EFFECT OF DIVALENT CATION- AND ANION-SUBSTITUTING IMPURITIES ON THE PROCESS OF FORMATION OF \(F\)-CENTERS IN AHC

I. Ya. MELIK-GAIKAZYAN, L. I. ROSHCHINA

The effect of impurities \(Pb^{++}\), \(Sr^{++}\), and \(S^{--}\) on the shape of the kinetic curve of accumulation of \(F\)-centers in KCl single crystals irradiated with x-rays has been investigated. By the method of least squares, from the experimental kinetic curves and Mitchell’s equation, the parameters of the most effective source of \(F\)-centers in pure and doped crystals were determined: the concentration of potential anion vacancies, the probability per unit time of localization of an electron on an anion vacancy, and the probability per unit time of radiation destruction of an \(F\)-center.

On the basis of a comparison of the concentration of potential vacancies in doped crystals with the concentration of single cation vacancies, the conclusion is drawn that single cation vacancies do not make a substantial contribution to the formation of \(F\)-centers at the initial stage of coloration.

The growth of \(F\)-centers by x-irradiation and electrical conductivity were measured at room temperature in KCl, both pure and doped with \(Pb^{++}\), \(Sr^{++}\), and \(S^{--}\). The parameters of the centres source were estimated. From these results it was concluded that the isolated positive ion vacancies are not the source of the \(F\)-centres at the early of coloration.

As studies have shown [19], the initial stage of rapid accumulation of \(F\)-centers, characterized by a high rate and a small energy expended on the accumulation of one \(F\)-center (tens of eV/\(F\)-center), is due to \(F\)-centers formed at vacancies that existed in the crystal before irradiation.

On the one hand, vacancies of negative ions in the crystal before irradiation exist in the form of associations or in combination with other defects; on the other hand [1—3], at the initial stage of coloration there is also possible generation of anion vacancies by hole centers \(X_2^{-}\), oriented along [100], owing to displacement of ionized halide ions into isolated cation vacancies or vacancies of complexes \(Me^{++}V^{+}\). As shown in [4—11], the introduction of cation-substituting impurities into a crystal can substantially increase, and at high concentrations even decrease, the limiting concentration of \(F\)-centers accumulated in the first stage, i.e., at defects that existed in the crystal before irradiation.

A divalent cation-substituting impurity (for example, Pb, Sr) may be present in the crystal lattice, first, in a state bound with its cation vacancy; upon irradiation, both holes and electrons may be localized on such complexes; second, in a dissociated state with its cation vacancy, in which case the increase—

the number of isolated cation vacancies increases. Under irradiation, a hole can become localized at an isolated cation vacancy [12, 13].

It is known that lead and strontium ions have different acceptor properties with respect to electrons and holes. Thus, for example, upon irradiation of KCl·Pb crystals, a band appears in the absorption spectrum corresponding to light absorption by atomic lead centers [14]. From works [2, 3, 4] it is known that alkaline-earth metal ions form hole trapping centers. These properties of the impurities are manifested most clearly in the change in electrical conductivity under the action of radiation [12, 13].

The addition to the crystal of a divalent anion-substituting sulfur impurity increases the concentration of anion vacancies and, according to the law of mass action, decreases the concentration of isolated cation vacancies. This is accompanied by a two-orders-of-magnitude decrease in ionic conductivity and a deterioration in the colorability of KCl·S$^{--}$ crystals in comparison with pure KCl [15].

Thus, the introduction into the crystal of divalent cation-substituting Pb and Sr impurities increases the defectiveness of the cation sublattice, while the introduction of an anion-substituting sulfur impurity decreases it.

On possible sources of radiation vacancies in doped alkali-halide crystals

To clarify the question of the predominant influence on the limiting concentration of $F$ centers accumulated at the first stage—whether by the increase in the defectiveness of the cation sublattice or by the radiation stability of $F$ centers—we quantitatively determined the probabilities of the elementary processes of formation and destruction of $F$ centers, as well as the concentration of pre-irradiation defects ($N_1$) capable of being converted into $F$ centers at the first stage. The calculations of the parameters $N_1$, $b_1$, $\beta$ were performed for “pure” KCl crystals and for crystals with Pb, Sr, and S impurities.

In Fig. 1 are presented the kinetic curves of accumulation of $F$ centers at different intensities for a pure KCl crystal (for the other crystals the ratio of the kinetic curves at different intensities is analogous and is therefore not given here); in Fig. 2—for one intensity and different crystals. By the method of least squares, the parameters of equation (1), $n_i$ and $B_1$, were calculated [19].

Fig. 1. Kinetic curves of accumulation of $F$ centers in a KCl crystal at different X-ray intensities.
$I_1:I_2:I_3:I_4:I_5 = 1:1.5:2:2.5:3$.

\[ n_i=\frac{N_1 b_1}{b_1+\beta_1}\left[1-e^{-(b_1+\beta_1)t}\right] = n_1\left(1-e^{-B_1 t}\right). \tag{1} \]

At a sufficiently long time and low irradiation intensity, the concentration of $F$ centers reaches a limiting value:

\[ n_1=\frac{N_1}{1+\beta_1/b_1} \quad \text{or} \quad \frac{1}{n_1}=\frac{1}{N_1}+\frac{1}{N_1 b_1/\beta_1}. \tag{2} \]

Since the initial defectiveness of the crystals \(N_1\) in equation (2) does not depend on the intensity, the initial defectiveness of the crystals can be determined from the segment cut off by the straight line \(\frac{1}{n_1}=f\left(\frac{I_1}{I_i}\right)\) on the coordinate axis. Figure 3 presents the dependences of \(\frac{1}{n_1}\) for some crystals on the reciprocal intensity. These straight lines were calculated by the least-squares method, and \(N_1\) was determined.

The results of the calculations are summarized in Table 1, from which it is evident that all the investigated impurities promote an increase in the density of the source of anion vacancies.

The increase in the density of the source may occur:

1) through an increase, in all impurity crystals, in the concentration of neutral pairs \(V^+V^-\) [16, 20], whose magnitude is commensurate with \(N_1\) [21]. The hole mechanism of pair decomposition [17] causes the appearance of two anion vacancies. Therefore, the neutral complex constitutes an effective source for the formation of anion vacancies;

2) through an increase in the defectiveness of the anion sublattice and, consequently, in the concentration of trapping centers in the crystal KCl·S\(^{--}\);

Fig. 2. Accumulation curves of \(F\)-centers at intensity \(I_1\) in crystals.
1 — KCl; 2 — KCl + \(1.5\cdot10^{-3}\) mol% Pb;
3 — KCl + \(3\cdot10^{-3}\) mol% Sr; 4 — KCl + 0.1 mol% S

3) through an increase in the concentration of complexes \(\mathrm{Sr}^{++}V^+\) in KCl·Sr crystals, capable of interacting with holes [2]. As a result

Table 1

Comparison of the concentrations of various defects in doped KCl crystals

as a result of rearrangement, \(V_2\)-centers are formed, comprising cation vacancies and anion vacancies on which electrons are localized. The concentration of complexes [22] coincides in magnitude with \(N_1\).

4) Due to an increase in the concentration of \(\mathrm{Pb}^{++}V^+\) complexes in \(\mathrm{KCl}\cdot\mathrm{Pb}\) crystals [23]. The radiation decomposition of the complexes occurs through interaction with electrons [18]; in this process the cation vacancy of the complex migrates and can interact with an ionized halogen. The action of this source ends with the transfer of the ionized halide into the cation vacancy and diffusion of the anion vacancy;

5) isolated cation vacancies cannot be the cause of the increase in \(N_1\) in doped crystals, since, according to the electrical-conductivity data obtained by us [15, 24], their concentration \((10^{14}\div10^{15}\ \mathrm{cm}^{-3})\) is two orders of magnitude smaller than \(N_1\).

It should be noted that the possibility is not excluded of the simultaneous realization of several sources of radiation \(F\)-centers, which may differ in the rate and efficiency of formation of anion vacancies.

Influence of changes in the localization conditions of holes and electrons on the probabilities of elementary processes of formation and destruction of \(F\)-centers

The probability per unit time of transformation of an anion vacancy into an \(F\)-center \((b_1)\) depends on the concentration of electrons capable of being localized at an anion vacancy, which, in turn, is determined by the number of electron-localization sites and by the probability of their recombination with holes. An increase in the number of electron capture levels and a decrease in the number of hole capture levels should lead to a decrease in the parameter \(b_1\).

Radiation stability of \(F\)-centers also depends on the concentration of free holes in the filled band, since one of the possible mechanisms of destruction of \(F\)-centers is the hole mechanism. From this point of view it is of interest to follow the change in the parameters \(b_1\) and \(\beta_1\) in crystals with different localization conditions for holes and electrons.

In a \(\mathrm{KCl}\cdot\mathrm{Pb}\) crystal, the conditions for electron localization are improved owing to the acceptor properties of lead; in \(\mathrm{KCl}\cdot\mathrm{Sr}\), the conditions for hole localization are improved through their interaction with \(\mathrm{Sr}^{++}V^+\) complexes. In a \(\mathrm{KCl}\cdot\mathrm{S}\) crystal, the concentration of cation vacancies is reduced.

Fig. 3. Dependence of \(1/n_1\) on \(I_1/I\). The designations are the same as in Fig. 2.

It follows from Table 2 that improvement of the hole-localization conditions in the \(\mathrm{KCl}\cdot\mathrm{Sr}\) crystal leads to a decrease in the probability of radiation destruction of \(F\)-centers \((\beta_1)\) in comparison with “pure” KCl, whereas worsening of the hole-localization conditions in \(\mathrm{KCl}\cdot\mathrm{S}\) leads to a sharp increase in the parameter \(\beta_1\).

Table 2

Concentrations of potential vacancies \((N_1,\ \mathrm{cm}^{-3})\) and probabilities of radiation-induced formation \((b_i,\ \mathrm{hcl}^{-1})\) and destruction \((\beta_i,\ \mathrm{hcl}^{-1})\) of \(F\)-centers in “pure” and doped KCl crystals irradiated with pulsed light at room temperature. The ratio of the intensities of the doubled beams satisfies the condition \(I_1:I_2:I_3:I_4:I_5 = 1:1.5:2:2.5:3\).

For all KCl crystals with impurities, a decrease in the parameter \(b_1\) is observed in comparison with “pure” KCl. The decrease in the probability of electron capture by anion vacancies in KCl·Pb crystals with increasing impurity concentration occurs because of localization of electrons on activator levels, which is accompanied by an increase in the intensity of the absorption band of atomic lead centers. In KCl·Sr crystals, the decrease in \(b_1\) may be associated with electron capture by microdefects that include Sr.

An especially strong decrease in the probability of electron localization at an anion vacancy per unit time is observed for KCl·S crystals. The decrease in \(b_1\) and the increase in the probability of radiation destruction of \(F\)-centers, \(\beta_1\), cause such a sharp increase in the ratio \(\beta_1/b_1\) (equation 1) that, despite the increased density of the first source of radiation vacancies \((N_1)\), the limiting concentration of \(F\)-centers accumulated in the first stage is considerably reduced in the KCl·S crystal in comparison with “pure” KCl (Fig. 2).

REFERENCES

1. I. H. Crawford, C. M. Nelson. Phys. Rev. Lett., 5, 314 (1960).
2. W. Hayes, G. M. Nelson. Phys. Rev., 117, 993 (1960).
3. W. Hayes. J. Appl. Phys. Suppl., 33, 329 (1962).
4. D. Schulman. J. Phys. Chem., 57, 8 (1953).
5. E. E. Schneider. Disc. Far. Soc., 31, 176 (1961).
6. L. M. Shamovskii. Dokl. Akad. Nauk SSSR, 99, 235 (1954).
7. M. L. Kats, B. Z. Semenov. Physics of alkali-halide crystals. Proceedings of the Second All-Union Conference, 1961, 191, Riga, 1962.
8. I. A. Parfianovich. Optics and Spectroscopy, 4, 253 (1958).
9. Ch. B. Lushchik. Tr. IFA AN ESSR, No. 3, 3 (1955).
10. L. V. Grigoryuk, I. Ya. Melik-Gaikazyan. Optics and Spectroscopy, 15, 394 (1963).
11. I. Ya. Melik-Gaikazyan, M. I. Ignat’eva et al. Proceedings of the First Conference on Radiation Physics, Kiev, 1965.
12. I. Ya. Melik-Gaikazyan, E. K. Zavadovskaya, M. I. Ignat’eva. Soviet Physics—Solid State, 6, 1243 (1964).
13. M. I. Ignat’eva. Author’s abstract, Tomsk, 1965.
14. L. V. Grigoryuk. Author’s abstract, Tomsk, 1964.
15. I. Ya. Melik-Gaikazyan, L. I. Roshchina, M. I. Ignat’eva. Soviet Physics—Solid State, 7, 3465 (1965).
16. I. E. Caffin, B. K. Ridley. Proc. Phys. Soc., 77, 153 (1961).
17. R. O. Vilu, M. A. Elango. Soviet Physics—Solid State, 7, 3673 (1965).
18. I. Ya. Melik-Gaikazyan, M. I. Ignat’eva. Crystallography, 11, issue 3 (1966).
19. R. Mitchell, D. Wiegend, R. Smoluchowski. Phys. Rev., 121, 484 (1961).
20. G. A. Andreev. Soviet Physics—Solid State, 8, No. 2, 327 (1966).
21. V. M. Matsonashvili, G. I. Skanavi. “Physics of Dielectrics.” Proceedings of the Second All-Union Conference, November 1958, p. 7. Publishing House of the Academy of Sciences of the USSR, Moscow, 1960.
22. K. G. Kladov. Diploma thesis, TPI, 1964.
23. S. S. Serg. Diploma thesis. Institute of Steel and Alloys, Department of Crystallography, 1966.
24. M. I. Ignat’eva, L. I. Roshchina. Izv. TPI, 140, 109 (1965).