RADIATION DEFECTS IN IONIC CRYSTALS

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

§1. Introduction

In the branch of solid-state physics devoted to the study of crystal imperfection, various methods of energetic action on a material are widely used. In addition to such types of action as heat treatment, plastic deformation, and the introduction of various kinds of impurities, irradiation can be employed, producing a dosed number of defects in a solid and studying their behavior. The investigation of radiation-induced imperfection is necessary for the development of the theory of the real crystal and is of great practical interest in connection with the application of atomic energy.

Intense changes in the physicochemical properties of solids under irradiation make it possible to develop technological processes for obtaining materials with specified characteristics. Radiation technology is being developed on the basis of the laws of the physics and chemistry of solids.

Under the action of irradiation by fast particles and $\gamma$-quanta, radiation defects arise in solids, leading to changes in the properties of materials.

Dielectric and metallic crystals have different sensitivities to the action of radiation.

In metals, disturbances associated with ionization of atoms and changes in electronic states rapidly disappear due to radiationless transitions that lead to the transfer of radiation energy to the crystal lattice. Stable radiation defects arise in metals only through the direct transfer of energy to lattice sites, sufficient to move an atom into an interstitial position. The energy of ionizing radiations in metals is spent only to a small degree on defect formation.

Dielectrics, and in particular ionic crystals, are characterized by the relative ease of generation of irradiation defects and by their great variety. For many dielectrics, the threshold energy of particles and quanta leading to the formation of defects amounts to several electronvolts.

An example is the long-known fact of the creation of F-centers in alkali-halide crystals under ultraviolet irradiation [1].

These circumstances led Seitz to the conclusion that the formation of radiation defects in ionic structures under the action of ioniz-

...ionizing radiation proceeds in a substantially different manner than in metals.

If in metals the displacement of atoms from lattice sites is achieved by elastic collision with the bombarding particle, then in LiF crystals irradiated with a beam of \(10^{14}\) protons with an energy of 7 MeV, the number of displacements due to elastic collisions is \(6.2 \cdot 10^{16}\ \mathrm{cm}^{-3}\). This value should be taken as an upper limit, without allowing for radiation annealing of defects [2].

Since in alkali-halide crystals after their irradiation with protons of energy \((4—7)\) MeV the density of F centers reaches \(10^{18}—10^{19}\ \mathrm{cm}^{-3}\), the role of direct displacements in radiation defect formation may be neglected.

Unlike in metals, in ionic crystals the mechanisms of formation of radiation defects by electronic excitation predominate.

Electronic excitations in dielectrics are divided into two classes:

1. Stable excitations—excitons and electron-hole pairs. Their lifetime, amounting to nanoseconds, is sufficient for them, upon interaction with lattice defects, to form stable defects.

2. Unstable electronic excitations. There are very many varieties of them. They are of low stability and, before interacting with lattice defects, decay into stable electronic excitations.

Radiation effects in ionic crystals are due to a superposition of elementary processes, the number of which increases sharply as the structure becomes more complex. Since the materials used in practice are, as a rule, multicomponent systems, the interpretation of experimental results for them is considerably complicated. Therefore, the solution of nodal problems of radiation physics is most promisingly carried out on “model” crystals. Such substances, in the case of covalent semiconductors, are germanium and silicon, and for the class of ionic dielectrics—alkali-halide compounds. Subsequently, the principal conclusions and aspects of the theory are supplemented and refined in the study of materials having direct practical application.

It is precisely in this direction that research in radiation physics is being conducted by leading groups in the Soviet Union and abroad.

In the radiation physics of ionic structures, three closely related directions may be distinguished:

a) investigation of the microstructure of radiation damage and the kinetics of its accumulation and annealing;

b) study of the mechanisms of generation of irradiation defects;

c) the influence of radiation defects on the properties of materials.

There is a large number of works in the literature on the influence of radiation on the optical, electrical, mechanical, and thermal properties of ionic structures. In some cases, regularities in the behavior of radiation defects obtained on one crystal are extended to all compounds of a given class. Such generalizations may not always prove correct, since cases are not excluded in which the observed effect is typical only of the crystal under study.

The processes of radiation defect formation are more productively studied using homologous series of crystals as examples. In this case the hypotheses advanced can be interpreted with greater reliability.

In addition, the study of radiation defects in crystals of different chemical composition makes it possible to determine the most general regularities of radiation-induced disruption of ionic structures, which can be used in developing materials with specified properties.

At the Tomsk Polytechnic Institute, systematic studies of radiation defects in ionic crystals of various chemical composition have been carried out for many years. These studies are based on the idea of a relationship between the radiation resistance of ionic structures and the chemical composition of the compound, conveniently expressed through the energy of the crystal lattice. This proposition is fundamental to the presentation of the material in this article.

Radiation defects in ionic crystals are considered using as examples alkali-halide crystals and compounds with a fluorite-type lattice, since at present the results of studies of radiation damage in other ionic structures are not numerous and cannot yet be systematized and presented in the form of scientific generalizations.

§2. Stored Energy in Alkali-Halide Crystals

The energy of radiation absorbed in a crystal is partially expended in the formation of lattice defects. The latter strongly alter the macroscopic properties of the material: its density, viscosity, hardness, optical density, electrical conductivity, dielectric losses, various types of strength, thermal conductivity, and so on. Comprehensive studies of the properties of irradiated crystals provide rich information on the structure and on the processes by which radiation damage is generated.

It is known that, when a crystal is irradiated, its energy balance changes by the amount of the total energy of formation of all possible defects.

The magnitude of the radiation energy stored in a crystal is an integral characteristic of the degree of radiation defectiveness and can be determined by calorimetric methods during dissolution or thermal annealing of the irradiated crystal.

Calorimetric installations constructed at TPI made it possible to study the laws of energy storage of \(\gamma\)-quanta and protons in ionic crystals of various chemical composition [3—8].

The stored energy has been determined in alkali-halide crystals and in a number of solid solutions, in crystals of compounds of metals of the second group, and in glasses.

In the crystals studied, the values of the stored energy are higher in compounds with higher lattice energy.

For NaCl and KCl crystals, the stored energy is released in two stages: \((20—150)^\circ\mathrm{C}\) and \((200—400)^\circ\mathrm{C}\). The low-temperature maximum, in contrast to the high-temperature one, increases with increasing irradiation dose.

For many ionic crystals, the laws of energy storage after irradiation with protons of energy \(4.5\) MeV at room temperature have been studied [7].

The integral proton flux was varied within the range \((1.2 \cdot 10^{13}—9 \cdot 10^{14})\) \(pr/\mathrm{cm}^2\). It was established that the dependence of the stored energy on the absorbed energy has the same character as under \(\gamma\)-irradiation; that is, a larger amount of energy is stored in crystals with higher lattice energy.

For crystals of the potassium series, two stages of accumulation of stored energy are observed: a rapid growth of the stored energy in the first stage of irradiation, and then a slow linear growth or saturation for KJ crystals (Fig. 1).

Fig. 1. Dependence of stored energy on the irradiation dose for crystals of the potassium series

In solid solutions of alkali-halide compounds, as compared with their components, owing to the weakened bonding forces between ions and the lower stability of radiation defects, the stored energy is smaller. The magnitude of the stored energy in solid solutions increases linearly with increasing irradiation dose. This experimental fact may find application for dosimetric purposes.

A comparison of the kinetics of accumulation and annealing of color centers and of stored energy in alkali-halide crystals, as well as quantitative calculations, indicates that in the region of small and medium irradiation doses up to \((10^{10}—10^{11})\) erg/cm\(^3\), the radiation energy is stored mainly in the formation of color centers. Under these conditions the role of radiation-chemical transformations is insignificant.

Consequently, in alkali-halide crystals the most abundant radiation defects are the various color centers.

§ 3. Models of color centers in alkali-halide crystals

In ionic crystals, glasses, and many organic materials, selective coloration arises under the action of ionizing radiation. The coloration of a material is explained by the fact that point defects created by radiation cause selective absorption of light. The various types of radiation defects give rise to absorption bands in the spectral region lying between the edges of intrinsic absorption in the ultraviolet and infrared wavelength ranges.

Fig. 2. Schematic spectrum of optical absorption of alkali-halide crystals.

Figure 2 schematically shows the positions of the optical-absorption bands in a KBr crystal after its irradiation at room temperature or at very low temperature. A pure, defect-free KBr crystal has absorption in the ultraviolet and infrared regions of the spectrum. At the edge of the intrinsic, fundamental absorption in the ultraviolet region of the spectrum (A) there are two peaks caused by exciton excitation. They are located at an energy of about 10 eV. In the infrared region, at photon energies close to \(10^{-2}\) eV, there is an absorption band (B) caused by optical vibrations of lattice ions.

The region lying between the indicated edges of the absorption bands is transparent to fluxes of electromagnetic radiation. After irradiation, absorption bands appear in the absorption spectra of ionic crystals; among them the most intense is the \(F\)-band.

On the short-wavelength side of the \(F\)-band lie the \(K\) and \(L\) bands, 1, 2, 3, which represent transitions to the outer excited levels of the electron in the \(F\)-center. Next the hole \(V\)- and \(H\)-color centers manifest themselves. On the long-wavelength side of the \(F\)-band lie absorption bands due to complex electronic color centers (\(M\)-, \(R\)-, \(N\)-centers).

Similar optical-absorption spectra are characteristic of all alkali-halide crystals. All absorption bands of the same type shift into the region of shorter wavelengths on going to crystals with a higher lattice energy.

At present a great variety of color centers in alkali-metal halides is known. Conventionally, these defects may be divided into electronic, hole, and impurity defects.

Fundamental reviews of studies of color centers have been given by Pohl [9], L. S. Tartakovskii [10], Seitz [11], S. I. Pekar [12], Mott and Gurney [13], and others. Seitz was the first to put forward assumptions concerning the structure of color centers, taking the band theory of the solid as a basis. For a long time these models were generally accepted. The application of new research methods compelled the abandonment of most of the color-center models proposed by Seitz.

Let us consider the structure of color centers within the framework of modern concepts.

Various electron centers formed when electrons are captured by defects of the crystal lattice give rise, in the long-wavelength region of the crystal absorption spectrum, to bands: $F$, $F^{1}$, $K$, $M$, $R_{1}$, $R_{2}$, $N$.

The most sharply pronounced and intense band is the $F$ band. The de Boer model of the $F$ center, well confirmed by experiment, represents an electron captured by a vacant halide site.

The theoretical studies of S. I. Pekar [12], based on L. D. Landau’s hypothesis of electron self-localization in an ideal lattice, introduced certain changes into the de Boer model. According to S. I. Pekar, the $F$ center may be regarded as a polaron localized at the site of a missing halide ion. The model of the $F$ center proposed at TPI [19] proceeds from the hypothesis that this center is a formation consisting of an electron and the fictitious positive charge characteristic of an anion vacancy. These two charges in the anion vacancy form a positronium-type system. It is significant that such a system is long-lived, whereas positronium has a short lifetime.

Studies of polarized luminescence, dichroism of absorption bands, and EPR made it possible to establish that complex electron color centers $(M, R, N)$ are aggregates of $F$ centers [14, 15].

Van Doorn and Haven [14, 16] showed that an $M$ center consists of two combined $F$ centers arranged along the $\langle 110\rangle$ axis. This model is confirmed by measurements of magnetic susceptibility, by the absence of a dipole moment, and by investigation of the reactions of mutual transformation of $F$ and $M$ centers. Since the $M$ center has three excited states, three absorption bands associated with electron transitions to each of the excited levels should be observed. Theoretical calculations indicate that two absorption bands of the $M$ center lie in the region of the $F$ band. These conclusions were experimentally confirmed by P. N. Gorbenko [17].

$R$ and $N$ centers consist of three and four $F$ centers, respectively, as confirmed by experiments on the study of the dynamic equilibrium between their concentrations [18].

Thus, complex electron color centers are aggregates of $F$ centers.

Proceeding from our model of the $F$ center, according to which the $F$ center is an atom of quasipositronium, complex electron centers may be regarded as molecules composed of quasipositronium atoms. A colored crystal of an alkali-halide compound is thus a volume containing atoms and molecules of this type of chemical compounds. With this way of considering the problem, the study of the properties of color centers already becomes an object of chemical investigation.

The final product of the coagulation of $F$ centers is colloidal particles.

In alkali-halide crystals colored additively or by radiation, $\alpha$ and $\beta$ absorption bands are observed at the long-wavelength edge of exciton absorption [20]. Since $\alpha$ and $\beta$ centers arise in additively colored crystals, they cannot have a hole nature. The conditions for separation of the $\alpha$ and $\beta$ bands and of the edge of intrinsic absorption improve when the temperature is lowered.

The $\beta$ band changes in the same way as the $F$ band. Accord-

the ratio of the absorption coefficients at the maxima of the \(F\)- and \(\beta\)-bands is \(7:6\). When a crystal is irradiated with light in the spectral region of the \(F\)-band, simultaneously with a decrease in the intensity of the \(F\)- and \(\beta\)-bands, the intensity of the \(\alpha\)-band increases.

The \(\alpha\)-band is interpreted as absorption associated with excitation of a halide ion located next to an empty halide site. The \(\beta\)-band arises upon excitation of a halide ion located next to an \(F\)-center.

Optical absorption at the low-energy edge of the exciton band depends strongly on the presence of defects in the lattice. Exciton absorption bands, when anion vacancies are present, are shifted toward longer wavelengths. Anion vacancies manifest themselves through this shift and through the appearance of the \(\alpha\)-band.

The exciton-excitation band, when \(F\)-centers are present in the crystal, shifts toward longer wavelengths, which leads to the appearance of the \(\beta\)-band.

The hole color centers arising in alkali-halide crystals after irradiation may, conventionally, be divided into two equivalent groups:

1. Centers stable only at low temperatures (\(H\), \(V_1\), \(V_4\), \(V_k\), Hayse–Nichols centers).
2. Centers stable at temperatures close to room temperature (\(V_2\), \(V_3\)).

A new approach to understanding the structure of hole centers was developed in the work of Hersh [21]. It turned out that in hole centers the degree of covalent bonding is large. Comparison of the absorption spectra of halide solutions with the absorption spectra of irradiated crystals made it possible to propose molecular models for the structure of hole centers (Fig. 3).

Fig. 3. Models of hole color centers in alkali-halide crystals

By means of electron paramagnetic resonance, Kanzig demonstrated the possibility of autolocalization of holes in alkali-halide crystals [22]. In ionic crystals, according to Hersh’s hypothesis, valence chemical bonds may arise: a hole may be “smeared out” over two halide ions, which leads to the formation of a quasimolecule \(X_2^{-}\), oriented along the \(\langle 110\rangle\) direction and called a \(V_k\)-center.

At low temperatures, when the thermal vibrations of the lattice are frozen out, \(V_k\)-centers can remain at a definite point

of the crystal for a long time. Under these conditions, holes in alkali-halide crystals are in a self-localized state. The work of the Tartu physicists experimentally demonstrated the possibility of self-localization of anion excitons in alkali-halide crystals. At low temperatures excitons interact only weakly with lattice defects. It may be assumed that at low temperatures anion excitons in KJ crystals are self-localized. A self-localized anion exciton may be represented as an electron in the field of an \(X_2^{-}\) molecule.

The structure of \(H\)-centers has been investigated by the method of electron paramagnetic resonance [23].

It was found that the \(H\)-center is oriented in the \(\langle 110\rangle\) direction and is a molecular halide ion \(X_2^{-}\) located at an anion site. In other words, this center may be represented as an interstitial halide atom. The existence of an \(H\)-center is direct evidence for the generation of defects according to Ya. I. Frenkel at low temperatures.

With regard to the structure of the \(V_1\)-center there are two opinions: 1) a halide molecule \(X_2\) located in an anion vacancy [24], 2) a negative halide ion \(X^{-}\) in an interstitial position \((1/4, 1/4, 1/4)\) [25]. A choice between these models can be made if additional experiments are available.

In crystals doped with alkaline-earth ions, irradiation produces impurity hole centers, which have been named Hayes–Nichols centers [26]. Structurally this center is represented by a molecular ion \(X_2^{-}\), localized on the complex “divalent-metal ion—cation vacancy.” The Hayes–Nichols center has a preferred orientation along the crystallographic direction \(\langle 100\rangle\) owing to displacement of the halide into the cation vacancy.

At room temperature, in the ultraviolet region of the absorption spectrum of irradiated alkali-halide crystals only the \(V_2\)- and \(V_3\)-bands are observed. The structure of the centers responsible for these bands has not been studied sufficiently. Hypothetical models of the \(V_2\)- and \(V_3\)-centers are molecular ions \(X_3^{--}\) or \(X_3^{-}\), located in one cation and two anion vacancies [21]. The basis for such an interpretation is the similarity of the \(V\)-absorption bands and the spectra of halide molecules in aqueous solutions of halides. Recent studies [27] with polarized light confirmed the orientation of the \(V_2\)-center in the \(\langle 100\rangle\) direction. No anisotropy of the \(V_3\)-center was found, which contradicts the proposed model of this defect.

According to the models of Seitz and Varley, the \(V_2\)-center is a two-hole center, and the \(V_3\)-center a one-hole center. Therefore the consequence of recombination of an electron at a \(V_2\)-center should be the formation of a \(V_3\)-center. I. P. Kalabukhov and P. A. Yurachkovskii [28] showed that, after illumination with light from the \(F\)-band of x-irradiated KCl crystals in which the \(V_2\)-band predominates, the intensities of the \(V_2\)- and \(V_3\)-bands decrease without any changes in their shape and in the positions of the maxima. Thus, the results of earlier experiments by Casler, Pringsheim, and Yuster, according to which optical destruction of the \(V_2\)-band strengthens the \(V_3\)-band, are not confirmed.

Optical destruction of the \(V_2\)- and \(V_3\)-bands does not lead to the appearance in the spectral region \((200—1000)\,m\mu\) of new selective absorption bands. Apparently, such bands also do not arise in the vacuum ultraviolet, as is indicated by the investigation of Chiarotti and co-workers,

who found that after \(F\)-irradiation of X-rayed NaCl and KCl crystals, no new bands arise in the ultraviolet region of the spectrum down to \(160\,m\mu\), apart from the known \(\alpha\)-band.

Consequently, the \(V_2\)- and \(V_3\)-centers are single-hole formations. Indeed, assuming that any of the centers under consideration contains two holes, and taking into account that no new hole centers arise upon optical destruction, one must admit the occurrence of an improbable process—the simultaneous recombination of two electrons at a \(V\)-center.

In some works an attempt was made to identify the \(V_3\)-band with impurity centers. Thus, Lüty [29] believes that the \(V_3\)-band is due to \(U\)-centers. However, this assumption is poorly substantiated and is not consistent with the experimental data.

Thus, the structure of the \(V_2\)- and especially the \(V_3\)-centers has not been definitively clarified and remains a subject of discussion.

Between electron and hole color centers there exist various equilibrium relations, which are determined by the intensity of the electronic and ionic processes in the lattice.

For these reasons the absorption spectrum of an irradiated crystal depends strongly on its temperature and optical excitation. Electron–ion processes have a complex effect on the formation and stability of color centers, which makes an elementary interpretation of absorption spectra difficult.

§ 4. Kinetics of the Radiation Accumulation of Color Centers in Alkali-Halide Crystals

On the basis of the laws of radiation physics of the solid state, the scientific foundations of the radiation technology of materials are being developed.

The concentration of radiation defects in crystals of a given chemical composition at constant temperature is a function of the dose, the radiation intensity, and the treatment of the crystal. The principal task of radiation kinetics is to determine the form of this function and to express its parameters in terms of the microscopic characteristics of the processes of radiation damage. With such an approach to the solution of the problem, the effort required to create the scientific foundations of radiation technology is substantially reduced, since the need to establish numerous particular regularities disappears.

Below we shall present the results of studies of the kinetics of accumulation of electron color centers in alkali-halide crystals of different chemical composition. These defects receive special attention because the main part of the radiation energy is stored in \(F\)- and \(M\)-centers.

In alkali-halide crystals at room temperature, the formation of \(F\)-centers under the action of ionizing radiation proceeds according to a two-stage law.

Figure 4 shows the dependences of the density of \(F\)-centers in alkali-metal halides on the X-ray irradiation dose. The curves presented in the figure have two regions: an initial region of rapid accumulation of the concentration of \(F\)-centers and a second region of slow growth of the density of color centers.

Similar regularities in the formation of \(F\)-centers are also observed after irradiation of alkali-halide crystals with protons [2, 30]. The two-stage character of the kinetics of radiation formation of \(F\)-centers at room temperature indicates the action of two sources

Fig. 4. Kinetics of the growth of the \(F\) absorption band with increasing irradiation dose in crystals of different chemical composition

vacancies. The initial rapid growth of the concentration of \(F\)-centers is mainly associated with anion vacancies already present before irradiation; the subsequent stage of accumulation of \(F\)-centers is determined primarily by the radiation generation of new anion vacancies.

As follows from Fig. 4, under isodose X-ray irradiation of alkali-halide compounds, a clear correlation is observed between the density of \(F\)-centers and the chemical composition of the crystals.

When crystals are irradiated, not only the formation of color centers occurs, but also their decay. In crystals with a larger lattice energy, the process of destruction of color centers proceeds at a lower rate than in crystals characterized by weaker bonding forces between ions. For this reason, after irradiation more color centers are retained in compounds with a larger lattice energy. Accordingly, crystals with a small lattice energy have little radiation memory.

According to modern concepts, all possible mechanisms of formation of \(F\)-centers can be divided into two groups:

1) mechanisms associated with the presence of defects in the crystal;
2) mechanisms of formation of color centers in an undisturbed lattice.

For each of the possible mechanisms there may be a corresponding source of radiation vacancies and \(F\)-centers.

If there is only one source of radiation defects in the crystal, with capacity \(N_0\), then the kinetic equation for the accumulation of \(F\)-centers has the form [31]:

\[ n(t)=\frac{N}{BG}-\left[\frac{N}{B-G}\left(\frac{1-G\cdot t}{G}-\frac{1-Bt}{B}\right)\right] \]

\[ N=b\cdot g\cdot N_0;\qquad G=g+j;\qquad B=b+\beta \]

n — concentration of \(F\)-centers.
b — probability of electron capture by an anion vacancy.
g — probability of generation of one anion vacancy.
\(\beta\) — probability of radiation destruction of \(F\)-centers.
\(\gamma\) — probability of annealing of anion vacancies.

In the general case there may be several sources of radiation vacancies in a crystal; then the kinetics of accumulation of \(F\)-centers has a multistage character. Each step of the accumulation curve carries information about one of the micromechanisms of formation of \(F\)-centers.

Such complex kinetic accumulation curves of \(F\)-centers are observed in thin sections of KCl single crystals doped with divalent impurities (Fig. 5).

Fig. 5. Kinetics of growth of the \(F\) absorption band in potassium chloride crystals under X-ray irradiation

The source of anion vacancies in the second stage of coloration is the nodes of the crystal lattice. In view of the fact that the capacity of this source is large (\(\sim 10^{22}\,\text{cm}^{-3}\)), one should expect that the accumulation of \(F\)-centers in the second stage should proceed according to a linear law. However, at \(F\)-center concentrations above \(5\cdot 10^{17}\,\text{cm}^{-3}\) a decrease in the accumulation rate is observed. This phenomenon may be caused either by annealing of radiation vacancies or by the formation of coagulators of \(F\)-centers. Deviation from linearity in the kinetics of accumulation of \(F\)-centers occurs at smaller doses than the deviation from the linear course of the relative radiation expansion of the crystal, associated with the generation of vacancies [32]. Consequently, the decrease in the rate of formation of \(F\)-centers in alkali-halide crystals at large irradiation doses is associated with intensification of the coagulation of \(F\)-centers into complex centers.

Studies of the efficiency of reactions transforming \(F\)-centers into \(M\)-centers in crystals of different chemical composition have led to a very fruitful idea: to take into account the influence of the process of multiple localization of radiation energy in a solid. It has been shown that at room temperature, when the coagulation volumes are large, the distribution of \(F\)-centers among multiple centers is Poissonian.

Therefore the accumulation of \(F\)-centers must proceed along a curve with

maximum, as is observed experimentally for LiF crystals [2].

It has been established that at temperatures below the temperature of hole autolocalization, the accumulation of \(F\)-centers in alkali-halide crystals proceeds from a single source. In this case the source of \(F\)-centers is all the sites of the crystal lattice.

Fig. 6. Dependence of the optimum coloration temperature on the irradiation dose

There exists an optimum temperature \((T_{\mathrm{opt}})\) at which the efficiency of accumulation of \(F\)-centers, determined from their concentration in isodose-irradiated specimens, is maximal [33].

The optimum temperature shifts regularly toward lower temperatures with increasing irradiation dose (Fig. 6). This fact is explained as follows. In the low-temperature region the rate of accumulation of \(F\)-centers has the form:

\[ dn/dt=\frac{gN}{1+\beta/b}. \]

As the temperature of the irradiated crystal is raised, both the parameter \(q\) increases (owing to an increase in the probability of nonradiative electron–hole recombination) and the parameter \(\beta\) increases (owing to an increase in hole mobility). Therefore an optimum temperature is possible for the rate of formation of \(F\)-centers. On the other hand, it has been experimentally established that with increasing temperature the limiting concentration of \(F\)-centers decreases. The combination of these effects accounts for the shift of \(T_{\mathrm{opt}}\) toward lower temperatures with increasing irradiation dose.

§ 5. Mechanisms of the radiation formation of defects in alkali-halide crystals

When crystals are irradiated with ionizing and ultraviolet radiation, vacancies, interstitial ions, atoms, and their aggregates are formed in them. When these defects interact with electrons, holes, and excitons, electron and hole color centers arise.

To explain the processes of generation of radiation defects in alkali-halide crystals, a large number of hypotheses have been advanced, which can be divided into two groups.

The first group comprises processes whose realization is possible in the presence of imperfections of the crystal lattice (point defects, dislocations).

The second group includes mechanisms of formation of radiation defects in a perfect lattice disturbed by irradiation.

1. Structure-sensitive and catalytic mechanisms

1. Formation of color centers as a result of the interaction of electron-hole pairs and excitons with vacancy associates. In the interaction of electronic excitations with vacancy complexes, bonds are broken into single vacancies; localization of electrons or holes on these vacancies leads to the creation of stable color centers. This process proceeds most intensively at elevated temperatures and determines the rate of accumulation of \(F\)-centers in the first stage of coloration at room temperature.

2. According to Seitz, a dislocation step is capable of trapping an electron or a hole. Electron-hole recombination at a dislocation step is accompanied by the release of energy sufficient to generate either an anion or a cation vacancy. According to the Seitz mechanism, the rate of formation of \(F\)-centers in the linear stage of coloration should increase after deformation of the crystals. However, in a number of works the opposite dependence was observed. In addition, coloration by x-rays of filamentary dislocation-free NaCl crystals indicates radiation generation of anion vacancies in crystals containing no dislocations. Apparently, the efficiency of the Seitz mechanism is rather limited.

3. Structure-sensitive mechanisms also include mechanisms in which lattice defects participate that, after completion of the act of generation of an \(F\)-center, are restored and can again take part in coloration. Such mechanisms are called catalytic.

a) A mechanism for creating anion vacancies in crystals doped with divalent cation-substituting impurities was proposed by Crawford and Nelson [34]. The authors believe that the formation of Hays–Nichols centers in crystals is accompanied by generation of free anion vacancies.

In such a process the number of anion vacancies increases as a result of displacement of neutral halogen atoms into cation sites of the lattice.

Schneider [35] holds the view that the Hays–Nichols center at room temperature dissociates into a hole center and an impurity ion. The divalent metal ion associates with a free cation vacancy; the impurity complex is restored and is capable of participating again in the process of vacancy generation.

The Schneider mechanism is confirmed by an increase in the growth rate of the density of \(F\)-centers in the linear stage of accumulation in KCl—Ca and KBr—Sr\(^{++}\) crystals [36].

For the Schneider mechanism to operate, the complex must be periodically restored during irradiation. However, in irradiated KBr—Sr\(^{++}\) crystals, dielectric relaxation caused by the orientation of impurity complexes is not observed [37].

This fact indicates radiation destruction of complexes and is an argument against the universality of Schneider’s mechanism.

b) The divacancy mechanism was proposed by Ch. B. Lushchik and co-workers [38]. At comparatively high temperatures and high irradiation intensities, the probability of encounter of two holes (centers \(X_2^-\)) at neighboring lattice sites is rather high. In this case a divacancy center may be formed, which is capable of being located not in four, but in three anion vacancies. The freed halide site may capture an electron and form an \(F\)-center. The principal obstacle to the realization of this mechanism consists in overcoming the Coulomb repulsion forces of like-charged \(V\)-centers.

This obstacle is removed if one assumes that a \(V_k\)-center is captured by a cation vacancy with the formation of a \(V_2\)-center. In this case the interaction of the second \(V_k\)-center with the \(V_2\)-center is not hindered by Coulomb repulsion forces.

Thus a hole center arises, occupying three anion vacancies. The bivacancy formed in this process migrates away from the center under consideration and, upon capturing an electron, dissociates into an \(F\)-center and a cation vacancy.

Experimental data do not contradict the possibility of realization of the divacancy mechanism. Indeed, the efficiency of generation of \(F\)-centers increases with increasing irradiation intensity and decreases when the crystal is cooled below the temperature of hole autolocalization. Increasing the vacancy density in the crystal (by doping the samples with divalent impurities) increases their colorability.

2. Structure-insensitive mechanisms

To explain the processes of formation of radiation defects in a perfect lattice, Varley [30] proposed a mechanism according to which multiple ionization of a halide ion leads to its displacement into an interstitial position. Seitz and Koehler [40] questioned whether the displaced ion could reach a stable position in the interstitial and not diffuse back into the vacancy it had left. Smoluchowski and co-workers [41] substantiated the possibility of separation of a positive halide ion and a vacancy by means of a series of focused collisions. In this process an interstitial atom and an anion vacancy are formed at a small distance from one another. Another objection was put forward by Dexter [42]; its essence is as follows: the probability of electron capture by a positive halide ion is so high that it is neutralized before being displaced into an interstitial position.

A modification of Varley’s mechanism formulated by Klick [43] is free from the objections indicated above. Klick allows for the possibility of single ionization of neighboring halide ions, which leads to the subsequent placement of an \(X_2^-\) molecule in one anion site. Localization of an electron at an anion vacancy leads to formation of an \(F\)-center; as a result of capture of another electron by the molecule, an \(H\)-center is formed. According to Klick’s mechanism, \(F\)- and \(H\)-centers are generated at short distances, but analysis of EPR spectra of irradiated crystals indicates that the centers are separated from one another by several lattice constants.

Williams [44] proposed a mechanism for separation of an interstitial atom and a vacancy in the following form. In the anion sublattice two

molecular ion of the type \(X_2^-\). Owing to its interaction with the asymmetric crystalline field, the molecular ion \(X_2^-\) acquires momentum in the direction of the crystallographic axis \(\langle 110\rangle\), which leads to separation of the Frenkel pair by means of elastic collisions.

The possibility of realization of the Varley mechanism and its variants is confirmed by the presence of interstitial defects in crystals irradiated at low temperatures and by the correlation between the efficiency of formation of \(F\)-centers and the geometrical parameters of the crystal lattice.

Vitols and co-workers [45] showed that in the temperature range \((110\text{--}210)^\circ\mathrm{K}\) the density of \(F\)-centers in X-irradiated KCl crystals increases exponentially with increasing irradiation temperature. The activation energy of the process changes very little when the impurity content in the crystal and the excitation conditions are changed. This gives grounds to suppose that in the low-temperature region the generation of \(F\)-centers is governed by a fundamental mechanism.

Vitols and Hersh [46, 47] advanced a hypothesis on the possibility of formation of \(F\)- and \(H\)-centers by an exciton mechanism:

\[ \begin{gathered} Q\\ e^0 \to F + H . \end{gathered} \]

An excited quasi-molecule of halogen (a relaxed exciton) decomposes into \(F\)- and \(H\)-centers.

It is possible that the exciton mechanism of radiation generation of color centers predominates at low temperatures. It should be noted that the exciton mechanism is also possible at temperatures below the temperature of exciton self-localization.

The mechanisms considered for the generation of radiation defects are based on electronic phenomena.

In Balarin’s work it was shown that in ionic crystals elastic interactions may arise in the form of chains of focused collisions.

Calculated and experimental data have been obtained on elastic focused collisions in ionic crystals, on the threshold energy for focusing, and on the formation of Frenkel defects.

In focusing collisions, elastic interaction of photoelectrons with lattice anions takes place, with transfer of kinetic energy to them. Focused collisions are produced only in anion rows in the \(\langle 111\rangle\) direction. In the course of such a process, an anion vacancy is created at the beginning and an interstitial ion at the end of the collision chain. It turned out that, in focused collisions of ions, the threshold energy for the formation of Frenkel defects in the lattice of alkali-halide crystals is several eV, instead of the 25 eV previously accepted according to the Seitz and Koehler theory.

§ 6. Lattice Energy and Crystal Structure

Systematic investigations of alkali-halide crystals have by the present time made it possible to find reasonable explanations for many physical phenomena occurring in these crystals and, in a number of cases, to confirm them theoretically and experimentally. In the field of radiation physics of alkali-halide crystals, the structure of certain color centers \((F, M, R, H, V_k^-)\),

hypotheses concerning the processes of formation of radiation defects, in good agreement with the experimental results, have been put forward; it has proved possible to calculate theoretically the state of electrons in the \(F\)-center. The large amount of experimental results accumulated in studying the properties of alkali-halide crystals has made it possible to find a way of systematizing the properties in a series of crystals. The systematization is based on a quantity that determines the energetics of the ionic lattice. Using the lattice energy as the basis for systematizing the properties, it has been possible to establish regularities in the variation of many optical, mechanical, electrical, and other properties over a wide range of crystals.

Systematization of the physical properties of crystals on the basis of the lattice energy is complete only for crystals possessing a single type of lattice. The regularities in the variation of properties for crystals with different lattice types as a function of the lattice energy usually undergo discontinuities on passing from one lattice type to another. For example, the dependence of the energy stored under irradiation in alkali-halide crystals and in crystals of alkaline-earth metal fluorides on the lattice energy undergoes a discontinuity on passing from crystals with the rock-salt lattice to crystals with a fluorite-type lattice. At the same time, the dependence of the energy stored in crystals changes monotonically with increasing lattice energy for crystals with the same lattice type (Fig. 7). The dependence on the lattice energy of the position of the edge of intrinsic optical absorption undergoes a discontinuity on passing from alkali-halide crystals to crystals of alkaline-earth metal fluorides and then to crystals of oxides of metals of the second group (Table 1).

Fig. 7. Dependence of the stored energy on the lattice energy of crystals

Table 1. Position of the edge of intrinsic absorption for compounds of metals of the first and second groups of D. I. Mendeleev’s system at room temperature.

Within a group of crystals with the same type of lattice, the dependence of the position of the edge of intrinsic absorption on the lattice energy is described by a continuous function.

The study of the physical properties of ionic crystals with a lattice different from that of rock salt has made it possible to establish that, within a group of crystals possessing a single lattice type, the dependence of a number of properties on the lattice energy is fully obeyed. As an illustration, Table 2 may be cited, in which certain properties of crystals of alkaline-earth-metal fluorides are systematized (compiled by N. M. Timoshenko) [46]. The radiation-induced change in the conductivity of alkaline-earth-metal fluorides irradiated with x-rays increases with increasing lattice energy [49]. Thus, by simple extrapolation, changes in physical properties can be predicted only within a group of crystals possessing the same type of lattice. In passing to crystals with a different lattice type, possible discontinuities in the function describing the dependence of changes in properties on lattice energy must be taken into account. It is therefore very important, in systematizing the physical properties of crystals of various kinds, to determine the possibility of allowing for the role of structure. This fact makes it necessary to carry out careful, comprehensive investigations of ionic crystals of more complex structure than the alkali halides. The next class of compounds having a more complex lattice structure than the alkali halides and convenient for study is represented by crystals with the fluorite-type lattice: CaF₂, SrF₂, BaF₂. For this reason, a considerable number of works have recently been devoted to the study of the physical properties of these crystals.

Although the physical properties of complex crystals cannot be predicted by simple extrapolation from the known properties of alkali halides, the general qualitative picture of possible changes in properties under the action of external factors can be presented fairly clearly.

The question of the structure of color centers in crystals of alkaline-earth-metal fluorides has not yet been definitively resolved. Nevertheless, on the basis of the results available at present, assumptions can be made concerning possible models of color centers in alkaline-earth-metal fluorides. Fluorides

Table 2

Properties of fluorides of alkaline-earth metals

alkaline-earth metals are typical ionic compounds (the degree of ionic bonding exceeds 90% in \( \mathrm{CaF}_2 \)). It should therefore be expected that in these crystals the radiation-induced formation of defects occurs mainly in the anion sublattice. Consequently, the structure of radiation defects in crystals of alkaline-earth metal fluorides is similar to the structure of defects formed in alkali-halide crystals under the action of ionizing radiation. It seems entirely possible to assume that the point radiation defects in fluorite-type crystals are the following:

1. Single anion vacancies and complexes of anion vacancies with electrons localized on them (analogues of \(F\), \(M\), \(R\), \(F'\), \(M'\), etc., complex electron centers in alkali-halide crystals).

2. Single interstitial anions, complexes of anions and vacancies of both signs with holes localized on them (analogues of \(H\) and \(V\), etc., hole centers in alkali-halide crystals).

3. Individual impurity ions in various states in the lattice, as well as complexes of impurity ions, vacancies, and ions in interstitial positions that have captured electrons and holes during irradiation (analogues of \(Z_1\), \(Z_2\), \(Z_3\), \(A\), etc., color centers in alkali-halide crystals).

It should not, of course, be assumed that the properties of radiation defects in alkaline-earth metal fluorides will be completely analogous to the properties of the corresponding color centers in alkali-halide crystals. The distinctive character of the crystal structure causes some difference in the properties of the corresponding defects.

Crystals of alkaline-earth metal fluorides have a fluorite-type crystal lattice, which is a face-centered cubic lattice of divalent cations, within which a cubic lattice of negative halide ions is inserted (Fig. 8).

Fig. 8. Structure of the fluorite lattice

The large difference in lattice energies and in structure between alkali-halide crystals and alkaline-earth metal fluorides must affect the process of formation of radiation defects. Indeed, in alkali-halide crystals at room temperatures the presence of Schottky defects is thermodynamically favorable, whereas in crystals of alkaline-earth metal fluorides at room temperature Frenkel defects exist predominantly. Frenkel defects in this group of compounds consist of equal concentrations of anion vacancies and halides in interstitial positions. The binding energy of the anion-vacancy–interstitial-halide complex is about 1.65 eV. Apparently, more complex complexes also exist in the crystals, which decompose as the temperature is raised.

§ 7. Color Centers in Alkaline-Earth Metal Fluorides

The most common and well-studied radiation defect in alkali-halide crystals is the \(F\)-center. The \(F\)-center is the simplest point defect formed in the crystal lattice under the action of ionizing radiation. The problem of the formation of radiation defects in crystals is practically reduced to the problem of the formation of the simplest \(F\)-centers and the corresponding hole centers, as well as to the problem of the transformation of these simplest centers into more complex ones. Therefore, one of the most important tasks in the radiation physics of alkaline-earth metal fluorides is to determine the properties of a center analogous to the \(F\)-center in alkali-halide crystals.

The most successful attempt to determine the absorption bands corresponding to \(F\)-centers in crystals of the fluorite type is the work of Arends [50]. Arends studied the optical and EPR spectra of additively and electrolytically colored crystals of CaF\(_2\) and BaF\(_2\). The optical absorption spectrum of a colored CaF\(_2\) crystal was a typical Mollwo spectrum with maxima of two absorption bands at 375 and 520 nm. The study of paramagnetic absorption in colored CaF\(_2\) crystals led to the following results. The spectrum consists of 7 lines symmetrically arranged with respect to the central one, which corresponds to a \(g\)-factor \(= 1.998 + 0.001\). Analysis of the results obtained led to the following explanation.

In a lattice of the fluorite type, each cation is localized at the center of a cube with 8 F ions at the corners. Each fluorine ion is located at the center of a tetrahedron of cations. Under the action of ionizing radiation, a fluorine ion is displaced from the center of the tetrahedron of cations; an electron is localized at the vacancy thus created, forming a center similar to an \(F\)-center in alkali-halide crystals. The presence of seven lines in the paramagnetic absorption spectrum is due to the superhyperfine splitting of the absorption line of the electron of the \(F\)-center as a result of the interaction of this electron with the magnetic moments of the six nearest fluorine nuclei, with nuclear spins \(1/2\). The assumption that the seven spectral lines are due to the interaction of the electron with the surrounding fluorine ions is confirmed by the intensity ratio between the spectral lines \(1:6:15:20:15:6:1\).

Thus, by studying EPR spectra it was found that in colored crystals there is a color center of the \(F\)-center type. The center is an anion vacancy with an electron localized on it, surrounded by a tetrahedron of divalent cations. The electron belongs with equal probability to all surrounding cations and interacts with the nuclear magnetic moments of the six surrounding fluorine ions.

In order to find the optical absorption band due to centers of the \(F\)-type, Arends investigated the optical destruction of the optical and EPR absorption bands. It turned out that bleaching the crystal with light from the \(\alpha\)-band (375 nm) causes a simultaneous decrease in the \(\alpha\)-absorption band and in the EPR signal; when the crystal is irradiated with light from the \(\beta\)-band, the EPR signal does not change.

It should be noted, however, that the results of the bleaching experiment agree only qualitatively. This fact does not make it possible to establish definitively the identity of the centers responsible for absorption in the region of 375 nm and for paramagnetic absorption in the microwave region.

Despite the fact that Arends’ work does not give a definitive answer to the question of the identity of the optical and EPR spectrum bands, in a number of studies theoretical calculations were carried out of the transition energy of the \(^{1}S—2p\) electron in an \(F\)-center. The calculations were performed on the basis of the method proposed by Gourary and Adrian [51] for calculating the position of the \(F\)-band in the spectrum of an irradiated alkali-halide crystal. It turned out that, with an appropriate choice of the electron wave functions in the anion vacancy, as Fleming [52] did, or with a suitable choice of the form of the lattice potential inside the anion vacancy in accordance with [53], very good agreement can be obtained between the calculated positions of the \(F\)-band and the measurements. But since the optical absorption bands corresponding to \(F\)-centers in crystals of alkaline-earth metal fluorides have not yet been definitively established experimentally, theoretical calculations cannot give the complete energy structure of the \(F\)-center.

Thus, the assumption is experimentally confirmed that radiation defects analogous to \(F\)-centers in alkali-halide crystals can be formed in crystals of alkaline-earth metal fluorides. However, it has still not been possible to establish definitively the position of the absorption bands caused by these centers.

Undoubtedly, in the process of coloration of a crystal under the action of radiation, hole centers are also created simultaneously with electron centers. Hayes and Twidell, by means of a comprehensive study of optical and EPR spectra, succeeded in detecting in CaF\(_2\) crystals centers stable up to 138° K, similar to \(V_k\)-centers in alkali-halide crystals, to which an absorption band at 350 nm corresponds. The self-localized hole \(V_k\)-center in BaF\(_2\) is a molecular ion \(X_2^{-}\) oriented along the \(\langle 100\rangle\) axis. Another type of hole center, similar to the \(V_1\)-center in alkali-halide crystals, may exist in crystals of alkaline-earth metal fluorides activated by yttrium, as Smakula believes. Indeed, in such crystals, to compensate the excess positive charge of the \(Y^{3+}\) ion, an additional number of \(F^{-}\) ions are present in interstitial positions. Under irradiation, an electron may be detached from an interstitial \(F^{-}\) ion and this electron may attach to a yttrium ion. In this process \(Y^{2+}\) is obtained at a lattice site and \(F^{0}\) in an interstitial position. The latter defect is similar to the \(V_1\)-center in alkali-halide crystals. Apparently this center can exist in crystals of alkaline-earth-metal fluorides even at room temperatures, since interstitial anions are stable at these temperatures.

§ 8. Formation of Radiation Defects in Crystals of Alkaline-Earth Metal Fluorides

In studying the action of radiation on the optical, electrical, and other properties of crystals of alkaline-earth fluorides, it was found that these compounds possess a rather high radiation resistance after irradiation in comparison with alkali-halide crystals. Since crystals of alkaline-earth metal fluorides have a larger lattice energy than alkali-halide crystals, this effect is natural. Indeed, the greater the lattice energy of a compound, the greater its stability should be as well,

radiation defects and, consequently, more of them should accumulate in the course of irradiation.

It has been shown experimentally that optical-absorption spectra obtained a few microseconds after the cessation of irradiation and a long time after irradiation are identical [54]. Consequently, the stability of the induced radiation defects is high, which is consistent with the large lattice energy in crystals of alkaline-earth-metal fluorides. Apparently, the low coloring efficiency of these crystals is due to the peculiarities of their structure.

To solve the problem of the formation of radiation defects, it is necessary first of all to identify the absorption bands caused by radiation defects created in the lattice itself.

At present, work to elucidate the influence of irradiation on various properties of alkaline-earth-metal fluorides is being carried out mainly on \(\mathrm{CaF_2}\) crystals. It has been established that in colored \(\mathrm{CaF_2}\) crystals, depending on the experimental conditions and the previous history of the specimen, two types of spectra may be observed: the so-called Smakula spectrum, consisting of four absorption bands at 225, 335, 400, and 580 nm (Fig. 9), and the Mollow spectrum, consisting of \(\alpha\)- and \(\beta\)-absorption bands (Fig. 10). According to data from various authors, the \(\alpha\)-band lies in the interval \((370 + 385)\) nm, and the \(\beta\)-band in \((520 + 560)\) nm.

Fig. 9. Absorption spectrum of an irradiated calcium fluoride crystal

Some experimenters believe that all bands of the Smakula spectrum are of impurity origin and are due to electron transitions on the trivalent yttrium ion. The following evidence is available for this assumption:

1. The spectra of \(\mathrm{CaF_2}\) and \(\mathrm{CaF_2—Y}\) crystals before and after irradiation are similar.

2. It has been shown that natural \(\mathrm{CaF_2}\) crystals always contain yttrium because of the closeness of the radii of calcium and yttrium ions. Repeated-

Fig. 10. Absorption spectrum of an irradiated calcium fluoride crystal

zone refining does not make it possible to purify the crystal of this impurity.

1. The saturation of all four absorption bands with the X-ray irradiation dose indicates a finite concentration of the defects responsible for these bands.

2. On the basis of a study of EPR spectra in CaF$_2$ crystals, the conclusion is drawn that there are four levels for electron transfer to the divalent yttrium ion, which corresponds to the four bands in the Smakula spectrum.

3. The identical temperature of destruction of all four bands in photochemically and additively colored crystals is consistent with this assumption.

Another group of scientists is inclined to believe that intrinsic radiation defects of the lattice give rise to the $\alpha$- and $\beta$-absorption bands of the Molwo spectrum [50, 52, 53].

However, the latest results of our investigations, carried out at TPI, suggest that the bands of the Molwo spectrum are due to defects associated with the presence of an oxygen impurity in the crystals. Thus, these bands are not due to intrinsic radiation defects [56, 57].

The work of researchers at TPI, as well as the work of Arkhangel’skaya, succeeded in showing that at least the band with a maximum at 580 nm in the Smakula spectrum is due to intrinsic lattice defects. Under irradiation by $\gamma$ rays and by protons of low intensity, the growth curve with irradiation dose of the absorption band at 580 nm has a clearly expressed two-stage character: a stage of rapid growth and saturation; moreover, the ratio among all four bands remains unchanged as the irradiation dose increases. With an increase in the intensity of the proton beam, the picture changes qualitatively: as the irradiation dose increases, the maximum of the band shifts from 580 to 560 nm. With the irradiation dose, absorption in this wavelength region increases by

according to the following law: a stage of rapid growth, saturation, and then further growth of the band; moreover, the rate of growth in the third stage is strongly determined by the irradiation intensity (Fig. 11).

The study of the microhardness of CaF$_2$ crystals shows that, as the irradiation dose increases, a qualitative analogy is observed in the change of the microhardness and of the band in the region of 560–580 nm [58]. It is known that the change in the microhardness of crystals is determined to a large extent by the defectiveness of the ionic lattice induced during irradiation. Consequently,

Fig. 11. Kinetics of the growth of absorption bands in a calcium fluoride crystal under proton irradiation.

the band with a maximum at 560 nm is due to ionic-type defects produced by irradiation. The shift of the band from 580 nm in CaF$_2$ crystals with increasing irradiation dose is due to the superposition, in this region of the spectrum, of two absorption bands with maxima at 580 and 560 nm and to the difference in the kinetics of their growth.

It should be emphasized that continuous growth of the band with a maximum in the interval 560–580 nm with irradiation dose is observed only at sufficiently high radiation intensities. The strong dependence of the band-growth rate on the radiation intensity can be explained as follows. For alkali-halide crystals, the dependence of the growth rate of $F$ centers in the third stage on the radiation intensity is expressed by the law $a = I^\delta$, where $\delta = 1 \div 2$ (in particular, under proton irradiation $\delta$ is equal to $1.2 \div 1.5$). For fluorides of the alkaline-earth metals, because of the structural features of the lattice, $\delta$ should take values from 1 to 9, since in the anion sublattice of the crystal-

for CaF$_2$, at least ninefold ionization of the ions in the unit cell is necessary, if the mechanism of defect generation by multiple ionization is predominant. From our experiments $\delta = 2.4$, which means that, to create defects in a fluorite-type lattice, a higher ionization density is needed than to create defects in alkali-halide crystals. The formation of radiation defects in single crystals of fluorides of alkaline-earth metals is made more difficult for the following reason as well. It is known that one of the most essential acts in defect generation is the process of separation of the vacancies formed and of the halide into interstices. It should be thought that the separation of these defects by means of a series of focused collisions is the most active process. However, the propagation of focused collisions is improbable in a fluorite-type lattice because of the features of the crystal-lattice structure. Therefore, impact mechanisms make a substantial contribution to the process of defect formation.

§ 9. Toward the scientific foundations of radiation technology for solids with ionic bonds

The ability of bodies to change their properties under the action of ionizing radiation is characterized by radiation resistance. By the radiation resistance of a substance one usually understands the ability of the substance to undergo only a small change in any property upon irradiation. However, this definition is incomplete and can lead to contradictory conclusions. In fact, a KI crystal, in which little energy is stored during irradiation, appears, according to the definition, more radiation-resistant than an LiF crystal. But in KI, under the action of radiation, irreversible processes occur to a greater extent than in LiF, i.e., KI is radiation-unstable in the chemical sense. Such a contradiction arises because some changes in properties are determined during the process of irradiating the crystal, others after irradiation.

Therefore two definitions are proposed:

1. Radiation resistance after irradiation—radiation memory—is determined by the stored energy. This characteristic has an analogy with the fatigue of bodies and aging under other types of testing. Large relative changes in physical properties will be observed for bodies with a larger lattice energy.

2. Radiation resistance during testing. It is determined by the absorbed energy, the absorption coefficient, or the attenuation of the radiation flux. The greatest changes will occur in bodies with a smaller lattice energy.

The fact of an intense change in the properties of solids under irradiation makes it possible to use radiation in the technological process of obtaining materials with specified characteristics.

Radiation physics of the solid state makes it possible to describe in detail the microprocesses in a solid located in the irradiation zone, and establishes connections between the kinetics of the microprocesses and the kinetics of change of macroscopic properties. It is possible to choose such irradiation conditions for materials under which either the disordering of ordered crystals or the restoration of order in disordered structures (for example, alloys) will predominantly occur.

At the present state of radiation physics of the solid state, there is no longer any need to study the kinetics of change of each characteristic of the irradiated material. There appears to be a possibility of develop-

create the scientific foundations of radiation technology, which make it possible to correctly predict and calculate changes in many properties of the irradiated material.

All other conditions being equal, the magnitude of the absorbed energy determines the effectiveness of the action of radiation and, consequently, the effectiveness of radiation technology. If the absorbed energy is small, then the change in properties, i.e., the technological effect, will also be small.

During irradiation, simultaneously with the change in the properties of the material, scattering of the absorbed energy and annealing of the radiation-induced change in properties take place.

It is therefore essential to determine not only how much radiation energy is absorbed by the body, but also how long the changes in the properties of the material that occurred during irradiation are retained.

In light of the foregoing, in developing the scientific foundations of radiation technology the principal characteristics should be the absorbed energy of radiation and the energy stored in the material.

The change in properties during irradiation is characterized by the magnitude of the absorbed energy.

It is known that the linear absorption coefficient of radiation increases with increasing atomic numbers of the elements making up the compound. On the other hand, as the effective atomic number increases, the strength of the chemical bond in crystals decreases. Therefore, in bodies with weak chemical bonds (low lattice energy), large changes in properties occur in the radiation field; however, the stability of the change is small.

The processes occurring in solids during irradiation should be of primary interest for radiation-chemical technology.

Radiation technology aimed at obtaining stable changes in the physical properties of materials must be based on the study of the energy stored in the body.

The magnitude of the stored energy under isodose irradiation increases with increasing bond energy between the elements of the structure in general and with increasing lattice energy in particular.

Ionic compounds with high lattice energy have good radiation memory and will long retain the effect of changes in properties caused by radiation. Such substances may serve as the basis for the search for bodies for radiation-energy accumulators. At the same time, the amount of absorbed energy in such bodies will be small; therefore the change in properties during irradiation will be relatively insignificant.

The accumulation of stored energy in ionic crystals in the overwhelming majority of cases proceeds along a curve with saturation. Such a course of the kinetic curve is a consequence of the fact that the rates of the processes of accumulation of radiation defects and of reduction of their concentration at different stages of irradiation do not remain constant.

At small doses, the rate of the processes of accumulation of energy-storage centers is higher than the rate of the processes reducing their concentration. If these rates are equal, then the magnitude of the stored energy is observed to be independent of the irradiation dose.

The maximum effect of radiation-induced change in the physical properties of solids is achieved in substances characterized by a high bond energy between particles.

The regime of radiation treatment of materials is selected according to cri-

with saturation. Upon reaching saturation, the economic expediency of further irradiation of the material disappears.

As an example of radiation technology, we may cite the increase in the hardness of diamonds, hard alloys, and abrasive materials by irradiating them with nuclear and ionizing radiation. These substances are characterized by a high binding energy between particles. Therefore the relative magnitude of the increase in hardness induced by irradiation of these hard bodies is large.

REFERENCES

1. A. A. Vorob'ev. Color Centers, TTU Publishing House, Tomsk (1968).
2. D. I. Vaisburd. Dissertation, Tomsk (1968).
3. E. K. Zavadovskaya, A. V. Kuz'mina, E. M. Golovchanskii, PTE, 5 (1966).
4. E. K. Zavadovskaya, A. V. Kuz'mina, FTT, 6, 3348 (1964).
5. E. K. Zavadovskaya, N. M. Timoshenko, Izv. TPI, 139 (1965).
6. E. K. Zavadovskaya, E. M. Golovchanskii, A. V. Kuz'mina, V. G. Vakhromeev. Radiation Physics of Nonmetallic Crystals. Proceedings of the Conference, Kiev, Naukova Dumka (1965).
7. E. K. Zavadovskaya, E. M. Golovchanskii, A. V. Kuz'mina. Izv. vuzov, Fizika, 4 (1966).
8. A. A. Vorob'ev, E. K. Zavadovskaya et al. Izv. TPI, 170 (1967).
9. Rohl R. W., Metallkund. 26, 217 (1934).
10. P. S. Tartakovskii, The Internal Photoeffect in Dielectrics, Gostekhizdat, Moscow (1940).
11. Seitz F., Rev. Mod. Phys. 26, 7 (1954).
12. S. N. Pekar. Studies on the Electron Theory of Crystals. Moscow–Leningrad (1961).
13. N. Mott, P. Gurney. Electronic Processes in Ionic Crystals. IL, Moscow (1950).
14. Van Doorn C. Z., Philips Rev. Repts. 12, 369 (1957).
15. Pick H., Z. Phys. 159, 69 (1960).
16. Van Doorn C. Z., Haven Y., Phys. Rev. 100, 753 (1955).
17. P. K. Gorbenko, N. P. Kalabukhov. Optics and Spectroscopy (in press).
18. Shnatterly S. S., Compton W. D. Phys. Rev. 135, A 227 (1964).
19. A. A. Vorob'ev, S. A. Vorob'ev, E. K. Zavadovskaya. Izv. vuzov, Fizika, 7, 156 (1967).
20. B. V. Budylin, A. A. Vorob'ev. The Effect of Radiation on Ionic Structures, Gosatomizdat, Moscow (1962).
21. Hersh H. N., Phys. Rev. 105, 1410 (1957).
22. Känzig W., T. Woodruff, J. Phys. Chem. Solids 9, 70 (1957).
23. I. Castrer, W. Känzig, J. Phys. Chem. Solids 3, 178 (1957).
24. W. Känzig, T. Woodruff, Phys. Rev. 109, 220 (1958).
25. F. Seitz, Phys. Rev. Letters 2, 282 (1961).
26. W. Hayes, G. M. Nichols, Phys. Rev. 117, 993 (1900).
27. Christy R. W., Shaw E. D., Winter E. M., Color Centers in Alkali Halides, 1965, Internat. Symposium Urbana, Illinois 1965.
28. P. A. Yurachkovskii, Abstract of dissertation, Odessa, 1968.
29. F. Luty, Z. Phys. Chem. Sol. 23, 677 (1962).
30. V. M. Lisitsyn, Dissertation, Tomsk, 1966.
31. I. Ya. Melik-Gaikazyan, Kinetics of Radiation Accumulation of F-Centers. Proceedings of the Conference on Radiation Physics, Tomsk, 1967.
32. I. Ya. Melik-Gaikazyan, Radiation Physics of Nonmetallic Crystals (conference proceedings), Kiev, Naukova Dumka (1967).
33. A. N. Kravets. Dissertation, Tomsk (1967).
34. Crofword J. H., Nelson C. M., Phys. Rev. Let. 5, 314 (1960).
35. E. E. Schneider, Disc. Faraday Soc. 31, 176 (1961).
36. I. Ya. Melik-Gaikazyan, V. M. Lisitsyn. FTT, 7, 1964, 1965.
37. E. K. Zavadovskaya, Yu. M. Annenkov. Radiation Physics of Nonmetallic Crystals, Kiev, Naukova Dumka (1967).
38. Ch. B. Lushchik, M. A. Elango. Proceedings of the Conference on Radiation Physics, Tomsk (1967). (In press).
39. Varley I. H. O., J. Nucl. Energ. 1, 2, 130 (1954).
40. Seitz F., Koechler I. S., Solid. State Phys. 2, 442 (1956).
41. R. Smolukhovskii, Materials of the Conference on the Broad Use of Atomic Energy, vol. 7, Nuclear Chemistry and the Action of Radiation.

1. Dexter D. L., Phys. Rev. 118, 934 (1960).
2. Klick C. C., Phys. Rev. 120, 760 (1960).
3. Williams K. Phys. Rev. 126, 70 (1962).
4. I. K. Vitol et al. Proceedings of the Conference on Radiation Physics, Tomsk, (1967) (in press).
5. I. K. Vitol, Izv. AN SSSR, Ser. fiz. 30, 565 (1966).
6. H. N. Hersh, Phys. Rev. 148, 928 (1966).
7. N. M. Timoshenko, Dissertation, Tomsk (1967).
8. E. K. Zavadovskaya, V. A. Chernyshov, L. A. Lisitsyna. Radiation Physics of Nonmetallic Crystals. Kiev, Naukova Dumka (1967).
9. Arends I., Phys. Stat. Soc. 7, 805 (1964).
10. Gourary B. S., Adrian F. I., Phys. Rev. 105, 1180 (1957).
11. Fleming R. I., Phys. Stat. Sol. 18, K 139 (1966).
12. Hartog H. W., Arends I. Phys. Stat. Sol. 22, 131 (1967).
13. Patterson D. A., Fuller R. G. Phys. Rev. Letters, 18, 1123 (1967).
14. I. R. O’Connor, I. H. Chen, Phys. Rev. 130, 1790 (1963).
15. L. A. Lisitsyna, Optics and Spectroscopy, 19, 295 (1965).
16. A. A. Vorob’ev, E. K. Zavadovskaya, V. M. Lisitsyn, L. A. Lisitsyna, Izv. vuzov. Fizika, 4, 56 (1969).
17. E. K. Zavadovskaya, L. A. Lisitsyna, A. T. Ovcharov, V. M. Lisitsyn, Izv. vuzov. Fizika, 11, 132 (1967).

ERRATA NOTED