of accumulation of \(F\)-centers at the slow stage of coloration, \(a\) is the rate of vacancy generation, \(c\) is the rate of conversion of the generated vacancies into \(F\)-centers, and \(\beta\) is the rate of radiation bleaching of \(F\)-centers. From expression (1) it is seen that a change in the slope of the accumulation curve at the second stage \(|a^*|\) does not uniquely determine a change in the rate of vacancy generation, since deformation, as will be shown below, can cause a change in the parameters \(c\) and \(\beta\).

Indeed, deformation, simultaneously with a change in the dislocation density, also changes the state of the impurity in the crystal. In [16] it was convincingly shown that deformation of “pure” crystals leads to the introduction into the crystal lattice of impurity that had precipitated on dislocations during the growth and storage of the crystal. In the case when an impurity possessing high acceptor properties with respect to electrons is incorporated into the lattice, the rate of electron capture by anion vacancies [16] decreases, i.e., the parameter \(c\) decreases. When the concentration in the lattice of impurities that improve the conditions for hole localization is increased, the rate of radiation destruction of \(F\)-centers decreases, i.e., the parameter \(\beta\) [17].

Thus, deformation of alkali-halide crystals, which as a rule contain about \(10^{17}\) impurity defects in \(1\ \mathrm{cm}^3\) [14], can significantly change the value of \(a^*\) even in the case when dislocations take no part whatever in the radiation generation of vacancies. It is important to note that the influence of one or another effect associated with the entry of impurity into solution during deformation depends substantially on the irradiation conditions, namely on the absorbed dose rate. (Unfortunately, this very important characteristic of the interaction of radiation with matter is, as a rule, not indicated in most domestic and foreign works.)

Let us confirm the foregoing by the following analysis. In the work of Abramson and Kaspari [14] it was shown that the parameter \(c\) can be expressed as follows: \(c=\kappa I\), where \(\kappa\) is a certain constant depending on the nature of the crystal, its purity, and the irradiation temperature, and \(I\) is the absorbed dose rate.

If one assumes that \(a = gl\) [14] and that \(g\) does not depend on the dislocation density, as was obtained in the same work from experiments on radiation expansion of crystals, then \(a^{*}\) can be written as

\[ a^{*}=\frac{\kappa g l^{2}}{\kappa l+\beta}\quad \text{or}\quad a^{*}=\frac{g l^{2}}{l+\beta/\kappa}. \]

For \(l \gg \beta/\kappa\), i.e., at high absorbed-dose rates, a change in the parameters \(\beta\) or \(c\) \((c=\kappa l)\) due to the introduction of impurities into the solution cannot substantially change the rate of accumulation of \(F\)-centers. This case is apparently realized in the experiments of Abramson and Kaspari, who used irradiation intensities large in comparison with those of other experimenters, and also in that part of the experiments of Davidge and Pratt [15] in which soft X-rays were used.

For \(l\) comparable with \(\beta/\kappa\), a change in these parameters must also cause a noticeable change in \(a^{*}\), the sign of the effect being determined by the properties of the impurity. An increase in \(\beta\) will lead to a decrease in \(a^{*}\) in deformed crystals (the result of Mitchell and his coauthors), while a decrease will lead to an increase of this quantity (the result of Nowick [12], Gordon and Nowick [18], and Brown [11]). It should be noted that in the work of the latter authors the correctness of the conclusion about a change in the value of \(a^{*}\) as a result of deformation is doubtful, since they studied the slope of the accumulation curve corresponding to doses insufficient for the manifestation of a strictly linear accumulation of \(F\)-centers in the second stage. This may also be the cause of many misunderstandings in estimating the influence of deformation on the kinetics of accumulation of \(F\)-centers.

For example, from a comparison of the curves presented in the works of Brown [11] and Mitchell [14], taking into account the irradiation conditions, it is evident that in the work of the former the intensities and doses used did not permit observation of the linear portion of the second stage in pure form, whereas in the second work an increase in the density of \(F\)-centers was undoubtedly observed owing to localization of electrons at radiation vacancies, and the parameter \(a^{*}\) was determined not only from the slope of the linear portion of the accumulation curve but also by the least-squares method. Mitchell’s results testify to an increase (and not a decrease) in the coloration rate in deformed crystals on the portion of the accumulation curve corresponding to that studied by Brown (Figs. 1 and 2).

Fig. 1. Data of N. E. Brown [11] on the influence of plastic deformation on the growth of the absorption coefficient at the maximum of the \(F\)-band in KCl irradiated with soft X-rays.

From the analysis presented it follows that it is necessary:

1. To approach very cautiously the evaluation of the parameter \(a^{*}\) from the slope of the accumulation curve. This quantity can be found most correctly by the least-squares method.

2. To take into account that at comparatively low absorbed-dose rates the influence of redistribution of impurities in the crystal as a result-

the deformation stage can make a substantial contribution to the change in the value of the rate of accumulation of \(F\)-centers in the slow stage.

1. One should strictly distinguish the change in the rate of accumulation of \(F\)-centers in the second stage \((\alpha^*)\) and the rate of vacancy generation \((\alpha)\), which is not determined directly from radiation-coloration experiments.

Fig. 2. Data of P. V. Mitchell et al. [13] on the effect of plastic deformation on the growth of the absorption coefficient at the maximum of the \(F\)-band in KCl irradiated with X-rays. The dashed line \(AB\) marks the portion of the graph on which deformation leads to an increase in the rate of generation of \(F\)-centers.

On the basis of the analysis presented, it may be concluded that the current state of the question of the influence of deformation on the kinetics of accumulation of \(F\)-centers does not allow one to decide unambiguously in favor of one of the above-mentioned mechanisms of vacancy generation.

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