STORED ENERGY IN SINGLE CRYSTALS OF ALKALINE EARTH METAL FLUORIDES AFTER EXPOSURE TO VARIOUS TYPES OF RADIATION

A. A. Vorob’ev, E. K. Zavadovskaya, N. M. Timoshenko

In the process of interaction of radiation with a solid, a certain fraction of the radiation energy is irreversibly dissipated. Part of the radiation energy is expended on the formation of defects in the solid; a certain number of these defects remain after irradiation is stopped, thereby increasing the store of potential energy. This energy, called stored energy, represents the total disturbances produced by radiation in the solid. The energy stored in a solid is released when it is heated or dissolved [1].

The total stored energy \(Q\), released from a specimen in the temperature interval between \(T_1\) and \(T_2\), can be determined from the equation

\[ Q = \int_{T_1}^{T_2} C \cdot dT - \int_{t_1}^{t_2} R \cdot dt . \tag{1} \]

The first term on the right-hand side represents the amount of heat accumulated by the specimen in the temperature interval between \(T_1\) and \(T_2\); the second term corresponds to the amount of heat supplied to the specimen during the time \(t_2 - t_1\) at a rate \(R\) cal/sec [2].

\(C\) is the heat capacity of the substance; it is assumed that annealing does not affect the heat capacity.

When irradiated and unirradiated specimens are heated together in the same way up to the temperature \(T_1\), at which the release of stored energy begins, the temperature of the irradiated specimen becomes higher than the temperature of the unirradiated specimen and reaches a maximum approximately at the temperature \(T_2\), at which the release of energy ceases. If the temperature rise occurs rapidly \((t_2 - t_1 \simeq 0)\), then the amount of heat transferred to the specimen from the furnace during this temperature rise,

\[ \int_{t_1}^{t_2} R \cdot dt, \]

is negligibly small, and the quantity \(Q\) can be determined from

\[ Q = \int_{T_1}^{T_2} C dt = \overline{C}(T_2 - T_1). \tag{2} \]

The study of the laws governing energy storage and its magnitude, in conjunction with changes in certain other properties of a solid, makes it possible to obtain valuable information about the nature of the disturbances and their stability [3].

Studies of the energy stored in metals during plastic deformation and irradiation have made it possible to draw conclusions by analogy regarding their action. Information on stored energy in dielectrics pertains mainly to NaCl crystals subjected to radiation [4, 5, 6, 7]. These studies do not reveal regularities in the storage of energy in ionic crystals and may be useful only for a certain evaluation of quantitative results. In addition, the experimental results obtained by various authors are difficult to compare because of differences in research methods and in the prior history of the material studied.

Studies of the magnitude of the stored energy and of its variation with the chemical composition of a compound were carried out by A. V. Kuz’mina [8] for alkali-halide crystals irradiated with $\gamma$ rays. The author established a regularity in the change in the magnitude of the stored energy in the series of alkali-halide crystals: namely, in crystals with greater lattice energy, a greater amount of energy is stored under the action of radiation.

Formulation of the investigations

In our investigations the following questions were considered:

1. Whether the dependence of the magnitude of the stored energy on chemical composition, established for alkali-halide crystals, is preserved for another group of ionic crystals, differing from the alkali halides in lattice type and energy.

2. To establish the character of the change in the magnitude of the stored energy with irradiation dose, and to estimate the fraction of stored energy relative to the radiation energy absorbed by the substance.

3. To determine the action of different types of radiation on the character of radiation-induced disturbances in one and the same material.

The stated problems were solved by studying the stored energy in crystals of the fluorides of alkaline-earth metals CaF$_2$, SrF$_2$, and BaF$_2$, grown by the authors by the Stockbarger method [9] in graphite crucibles in a vacuum of $10^{-4}$ mm Hg.

The crystals were irradiated in the IRT-2000 reactor of the Institute of Nuclear Physics with a mixed flux (fast-neutron flux $nV = 10^{11}$ neutrons/cm$^2$ sec. Thermal-neutron flux $nV = 1.6 \cdot 10^{13}$ neutrons/cm$^2$ sec). Irradiation with $\gamma$ rays was carried out using a “Cobalt-60” source with a ray energy of 1.24 MeV; the source of x-rays was a RUP-200 installation (irradiation conditions: voltage in the dose field with an intensity of 450 R/sec; x-ray tube—200 kV, current—20 mA). The absorbed energy in the case of x-rays and $\gamma$ rays was determined by calculation [10].

The stored energy was measured by the method of differential thermal analysis in a high-temperature vacuum calorimeter [19].

Experimental results

Dependence of stored energy on the chemical composition of the compound

Heating of irradiated crystals is accompanied by annealing of the defects produced by radiation and preserved in the crystal after the cessation of irradiation; in other words, by the release of stored energy.

Figure 1 shows the dependence of the rate of release of stored energy

$$ \frac{dQ}{dT} $$

on temperature for CaF$_2$, SrF$_2$, and BaF$_2$ crystals irradiated with $\gamma$ rays to an absorbed dose of $6.25 \cdot 10^7$ rad. The areas bounded ...

measured along the abscissa axis and by the energy-release-rate curves \(dQ/dT\), constitute the energy stored by the crystal.

As can be seen from Fig. 1, for alkaline-earth metal fluorides there is a dependence of the stored energy on the chemical composition. At the same absorbed energy, in \(\mathrm{CaF_2}\)—a material with a higher lattice energy—more energy is accumulated than in \(\mathrm{BaF_2}\), the material with the lowest lattice energy in the series of fluorides.

This dependence is also preserved in the case of irradiation of the crystals in a reactor. From the dependence of stored energy on the lattice energy of the compound shown in Fig. 2, it follows that, in the case of irradiation in a reactor, there are more radiation defects in \(\mathrm{CaF_2}\) than in \(\mathrm{BaF_2}\).

Stored energy under irradiation with X-rays was measured in \(\mathrm{CaF_2}\) and \(\mathrm{SrF_2}\) crystals. At equal exposure dose of irradiation, a smaller fraction of the X-ray energy is absorbed in \(\mathrm{CaF_2}\) than in \(\mathrm{SrF_2}\); however, the stored energy in \(\mathrm{CaF_2}\) is greater than in \(\mathrm{SrF_2}\), i.e., the dependence of the magnitudes of reversible radiation defects on the lattice energy of the compound is preserved (Table 1).

When irradiating with X-rays, the ratio of stored energy to absorbed energy is of interest. As can be seen from Table 1, even at a smaller absorbed dose, the ratio of stored energy to absorbed energy \((\eta)\) for \(\mathrm{CaF_2}\) is an order of magnitude greater than for \(\mathrm{SrF_2}\). The foregoing gives grounds to suppose that: 1) if, under irradiation with X-rays at the indicated doses, only the formation of radiation defects on structural defects already present before irradiation takes place, then their concentration in \(\mathrm{CaF_2}\) exceeds the concentration in \(\mathrm{SrF_2}\).

Fig. 1. Spectra of release of stored energy in \(\mathrm{CaF_2}\), \(\mathrm{SrF_2}\), and \(\mathrm{BaF_2}\) crystals irradiated with \(\gamma\)-rays (absorbed dose \(6.25 \cdot 10^7\) rad; sample weight: \(\mathrm{CaF_2}\), \(m = 5.136\) g; \(\mathrm{SrF_2}\), \(m = 5.718\) g; \(\mathrm{BaF_2}\), \(m = 7.502\) g).

Fig. 2. Stored energy in crystals of alkaline-earth metal fluorides irradiated in a reactor for 9 hours.

In favor of this supposition are the results of measurements of electrical conductivity [11]. The electrical conductivity (and consequently also the defect concentration) in unirradiated crystals decreases in the fluoride series in going from a compound with a higher lattice energy to a compound with a lower lattice energy;

2) if, however, irradiation at the indicated doses is accompanied by the formation of new defects, then their concentration in \(\mathrm{CaF_2}\) is greater than in \(\mathrm{SrF_2}\). True, it is difficult to imagine that the generation of new defects in \(\mathrm{CaF_2}\) proceeds more vigorously than in \(\mathrm{SrF_2}\), since the binding energy of ions in the re-

Stored energy in crystals of alkaline-earth fluorides after exposure to various types of radiation

Table 1

Note: \(D\) — exposure dose;
\(D_n\) — absorbed dose;
\(Q\) — stored energy;
\(\eta\) — ratio of stored energy to absorbed energy.

is greater for CaF₂ than for SrF₂; therefore this bond is evidently more difficult to disrupt in CaF₂. However, the reverse process—radiation-thermal annealing in CaF₂—should proceed more slowly than in SrF₂ (the relative free volume in CaF₂ is smaller than in SrF₂; therefore diffusion processes will proceed more slowly in CaF₂).

It is possible that the simultaneous presence of both factors (items 1 and 2) ensures a higher concentration of defects in irradiated CaF₂ than in SrF₂, which is manifested not only in the magnitude of the stored energy. Thus, studies of thermoluminescence of CaF₂ and SrF₂ specimens irradiated with x rays indicate that the stored light sum in CaF₂ is several times greater than in SrF₂.

Studies of stored energy on a new group of ionic crystals—alkaline-earth metal fluorides—confirmed the propositions advanced in a number of works [1, 11, 12] concerning the regular relationship between changes in the properties of materials under the action of radiation and the energy of their crystal lattice.

According to these propositions, the physicochemical properties of compounds are determined by their chemical composition and by the binding energy of the ions in the lattice; the same dependence is also retained in the case of changes in the properties of materials under the action of radiation. The authors [1, 11, 12] assume that in crystals with a higher lattice energy more defects are retained after irradiation and, consequently, the change in properties will be more substantial than in crystals with weak bonding of the ions in the lattice.

Our studies have shown that under the action of various types of radiation—x rays, γ rays, and reactor irradiation—in the series of alkaline-earth metal fluorides the greatest energy is stored in CaF₂, less in SrF₂, and still less in BaF₂.

It may be assumed that, after the cessation of irradiation, more defects are retained in the more stable compound—CaF₂—than in the less stable one—BaF₂.

Kinetics of stored energy under irradiation

The change in the magnitude of stored energy upon irradiation with different doses makes it possible to judge the behavior of the material in a radiation field, which is of definite theoretical and practical interest.

The dependence of stored energy in CaF₂, SrF₂, and BaF₂ crystals on dose was investigated by us for γ radiation.

As can be seen from Fig. 3, over the entire range of doses studied the stored energy in CaF₂ exceeds the stored energy in SrF₂ and, still more, in BaF₂; that is, the dependence on the lattice energy of the compound considered above is retained. The kinetics of stored energy as a function of absorbed dose has the same form for all three compositions: a rapid increase in stored energy at the beginning of irradiation up to doses of \(3 \cdot 10^8\) rad, and saturation at higher doses.

In CaF₂ there is a slow, almost linear increase in stored energy at doses above \(3 \cdot 10^8\) rad. The magnitude of the stored energy in CaF₂ at the maximum irradiation dose of \(8.7 \cdot 10^8\) rad (\(10^9\) roentgens) is 12 J/g.

It may be assumed that the increase in stored energy with dose is due to the predominance of the defect-generation process over radiation-thermal annealing. The tendency of the stored energy toward saturation in SrF₂ and BaF₂ is apparently due to the establishment of equilibrium between these two processes. For CaF₂, no saturation of the stored energy is observed, possibly because, in the investigated range of absorbed doses, the process of defect generation predominates over the process of radiation-thermal annealing.

The kinetics of the change in stored energy with increasing absorbed energy makes it possible to determine the fraction of stored energy in the absorbed energy and its variation with irradiation dose. From the dose dependence of the ratio of stored energy to absorbed energy shown in Fig. 4, it follows that, for the same absorbed dose, the percentage of stored energy is greater for

Fig. 3. Dependence of the stored energy in alkaline-earth metal fluorides on the absorbed dose under irradiation with γ-rays

Fig. 4. Dependence of the ratio of stored energy to absorbed energy on the absorbed dose of γ-radiation

CaF$_2$ and smaller for BaF$_2$ (see also Table 1), i.e., CaF$_2$ is a more effective accumulator of radiation energy.

With increasing absorbed dose, the stored energy increases, but the ratio of the stored energy to the absorbed energy ($\eta$) decreases. Figuratively speaking, as the irradiation dose increases, the efficiency of energy storage, or the coefficient of performance of energy accumulation by the crystal, decreases.

If $\eta$ for SrF$_2$ and BaF$_2$ changes only weakly with irradiation dose, then for CaF$_2$ the dependence of $\eta$ on irradiation dose approaches an exponential in character. CaF$_2$ is a more effective accumulator of energy at small absorbed doses (Table 1).

At small absorbed doses, $\eta$ for CaF$_2$ amounts to several percent, whereas for SrF$_2$ it is almost an order of magnitude smaller. At large absorbed doses, the stored energy amounts, for CaF$_2$ and SrF$_2$, to tenths of a percent, and for BaF$_2$ even hundredths of a percent of the energy absorbed by the crystal.

The large value of $\eta$ for small absorbed doses can evidently be explained as follows. As is known, in a real crystal there is always a certain number of defects; therefore, at small absorbed doses, defect formation under the action of radiation will occur primarily at structural imperfections already present in the crystal before irradiation. This includes, for example, the formation of color centers at vacancies present in the crystal, and the formation of vacancies at various structural imperfections [13]. These processes occur with small energy expenditures.

Further irradiation is accompanied by the formation of defects at the expense of disruption of the structure of the substance itself, which evidently requires greater expenditures of radiation energy; moreover, with increasing irradiation dose the concentration of defects increases, which in turn leads to enhancement of radiation-thermal annealing, whose contribution in the initial stage of irradiation is apparently insignificant.

Effect of Various Types of Radiation on the Stability of Defects in Crystals of CaF₂, SrF₂, and BaF₂

The spectra of the release of stored energy can serve as a characteristic of defects produced by irradiation.

As can be seen from Fig. 1, in the spectra of stored-energy release in fluoride crystals irradiated with γ-rays, four peaks are observed, corresponding either to four different types of defects or, at least, to one and the same type of defect in its different energy states. For alkaline-earth fluorides this question remains open up to the present time. The identical number of peaks in the spectra of all three crystals indicates that in materials with the same structure, analogous defects are formed under the action of radiation.

The maxima of the stored-energy release peaks in SrF₂ and BaF₂ coincide and occur at temperatures of 120°C, 200°C, 280°C, and 400°C. The maxima of three peaks of stored-energy release in CaF₂ are shifted into the region of higher temperatures than in SrF₂ and BaF₂, and occur at temperatures of 220°C, 360°C, and 520°C. This makes it possible to assume that the defects in CaF₂ induced by γ-irradiation are thermally more stable than in SrF₂ and BaF₂. This assumption is also supported by the fact that the release of stored energy, and consequently the annealing of defects in SrF₂ and BaF₂ irradiated with the indicated dose, ceases upon heating to 520°C, whereas in CaF₂ it ceases only upon heating above 600°C.

In the spectra of stored-energy release of CaF₂ and SrF₂ crystals irradiated with X-rays, only three peaks are observed: in CaF₂ with maxima at temperatures of 120–130°C, 220°C, and 310°C; in SrF₂, respectively, 100–130°C, 200°C, and 280°C (Figs. 5 and 6). Upon irradiation

Fig. 5. Spectrum of stored-energy release in a CaF₂ crystal irradiated with X-rays (absorbed dose \(6.6 \cdot 10^6\) rad, \(m = 4.07\) g)

Fig. 6. Spectrum of stored-energy release in an SrF₂ crystal irradiated with X-rays (absorbed dose \(3 \cdot 10^7\) rad, \(m = 3.65\) g)

with X-rays, the dependence of the thermal stability of defects on the chemical composition of the compound is also preserved.

Comparing the spectra of stored-energy release of CaF₂ and SrF₂ crystals irradiated with X-rays and γ-rays, one may conclude that the peaks in the low-temperature region (up to 300°C) have maxima at the same temperatures; under the action of electromagnetic radiation, analogous defects are formed in this region.

In the temperature region above 300°C, in SrF₂ irradiated with X-rays, there is no peak at a temperature of 400°C, while in CaF₂ the peak at

520°C. The intense peak at a temperature of 360°C in CaF$_2$ irradiated with $\gamma$ rays is weakly intense and has a maximum at 310°C under irradiation with X-rays. It should be noted that the peaks in the temperature region up to 220°C have approximately the same intensity in crystals of one and the same composition irradiated with the indicated types of radiation.

The results presented above can be explained as follows. Under irradiation with X-rays (the absorbed dose is small), the contribution to the stored energy is made by defects produced by the radiation at structural disturbances already present in the crystal before irradiation. Since these defects are formed with minimal energy expenditures, their destruction also occurs easily. These defects, apparently, also determine the peaks in the stored energy at temperatures up to 220°C.

The structural disturbances produced by irradiation with X-rays are evidently insignificant, which accounts for the weak peaks in the stored energy in CaF$_2$ at a temperature of 310°C and in SrF$_2$ at 280°C, and for the absence of peaks in the high-temperature region. Irradiation with $\gamma$ rays (larger absorbed doses), however, is accompanied by disturbances of the structure of the substance and by the appearance, apparently, of new defects; this is manifested in CaF$_2$ by the appearance of a peak at a temperature of 520°C and of a strong peak at 360°C. In SrF$_2$ two peaks also appear: at temperatures of 380–400°C and 500°C (Fig. 7, curves 1 and 3). The results of Fong’s work [14] on the optical absorption of CaF$_2$ irradiated with $\gamma$ rays, as well as our studies of the radiolysis of fluoride powders, support this supposition.

It is of interest to trace the change in peak intensity with irradiation dose, which we shall do using SrF$_2$ as an example. Comparing Figs. 6 and 7, we note that in SrF$_2$ irradiated with X-rays the peaks at temperatures of 100–130°C and 200°C are the most intense. In SrF$_2$ irradiated with $\gamma$ rays (Fig. 7, curves 1 and 3), the intensity of these peaks changes almost not at all (the discrepancy between peak intensities in the figures is due to the difference in the weight of the specimens studied). If the peak at a temperature of 280°C in SrF$_2$ irradiated with X-rays is weak, then in the specimen irradiated with $\gamma$ rays it begins to grow and also reaches saturation: the intensity of the peak at absorbed doses of $6.25 \cdot 10^7$ and $1 \cdot 10^9$ rad is almost the same (Fig. 7, curves 1 and 3).

Fig. 7. Spectra of release of stored energy in SrF$_2$ crystals irradiated with $\gamma$ rays and in a reactor:
1 — irradiation with $\gamma$ rays, absorbed dose $6.25 \cdot 10^7$ rad, $m = 5.7189$ g;
2 — irradiation in a reactor for 9 h, $m = 6.692$ g;
3 — irradiation with $\gamma$ rays, absorbed dose $1 \cdot 10^9$ rad, $m = 5.718$ g.

The peak at a temperature of 400°C, which is absent in SrF$_2$ irradiated with X-rays, appears in the specimen irradiated with $\gamma$ rays to a dose of $6.25 \cdot 10^7$ rad (its intensity is somewhat less than the intensity of the peak at a temperature of 280°C) and continues to grow under further irradiation. If in SrF$_2$ irradiated with $\gamma$ rays (absorbed dose $6.25 \cdot 10^7$ rad) there is no peak at a temperature of 500°C, then in the specimen irradiated to an absorbed dose of $1 \cdot 10^9$ rad this peak reaches a considerable magnitude.

Thus, in the stored-energy spectrum of an SrF$_2$ crystal irradiated with electromagnetic radiation (X-rays and $\gamma$ rays), as the absorbed dose increases, new peaks appear, and each newly appearing-

ing peak has a higher temperature than the preceding peaks. An analogous phenomenon is also observed for CaF₂. It may be assumed that in alkaline-earth fluorides, as the absorbed dose increases, some defects are transformed into others that are thermally more stable.

To elucidate the influence of corpuscular radiation on the spectra of release of stored energy, investigations were carried out on CaF₂, SrF₂, and BaF₂ samples irradiated in a reactor.

In one of our works [10] it was established that the optical-absorption spectra of CaF₂ crystals irradiated with x rays and with protons are similar. In the optical-absorption spectra of CaF₂ crystals irradiated with γ rays and in a reactor, in the wavelength region from 220 to 1100 mμ, as in crystals irradiated with x rays and protons, four absorption bands are observed, with maxima at 225, 335, 400, and 580 mμ. Such an analogy in the optical-absorption spectra of CaF₂ crystals irradiated with different types of radiation makes it possible to suggest an analogy of the radiation-induced disturbances. This suggestion is also supported by studies of the spectra of release of stored energy, the results of which are given in Fig. 8.

The regular difference in the areas bounded by the curves \(dQ/dT\) for the crystals investigated indicates the existence, for irradiation in a reactor, of a dependence of the magnitude of the stored energy on the chemical composition of the compound.

In the spectra of release of stored energy, five peaks are observed for each material. In going from BaF₂ to CaF₂, i.e., as the lattice energy of the compound increases, the maxima of the peaks shift toward higher temperatures (see Fig. 8 and Table 2). This circumstance indicates that the defects produced by irradiation in a reactor are thermally more stable in the material with the higher lattice energy, CaF₂; i.e., an analogy is observed in the properties of the defects, as in the case of x and γ irradiation.

Table 2

Temperatures of the maxima of the peaks of stored-energy release in CaF₂, SrF₂, and BaF₂ crystals irradiated with different types of radiation

In the optical-absorption spectra of CaF₂ and SrF₂ crystals, shown in Fig. 9, four absorption bands are observed with maxima that, in CaF₂, occur at wavelengths of 225, 335, 400, and 580 mμ, and in SrF₂ at 330, 400, 500, and 630 mμ.

The analogy in the optical-absorption spectra and in the spectra of release of stored energy of crystals irradiated in a reactor confirms the assumption of an analogy of the defects in alkaline-earth metal fluorides induced by a particular type of radiation. Even from the optical-absorption spectra of CaF₂ and SrF₂ irradiated in a reactor, it follows that, under equal irradiation conditions, the defect concentration in CaF₂ is considerably greater than in SrF₂, which is also manifested in the magnitude of the sto-

stored energy (we judge the concentration of defects by the intensity of the absorption bands).

Comparing the spectra of stored-energy release in crystals of CaF$_2$, SrF$_2$, and BaF$_2$ irradiated with $\gamma$ rays and in a reactor (Figs. 1, 7, 8, Table 2), one can judge the similarity of the defects produced by the various types of radiation. Thus, for example, for SrF$_2$ the maxima of the peaks of stored-energy release correspond to the same temperatures (Fig. 7, Table 2). The same is true for the BaF$_2$ crystal, with the only difference that, under reactor irradiation, a weak peak is observed at a temperature of 50°C, which is not observed in the case of irradiation of crystals with $\gamma$ rays.

Fig. 8. Spectra of stored-energy release in crystals of CaF$_2$, SrF$_2$, and BaF$_2$ irradiated in a reactor for 9 hours. (CaF$_2$, $m = 5.136$ g; SrF$_2$, $m = 5.718$ g; BaF$_2$, $m = 7.502$ g)

Fig. 9. Optical absorption spectra of CaF$_2$ and SrF$_2$ crystals irradiated in a reactor

The peak at a temperature of 300°C, observed for CaF$_2$ irradiated in a reactor, is absent in the $\gamma$-irradiated sample, but is observed for x rays (Table 2). It should be noted that, whereas for SrF$_2$ and BaF$_2$ the temperatures of the peak maxima coincide under irradiation with $\gamma$ rays and in the reactor, in CaF$_2$ under reactor irradiation the peaks in the temperature interval up to 400°C are shifted toward higher temperatures than in the case of $\gamma$-ray irradiation (Table 2).

An analogous phenomenon is observed for CaF$_2$ crystals in the thermoluminescence curves (Fig. 11). As is seen from Fig. 11, the maxima of the thermoluminescence peaks for CaF$_2$ irradiated in a reactor are shifted toward higher temperatures than for CaF$_2$ irradiated with $\gamma$ rays. At the same time, an analogy is observed not only in the number of peaks but also in the ratio of their intensities for CaF$_2$ irradiated with $\gamma$ rays and in a reactor, which testifies to the similarity of the action of these types of radiation.

It is not yet possible to explain this shift of the peaks, but it is quite possible that, for CaF$_2$, reactor irradiation introduces some specificity in comparison with irradiation of SrF$_2$ and BaF$_2$. Thus, for example, we have observed that CaF$_2$ crystals irradiated in a reactor possess stronger induced activity than SrF$_2$ and BaF$_2$ crystals.

As is known, in the case of reactor irradiation it is very difficult to carry out dosimetry of the radiation. For these purposes it is quite expedient to use the calorimetric method. Knowing the dependence of the stored energy on the absorbed dose of $\gamma$ radiation (Fig. 3), one can determine, from the magnitude of the stored energy released from a crystal irradiated in a reactor, what absorbed dose this material received in the reactor. Here we proceed from the assumption that irradiation with $\gamma$ rays and in a reactor is analogous, equivalent. Thus, for CaF$_2$ irradiated in a reactor for

9 h, the stored energy is 6.5 J/g. In the case of $\gamma$-irradiation this corresponds to an absorbed dose of $4.8 \cdot 10^7$ rad. It may evidently be assumed, with a certain approximation (since the radiation intensities are different), that at the site of irradiation of CaF$_2$ in the reactor the dose rate of irradiation corresponds to 1700 r/sec.

What has been said above is only a recommendation that broadens the possibilities of calorimetric studies of stored energy for dosimetric purposes, and it requires detailed and careful verification and elaboration.

On the nature of the defects responsible for the stored energy in CaF$_2$, SrF$_2$, and BaF$_2$ crystals

The presence of particular defects in a solid can be determined from a change in some property. For the fluorides of the alkaline-earth metals, the optical properties have been studied in the greatest detail. However, these studies do not allow the authors to draw unambiguous conclusions about the nature of the defects. Thus, for example, the difference noted by Lisitsyna [15] in the kinetics of growth of the absorption bands of CaF$_2$ crystals irradiated with protons permits the assumption that the defects responsible for the absorption bands at 225, 335, and 400 mµ are different in nature from the defects responsible for the absorption band at 560 mµ.

Other authors [16] attribute to all four absorption bands observed in the wavelength region 220–1000 mµ one and the same type of defect.

Studies of stored energy, in combination with other studies carried out by us (optical absorption, thermobleaching), make it possible to state certain assumptions concerning the nature of the defects responsible for the stored energy.

In the works of Golovchanskii et al. [20] it is suggested that color centers (F, M-centers and more complex centers) are responsible for the stored energy in alkali-halide crystals irradiated with protons. It is of interest to establish whether this proposition is also valid for the fluorides of the alkaline-earth metals.

For this purpose, from the absorption spectrum of a CaF$_2$ crystal irradiated with $\gamma$-rays (Fig. 10), the concentration of color centers responsible for absorption in the wavelength region 220–1100 mµ was calculated (Table 3). The calculation was made using Smakula’s formula [17], which, under the assumption that the oscillator strength for CaF$_2$ is equal to 1 for all absorption bands, takes the form

Table 3

\[ N = 1.06 \cdot 10^{16} k w, \tag{18} \]

where $k$ is the absorption coefficient at the band maximum (cm$^{-1}$);
$w$ is its half-width (eV).

The total concentration of color centers is \(3 \cdot 10^{17}\ \mathrm{cm}^{-3}\). The stored energy for this case is \(2 \cdot 10^{19}\ \mathrm{eV}\). If simple centers (of the type of \(F\)-centers in alkali-halide crystals) are considered responsible for the stored energy in \(\mathrm{CaF}_2\) crystals, then their concentration, for the case indicated, should be on the order of \(1.5 \cdot 10^{18}\ \mathrm{cm}^{-3}\) (assuming that the energy of such a center does not exceed the band-gap width of \(\mathrm{CaF}_2\), \(\Delta = 13.5\ \mathrm{eV}\)).

As we see, the concentrations of color centers determined by the optical method and by an approximate calculation from the magnitude of the stored energy do not coincide. This circumstance permits the following assumptions to be made:

1. In alkaline-earth fluoride crystals, not only simple but also complex color centers (possibly coagulates of simple centers) are responsible for the stored energy.

2. Not only defects determined by the optical method in the wavelength interval \(220\)—\(1100\ \mathrm{m\mu}\) are responsible for the stored energy. In support of this assumption are the data of L. A. Lisitsyna, according to which in the optical absorption spectrum of \(\mathrm{CaF}_2\) crystals irradiated with protons, in addition to the “traditional” bands with maxima at 225, 335, 400, and \(560\ \mathrm{m\mu}\), two new bands are observed in the far ultraviolet region of the spectrum, with maxima at \(193\ \mathrm{m\mu}\) (\(6.4\ \mathrm{eV}\)) and \(187\ \mathrm{m\mu}\) (\(6.7\ \mathrm{eV}\)). The author also found that, at large irradiation doses (beginning with \(10^{15}\ \mathrm{protons}/\mathrm{cm}^2\)), an additional band appears with a maximum at \(800\ \mathrm{m\mu}\). The appearance of this band was also observed by Fong [14] in \(\gamma\)-irradiated \(\mathrm{CaF}_2\) crystals.

Obviously, the defects responsible for the indicated bands also make a certain contribution to the total amount of stored energy.

A joint study of stored energy, optical absorption, and thermoluminescence allowed us to answer the question: are electron-hole defects responsible for the stored energy, or are some other additional defects also involved?

First of all, measurement of the optical absorption spectra during thermal annealing of \(\gamma\)-irradiated \(\mathrm{CaF}_2\) indicates that, in the temperature region up to \(360^\circ\mathrm{C}\), a decrease in the intensity of the absorption bands is observed (Fig. 10). At the same time, no preferential change in the intensity of any one of the four bands is observed; the intensities of the bands decrease uniformly; in the indicated temperature region their annealing is complete.

Fig. 10. Change in the optical absorption spectra of \(\mathrm{CaF}_2\) crystals irradiated with \(\gamma\)-rays during thermal annealing.

Fig. 11. Thermoluminescence curves of \(\mathrm{CaF}_2\) crystals irradiated with \(\gamma\)-rays and in a reactor \((g = 5^\circ\mathrm{C}/\mathrm{min})\).

When irradiated CaF₂ crystals are heated, four peaks are found on the thermoluminescence curve in the temperature region from room temperature to 300–360°C (Fig. 11, curve 2). Since the thermoluminescence of crystals is due to the destruction of electron–hole centers, it may be assumed that electron and hole centers in CaF₂ crystals are responsible for the absorption bands at 225, 335, 400, and 560 mμ.

Heating CaF₂ crystals in the temperature region 360–550°C is not accompanied by luminescence. This gives grounds to suppose that other defects, but not of the electron–hole type, are responsible for the peaks of stored-energy release at temperatures of 360°C and 520°C in CaF₂ crystals. It is possible that, in the indicated temperature region, defects responsible for optical absorption at wavelengths of 193 mμ and 187 mμ, whose nature has not been clarified, are annealed.

The observed intense gas evolution upon heating CaF₂ powder irradiated with γ rays in the temperature region around 360°C makes it possible to assume that in this temperature region and above, annealing evidently occurs of more complex disturbances of the CaF₂ structure than electron–hole centers.

Conclusions

1. Using ionic crystals—fluorides of alkaline-earth metals—as an example, the dependence, established for alkali-halide crystals, of changes in properties under the action of radiation on the chemical composition of the compounds has been confirmed. Stored energy was chosen as the characteristic of the change in properties under the action of radiation.

2. Stored energy characterizes the stability of radiation defects in ionic crystals of different composition and is a characteristic of the total radiation defects retained in the crystal after exposure to radiation.

3. For alkaline-earth fluorides irradiated with x rays, γ rays, and in a reactor, a decrease in stored energy is observed in the transition from the material with the greatest lattice energy, CaF₂, to the material with the lowest lattice energy, BaF₂.

4. The spectra of stored-energy release of CaF₂, SrF₂, and BaF₂ crystals irradiated with γ rays and in a reactor are analogous, which gives grounds to speak also of the analogous nature of the defects created by kinds of radiation that differ in nature.

5. The maxima of the stored-energy release peaks in CaF₂ are shifted to the region of higher temperatures than in SrF₂ and BaF₂, which makes it possible to assume a greater stability of the defects induced by radiation in CaF₂—a material with a higher lattice energy.

6. The kinetics of stored energy as a function of radiation dose has two stages. Under γ irradiation in the interval of absorbed doses up to \(3 \cdot 10^{8}\) rad, intense storage of energy is observed. Further irradiation is accompanied by a tendency of the stored energy in SrF₂ and BaF₂ toward saturation; in CaF₂, saturation of the stored energy is not observed.

7. The dependence of stored energy on absorbed dose makes it possible to use the calorimetric method for dosimetry.

8. Using SrF₂ as an example, it has been shown that, with increasing absorbed dose, new peaks appear in the stored-energy spectrum, apparently due to the appearance of new defects.

9. Among the alkaline-earth fluorides, CaF₂ is the most effective accumulator of radiation energy. The most effective storage of energy is observed at small absorbed doses (x-

X-rays). As the radiation dose increases, the percentage of stored energy relative to the absorbed energy decreases. Under irradiation with $\gamma$-rays, the energy stored as a fraction of the energy absorbed by the crystal ranges from hundredths of a percent for $\mathrm{BaF_2}$ to several percent for $\mathrm{CaF_2}$.

1. The contribution to the stored energy in $\mathrm{CaF_2}$ is made not only by the defects responsible for optical absorption at the given wavelengths 225, 335, 400, and 560 m$\mu$. The defects responsible for these absorption bands are of electron-hole character and account for the stored energy in the temperature range from room temperature to 300–330°C.

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