DEPENDENCE OF THE ACCUMULATION RATE OF F-CENTERS IN KCl SINGLE CRYSTALS IRRADIATED WITH PROTONS ON THE IRRADIATION TEMPERATURE

A. N. Kravets, I. Ya. Melik-Gaikazyan

(Presented by the scientific seminar of the Research Institute of Nuclear Physics)

One of the urgent but least solved problems of radiation physics is the establishment of the micromechanisms of defect creation in solids under the action of radiation. To solve this problem it is expedient to use alkali-halide crystals, in which models of the principal radiation defects have been reliably established [1—5]. Some of the proposed mechanisms make it possible to assume that the process of radiation generation of F-centers in ionic crystals, both at pre-radiation vacancies [6] and at vacancies generated by radiation [7], proceeds most effectively at temperatures corresponding to deautolocalization of holes. To test this assumption, we investigated the accumulation of F-centers in KCl crystals under the action of protons at fixed temperatures (with an accuracy of up to 0.5°K) in the range 80–300°K and over a wide interval of F-center concentrations \((10^{16} \div 0.5 \cdot 10^{19}\ \text{cm}^{-3})\). The crystals were cut from a single boule grown by the Kyropoulos method from chemically pure salt and were irradiated in a cryostat [8] under identical conditions. Crystal 1 (Fig. 1) is pressed tightly against crystal holder 2 by screw 3 and stop 4. The position of the crystal is strictly fixed by projections on the crystal holder. Cooling of the crystal is carried out by pressing a vessel with liquid nitrogen against the crystal holder. Temperature stabilization is accomplished with the aid of furnace 5. The crystal is irradiated with protons through slit 6, the width of which can be set from 10 µm to 2 mm. The height of the slit is 14 mm. Photometry of the colored layer is carried out in a direction perpendicular to the irradiation by means of microslit 8, the width of which can also be varied from 30 to 100 µm. This slit, with the aid of a micrometer screw with a division value of 10 µm, is moved along the crystal parallel to its front edge. The entire device is mounted on a Plexiglas flange, by means of which it is introduced into the cryostat. Adjustment of the microslits and positioning of the crystal are carried out with an MBI-3 microscope equipped with a screw optical micrometer of the MOV-1-15* type. Rigid mounting of the cryostat on the ion guide of the cyclotron makes it possible to move the spectrophotometer on a special stand so that the light from the monochromator falls perpendicular to the surface of the crystal. The use, as a collimator, of 6 plates made of LiF crystals with mirror cleavage,

made it possible to obtain a uniformly colored layer. The proton current is measured on five samples placed in the ion guide in front of the cryostat and calibrated with a Faraday cylinder [8]. This method was developed by us jointly with D. I. Vaisburd and makes it possible to measure the absorption coefficients of irradiated crystals from 0.1 to \(10^4\ \mathrm{cm}^{-1}\).

Fig. 1. Experimental scheme

Figure 2 presents the relative distribution of the concentrations of F-centers in KCl irradiated with protons at \(80^\circ\mathrm{K}\) over the depth of the colored layer at different irradiation doses. From the data of this figure it follows—

Fig. 2. Relative distribution of the concentration of F-centers \((\alpha/\alpha_0)\) over the depth of the proton-colored layer of a KCl crystal. Curves 1 and 2 correspond respectively to doses \(3.75\cdot10^{12}\) and \(7.5\cdot10^{13}\) protons \(\mathrm{cm}^{-2}\). Curve 3 is the relative distribution of the specific ionization losses of protons in KCl, calculated from the data of work [12].

indicates that with increasing irradiation dose the concentration of \(F\)-centers over the depth of the colored layer becomes equalized, since their accumulation, according to the data of Fig. 3, b, becomes saturated.

Figure 3, a presents the kinetic curves for the accumulation of \(F\)-centers in KCl irradiated with protons of energy \(6.7\) MeV and intensity \(4.1 \cdot 10^9 \dfrac{\text{protons}}{\text{cm}^2 \text{s}}\), and Fig. 3, b for irradiation with protons of energy \(1.0\) MeV and intensity \(10.4 \cdot 10^{10} \dfrac{\text{protons}}{\text{cm}^2 \text{s}}\).

Fig. 3. Kinetics of accumulation of \(F\)-centers in KCl under the action of protons at different temperatures.

The radiation energy expended on the accumulation of one \(F\)-center at the initial stage (Fig. 3, a) is 150 and 980 eV at tem-

temperatures of 230 and 80°K, respectively; however, the rate of accumulation of \(F\)-centers at a temperature of 230°K decreases more rapidly than at lower temperatures (Fig. 3, б), so that the value of the optimum temperature for the formation of \(F\)-centers is not constant and shifts with increasing dose toward lower temperatures. According to our measurements, the concentration of \(M\)-centers in this case is 2–3 orders of magnitude lower than the concentration of \(F\)-centers; therefore, the limitation of the accumulation of \(F\)-centers at low temperatures cannot be due to their coagulation into multiple electron centers [9]. According to the data of [5, 10, 11], it may be assumed that the process limiting the accumulation of \(F\)-centers in KCl crystals in the interval 80–200°K is their recombination with hole centers of the \(V_4\) type, with the concentrations of \(F\)-centers \((n_F)\) and \(V_4\)-centers \((n_V)\) being equal [10]. In this case the kinetic equation for the accumulation of \(F\)-centers may be written in the form:

\[ \frac{dn_F}{dt}=j\left[\eta_0P_0+\eta_1P_1+\eta_2P_2+\ldots+\eta_iP_i+\ldots\right] \tag{1} \]

with the initial condition \(n_F=0\) at \(t=0\), where \(t\) is the irradiation time; \(j\) is the proton flux density; \(\eta_i\) is the number of \(F\)-centers formed per unit length of the proton track in a volume of \(i\)-fold localization of proton energy; \(P_i=\dfrac{\lambda^i}{i!}l^{-\lambda}\) is the probability of finding such a volume in the crystal, and \(\lambda=v_F\eta_0jt\); \(v_F\) is the reaction volume for destruction of an \(F\)-center,

\[ v_F=\frac{\Delta n_F}{n_F n_V}, \]

\(\Delta n_F\) is the decrease in the concentration of \(F\)-centers as a result of their recombination with \(V_4\)-centers. At the initial stage of radiation accumulation of \(F\)-centers, when \(\lambda\ll 1\), and \(P_0=1;\ P_1=P_2=P_3=\ldots=P_i=0\), the solution of equation (1) is

\[ n_F=\eta_0jt, \tag{2} \]

i.e., a straight line, which is what is observed in Fig. 3, а. If the upper value of \(\lambda\) is not limited, then equation (1) can be solved in the approximation

\[ \eta_i=(-1)^i|\eta_1|;\quad i=1,2,3\ldots \tag{3} \]

The solution obtained in this case,

\[ n_F=\frac{1}{v_F}\left[1-l^{-\lambda}-\frac{1}{2}\frac{\eta_1}{\eta_0}\left(1-2l^{-\lambda}+l^{-2\lambda}\right)\right], \tag{4} \]

describes well the experimental kinetic curves for the accumulation of \(F\)-centers. The calculations were performed on an M-20 electronic computer. It was found that the limiting distance at which \(F\)- and \(V_4\)-centers can be located without recombining with each other,

\[ r_F=\left(\frac{3v_F}{4\pi}\right)^{\frac{1}{3}}, \]

is 30–40 Å.

The results presented indicate that the intensification of electron-hole processes with increasing irradiation temperature increases not only the efficiency of formation of \(F\)-centers, but also the probability of their radiation destruction.

References

1. C. Feher, Phys. Rev. 105, 1122, 1957.
2. C. Z. van Doorn, Phil. Res. Rep. 112, 309, 1957.
3. B. J. Faraday, H. Rabin, W. D. Compton. Phys. Rev. Letters, 7, 57, 1961.
4. W. Känzig, T. O. Woodruff, J. Phys. Chem. Solids 9, 70, 1958.
5. N. Itoh, J. Phys. Chem. Solids 27, 197, 1966.
6. P. O. Vilyu; M. A. Elango, FTT, 7, 3673, 1965.
7. T. P. P. Hall, D. Pooley, P. T. Wedepohl, Proc. Phys. Soc. 83, 635, 1964.
8. A. N. Kravets, Zavodskaya laboratoriya, 6, 767, 1966.
9. D. I. Vaisburd, I. Ya. Melik-Gaikazyan, DAN SSSR, 165, 1029, 1965.
10. B. J. Faraday, W. D. Compton, Phys. Rev., 138, A893, 1965.
11. J. D. Kingsly, J. Phys. Chem. Solids, 23, 949, 1962.
12. D. I. Vaisburd, N. L. Terent’ev. Proceedings of the All-Union Conference on Dosimetry of High Doses. Tashkent, 1966.