ELECTRICAL PROPERTIES OF ALKALINE-EARTH METAL FLUORIDES AND THEIR CHANGES UNDER $\gamma$-IRRADIATION

E. K. ZAVADOVSKAYA, V. A. CHERNYSHEV

For one group of ionic crystals, namely the alkali halides, the dependence of their properties on chemical composition has been established, and radiation-induced changes in their properties have been studied. In the present work, the possibility is considered of extending these regularities to other, more complex ionic compounds. To answer the question posed, a series of alkaline-earth metal fluorides was chosen as the material under investigation. These materials, while being representatives of ionic compounds, at the same time differ from alkali-halide crystals in the type of crystal lattice, the greater binding energy of the ions in it, the higher melting temperature, greater chemical stability, etc.

Another equally interesting question is that of radiation-induced changes in the physical properties of these materials; solving it will make it possible to judge whether the established regularities of radiation-induced changes in properties for alkali-halide crystals are common to all ionic compounds, or whether they are valid only for alkali-halide crystals. This is of great practical importance.

Owing to their very interesting physical properties, alkaline-earth metal fluorides are at present finding ever wider application in technology. These materials are used mainly as laser materials, since they most fully meet the requirements imposed on laser systems with a solid working substance. Namely: (a) a sharp fluorescence line; (b) a good quantum yield of fluorescence, i.e., the ratio of photons emitted during fluorescence to the number of photons absorbed in the absorption band; (c) a relatively intense absorption band, by means of which energy can be effectively transferred to the crystal. Very few materials meet all these requirements. Suridii used CaF$_2$ with a 3% manganese addition for fast-neutron dosimetry. He created a dosimetric instrument for which the lower limit of the neutron dose is 150 mrem [1]. Brown and Whiting developed an infrared quantum counter based on CaF$_2$ with an ErF$_2$ impurity [2].

Up to the present time, particularly great attention in the study of these materials has been devoted to optical properties and related

with the electronic processes associated with them. The principal works in this direction belong to Feofilov [3], Smakula [4], Schulman [5], Bontinck [7], Fong [6], Yakom [7], and others. There are very few systematic studies devoted to the investigation of the electrical properties of CaF₂, and, as a rule, they are exploratory in character [8].

We have carried out a study of the dielectric properties of these materials and of their changes under the action of γ-irradiation. γ-irradiation was chosen by us on the basis of the possibility of uniform coloration of the crystals, the simplicity of varying the irradiation dose, and the possibility of obtaining practically any dose values.

These crystals have a higher lattice energy that varies with composition; therefore it is possible to trace the dependence of the physical properties of these materials on their chemical composition. Investigation of the dielectric properties makes it possible to determine the resultant effect of γ-irradiation on these materials. This resultant effect is composed of two mutually opposing processes, namely, the process of defect creation under irradiation and the process of their destruction.

The process of destruction of defects under the action of thermal energy, storage time, and exposure to light, just like the process of creation, can proceed with different intensity in crystals with different lattice energies. If the influence of the prior history of the specimen and of small amounts of impurities does not mask the principal effect of the binding forces of the ions in the lattice, then radiation-induced changes will be substantial in the group of alkaline-earth metal fluorides, and a dependence of the electrical properties on the lattice energy will occur.

The presence of ions of different valence in the crystal lattice of single crystals of alkaline-earth metal fluorides gives rise to a more complex structure than that of the rock-salt lattice, which affects the type of defects in it. Whereas Schottky defects are characteristic of the rock-salt crystal lattice, Frenkel defects are characteristic of the fluorite-type crystal lattice.

The conductivity of ionic compounds, according to modern concepts, is determined entirely by the defectiveness of the crystal lattice.

It has been suggested [8] that in CaF₂ single crystals several mechanisms of electric-charge transport through the crystal are possible. One possible mechanism is transport of electric charge through the motion of weakly bound ions along the boundaries of blocks, mosaic grains, and dislocations. The mobility of an ion located at the boundaries of blocks, mosaic grains, and dislocations is 100 times greater than that of an ion located in the regular lattice [9]. This mechanism is observed at rather low temperatures (up to 100°C) and is characterized by a very low activation energy for the carriers of electric charge (0.26 eV).

A second possible mechanism is the vacancy mechanism, i.e., the motion of charge carriers over vacant sites of the crystal lattice. This mechanism of electric-charge transport is the principal one for single crystals of alkaline-earth metal fluorides, since it is caused by the presence of Frenkel defects in the crystal. But since the mobility of interstitial fluorine ions is small at temperatures up to 600°C [8], the carriers of electric charge are predominantly only anion vacancies. An increase in the number of anion vacancies upon the introduction of monovalent alkali-metal ions into the crystal lattice increases the conductivity of these crystals in this temperature interval.

The presence of interstitial fluorine ions in the crystal lattice

CaF$_2$ can contribute to the development of a third conduction mechanism, which is determined by the motion of an interstitial fluorine ion through the interstices of the crystal lattice. This conduction mechanism develops at sufficiently high temperatures (for CaF$_2$ above 600°C) and is characterized by a high activation energy (about 1.9 eV) [8].

Figure 1 shows the dependence of the logarithm of conductivity on temperature for CaF$_2$ single crystals. At temperatures of 80–90°C a break is observed in the dependence of the logarithm of conductivity on temperature. The activation energies, calculated from the slope of

\[ \lg \sigma = f\left(\frac{1}{T^\circ K}\right), \]

are: up to the temperature of the break point, $-0.26$ eV, and above the temperature of the break point, 1.2 eV. The low activation energy up to the temperature of the break point makes it possible to assume that the conductivity in this temperature interval is due to the motion of weakly bound fluorine ions along the boundaries of blocks, mosaic grains, and dislocations, while above the temperature of the break point this type of conductivity is supplemented by conductivity caused by the motion of fluorine ions through vacant sites of the crystal lattice. The same low-temperature break in the dependence

\[ \lg \sigma = f\left(\frac{1}{T^\circ K}\right) \]

for CaF$_2$ was later obtained by Champion [11].

Fig. 1. Dependence of $\lg \sigma$ on temperature:
1 — for unirradiated CaF$_2$;
2 — for CaF$_2$ irradiated with $\gamma$ rays to a dose of $3.34 \cdot 10^7$ rad.

Preliminary $\gamma$ irradiation of CaF$_2$ single crystals in the dose range from $5.7 \cdot 10^6$ rad to $4.3 \cdot 10^8$ rad increases their conductivity only up to the temperature of the break point (Fig. 1). The activation energies for irradiated and unirradiated CaF$_2$ crystals up to the temperature of the break point do not differ from one another; consequently, the type of current carriers does not change upon irradiation of the crystals, but only their number increases. The ratio $\sigma_{\text{irr}}/\sigma$ in this temperature interval reaches saturation with increasing dose (Fig. 2).

Fig. 2. Dependence of $\sigma_{\text{irr}}/\sigma$ on the dose of $\gamma$ irradiation for CaF$_2$
($t = 70^\circ$C)

Above the temperature of the break point, where the conductivity is mainly due to the motion of the fluorine ion through vacant sites of the crystal lattice, even large absorbed doses of $\gamma$ rays on the order of $4 \cdot 10^8$ rad almost do not change the conductivity of these crystals. Evidently, upon irradiation of CaF$_2$ crystals with $\gamma$ rays, free anion vacancies are not formed according to the Varley mechanism, which occurs upon irradiation of alkali-halide crystals. However, under the action of ionizing radiation, these crystals acquire coloration, which is determined by the appearance in

in the absorption spectra in the range 200–1000 mµ of four absorption bands with maxima at 225, 335, 400, and 580 mµ. The growth curves of the absorption bands tend toward saturation, as shown by the work of Fong and his co-workers [6]. They also showed that in CaF₂ only 5–8% of the rare-earth impurity ions contained in the crystal pass, under the action of γ-radiation, into the divalent state; in this case the compensating interstitial fluorine ions may leave the crystal lattice for the boundaries of blocks, mosaic grains, and dislocations. This circumstance may lead to an increase in conductivity up to the temperature of the break point. We calculated the concentration of trivalent rare-earth ions required for the greatest change in conductivity observed up to the temperature of the break point. For an absorbed dose of \(4.3 \cdot 10^8\) rad, approximately \(10^{14}\) rare-earth ions per cm³ are required, which amounts to \(10^{-6}\)%. Thus, the mechanism described above may take place, since the presence of such a small amount of rare-earth impurities can produce the increase in conductivity that we observed after the action of γ-radiation on CaF₂ crystals.

In the dependence of the dielectric loss tangent on temperature, presented in Fig. 3, for CaF₂ crystals two sharply pronounced regions are observed: the region of relaxation losses and the region of conductivity losses, as also for alkali-halide crystals. The dielectric losses in the low-temperature region are probably connected with the relaxation of weakly bound ions and complex complexes possessing a definite dipole moment. The nature of these complexes has not yet been precisely established, although some authors believe that one of the possible complexes may be the complex \(2\mathrm{Al}^{+++}\) and a vacancy of a divalent-metal ion. But one must not ignore the complex oxygen ion + fluorine-ion vacancy, i.e., a complex analogous to the complex divalent-metal ion + cation vacancy in alkali-halide crystals.

Upon γ-irradiation, the dielectric loss tangent for CaF₂ single crystals in the relaxation temperature region changes with dose in a complicated manner. At small doses, approximately up to \(5 \cdot 10^7\) rad, the dielectric absorption increases, whereas at larger doses, beginning with \(5 \cdot 10^7\) rad, the dielectric absorption decreases. In the temperature region of conductivity losses, the dielectric absorption is entirely determined by the change in the conductivity of these materials with temperature (Fig. 3).

Figure 4 presents the relaxation maxima observed for some CaF₂ crystals after their irradiation with γ-rays; upon heating the given crystal to 400°C, these maxima disappear, and upon repeated irradiation with the same dose the same maxima arise, of the same magnitude and at the same temperatures. There is no doubt that this type of relaxator must be associated with small amounts of impurities present in the material.

Let us consider the possible types of compensation of trivalent rare-earth ions present in these crystals:

1. The excess charge of a trivalent rare-earth ion is compensated by an interstitial fluorine ion [6].

2. Two excess charges of two closely spaced trivalent rare-earth ions are compensated by one calcium-ion vacancy [10].

3. Instead of a monovalent fluorine ion, a divalent oxygen ion enters the lattice. The possibility of such substitution is ensured by the closeness of the ionic radii (1.33 Å and 1.36 Å) [3].

When a trivalent rare-earth ion changes to the divalent state, the first type of compensation cannot give a dipole, since the interstitial ion leaves the crystal lattice and the latter remains, as it were, in its normal position. With the second type of compensation, and upon the transition of even one rare-earth ion from the trivalent state to the divalent one, an anion vacancy must be formed in order to preserve electroneutrality; as a result a pair of vacancies is formed, the relaxation of which may give the maxima observed by us. With

Fig. 3. Dependence of $\operatorname{tg}\delta$ on temperature:
1 — for unirradiated CaF$_2$;
2 — for CaF$_2$ irradiated with $\gamma$ rays at a dose of $6.72\cdot10^6$ rad;
3 — for CaF$_2$ irradiated with $\gamma$ rays at a dose of $10^8$ rad.

Fig. 4. Dependence of $\operatorname{tg}\delta$ on temperature:
1 — for unirradiated CaF$_2$;
2 — for CaF$_2$ irradiated with $\gamma$ rays at a dose of $6.7\cdot10^7$ rad.

the third type of compensation, and upon the transition of a rare-earth ion from the trivalent state to the divalent one, an anion vacancy must be formed in order to preserve electroneutrality, and a complex analogous to the complex consisting of a divalent-metal ion plus a cation vacancy in alkali-halide crystals may be formed.

Thus, we have two equally probable mechanisms for the formation of dipoles upon irradiation of CaF$_2$ single crystals with $\gamma$ rays. Which of them is responsible for the maxima observed by us in the dependences $\operatorname{tg}\delta=f(t^\circ\mathrm{C})$? If it is assumed that the dipole giving the maxima observed by us is the complex oxygen ion plus fluorine-ion vacancy, then such maxima would be observed for all crystals, since the amount of oxygen present in them under the growth conditions is the same. Consequently, the more probable type of dipole is a Ca$^{++}$ ion vacancy plus a fluorine-ion vacancy.

Jackobs [10], who measured the tangent of the dielectric-loss angle in the acoustic frequency range for unirradiated CaF$_2$, found relaxation maxima which, in his opinion, are caused by relaxation of the complex trivalent Al$^{+++}$ ion plus Ca$^{++}$ ion vacancy. This complex is more “heavy,” and it relaxes at higher temperatures, 160–220°C. In order to determine the nature of the change in the electrical characteristics under the action of irradiation, CaF$_2$ crystals were subjected to more powerful neutron irradiation in a reactor. The integral irradiation doses with an unfiltered neutron beam were $3.24\cdot10^{17}$ n/cm$^2$, $6.5\cdot10^{17}$ n/cm$^2$, and $13\cdot10^{17}$ n/cm$^2$.

Preliminary irradiation with fast neutrons somewhat increases the conductivity (Fig. 5) in the temperature range from 20 to 100°C, while in the range from 100 to 380°C a rather substantial decrease in conductivity is observed. Moreover, the slope of the dependence $\lg \sigma = f\left(\dfrac{1}{T^\circ K}\right)$ decreases with increasing dose of preliminary irradiation. The increase in the activation energy for the current carriers indicates more complex processes occurring in the preliminarily irradiated crystal. In the temperature range from 380 to 530°C, intensive annealing of radiation defects takes place. If an analogy is drawn with alkali-halide crystals, it may be assumed that in CaF$_2$ single crystals the decrease in conductivity is associated with the formation, during irradiation, of traps for anion vacancies similar to Smoluchowski traps in alkali-halide crystals for cation vacancies. When anion vacancies are captured by traps, rather large aggregates of vacancies may form. If the process of formation of such aggregates in alkali-halide crystals takes place in the temperature range from 20 to 100°C, then in CaF$_2$ single crystals this process occurs from 90 to 380°C, while their destruction occurs at higher temperatures (about 400°C), which is evidently connected with the higher lattice energy.

Fig. 5. Dependence of $\lg \delta$ on temperature:
1 — for unirradiated CaF$_2$;
2 — for CaF$_2$ irradiated in a reactor with a dose of $13 \cdot 10^{17}$ n/cm$^2$

Some authors [12] associate the decrease in conductivity of CaF$_2$ single crystals containing an oxygen impurity with neutralization of an anion vacancy by an electron, with formation of an $F$-center. But color centers have a definite narrow temperature range in which they are intensively destroyed; consequently, the conductivity of CaF$_2$ crystals should increase abruptly. In actual fact we observed a monotonic increase in the conductivity of the irradiated CaF$_2$ crystal.

The dielectric absorption in the region of relaxation losses decreases somewhat at small doses of neutron irradiation, and increases at large doses. In the region of conduction losses the dielectric absorption of crystals preliminarily irradiated with neutrons is lower than that of unirradiated crystals (Fig. 6).

It should be noted that, for CaF$_2$ single crystals, the character of radiation damage is the same as for alkali-halide crystals, except that to produce the same effect as in alkali-halide crystals considerably larger doses of preliminary irradiation are required, which is evidently connected with the higher energy of the crystal lattice.

For SrF$_2$ single crystals, as for CaF$_2$, in the linear dependence of $\lg \sigma$ on temperature a temperature break is observed at 80–90°C (Fig. 7). If for CaF$_2$ single crystals preliminary irradiation with $\gamma$ rays changes the conductivity only in the temperature range from 20 to 100°C, then for SrF$_2$ crystals preliminary irradiation with $\gamma$ rays causes more complex changes in conductivity as a function of temperature.

At low irradiation doses, in the temperature range from 20 to 80°C, increases in conductivity are observed, while in the temperature range from 80 to 240°C there is a decrease. At higher irradiation doses, in the temperature range from 20 to 80°C there is first an increase and then a decrease, which does not reach the conductivity value of the unirradiated crystal. In the temperature range from 80 to 240°C the decrease is still greater. The ratio $\sigma_{\text{irr}}/\sigma$ with increasing dose of preliminary irradiation, at the temperatures of the greatest change in conductivity, 60 and 130°C, tends toward saturation.

Fig. 6. Dependence of $\operatorname{tg}\delta$ on temperature:
1 — for unirradiated CaF$_2$;
2 — for CaF$_2$ irradiated in a reactor with a dose of $3 \cdot 10^{17}\ \text{n}/\text{cm}^2$;
3 — for CaF$_2$ irradiated in a reactor with a dose of $13 \cdot 10^{17}\ \text{n}/\text{cm}^2$.

For the dependences of the tangent of the dielectric-loss angle for SrF$_2$ single crystals, as also for CaF$_2$ single crystals, two sharply expressed regions are observed: the region of conduction losses and the region of relaxation losses. At low doses of preliminary irradiation with $\gamma$ rays, the dielectric absorption in the relaxation region increases somewhat, while at higher doses it decreases. In the region of conduction losses, the dielectric absorption of preliminarily irradiated SrF$_2$ crystals is completely determined by the change in the conductivity of these crystals. In this region there is also a sharp increase in dielectric absorption at the temperatures where a sharp increase in conductivity occurs.

Fig. 7. Dependence of $\lg \sigma$ on temperature:
1 — for unirradiated SrF$_2$;
2 — for SrF$_2$ irradiated with $\gamma$ rays at a dose of $3 \cdot 10^{6}$ rad;
3 — for SrF$_2$ irradiated with $\gamma$ rays at a dose of $7.5 \cdot 10^{17}$ rad.

It is difficult to give an unambiguous interpretation of the data obtained for SrF$_2$ single crystals. The rather rapid increase in conductivity in the first temperature region for irradiated SrF$_2$ crystals may be caused by two reasons:

1. The lower lattice energy and the larger relative free volume of SrF$_2$ single crystals probably facilitate the formation of free anion vacancies according to the Varley mechanism, which cause the increase in conductivity observed by us. As the temperature increases, their mobility increases and they can be captured by traps of anion vacancies, which leads to a decrease in the number of current carriers and to the formation of neutral complexes. Further incre-

an increase in temperature leads to the destruction of complexes owing to an increase in the kinetic energy of the ions of the crystal lattice. At these same temperatures, where the destruction of these complexes occurs, 130–240°C, a sharp rise of dielectric absorption is observed in the dependences $\operatorname{tg}\delta = f(t^\circ C)$, which may be associated with an increase in the number of charge carriers.

Fig. 8. Dependence of $\operatorname{tg}\delta$ on temperature:
1—for unirradiated $\mathrm{SrF_2}$;
2—for $\mathrm{SrF_2}$ irradiated with $\gamma$-rays at a dose of $4.2 \cdot 10^7$ rad.

1. At the same time, the considerable increase in conductivity in the temperature range from 20 to 80°C may be associated with the destruction of complex color centers, which give an excess of anion vacancies. In this process, not only anion vacancies may play a role, but also electrons released during the destruction of complex color centers.

For $\mathrm{BaF_2}$ single crystals, the radiation-induced changes are analogous to the radiation-induced changes in $\mathrm{SrF_2}$ single crystals. It should be noted that, while absorbed doses of $\gamma$-rays of $3 \cdot 10^7$ rad are not sufficient for $\mathrm{CaF_2}$ and $\mathrm{SrF_2}$ to reduce the dielectric absorption in the relaxation region, for $\mathrm{BaF_2}$ single crystals these doses noticeably reduce the dielectric absorption.

In the temperature region where the assumed complexes are destroyed, a sharp rise in dielectric absorption is also observed in the dependences $\operatorname{tg}\delta = f(t^\circ C)$.

On the basis of the above, the following conclusions may be drawn:

1. For crystals of alkaline-earth metal fluorides, as also for alkali-halide crystals, a regular relationship is observed between the electrophysical properties and the lattice energy.

2. Under isodose irradiation of $\mathrm{CaF_2}$, $\mathrm{SrF_2}$, and $\mathrm{BaF_2}$ single crystals, the degree of radiation damage increases as the energy of the crystal lattice decreases.

3. Preliminary irradiation of $\mathrm{CaF_2}$ single crystals with $\gamma$-rays leads to insignificant changes in $\operatorname{tg}\delta$ and $\sigma$, and only preliminary irradiation with a powerful flux of fast neutrons leads to substantial changes in $\sigma$ and $\operatorname{tg}\delta$.

4. Preliminary irradiation of $\mathrm{SrF_2}$ and $\mathrm{BaF_2}$ single crystals with $\gamma$-rays leads to a noticeable change in the conductivity and $\operatorname{tg}\delta$, which is evidently associated with their lower lattice energy in comparison with $\mathrm{CaF_2}$.

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