PHYSICAL PHENOMENA OCCURRING IN LiF CRYSTALS IRRADIATED WITH γ-RAYS DURING THERMAL ANNEALING

E. K. ZAVADOVSKAYA, N. M. TIMOSHENKO, V. A. CHERNYSHEV

The paper presents the results of investigations of stored energy, optical absorption, microhardness, and electrical properties during the thermal annealing of LiF crystals irradiated with gamma rays.

The change in the above-listed properties is associated with a definite type of radiation damage.

In the work the results of the investigations of stored energy, optical absorption spectra, microhardness and electrical properties crystals LiF irradiated with H-rays in the process of quenching are given.

The change of the above mentioned properties in connected with the definite kind of irradiation disturbances.

The present work is devoted to a further clarification of the nature of radiation damage and of the processes of its destruction during thermal annealing in ionic dielectrics. Lithium fluoride was chosen as the material studied; its radiation damage has been the subject of investigations in a number of works [1—5].

To solve the problem posed, a complex of research methods was applied, making it possible to study the electrical, mechanical, optical, and energetic properties of LiF crystals irradiated at a Co\(^{60}\) source with γ-rays of \(E = 1.24\) MeV in a field with a dose-rate of 450 r/sec.

Experimental results

1. Stored energy (SE). Investigations of stored energy make it possible to estimate the total radiation damage retained in the crystal after the action of radiation, as well as the stability of defects during their thermal annealing. The SE release spectrum of a LiF crystal irradiated with small doses (of the order of \(10^6\) roentgen) has a simple form (Fig. 1, curve 1): an increase in the rate of SE release in the temperature interval from 60 to 220°C is accompanied at higher temperatures by a decrease in

\[ \frac{dQ}{dT}. \]

In the dose interval up to \(8 \cdot 10^6\) rad, with increasing absorbed dose of γ-radiation there occurs an increase in SE and in the absorption coefficient \((K_F)\) at the maximum of the \(F\)-band; moreover, the change of \(Q\) and \(K_F\) with dose has an analogous character (Fig. 2).

The SE release spectrum of a crystal irradiated with doses of the order of \(10^8\) roentgen and higher has a complex character: three peaks are observed, max-

maxima of which occur at temperatures of 130–150°C, 220 and 280°C (Fig. 1, curves 2, 3) [8].

2. Optical absorption spectra. In the optical absorption spectra of LiF crystals irradiated with γ-rays at doses up to \(5 \cdot 10^7\) roentgens,

Fig. 1. Dependence of the rate of release of stored energy in LiF crystals irradiated with γ-rays at doses: 1—\(2.7 \cdot 10^6\) roentgens, 2—\(3.9 \cdot 10^8\) roentgens, 3—\(1.25 \cdot 10^9\) roentgens.

two bands, \(F\) and \(M\), are observed, the maxima of which occur at wavelengths of 240 and 450 mµ. During thermal annealing, destruction of the \(F\)-centers begins at a temperature of about 80°C (Fig. 3). The annealing curve of the \(F\)-band in the temperature interval from room temperature to 400°C has a complex character, namely: two temperature regions are observed with different rates of destruction of \(F\)-centers; the first region is 80–220°C and the second is 200–300°C.

The intensity of the \(M\)-band remains unchanged during annealing up to 160°C. Beginning at a temperature of 160°C, the rate of destruction of the \(M\)-band increases up to 250°C. After 250°C the rate of destruction of the \(M\)-band becomes constant and has its maximum value (Fig. 3). The final destruction of the \(M\)-band occurs at a lower temperature than that of the \(F\)-band.

Fig. 2. Dependence of the stored energy \(Q\) and of the absorption coefficient at the maximum of the \(F\)-band, \(K_F\), on the absorbed dose \(D_n\) of γ-radiation.

The optical absorption spectrum of a LiF crystal irradiated with γ-rays at doses greater than \(5 \cdot 10^7\) roentgens presents a complex picture: along with the \(F\)- and \(M\)-bands, \(R_1\) (320 mµ) and \(R_2\) (380 mµ) bands appear, the annealing of which begins in the temperature region of 120°C and ends at temperatures of 220–240°C (Fig. 3).

3. Change in microhardness and stored energy after preliminary annealing. Simultaneously with the study of the change in optical absorption of LiF crystals during thermal annealing, studies were carried out of the change in microhardness and the magnitude of the SE.

For this purpose, LiF crystals irradiated with γ-rays at a dose of \(5.45 \cdot 10^8\) roentgens were annealed for different times at a constant temperature, or for the same time but at different temperatures. The EE and microhardness were then measured on crystals treated in this way.

Fig. 3. Annealing kinetics of the optical absorption bands of irradiated LiF crystals: the F band—crystal irradiated with a dose of \(5.4 \cdot 10^6\) roentgens; the M-, \(R_1\)-, and \(R_2\)-bands—crystal irradiated with a dose of \(5.45 \cdot 10^8\) roentgens.

It follows from Fig. 4 that preliminary annealing at a temperature of \(230^\circ\mathrm{C}\) of irradiated crystals is accompanied by a decrease in the magnitude of the EE \((Q)\) and the microhardness \((H)\). The intensive change in \(Q\) and \(H\) observed during annealing up to 3 hours is then accompanied by a tendency toward saturation in the change of the quantities \(Q\) and \(H\). Under the indicated annealing conditions, the change in the EE is more significant than that in the microhardness.

The weak change in the quantities \(Q\) and \(H\) as a result of preliminary annealing in the temperature range up to \(230^\circ\mathrm{C}\) is replaced by an energetic change in these quantities after annealing at higher temperatures (Fig. 5); in this case, the character and relative magnitude of the change in \(Q\) and \(H\) in the temperature range above \(230^\circ\mathrm{C}\) are the same.

Fig. 4. Change in microhardness \(H\) (curve 1) and stored energy \(Q\) (curve 2) as a function of the time of preliminary annealing at a temperature of \(230^\circ\mathrm{C}\) of LiF crystals irradiated with a dose of \(5.4 \cdot 10^8\) roentgens.

4. Electrical conductivity and dielectric losses. Figure 6 presents the dependence of \(\sigma_{\mathrm{irr}}/\sigma\) on temperature. From this dependence it is evident that, with increasing temperature, \(\sigma_{\mathrm{irr}}/\sigma\) decreases, and in the region

180°C reaches a minimum value. At the same time, the greater the dose of preliminary irradiation, the greater the decrease in \(\sigma_{\text{irr}}/\sigma\). With a further increase in temperature this ratio begins to increase, and in the temperature range from 220 to 400°C a maximum is observed in the dependence \(\sigma_{\text{irr}}/\sigma = f(t^\circ\mathrm{C})\), i.e., the conductivity of the preliminarily irradiated crystal becomes greater than that of the unirradiated one. This maximum also increases with increasing dose of preliminary irradiation.

Fig. 5. Change in the microhardness \(H\) (curve 1) and stored energy \(Q\) (curve 2) as a function of the temperature of preliminary annealing (annealing for 1 hour) of LiF crystals irradiated with a dose of \(5.45 \cdot 10^8\) roentgens.

Table 1 gives the activation energies calculated from the slope of the dependence \(\lg \sigma = f\!\left(\frac{1}{T^\circ\mathrm{K}}\right)\) for irradiated and unirradiated LiF crystals in the temperature range from 160 to 260°C. It is seen from the table that the activation energy increases with increasing dose of preliminary irradiation.

The tangent of the dielectric-loss angle (Fig. 7) of preliminarily irradiated LiF crystals in the relaxation region (20°C–180°C) is somewhat greater than that of unirradiated crystals; also, weak maxima with a very large half-width are observed in this temperature region. The magnitude of the maxima changes only slightly with increasing dose of preliminary irradiation, while the maximum itself shifts toward lower temperatures (Table 2).

Fig. 6. Dependence of \(\sigma_{\text{irr}}/\sigma\) on temperature.

In the temperature range from 180 to 350°C, the tangent of the dielectric-loss angle is governed by the magnitude of the through-conduction current. The activation energies calculated from the shift of the relaxation maxima with increasing frequency are given in Table 1. As is seen from Table 1, the ener-

Table 1

Table 2

gy of activation for relaxation of dipoles stimulated by irradiation decreases with increasing irradiation dose.

Fig. 7. Dependence of \(\tg \delta\) on temperature for LiF.
— unirradiated, \(f = 1000\) Hz;
○○○ — irradiated with a dose of \(5.8 \cdot 10^7\) roentgen, \(f = 1000\) Hz;
⊕⊕⊕ — irradiated with a dose of \(5.8 \cdot 10^7\) roentgen, \(f = 100\) Hz;
××× — unirradiated, \(f = 100\) Hz.

Discussion of the experimental results

The spectrum of SE release in LiF crystals irradiated with small doses of $\gamma$ rays differs from the SE-release spectrum of crystals irradiated with large doses (Fig. 1).

Analysis of the optical-absorption spectra shows that, in the case of small doses, only the $F$ band is observed in the optical-absorption spectra; the intensity of the $M$ band is insignificant and becomes noticeable only at a dose of $5.4 \cdot 10^6$ roentgens. Therefore, at small irradiation doses only $F$ centers contribute to the SE, and only an insignificant fraction of the energy is due to $M$ centers.

This is also indicated by the analogous character of the change in the SE $Q$ and in the absorption coefficient $K_F$ at the maximum of the $F$ band, shown in Fig. 2.

The calculation of the number of $F$ centers, carried out for LiF according to the formula proposed by Nad’ [5], made it possible to determine the energy attributable to one destroyed $F$ center,

\[ e_F=\frac{Q}{n_F}\;(\text{eV}), \]

where

$Q$ is the magnitude of the SE in $\text{cm}^3$;

$n_F$ is the concentration of $F$ centers in $1\ \text{cm}^3$.

For absorbed doses up to $10^6$ rad, $e_F = 9.7$ eV. Calculations performed for large doses give the value $e_F > 10$ eV. This circumstance is due to the fact that at doses above $10^6$ rad, $M$ centers begin to make a definite contribution to the value of the SE.

The high concentration of $F$ centers and $M$ centers, and the appearance of complex $R_1$ and $R_2$ centers (Fig. 3), determine the complex spectrum of SE release in LiF crystals at large irradiation doses (Fig. 1, curves 2, 3). At large irradiation doses, the concentration of defects in LiF at room temperature does not correspond to their thermodynamic equilibrium, the result of which is their destruction at room temperature and the release of SE (Fig. 1, curves 2 and 3). At small irradiation doses (Fig. 1, curve 1), annealing of defects (and, consequently, SE release) begins at higher temperatures.

The release of SE in LiF crystals irradiated with large doses in the temperature region from room temperature to 150°C evidently occurs owing to the transformation of simple defects into more complex ones, namely: $F$ centers coagulate into $M$ centers, and $M$ centers into $R_1$ and $R_2$ centers. Measurements of the optical-absorption spectra confirm this assumption. Thus, the concentration of $R_1$ and $R_2$ centers increases somewhat upon heating to 100°C (Fig. 3). We did not find a noticeable increase in the intensity of the $M$ band upon destruction of the $F$ band (Fig. 3), which is evidently due to the simultaneous destruction of $M$ centers (possibly their transformation into $R$ centers). Kobayashi [6], studying the annealing kinetics of absorption bands in NaCl crystals irradiated with protons, observed coagulation of $F$ centers, as a result of which the concentration of $M$ centers increased.

Consequently, the release of SE in the temperature region from room temperature to 150°C and the peak at a temperature of 130°C are evidently due to the transformation of simple defects into more complex ones, as well as to partial annealing of $R_1$ and $R_2$ centers, whose complete annealing occurs at a temperature of 200–250°C. Heating the crystals above 150°C is accompanied by the destruction of $F$ and $M$ centers. Therefore the rate of SE release, $\dfrac{dQ}{dT}$, begin-

starting from \(t = 130\text{–}150^\circ\mathrm{C}\), increases and becomes constant at a temperature of \(220^\circ\mathrm{C}\), which accounts for the appearance of a peak at \(220^\circ\mathrm{C}\).

Heating the crystal above \(220^\circ\mathrm{C}\) is accompanied by intensive destruction of \(F\)- and \(M\)-centers. The rate of TE emission reaches its maximum value at a temperature of \(270^\circ\mathrm{C}\) and decreases upon further heating. It should be noted that the \(M\)-centers are completely annealed at a lower temperature than the \(F\)-centers. The temperature of complete destruction of the \(M\)-band is \(320\text{–}340^\circ\mathrm{C}\), and that of the \(F\)-band is about \(400^\circ\mathrm{C}\). Complete annealing of the \(F\)- and \(M\)-centers is accompanied by the cessation of TE emission (Fig. 1).

Thus, the annealing of radiation damage in LiF presents a complex picture. A joint study of the TE emission spectra and optical absorption spectra makes it possible to indicate the temperature regions in which annealing of one defect or another occurs. A joint study of TE, microhardness, and optical absorption of LiF crystals makes it possible to confirm assumptions about the type of defects responsible for strengthening. First of all, complex centers (\(R_1\) and \(R_2\)) are not responsible for the microhardness of LiF crystals. Evidence for this assumption is the fact that the concentration of \(R_1\)- and \(R_2\)-centers during annealing first increases and then decreases (Fig. 3), whereas the microhardness decreases (Fig. 5). An intensive change in microhardness is observed at temperatures above \(230^\circ\mathrm{C}\); \(R_1\)- and \(R_2\)-centers are completely annealed up to this temperature.

Preliminary annealing at a temperature of \(230^\circ\mathrm{C}\) of an irradiated LiF crystal is accompanied by a greater change in TE than in microhardness (Fig. 4). If one adheres to the point of view of the authors of [5, 7], who associate the strengthening of alkali-halide crystals under the action of radiation with interstitial halogen atoms, the weak change in the microhardness of LiF in the temperature range up to \(230^\circ\mathrm{C}\) can be explained by the low-intensity return of interstitial fluorine (in LiF, Frenkel defects are formed under the action of radiation) to anion vacancies. This proposition is confirmed by the change in the electrical conductivity of irradiated LiF during annealing (Fig. 6). The decrease in electrical conductivity in the range up to \(230^\circ\mathrm{C}\) is due to a decrease in the number of cation vacancies as a result of their blocking by anion vacancies. In the indicated temperature range, the number of anion vacancies released owing to the destruction of \(F\)-, \(M\)-, and \(R\)-centers exceeds the number of fluorine ions returning from interstitial sites, as a result of which an excess number of free anion vacancies appears; these, in turn, block cation vacancies, thereby lowering the electrical conductivity.

In the temperature range above \(230^\circ\mathrm{C}\), intensive annealing of \(F\)- and \(M\)-centers and of interstitial fluorine occurs, which accounts for the considerable change in TE and microhardness (Fig. 5). An increase in the concentration of free cation vacancies is accompanied, in the temperature range above \(230^\circ\mathrm{C}\), by an intensive increase in the conductivity of the crystal (Fig. 6).

The presence of relaxation maxima in the dependence \(\operatorname{tg}\delta = f(t^\circ\mathrm{C})\) (Fig. 7) is due to the formation of large associations of positive and negative vacancies. The large half-width of these maxima indicates a broad spectrum of relaxation times, caused by the fact that the number of vacancies in the associations is not the same.

From Table 1 it is seen that, with an increase in the dose of preliminary irradiation, the activation energy for the relaxation of these associations decreases, while the activation energy calculated from the slope of the dependence \(\lg\sigma = f\left(\dfrac{1}{T}\right)\) increases.

Strictly speaking, the activation energy calculated from the slope of the dependence $\lg \sigma = f\left(\frac{1}{T}\right)$ in the temperature range from 160 to 260°C is not the energy $U_0$ that is necessary for the transfer of a cation from one equilibrium position to another, but is a more complex quantity. Since in this temperature range an isolated cation vacancy cannot exist, it is necessarily bound either to an impurity ion or to a vacancy of the opposite sign. Therefore, before the cation vacancy begins to participate in the charge-transfer process, it must be separated from the vacancy complex, which requires an additional energy $U_1$. Consequently, the activation energy $U$, determined on the basis of the formula $\sigma = A \cdot e^{\frac{U}{KT}}$, is equal to the sum of these two energies, $U = U_0 + U_1$.

The increase in the activation energy calculated from the slope of $\lg \sigma = f\left(\frac{1}{T}\right)$, and the shift of the relaxation maximum (Table 2) in the dependences $\operatorname{tg}\delta = f(t)$ toward lower temperatures with increasing dose of preliminary irradiation are evidently due to the fact that the number of sites for the formation of vacancy complexes increases and, consequently, a larger number of neutral complexes with a smaller number of vacancies is formed. The smaller the number of vacancies in a complex, the greater the energy of their coupling with one another, $U_1$, and the less energy is required for their relaxation. This assumption is supported by the fact that the maxima in the dependence $\operatorname{tg}\delta = f(t)$ shift toward lower temperatures as the dose increases.

Conclusion

Annealing of radiation-induced defects in LiF crystals is reflected in changes in properties such as microhardness, stored energy, optical absorption, electrical conductivity, and the tangent of the dielectric-loss angle.

At absorbed doses up to $10^6$ rad, the stored energy is formed by $F$-centers. At higher doses, more complex centers, such as $M$- and $R$-centers, begin to contribute to the value of the stored energy.

The stored-energy spectrum and the annealing kinetics of the absorption bands have a complex character, which is due to the complexity of the annealing process of radiation-induced defects.

An intense change in microhardness is observed in the temperature region above 230°C.

The change in electrical conductivity during the annealing of LiF also has a complex character, which is due to the predominance of the annealing of some defects over others in different temperature regions.

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