ELECTROPHYSICAL STUDIES OF RADIATION DEFECTS IN ALKALI-HALIDE CRYSTALS

A. A. VOROB'EV, E. K. ZAVADOVSKAYA, Yu. M. ANNENKOV

The present level of development of the radiation physics of alkali-metal halides has been achieved mainly through the application of methods of high-frequency spectroscopy and luminescence analysis. With this approach to clarifying the problem, experimenters judge a wide range of ionic processes indirectly, and a number of phenomena are not controlled at all. The use of electrophysical methods of investigation makes it possible to obtain useful, and in some cases unique, information about irradiation defects. The application to radiation physics of the theory of dielectrics developed by Maxwell, Debye, Brown, G. I. Skanavi, and Fröhlich has proved highly fruitful.

The physicochemical properties of crystals can be studied more productively using homologous series of alkali-halide compounds as examples. Investigation of irradiation effects in crystals of different chemical composition makes it possible to establish the most general regularities of radiation-induced disruption of ionic structures, which can be used in developing the scientific foundations of radiation technology.

This position is the guiding principle in studying the radiation-induced change in the electrical properties of alkali-halide crystals [1—10].

§ 1. Radiation Changes in the Electrical Conductivity of Alkali-Halide Crystals

The investigations carried out have made it possible to establish the principal laws governing the change in the electrical conductivity of alkali-metal halides over a wide range of doses and to consider the nature of the observed effects.

Short-term exposure to a beam of protons, electrons, or X-rays leads to a decrease in the electrical conductivity of NaCl, KCl, KBr, KI crystals and of solid solutions of the KCl—KBr system.

Intense proton and electron bombardment (absorbed dose above \(5 \cdot 10^{11}\) erg/cm\(^3\)) stimulates an increase in the conductivity of alkali-metal halides in the temperature region below \(200^\circ\)C.

Consequently, under the action of radiation on alkali-halide crystals, charge carriers (cation vacancies) become bound to radiation defects and new vacancies are generated. The efficiency of these processes is determined by the magnitude of the dose absorbed by the material and by its chemical composition.

We concentrated our attention on the study of the radiation-induced lowering of electrical conductivity (the region of small and medium doses), since the nature of this effect has not yet been finally clarified.

The superposition of the processes of generation and binding of free cation vacancies by holes leads to the fact that the electrical conductivity of irradiated crystals at a measurement temperature close to room temperature may be equal to, or less than, the conductivity of samples not disturbed by irradiation. Such a regularity is observed for all the alkali-halide compounds studied (NaCl, KCl, KBr, KJ, KCl—KBr), except for NaBr crystals (Figs. 1, 2).

Fig. 1. Temperature dependences of the electrical conductivity of NaCl crystals irradiated with protons.
—●—●—●— unirradiated crystals; —△—△— \(D = 7 \times 10^9\ \mathrm{erg/cm^3}\); —○—○—○— \(D = 3 \times 10^{10}\ \mathrm{erg/cm^3}\); —×—×—×— \(D = 2.3 \times 10^{11}\ \mathrm{erg/cm^3}\).

The electrical conductivity of sodium bromide, measured at temperatures below \(100^\circ\mathrm{C}\), increases considerably after irradiation (Fig. 3). This fact, which at first glance contradicts Seitz’s hypothesis [11], is satisfactorily explained within the framework of modern ideas on the structure of hole color centers.

Studies of the anisotropy of the \(V\)-absorption bands and EPR in irradiated crystals [12, 13] have shown that halide ions \(X_2^{-}\), \(X_3^{--}\) are constituent parts of a series of \(V\)-centers. The localization sites of the halide ions may be cation vacancies. Thus, the model of a \(V_2\)-center in the form of a molecular ion \(X_3^{--}\), having a preferential orientation along the crystallographic direction \(\langle 100\rangle\), has been confirmed in many works [14]. Consequently, in alkali-halide crystals, at least part of the hole color centers is formed at a temperature close to room temperature through the displacement of neutral halogen atoms into cation vacancies. The probability of this process is determined by the ratio of the size of the halogen and that of the cation vacancies. Table 1 gives the ratios between the ionic radius of the cation \((r_k)\) and the size of the halogen atom \((r_a)\) for alkali-halide crystals.

As can be seen from Table 1, only for NaBr crystals does the ratio \(\sqrt{r_a}/\sqrt{r_k}\) exceed unity, which makes it possible to regard the placement of bromine atoms at sites of the cation sublattice as unlikely. From this point of view, sta-

the anomalous increase in the electrical conductivity of NaBr crystals after their irradiation with small and medium doses (less than \(5\cdot 10^{11}\ \mathrm{erg/cm^3}\)) becomes understandable. The free cation vacancies generated by irradiation are, to a lesser extent than in other crystals, blocked by hole centers and take part in charge transport.

Table 1

Thus, the investigations carried out confirm Seitz’s viewpoint on the binding of cation vacancies by holes generated during irradiation of alkali-halide crystals. In this case, the cation vacancies lose mobility as a result of neutral halogen atoms being placed in them. The probability that free cation vacancies will bind with holes is greater for crystals with lower lattice energy.

Fig. 2. Temperature dependences of electrical conductivity for KBr crystals irradiated with protons.
—●—●—●—, unirradiated samples; —△—△—△— \(D = 5 \times 10^{9}\ \mathrm{erg/cm^3}\); —○—○—○— \(D = 5.2 \times 10^{10}\ \mathrm{erg/cm^3}\); —×—×—×— \(D = 2.1 \times 10^{10}\ \mathrm{erg/cm^3}\).

The mechanism of the radiation-induced decrease in the electrical conductivity of crystals proposed by Seitz takes place at the irradiation temperature. However, it alone cannot explain the experimental data on the change in electrical conductivity of irradiated crystals during annealing.

Indeed, as follows from Fig. 1, when NaCl single crystals irradiated with 4.5 MeV protons are heated, the ratio

\[ \frac{\sigma_{\text{unirr.}}}{\sigma_{\text{irr.}}} \]

passes through a maximum at \((100—120^\circ\mathrm{C})\) and tends to unity in the high-temperature region.

On the basis of the results of works [1—10], [15] it may be concluded that the effect under discussion is typical for alkali halide crystals subjected to the action of various types of radiation.

Fig. 3. Radiation-induced change in the electrical conductivity of NaBr crystals. —●—●—●— unirradiated specimens; —△—△—△— \(D = 5 \times 10^{10}\) erg/cm\(^3\); —○—○—○— \(D = 1.1 \times 10^{11}\) erg/cm\(^3\); —×—×—×— crystal irradiated with a dose \(1.1 \times 10^{11}\) erg/cm\(^3\) and heated to \(250^\circ\)C

As a working hypothesis, Smoluchowski [16] assumed that during annealing free cation vacancies associate with certain lattice defects that acquire a positive charge upon irradiation (traps).

In general, Smoluchowski’s theory agrees satisfactorily with the experimental data. However, the identification of cation-vacancy traps with ionized aggregates of vacancies raises objections. It is known that during irradiation vacancy aggregates are intensively destroyed—radiation-stimulated dissolution of supersaturated vacancies in the crystal lattice takes place. In this connection, the stability of the traps according to Smoluchowski is called into question. In addition, a bimolecular process of capture of charge carriers occurs only if all traps possess the same interaction cross section with cation vacancies. This requirement is not fulfilled in Smoluchowski’s theory.

These objections are removed if free anion vacancies, which arise during the thermal destruction of \(F\)-centers, are regarded as traps for cation vacancies. Taking as a basis the ionic mechanism of destruction of color centers [17], it appears possible to explain the temperature dependence of the electrical conductivity of irradiated alkali halide crystals. In order to confirm the proposed interpretation, the temperature changes in electrical conductivity, thermally stimulated luminescence, and thermal bleaching of \(F\)-centers were investigated under identical experimental conditions for KCl, KBr, and KI crystals irradiated with protons.

From the data of Fig. 4 it follows that the thermally stimulated release of the light sum stored in KBr crystals occurs in two stages. Similar curves are also characteristic of NaCl, KCl, and KI. The first thermoluminescence peak is observed at temperatures \((75—95)^\circ\)C; the second maximum of emission occurs at \((140—180)^\circ\)C. With increasing lattice energy of the alkali halide crystals, the position of the peaks shifts

toward higher temperatures. As a rule, the low-temperature luminescence maximum is more intense.

Fig. 4. Temperature dependences of the electrical conductivity (2), luminescence intensity (3), and maximum of the \(F\)-absorption band (4) for irradiated KBr crystals \(\left(D = 3.5 \times 10^{10}\ \text{erg}/\text{cm}^2\right)\).

With increasing temperature of the samples, the \(F\)-absorption bands for the crystals studied are annealed in two stages. The maximum rates of destruction of \(F\)-centers are observed in the region of the thermoluminescence peaks (Fig. 4). The main part of the \(F\)-centers dissociates at temperatures below \(100^\circ\text{C}\) (the heating rate of the samples was \((1–3)^\circ\text{C}\) per minute).

A comparison of the thermoluminescence curves, the bleaching of the \(F\)-band, and the temperature variation of the electrical conductivity of the irradiated crystals indicates that the greatest decrease in conductivity occurs at the temperature of the first bleaching peak and of the maximum destruction of \(F\)-centers.

On the basis of the investigations carried out, the following probable scheme is proposed for the thermal destruction of \(F\)-centers.

Divacancies present in the crystal after irradiation combine with \(F\)-centers into complexes, which are ionized as a result of thermal fluctuations. In this process free anion vacancies appear, capable of associating with cation vacancies. As the temperature increases, the mobility of divacancies increases, the rate of destruction of \(F\)-centers rises, and, as a consequence of these processes, the electrical conductivity of the irradiated samples decreases. The liberated \(F\)-electrons partially recombine with certain hole centers and are partially localized near neutral halogen atoms situated at cation sites, with the formation of centers \((X^{0}\cdot \square \cdot e)\). As will be shown below, such defects give rise to dielectric absorption of the resonance type in the region of acoustic frequencies.

At elevated temperatures the centers \((X^{0}\cdot \square \cdot e)\) are destroyed through ionic processes, cation vacancies are released, and the conductivity of the crystals increases to values corresponding to the conductivity of unirradiated samples.

Thus, the radiation-induced decrease in the electrical conductivity of alkali-halide crystals at small and medium irradiation doses is satisfactorily explained within the framework of the mechanisms of Seitz and of Smoluchowski. The effectiveness of the Seitz mechanism is determined to a considerable extent by the possibility of placing neutral halides at cation sites of the lattice.

The set of studies carried out on thermobleaching and electrical conductivity of irradiated KBr, KCl, and KI crystals made it possible to regard as traps of cation vacancies the anion vacancies that are released during the thermal destruction of $F$ centers.

§ 2. Dielectric losses in irradiated alkali-halide crystals

A large number of works have been devoted to the polarization and dielectric losses of dielectrics; these works formed the foundation of the modern theory of dielectrics.

In the theory of dielectrics, until recently the behavior of electrons in structural defects was not taken into account. However, in connection with the use of ionizing radiation for further investigation of the structure of a real crystal, the role of electronic phenomena in processes of slowly established polarization may be significant.

Indeed, the works of Garlik and Gibson [18], Kalman [19], V. A. Ioffe [20], Ya. N. Ksendzov [21], and others indicate that electrons localized at capture levels lead to low-frequency dielectric absorption of the resonance type.

From the theoretical works of Fröhlich [22] and Zussman [23] it follows that resonant dielectric losses of electronic character can arise at low frequencies if:

a) the energy state of the localized electron is degenerate. This condition requires strict symmetry of the electron-localization site;

b) the vibration frequency of the ions surrounding the electron-localization site differs from the vibration frequency of the ions in the undisturbed lattice.

Below it will be shown that low-frequency dielectric losses of resonant character are observed under certain conditions in irradiated alkali-halide crystals.

Crystals of NaCl, KCl, KBr, and KI were irradiated with protons of energy 4.5 MeV. The dielectric losses were studied in the acoustic frequency range.

Radiation-induced changes in the dielectric properties of NaCl and KCl crystals, on the one hand, and KBr and KI crystals, on the other, are qualitatively different.

1. Irradiation of sodium and potassium chlorides with protons stimulates a decrease in dielectric losses in the temperature interval from room temperature to $(140\text{–}200)^\circ\mathrm{C}$ (Fig. 5).

At acoustic frequencies, in the temperature region above $100^\circ\mathrm{C}$, the dielectric losses of alkali-metal halides have an ohmic character; therefore, the radiation-induced decrease in ionic conductivity and in $\tan\delta$ at elevated temperatures is due to the same causes, the analysis of which was given above.

As follows from the data of Fig. 5, the loss angle measured at temperatures close to room temperature decreases as a result of irradiation of the crystals studied. This fact agrees well with the mechanism of structural dielectric losses proposed by us [9]. Indeed, the formation of hole color centers at cation vacancies localized near internal crystal surfaces

and those responsible for structural dielectric losses, should lead to a decrease in \(\tg \delta\).

Fig. 5. Temperature changes of \(\tg \delta\) for unirradiated (1) and proton-irradiated (2, 3, 4) KCl crystals.
2 — \(D = 8.6 \times 10^9\) erg/cm\(^3\); 3 — \(D = 5.2 \times 10^{10}\) erg/cm\(^3\);
4 — \(D = 2 \times 10^{11}\) erg/cm\(^3\).

1. Radiation treatment of KBr and KJ crystals leads to the appearance of intense dielectric absorption at audio frequencies (Figs. 6, 7).

Fig. 6. Dependence of \(\tg \delta\) on temperature for unirradiated (1) and proton-irradiated (2, 3, 4, 5) KBr crystals;
2 — \(D = 4.3 \times 10^9\) erg/cm\(^3\); 3 — \(D = 5.7 \times 10^{10}\) erg/cm\(^3\);
4 — \(D = 1.3 \times 10^{11}\) erg/cm\(^3\); 5 — \(D = 2.5 \times 10^{11}\) erg/cm\(^3\).

In the case of KBr crystals, at an absorbed dose equal to \(4.3 \cdot 10^9\) erg/cm\(^3\), the maximum of \(\operatorname{tg}\delta\) is observed at \(130^\circ\)C (measurement frequency 100 cps). With an increase in the integral proton flux, the peak of the loss angle increases monotonically and shifts into the region of high temperatures. Similar regularities have been found for KI single crystals (Fig. 7).

Fig. 7. Dependence of \(\operatorname{tg}\delta\) on temperature for unirradiated (1) and proton-irradiated (2, 3, 4) and X-ray-irradiated (5) KI crystals;
2 — \(D = 1.4 \times 10^{11}\) erg/cm\(^3\); 3 — \(D = 2.5 \times 10^{11}\) erg/cm\(^3\); 4 — \(D = 4.2 \times 10^{11}\) erg/cm\(^3\); 5 — \(D = 9.7 \times 10^8\) erg/cm\(^3\).

Dielectric absorption in KBr and KI crystals irradiated with protons cannot be attributed to simple relaxation phenomena. Indeed, an increase in the frequency of the external electric field does not affect the positions of the temperature maxima of \(\operatorname{tg}\delta\), but leads to a sharp decrease in their amplitude (Fig. 8).

Thus, after proton bombardment the electrical properties of alkali-halide crystals change nonuniformly. For alkali-metal chlorides, radiation exposure decreases dielectric losses.

In the temperature dependences of \(\lg \delta\) for irradiated KBr and KI crystals, an intense maximum is observed whose position does not depend on the frequency of the electric field.

We concentrated our attention on elucidating the nature of the radiation-stimulated dielectric absorption in KBr and KI crystals.

Data from measurements of the temperature dependences of the electrical conductivity of irradiated KBr and KI crystals indicate the polarization nature of the maxima of \(\operatorname{tg}\delta\).

On the basis of a comprehensive analysis of the experimental results and additional experiments on the study of the time dependences of the absorption current, the resonance type of the dielectric absorption under discussion has been unambiguously established. The experimental data indi-

indicate that the resonant oscillation frequency is below 50 Hz. The low resonance frequency does not make it possible to identify the resonating particles with ionic defects of the structure.

Fig. 8. Dependence of \(\operatorname{tg}\delta\) and \(\varepsilon\) on temperature for KBr crystals irradiated with protons \((D = 5.2 \times 10^{10}\ \text{erg}/\text{cm}^3)\).
1 — 50 Hz; 2 — 100 Hz; 3 — 500 Hz; 4 — 1000 Hz; the dashed lines show data for unirradiated samples.

As a working hypothesis it is assumed that the resonant absorption is due to electronic phenomena that are activated at elevated temperatures. The position and intensity of the temperature maximum of \(\operatorname{tg}\delta\) are determined by the relation between the efficiency of the processes of creation and destruction of electrically active defects. The increase of \(\operatorname{tg}\delta\) at temperatures below the temperature of the maximum is due to an increase in the number of oscillators \((N_{\text{osc.}})\), while the decrease of \(\operatorname{tg}\delta\) at higher temperatures is due to destruction of the oscillators.

From the data presented in Figs. 6 and 7 it follows that the increase in the number of oscillating defects upon heating irradiated KBr and KI crystals obeys an exponential dependence and is characterized by activation energies equal to 0.85 and 0.65 eV, respectively.

Table 2 gives the values of the activation energy for oscillator formation \((U_N)\) and the energy of thermal dissociation of \(F\)-centers \((U_F)\).

Table 2

The satisfactory agreement between \(U_N\) and \(U_F\) is hardly accidental and, in all likelihood, reflects the interrelationship between the processes of thermal destruction of \(F\)-centers and creation of oscillators responsible for resonant absorption at low frequencies. The data of Table 2 are an argument in favor of the view that, upon dissociation of \(F\)-centers in crystals, electrically active defects appear.

As follows from the data of Fig. 9, the temperature regions of destruction of \(F\)-centers, of changes in electrical conductivity, and of the appearance of a maximum of \(\operatorname{tg}\delta\) for irradiated KBr crystals coincide.

The studies carried out made it possible to adopt a model of oscillators responsible for resonant absorption in irradiated KBr and KJ crystals, in the form of a neutral halide atom situated in a cation vacancy, near which an electron is localized on 12 cations. Such a center \((X^0\cdot \Box \cdot e)\) arises as a result of thermal destruction of an \(F\)-center and is stable within a certain temperature range.

The proposed oscillator model satisfies the Fröhlich–Zusman conditions necessary for the occurrence of low-frequency resonant absorption.

In accordance with the adopted oscillator model, their mean statistical density \((N_{\mathrm{osc}})\) is expressed by the formula:

\[ N_{\mathrm{osc}}=\frac{dn_F}{dt}\cdot n_v\cdot \sigma_3\cdot \tau, \tag{1} \]

where

\[ \frac{dn_F}{dt} \]

is the rate of thermal destruction of electronic color centers;

\(n_v\) is the density of neutral halide atoms at cation sites \((X^0|\Box|)\);

\(\sigma_3\) is the cross section for capture of a free electron by the center \((X^0\cdot|\Box|)\);

\(\tau\) is the lifetime of the oscillators \((X^0\cdot|\Box|\cdot e)\).

Fig. 9. Change of \(\operatorname{tg}\delta\) (1), measured at a frequency of 50 Hz, electrical conductivity (2), and intensity of the \(F\)-absorption band (3) during isochronous annealing \((B=2\ \text{deg/min})\) of KBr crystals irradiated with protons \((D=3.5\times10^{10}\ \text{erg}/\text{cm}^2)\).

In the low-temperature region the \(F\)-centers are destroyed only slightly, and the loss angle is small. Heating of the crystals stimulates the growth of \(\frac{dn_F}{dt}\), which leads to an increase in the number of oscillators. At high temperatures the oscillators are destroyed owing to intensification of ionic processes (decrease of \(\tau\)). Consequently, a maximum should be observed in the temperature dependence of \(\operatorname{tg}\delta\). With increasing irradiation dose the density of color centers increases; therefore the maximum of \(\operatorname{tg}\delta\) should increase in magnitude, while its position should shift into the region of high temperatures. Precisely such dependences are observed for irradiated KBr and KJ crystals (Figs. 6, 7).

The dielectric loss angle near the maximum value is determined by the concentration of oscillators, which is expressed by the formu-

... field (1). By introducing impurities into crystals and subjecting the samples to various external perturbations, one can deliberately change the parameters of equation (1) and thereby unambiguously establish the applicability of the proposed oscillator model.

For this purpose the parameters of equation (1) were changed by varying the heating rate of irradiated KBr and KI samples during measurement of dielectric losses; by preliminary heat treatment and plastic deformation; by exciting the crystals with light from the \(F\)-absorption band during measurement of \(\operatorname{tg}\delta\); and by introducing into KBr crystals anion-substituting impurities \((\mathrm{OH}^-)\) and cation-substituting impurities possessing electron-acceptor \((\mathrm{Pb}^{++})\) and hole-acceptor \((\mathrm{Ca}^{++}, \mathrm{Sr}^{++})\) properties.

The experiments performed fully confirmed the proposed oscillator model.

As was indicated earlier, resonance absorption is not observed in irradiated NaCl and KCl crystals. In connection with this circumstance, it is of interest, using solid solutions of the KBr—KCl system as an example, to determine the conditions necessary for the formation in alkali-halide crystals of radiation defects that give rise to a resonant type of dielectric loss.

In studying dielectric losses in proton-irradiated crystals of KCl—KBr solid solutions, the following regularity was found: resonant dielectric absorption arises only for compositions with a predominant KBr content. All attempts to detect resonant dielectric losses in solid solutions containing potassium chloride in concentrations greater than 30 mole % proved unsuccessful [24].

The data on dielectric losses in irradiated KCl—KBr solid solutions, completely incomprehensible from the standpoint of ionic-relaxation processes, are fully explained within the framework of the proposed mechanism of resonant absorption.

As was indicated, the oscillator is modeled in the form of an electron localized on the 12 cations nearest to a cation vacancy, in which a halide atom \((X^0 + \cdot e)\) is situated. The resonance conditions formulated by Fröhlich and Zussman are fulfilled if the \(X^0 + \cdot e\) center is formed at a free cation vacancy; that is, the oscillator is in the symmetric field of the lattice. If, in the immediate vicinity of the oscillator, there are violations of the periodicity of the structure (impurity atoms, vacancies), then the degenerate state of the electron is lifted and low-frequency resonance is impossible.

Mixed crystals should be regarded as a set of a number of isostructures. Thus, in solid solutions of the KCl—KBr system there are seven isostructures: (1—the \(K^+\) ion is surrounded by 6 \(\mathrm{Br}^-\) ions, 2—the \(K^+\) ion is surrounded by 5 \(\mathrm{Br}^-\) ions and 1 \(\mathrm{Cl}^-\) ion, etc.).

It is not difficult to see that the Fröhlich—Zussman conditions can be fulfilled only for the first and seventh isostructures. Indeed, if the oscillator is surrounded by nonequivalent anions, elastic stresses arise that lift the degenerate state of the electron. The probability of finding, in crystals of solid solutions, regions belonging to the first isostructure is high only for compositions with a large KBr content. Consequently, for compositions close to equimolar, resonant absorption in the audio-frequency range should not occur, which is indeed observed experimentally.

As was noted, resonant absorption of the energy of an electric field in the audio-frequency region has not been detected for irradiated NaCl and KCl crystals. Probably, the conditions necessary for the occurrence...

resonance dielectric losses in alkali-metal chlorides are performed outside the temperature–frequency range used by us.

In this connection, a theoretical consideration of the question of the resonant type of dielectric losses in irradiated crystals of different chemical composition is of interest.

REFERENCES

1. A. A. Vorob'ev. Izvestiya Akademii nauk SSSR, physical series, XXIX, 3, 361, 1965.

2. A. A. Vorob'ev. Uspekhi khimii XXXVI, 6, 1065, 1967.

3. A. A. Vorob'ev. Izvestiya vysshikh uchebnykh zavedenii, “Fizika,” 10, 39, 1967.

4. A. A. Vorob'ev. Ionic and Electronic Properties of Alkali-Halide Crystals, Tomsk, 1968.

5. Yu. M. Annenkov, E. K. Zavadovskaya. Izv. TPI, 139, 304, 1965.

6. Yu. M. Annenkov. Izv. TPI, 140, 63, 1965.

7. E. K. Zavadovskaya, Yu. M. Annenkov. Radiation Physics of Nonmetallic Crystals (Proceedings of the conference), 310, Kiev, 1965.

8. V. A. Chernyshev. Izv. AN SSSR, physical series, 29, 1, 71, 1965.

9. Yu. M. Annenkov. Dissertation, Tomsk, 1968.

10. V. A. Grishukov. Dissertation, Tomsk, 1968.

11. Seitz F. Rev. Mod. Phys., 26, 7, 1954.

12. Känzig W., Woodruff T. J. Phys. Chem. Solids, 9, 70, 1957.

13. Hayes W., Nichols G. M. Phys. Rev., 117, 993, 1960.

14. Christy R., Phelps P. Phys. Rev., 117, 993, 1960.

15. B. V. Budylin, A. A. Vorob'ev. The Action of Radiation on Ionic Structures. Gosatomizdat, Moscow, 1962.

16. R. Smolukhovskii. Materials of the Conference on the Peaceful Uses of Atomic Energy, vol. 7, State Scientific-Technical Publishing House of Chemical Literature, Moscow, 1958.

17. Ch. B. Lushchik. Proceedings of the Institute of Physics and Astronomy, Academy of Sciences of the Estonian SSR, 1958.

18. Carlick G. F., Cibson A. F. Proc. Roy. Soc., 188, 485, 1947.

19. Kaliman H., Kramer B., Mark P. Phys. Rev., 99, 1328, 1955.

20. Ioffe V. A., Yanchevskaya I. S. FTT, 4, 3, 668, 1962.

21. Ya. N. Ksendzov. Izv. AN SSSR, 22, 3, 1958.

22. G. Fröhlich. Dielectric Spectroscopy, Moscow, 1960.

23. Sucman I. A. Proc. Phys. Soc., 79, 4, 1962.

24. Yu. M. Annenkov, V. A. Grishukov. Izv. TPI, 139, 318, 1965.