NEWS OF THE TOMSK POLYTECHNIC INSTITUTE NAMED AFTER S. M. KIROV, ORDER OF THE RED BANNER OF LABOR

Volume 140　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　1965

EFFECT OF DEFECTS ON RADIATION-INDUCED CHANGES IN THE OPTICAL PROPERTIES OF ALKALI-HALIDE SINGLE CRYSTALS*)

I. Ya. Melik-Gaikazyan

The principal processes that occur under the action of ionizing radiation and high-energy particles on an ionic crystal are: 1. The formation of electron–hole pairs, excitons, and their localization at microdefects of the crystal—vacancies present in the crystal before its irradiation, mainly as part of associations, and also at vacancies generated by the radiation—which leads to the creation of color centers. The most abundant radiation defect is the \(F\)-center, which, according to the well-verified de Boer model, is an electron weakly bound at the site of an anion vacancy [1—3]. Thus, from the number of \(F\)-centers generated during irradiation one can judge the rate of destruction of vacancy associations and the rate of generation of new vacancies in the irradiated crystal. 2. Destruction of color centers, i.e., de-excitation of the crystal [4—7]. It must be acknowledged that the processes of de-excitation have been studied much less than the former processes. Attention was drawn in [8] to the important role of these processes in explaining the observed regularity of the relationship between the density of \(F\)-centers and the chemical composition of the crystal. However, on the basis of these works it is still impossible either to draw unambiguous conclusions about the mechanism of radiation-induced destruction of \(F\)-centers or to form an idea of its kinetics. In the present article an attempt is made to relate the influence of cation impurities to the change in the radiation stability of \(F\)-centers in alkali-halide crystals.

From thermodynamic considerations there follows a differential equation whose solution relates the number of \(F\)-centers accumulated by a certain moment of irradiation to such radiation characteristics of the materials as the rates of filling of primary vacancies and vacancies created by irradiation—\(b\) and \(c\), and the rate constants

*) Part of the data presented was obtained in the Department of Electronics and Energetics of Ionic Structures of the Problem Laboratory of EDiP, headed by Professor Doctor E. K. Zavadovskaya.

destruction of the same centers, $\alpha$ and $\beta$, respectively, and the rate of vacancy generation, $a$.

\[ n_F = n^*(1-e^{-b^*t})+a^*t+\frac{a^*}{c^*}(1-e^{-c^*t}), \tag{9} \]

where

\[ n^*=\frac{bn_0}{b+\alpha};\quad b^*=b+\alpha,\quad c^*=c+\beta;\quad a^*=\frac{ac}{c+\beta}, \]

where $n_0$ is the concentration of vacancies in the unirradiated crystal.

A substantial change in the radiation constants $\alpha$ and $\beta$ is possible when additives are introduced into the crystal, which will lead to a change in the shape of the accumulation curve of $F$ centers. Let us consider the end of the first stage of coloration, when the irradiation time is sufficiently short that the contribution of the term $a^*t$ to the number of accumulated $F$ centers is not yet significant, but the terms $e^{-b^*t}$ and $e^{-c^*t}$ are close to 0. In this case

\[ n_F=\frac{bn_0}{b+\alpha}+\frac{a^*}{c^*}. \]

Obviously, there are three principal possibilities for the influence of a divalent impurity on the magnitude of $n_F$:

1. A divalent or higher-valent impurity introduces nonequilibrium free cation vacancies into an alkali-halide crystal; their interaction with positive holes will lead to an increase in the radiation stability of $F$ centers, i.e., to a decrease in $\alpha$.

2. The impurity may interact actively with electrons, which will lead to a decrease in the parameter $b$, i.e., to a decrease in $n_F$.

3. The impurity itself may create trapping levels for holes [10], [11], which, as in the first case, will lead to a decrease in $\alpha$ and to an increase in $n_F$.

Fig. 1. Dependence of the concentration of $F$ centers on the impurity concentration in X-rayed KBr crystals.

The analysis presented shows that the effect of an impurity on radiation coloration can be rather complex, depending on its nature and concentration in the crystal. In analyzing the data of various authors, we were unable to answer the question of by what criteria and in what percentage ratio additives should be selected for alkali-halide crystals so that they produce the effect of increasing or decreasing the density of $F$ centers under isodose irradiation of the crystals.

To solve the problem posed, a study was made of the dependences of the density of $F$ centers in isodose-irradiated crystals KCl·Pb, NaCl·Pb, NaCl·Cd, NaCl·Mn, KCl·Sr*) (Figs. 1–6). The nonmonotonic character of the indicated dependences shows, as does the analysis of equation (1) given above, that

*) The study of the KCl·Sr and KBr·Pb systems was carried out by M. I. Ignat’eva [12], [13], and that of the remaining systems by L. V. Grigoryuk [14], [15].

the complex character of the influence of an impurity on the process of accumulation of \(F\)-centers in alkali-halide crystals. For each impurity, depending on the degree of its isomorphism with the host, there corresponds a certain

Fig. 2. Dependence of the density of \(F\)-centers on concentration in X-irradiated NaCl·Pb crystals.

Fig. 3. Dependence of the density of \(F\)-centers on concentration in X-irradiated NaCl·Cd crystals.

optimal concentration. The study of concentration dependences of such structure-sensitive properties as ionic conductivity and microhardness showed that, at least up to the optimal

Fig. 4. Dependence of the density of \(F\)-centers on concentration in X-irradiated NaCl·Mn crystals.

Fig. 5. Dependence of the density of \(F\)-centers on concentration in X-irradiated KCl·Pb crystals.

concentration, incorporation of the impurity into lattice sites occurs [12]. This makes it possible to relate the increase in the concentration of \(F\)-centers to the localization of holes either on impurity ions or on free cation vacancies. From the standpoint of Seitz’s models of hole centers, it is precisely the latter mechanism that is relevant. It is known that at room temperature stable \(F\)-centers are those which, according to the indicated models, include

include two cation vacancies. Consequently, cation vacancies are very scarce, and an increase in the defectiveness of the cation sublattice will favor a decrease in the number $\alpha$, which will lead to an increase in $n_F$. According to new models of hole centers, substantiated by studies of electron-paramagnetic-resonance spectra [16], the site of localization of the hole is not a pair of cation vacancies, but halide ions exchange-coupled with one another. However, stable at room temperature hole centers $V_2$ and $V_3$, as well as some impurity hole centers (Hayes–Nichols centers), include cation vacancies. Let us try, using KCl·Pb and KCl·Sr crystals as examples, to determine the relative role of vacancies, free and impurity-bound, in changing the conditions for hole localization.

Fig. 6. Dependence of the concentration of $F$-centers on the impurity concentration in X-rayed KCl·Sr crystals.

A relatively small (by a factor of 0.7) increase in the density of $F$-centers in KCl·Pb corresponds to a noticeable change in ionic conductivity. The change in the ionic conductivity of KCl·Sr is smaller than in KCl·Pb; at the same time, the maximum increase in the density of $F$-centers in this crystal reaches 500%. This comparison suggests a significant role of impurity–cation-vacancy complexes in improving the conditions for hole localization. Localization of holes on these complexes occurs through the jump into the cation vacancy of a molecular halide ion exchange-coupled with another halide ion located at a normal site. Improvement of the conditions for hole localization leads above all to an increase in the radiation stability of $F$-centers in KCl·Sr. Indeed, in [17] it was shown that the radiation stability of $F$-centers in KCl·Sr is almost twice as high as in KCl, despite the reduced thermal and photostability of $F$-centers in these crystals.

In KCl·Pb crystals, hole impurity centers do not form at room temperature. The increase in the density of $F$-centers with increasing impurity concentration in KCl·Pb may be connected with the localization of holes on free excess cation vacancies.

In KCl·Sr, at impurity concentrations greater than the optimum, only a comparatively small decrease in the density of $F$-centers is observed, in accordance with the preferential ability of the ions to interact with holes, but not with electrons. A strong decrease in the density of $F$-centers may be expected if, as additives, one chooses salts of metals possessing high acceptor properties with respect to electrons, for example lead salts. Indeed, as is evident from the figures, in NaCl·Pb, KCl·Pb, and KBr·Pb crystals a significant ($\simeq 100\%$) decrease in the density

of \(F\)-centers in comparison with its maximum value, whereas in KCl·Sr crystals this decrease amounts to only 15%.

Impurities substituting regular sites of the crystal lattice may have acceptor properties; in this case the charge of the impurity ion is reduced and a so-called “atomic” center is formed. A comparison of the concentration dependences of the density of \(F\)-centers and “atomic” centers, whose concentration also varies along a curve with a maximum, led L. V. Grigorchuk and the author [15], [18] to the conclusion that the density of \(F\)-centers may decrease as a result of localization of electrons on impurity ions situated not only in the regular lattice, but also in special, defective places in the crystal. This, in turn, raises the question of for which states of the impurity its acceptor properties are most strongly expressed. Experiments on high-temperature quenching and subsequent irradiation of crystals of all the listed systems give an unambiguous answer to this question. When a crystal with a high impurity concentration is heated, the lattice in defective regions becomes enriched with the impurity; rapid cooling “freezes” this state.

If the “lattice” acceptor properties of the impurity are higher, then a decrease in the density of \(F\)-centers will occur in crystals in which the impurity concentration exceeds the optimum. Experiments showed that in all the cases considered, a decrease in the density of \(F\)-centers occurs with a simultaneous increase in the density of atomic centers. The effect is most significant and reaches 400–500% in the case of slightly isomorphous additives, for example, in NaCl·Mn and NaCl·Pb crystals.

The results considered above relate to the first stage of accumulation of \(F\)-centers. None of the currently discussed mechanisms of vacancy generation provides for an influence of impurities on the rate of this process. At the same time, in work on measuring stored energy in alkali-halide crystals irradiated with X-rays, Tęka found an increase in stored energy in NaCl·Ca crystals compared with NaCl. It is natural to associate this fact with an increased rate of vacancy generation in crystals containing an impurity. Using the Hayes–Nichols hole-center model, the generation of anion vacancies can be considered as follows. The holes formed upon irradiation of the specimen are captured by a halide ion neighboring a cation vacancy associated with an impurity ion. The anion vacancy thereby formed moves into the bulk of the crystal as a result of electrostatic repulsion forces. Thus, in contrast to the previously accepted mechanism, the generation of additional anion vacancies in the presence of impurity ions is proposed. In accordance with these ideas, V. M. Lisitsyn showed that, when KCl·Sr and KBr·Sr crystals are irradiated with protons, the rate of accumulation of \(F\)-centers in stage II increases, i.e., the parameter \(a\), proportional to the rate of vacancy generation, increases [19].

Conclusions

1. The density of \(F\)- and atomic centers accumulated in stage I of irradiation changes, with increasing content of divalent impurity and isodose irradiation, along a curve having a maximum.

2. The increase in the density of \(F\)-centers with increasing impurity concentration occurs as a result of the formation of additional levels for localization of holes: 1) chiefly by that part of the impurity that

which is located at the nodes of the crystal lattice, and 2) partly with excess cation vacancies.

1. In the case when, upon irradiation of the crystal, hole localization occurs at centers that include an impurity ion, an increase in the radiation stability of the \(F\)-centers is observed (KCl·Sr), corresponding to a significant increase in the density of \(F\)-centers in the irradiated crystals.

2. The decrease in the density of \(F\)-centers with increasing impurity concentration is due to the acceptor properties of the impurity, which is located both at regular nodes of the crystal lattice and at defect sites.

3. An impurity located at lattice nodes possesses the greatest acceptor properties with respect to electrons.

4. Additions of alkaline-earth ions cause an increase in the rate of accumulation of \(F\)-centers also at the second stage of coloration when crystals are irradiated with protons.

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