RADIATION DAMAGE AND RADIATION RESISTANCE OF ALKALI-HALIDE CRYSTALS

A. A. VOROB'EV

Introduction

Because of the ever-increasing practical use of alkali-halide crystals, in recent years the volume of scientific research on the effect of radiation on the properties of crystals and on the physical description of irradiation processes has increased considerably.

Ionic crystals have occupied, and continue to occupy, a special place in solid-state physics. Until recently, when people spoke of the theory of the solid state, they had primarily in mind the theory of a crystalline lattice of the NaCl type. At present the theory of chemical bonding in solids has advanced far. The theory of alkali-halide crystals has also progressed.

The interaction of radiation with the lattice of alkali-halide crystals is a new chapter in the theory of ionic structures, one that has been intensively developed in recent times.

Studies of the interaction of radiation with the solid state in Tomsk were begun in 1926 by Academician V. D. Kuznetsov and were continued by Professors P. S. Tartakovskii, V. M. Kudryavtseva, K. A. Vodop'yanov, and others.

Many studies of the action of radiation on ionic compounds are devoted to determining the nature of microdefects and their influence on the properties of bodies. Previously, the choice of research objects was made without taking into account the commonalities and differences in the properties of cations and anions and the periodicity in the variation of their parameters. The published experimental and theoretical materials do not make it possible to draw generalizing conclusions about the dependence of the radiation resistance of alkali-halide compounds on their chemical composition and the conditions of the experiment.

Comparison of results obtained by different researchers is also made difficult by the fact that measurements were carried out under different conditions. For example, results are usually presented as a function of exposure dose or irradiation time, whereas the absorption coefficient for radiation varies significantly with the chemical composition of the crystal and the radiation energy. Therefore, at the same exposure dose, different amounts of energy are absorbed in crystals of different composition, and, consequently, different densities of radiation defects arise.

Standardization of experimental conditions is necessary in studies of the influence of irradiation, and, in publication, it is essential to indicate the dimensions of the samples, the irradiation conditions, the magnitude of the absorbed dose, the dose rate, the temperature during irradiation and during the experiment, etc.

To assess radiation damage caused by various types of radiation, studies of the properties of crystals with the same color-center density should be carried out.

Among the emerging scientific trends in the study of radiation damage in alkali-halide crystals, one may note attempts at scientific generalization and at establishing a connection between the radiation resistance of ionic crystals and their chemical composition and structure through lattice energies, free volume, ionic radii, atomic numbers of the components of the compound, etc.

Of interest are methods for regulating the radiation resistance of crystals by changing their chemical composition, defectiveness, and the geometrical parameters of the lattice.

Studies of microprocesses in crystals under irradiation have become widespread.

The first line of research, important for practical technological applications, should be attributed more to the technical sciences and to materials science.

The second, physical line—studies of microprocesses under irradiation—uses, for solving its problems, the experimental and theoretical methods of modern nuclear physics, with preliminary deep mathematical treatment of the problem.

The synthesis of the two directions listed is of substantial interest, when macroscopic studies are carried out on the basis of a thorough physical treatment of the microscopic picture of physical processes.

Theoretical studies have been published in which the method of statistical trials (Monte Carlo) is used to study cascade showers of secondary particles and microdisturbances during the passage of a high-energy particle through a crystal.

The use of high-speed computers makes it possible to consider many variants of the problem and to choose the distribution function of displaced particles in the crystal during the passage of a high-energy particle that corresponds to the experimental data.

One result of these studies was that the periodic fields of the crystal lattice orient displaced atoms along certain crystallographic directions, as a result of which penetration of the bombarding particles and displaced atoms deep into the crystal over thousands of interatomic distances becomes possible. The motion of ions in a crystal lattice along certain preferential crystallographic directions has been called the focusing action of the crystal lattice. It should be noted that a qualitative physical theory of the motion of electrons in a lattice under the action of a voltage applied to the crystal and of internal electric fields along preferential crystallographic directions was developed by Hippel as early as the nineteen-thirties in the theory of breakdown.

The theory of radiation defects and dislocation theory make it possible to test the influence of point and linear lattice defects on thermal conductivity and electrical conductivity, and to explain satisfactorily the results of experiments.

At the I. V. Kurchatov Institute and abroad, methods have been developed for the direct recording, with the aid of an electron microscope, of individual

radiation damage—the track of a heavy particle in a metal. The tracks of the passage of high-energy particles in mica are revealed by etching.

The use of low temperatures makes it possible to separate the primary physical processes under irradiation from the secondary ones, and to bring the experimental situation closer to the theoretical scheme. The use of materials of very high purity for investigations also contributes to this, since impurities and defects in crystals may distort or completely conceal the primary effects.

S. V. Starodubtsev believes that under intense bombardment by heavy particles, whose penetrating power is small, the surface layer undergoes large radiation damage, bringing this layer into an amorphous state. Under electron bombardment, large damage is obtained not only in the surface layer, but also at the depth where maximum absorption of the electrons occurs.

Polymorphic transformations in alkali-halide crystals, when the free volume and the packing of the crystal change, make it possible to consider the question of the influence of free volume on radiation resistance.

It is likely that the application of the quantum-mechanical theory of anomalous dispersion and absorption, of the type of the Weisskopf and Wigner theory, to a model containing several centers could give positive results for explaining the spectra of alkali-halide crystals.

Irradiated alkali-halide crystals change their properties and, after receiving a large dose, are destroyed. It is necessary to introduce the concepts of radiation resistance of a body and radiation strength of crystals.

Radiation resistance, i.e., the ability of alkali-halide crystals under specified conditions to withstand the action of radiation without damage and without substantial change in physical properties, has not been scientifically defined. There is no clarity as to a crystal of what chemical composition is more radiation-resistant. Perhaps radiation resistance should be introduced not as a general characteristic, but as a particular one with respect to some property or group of properties. Radiation resistance and strength should be defined in such a way that these definitions are of the same type as analogous others, for example, heat resistance or, respectively, mechanical strength, etc.

Radiation resistance will be a function of the energy of the bombarding particle, the dose rate \(J\), and the properties of the material, and is one of its characteristics. If no changes occur in the chemical composition of the absorber, then radiation resistance should not depend noticeably on the irradiation time and, consequently, also not on the dose \(D\), since \(D = J \cdot t\). The number of radiation damages depends on the dose \(D\) and the irradiation time. Radiation strength may be defined as the value of the maximum dose that does not yet cause mechanical destruction of the crystal, or measured by the minimally absorbed dose that causes destruction of the crystal.

To determine the resistance and strength of crystals it is necessary to study the regularities in the change of the absorption and attenuation coefficients of radiation in crystals as a function of their chemical composition, the physical state of the crystal, and the irradiation conditions, and the change in the radiation as it passes through the crystal.

The mechanical, electrical, and thermal strength and resistance of alkali-halide crystals increase with increasing energy

bonds between ions. The dependence of radiation resistance and strength on chemical composition has not been studied.

Upon irradiation, radiation damage and its annealing occur simultaneously. For studying the kinetics of the radiation-damage process and the kinetics of changes in properties, it is of interest to determine the magnitude of the energy required for the formation of radiation damage and for its annealing.

Absorption of electromagnetic radiation in crystals

The interaction of electromagnetic waves, electrons, protons, and other high-energy particles with matter has been well described theoretically. X-radiation, interacting with individual atoms, is absorbed by a crystal through the photoelectric effect and Compton scattering.

In the absorption spectra of chlorine in the compounds CsCl, RbCl, KCl, NaCl, and LiCl, the edge of the absorption band shifts systematically toward higher energies as the atomic number of the metal decreases. In the energy range of X-rays, chlorine atoms can no longer be regarded as free. Their bond with the metal atoms in the crystal deforms the energy levels in the chlorine atom. At higher quantum energies the fine structure of the absorption spectrum will probably be absent.

The absorption of X-rays in alkali-halide crystals was studied by A. D. Shchelokov, E. K. Zavadovskaya, B. I. Yunenko, and others.

The mass attenuation coefficient of X-rays by alkali-halide crystals varies strongly with composition. On going to crystals with a larger total atomic number of the elements forming the compound, absorption of X-rays increases for wavelengths that are shorter than the wavelength of the K-absorption edge of the atoms entering the compound; for example, on going from LiF and KJ, the mass attenuation coefficient increases from \(1.18\ \text{cm}^2/\text{g}\) to \(5.11\ \text{cm}^2/\text{g}\) for

\[ \lambda = 0.22\ \mathring{\mathrm A}. \]

With increasing lattice energy of the crystals, the mass attenuation coefficient decreases.

The mass attenuation coefficient is proportional to the constant

\[ C = p_1 Z_1^{2.58} + p_2 Z_2^{2.58}, \]

where \(p_1\) and \(p_2\) are the weight fractions of the atoms constituting the compound, and \(Z_1\) and \(Z_2\) are the atomic numbers of the atoms in D. I. Mendeleev’s table (or the numbers of electrons in the atoms). Moreover, \(C\) does not depend on the X-ray wavelength \(\lambda\) if \(\lambda \leq \lambda_k\), where \(\lambda_k\) is the wavelength of the K-absorption edge of the atoms.

For the passage of X-rays of a continuous bremsstrahlung spectrum through a crystal, owing to the greater absorption of the long-wavelength part of the spectrum, the X-rays become more homogeneous and, correspondingly, the dependence \(\ln I/I_0 = f(d)\) becomes more nearly linear.

The X-ray attenuation coefficient increases rapidly with increasing wavelength.

At a certain wavelength for a given element, at which the quantum energy becomes insufficient to remove an electron from the \(K\)-shell of the atom, the value of the mass coefficient \(\mu/\rho\) decreases abruptly at the \(K\)-edge. With further increase in wavelength …

the atomic coefficient continues to increase steeply and monotonically up to the next abrupt drop (the \(L\)-edge) and the subsequent next rise.

V. A. Vorob’ev and V. N. Rudenko investigated the absorption of bremsstrahlung from a betatron of 10–30 MeV. A narrow radiation beam with an opening angle of \(5^\circ\) was cut out by a lead collimator with an exit aperture diameter of 20 mm and was absorbed in salt crystals: KCl, KBr, KI. The thickness of the absorbing layer of crystals was varied from 1 to 700 mm.

In the dependences of ionization in a thin-walled ionization chamber on the thickness of KCl, KBr, and KI crystals at an energy of 30 MeV, at depths of 7 mm for KI, 10 mm for KBr, and 13 mm for KCl, the “equilibrium wall” effect sets in and an ionization maximum is observed. The magnitude of the ionization maximum increases with increasing effective atomic number of the elements making up the compound in going from KCl, KBr, KI, while the thickness of the crystal layer at which the absorption maximum is observed decreases.

The growth of the ionization maximum is due to an increase in absorbing power with increasing effective atomic number of the stopping substance.

The decrease in the distance of the maximum position from the beam-entry surface is caused by a decrease in the range of secondary electrons on going to compounds of heavier elements, KCl, KBr, KI.

The falloff of ionization in the crystal occurs according to a law close to exponential. In this region the dependence of ionization in the chamber on the thickness of the absorber in front of it can be represented in the form

\[ I = I_0 \exp(-\mu x), \]

where \(I_0\) is the ionization in the chamber for that absorber thickness in front of it at which the exponential decrease of ionization begins;

\(I\) is the ionization after an absorber layer of thickness \(x\);

\(\mu\) is the attenuation coefficient—linear or mass, depending on the units in which \(x\) is expressed: in cm or in g/cm\(^2\).

The mass attenuation coefficient of 30 MeV radiation is, for KCl, \(\mu_m = 0.027\ \text{cm}^2/\text{g}\); for KBr, \(\mu_m = 0.029\ \text{cm}^2/\text{g}\); and for KI, \(\mu_m = 0.032\ \text{cm}^2/\text{g}\).

The increase in the attenuation coefficient with increasing atomic number of the atoms of the stopping substance is due to the increase in the cross section of the photoelectric effect, pair production, and Compton scattering processes.

The attenuation coefficient changes little with the maximum radiation energy of 10–30 MeV in KCl, KBr, and KI crystals, since, as the pair-production cross section increases with increasing photon energy, the cross sections of the photoelectric effect and Compton scattering decrease. The passage of X-ray or \(\gamma\)-radiation through a crystal is accompanied by the appearance of secondary electrons.

The presence of color centers in alkali-halide crystals gives rise to absorption bands in the visible and ultraviolet regions. The absorption spectra of crystals containing color centers are complex. As yet there is no theory capable of predicting the number, position, and shape of the absorption bands, their change and displacement when the chemical composition, temperature, or pressure is changed.

Under these conditions, experimental regularities and correlations of the energy levels of color centers in various groups of crystals with their other characteristics are of interest.

With a change in chemical composition, the onset and edge of intrinsic absorption and the positions of maxima of exciton absorption in the ultra-

in the violet and infrared regions, and the absorption maxima, with increasing lattice energy of the ionic compounds, shift into the short-wavelength part. The onset, edge, and maxima in the infrared part of the reflection spectrum of ionic crystals shift into the short-wavelength part with increasing lattice energy of the compound.

The refractive index of light in ionic crystals decreases on going to compounds with lower lattice energy.

The positions of the maxima of additional absorption bands that arise in ionic crystals after their coloration, caused by electron and hole centers or by exciton excitation, shift, on going along a series to a compound with lower lattice energy, into the long-wavelength region.

The positions of the maxima of absorption bands of alkali-halide crystals activated by tin, indium, and other impurities shift toward lower energies as the lattice energy of the compounds decreases.

Additional absorption bands arising in crystals with impurities as a result of irradiation shift toward shorter wavelengths with increasing lattice energy.

The spectral fluorescence bands of alkali-halide phosphors activated by impurities shift into the long-wavelength part of the spectrum as the lattice energy of the compound decreases.

On going to the X-ray and bremsstrahlung radiation of the betatron, the determining factor in the absorption of radiation quanta is the atomic number of the elements in the compound. The absorption coefficient of radiation by crystals increases with increasing atomic number and with an unchanged alkali metal.

The position of the maximum of the absorption bands is determined by the empirical Ivey formula. This relation can be obtained from a quantum-mechanical consideration of the behavior of an electron situated in a potential well.

S. I. Pekar, taking into account the electronic and atomic polarization and the effective mass of the electron, determined the position \(\lambda_{\max}\)

\[ \lambda_{\max} = \frac{4\pi C \varepsilon^{2}} {m^{*}\left(0.749 + 0.824\varepsilon C_{1} + 0.173\varepsilon^{2} C_{1}^{2}\right)}, \]

where \(C\) is the speed of light,

\(\varepsilon\) is the dielectric constant,

\(m^{*}\) is the effective mass of the electron.

\[ C_{1} = \frac{1}{n^{2}} + \frac{1}{\varepsilon}, \]

\(n\) is the refractive index.

For \(m^{*}=\mathrm{const}\), for alkali-halide crystals one obtains \(\lambda_{\max}\) as a function of \(n\) and \(\varepsilon\) and its regular displacement upon replacement of anions, but not cations.

The influence of anions and cations consists in the fact that, for crystals having the same cation, the points of the dependence \(\lambda_{\max}=f(\ln d)\) lie on a single straight line. The transition from lithium to sodium and further is accompanied by a shift of the line toward long wavelengths. The influence of cations on the spectrum is stronger than that of anions. The difference between lithium and sodium is greater than between Na and K.

High-energy electrons interact with the electrons of all shells of atoms. In the case when the radiative energy losses of electro-

... still do not play a significant role for us, the magnitude of the energy losses by electrons per unit path length is determined by the electron density in the stopping material and by the binding energy of the electrons in the atomic shells (the mean ionization potential).

Therefore, for alkali-halide crystals, in the series for each alkali crystal, on passing to a halide of higher atomic number, the electron energy losses for ionization and excitation decrease, whereas the energy losses for emission of bremsstrahlung quanta increase. Up to electron energies of 10 MeV, the radiation energy losses by electrons, compared with ionization losses, are small. In crystals, on passing to a halide of higher atomic number and with the alkali metal unchanged, theoretical calculations indicate that there should be an increase in the electron range (in g/cm²).

Experimental investigations by B. A. Kononov and V. N. Rudenko for electrons of energy 5–10 MeV showed that the penetration depth of electrons into crystals (in g/cm²) decreases on passing to a halide of higher atomic number and with the alkali metal constant. The discrepancy between the calculated electron range in crystals and the experimentally determined penetration depth arises because of the greater scattering of electrons in crystals that contain elements of higher ordinal number, i.e., because of the greater lengthening of the electron path in layers of identical thickness.

The increase in the intensity of electron scattering in crystals, as well as the difference between the range and the penetration depth of electrons in crystals on passing to a halide of higher atomic number, must be taken into account in determining the absorbed dose and in establishing quantitative relations between the magnitude of the absorbed radiation energy and radiation damage.

Electrons scattered in deeper layers of the irradiated crystal in the backward direction create an additional dose in the surface layers, the magnitude of which increases on passing to a compound containing elements of higher atomic number. Thus, for example, the contribution to the total dose from backscattered electrons when a NaCl crystal is irradiated with a beam of monoenergetic crystals (betatron) of 5.6 MeV is 8.5%, and for KJ—27%.

Backscattered electrons carry away part of the energy of the electron beam from the irradiated specimen. This must be taken into account when determining the absorbed dose. Electron scattering also leads to the fact that, in planes of the crystal perpendicular to the direction of the beam of bombarding electrons, the dose decreases from the center toward the edge. The dose at the center may exceed that at the edge by 40%.

The penetration depth of electrons into crystals is determined by scattering, and not only by the magnitude of the energy losses per unit path length. As a consequence, according to V. N. Rudenko’s data, the dose distribution in crystals does not coincide with the depth of coloration.

Proton scattering has no significant effect on their penetration depth into crystals or on the magnitude of the absorbed dose. Therefore, for protons, good agreement is observed between the calculated range in crystals and the penetration depth. Thus, according to measurements by D. I. Vaisburd, for protons of energy 5 MeV the penetration depth of protons into crystals (in g/cm²) increases in the alkali-metal series on passing to a halide of higher atomic number.

The absorption coefficient of beta rays increases with increasing sum of the atomic numbers of the metal and the halide.

With decreasing lattice energy, the heat capacity of crystals increases. Thus, with decreasing lattice energy, the absorption by a crystal of energy of all kinds increases; this is probably a consequence of the lowering of the Debye temperature and the decrease in the quantum of vibrational energy of the lattice.

The absorption of radiation of different energy and of heat is determined by substantially different physical processes in crystals. The general form of the dependence of energy absorption on chemical composition is determined by the fact that the final act of radiation absorption is the scattering of heat in the lattice.

Stored energy upon irradiation; stability of radiation damage

M. Born and Huang Kun showed that all the normal mechanical and electrical properties of a crystal and the temperature dependence of its characteristics can be described with the aid of its free energy, which is simply related to the lattice energy.

During plastic deformation or irradiation, energy is stored in crystals, the free energy increases, the stability of the system decreases, and their mechanical and electrical properties change.

The energy absorbed by crystals during their irradiation is expended on heating, on producing various radiation disturbances of the lattice and thereby increasing the internal energy of the crystal, and on the energy of elastic deformation. Thus, after irradiation the crystal possesses an additional, super-equilibrium free energy under the given conditions, which is customarily called hidden, stored, or Wigner energy. The magnitude of the stored energy is related to radiation disturbances and can serve as a measure of their number.

Many properties of alkali-halide crystals are related to the magnitude of their lattice energy. The strength and resistance of crystals to destruction increase with increasing lattice energy.

To produce identical microdisturbances of the lattice—for example, displacement of an ion from a site—more energy must be expended in crystals with higher lattice energy. In crystals with low lattice energy, microdisturbances under given conditions, for example at room temperature, will be preserved less well than in crystals with higher energy, in which radiation microdisturbances will be annealed less readily than in crystals with lower lattice energy. In the simplest case, the stored energy is proportional to the depth of the energy trap or to the product of the energy expended on the formation of one radiation defect by their number. In crystals with low lattice energy, both of these factors should be smaller than in crystals with higher lattice energy. In our view, after isodose irradiation the stored energy in crystals with higher lattice energy should accordingly be greater than in crystals with lower lattice energy.

By heating crystals and determining the stored energy released, one can compare the total amount of stored energy in crystals. By determining the positions of the maxima of heat release, one can estimate the energy \(kT\) characteristic of the type of radiation damage that releases heat.

E. K. Zavadovskaya and A. V. Kuz’mina measured the stored energy of LiF, NaCl, KCl, KBr, and KJ after their irradiation. The stability of radiation defects in the series of alkali-halide crystals should be greatest—

greater than in LiF. Changes in the stored energy in LiF crystals after their irradiation at room temperature with Co\(^{60}\) gamma rays at a dose of \(10^3\) roentgens and with X-rays at a dose of \(10^5\) roentgens confirmed our hypothesis of the high stability of the defects and, consequently, of the high density of stored energy. After the comparatively small exposure doses given above, the stored energy in LiF reached hundreds of cal/g.

In the absorption spectra of irradiated LiF crystals, \(F\), \(M\), \(R_1\), and \(R_2\) absorption bands are observed. The concentration of color centers changes little during storage of the crystals at room temperatures.

The high stability of radiation centers and the large amount of stored energy in irradiated LiF crystals make it possible to recommend them as memory elements for radiation fluxes that have passed through the crystals. From the magnitude of the stored energy one can judge the magnitude of the dose of ionizing radiation.

In NaCl crystals, the stored energy and the concentration of \(F\)-centers increase with increasing dose. In KCl crystals, whose lattice energy is smaller than that in NaCl crystals, the change in these properties already tends toward saturation, and the magnitude of the stored energy and the density of color centers are smaller than in NaCl and LiF.

In KBr crystals, after irradiation doses identical to those for NaCl and KCl, the increase in the density of \(F\)-centers and in stored energy is insignificant, and in KJ it is barely noticeable.

The stored energy serves as a measure of radiation damage.

Table 1 shows the decrease in the magnitude of the stored energy after irradiation with cobalt-60 \(\gamma\)-rays at a dose of \(5 \cdot 10^8\) roentgens.

Table 1

The heat of dissolution of irradiated crystals changes with the dose of \(\gamma\)-irradiation over the investigated range of irradiation doses from 1 to \(5 \cdot 10^8\) roentgens. At smaller irradiation doses the heat of dissolution of the irradiated crystal is less than that for the unirradiated one, whereas at larger irradiation doses the heat of dissolution of the irradiated crystal becomes greater than that of the unirradiated one and increases with increasing dose, as shown in Table 2.

In KCl and KBr crystals, the phenomenon of a change in sign of the difference in heats of dissolution \(\Delta Q\) is not observed because of the small amount of energy stored after irradiation.

Measurement of the stored energy released upon dissolution of irradiated crystals or upon their annealing made it possible to formulate the following regularities, establishing the relation of the stored energy to the chemical composition of the compounds.

1. The magnitude of the stored energy increases with increasing lattice energy of ionic crystals.

1. The amount of energy stored by radiation damage, which releases heat during annealing, increases with increasing lattice energy of the ionic compound. Annealing of radiation defects occurs at higher temperatures.

Table 2

CHANGE

in the difference of heats of solution \(\Delta Q = QH_{\text{irr.}} - Q_{\text{unirr.}}\) as a function of the gamma-irradiation dose

1. The stored energy in crystals increases with increasing exposure dose of irradiation. The increase in stored energy occurs differently in crystals of different chemical composition. In crystals with greater lattice energy, the stored energy accumulates more rapidly than in crystals with lower lattice energy.

At small irradiation doses the heat of solution of the irradiated crystal changes as a function of the irradiation dose. At lower doses it is greater for the irradiated crystal, while at higher irradiation doses the heat of solution of the irradiated crystal becomes smaller than that of the unirradiated one and decreases with dose.

At the temperature of liquid nitrogen and at room temperature, the energy expended on the formation of one \(F\)-center, determined calorimetrically from the value of the stored energy, or optically from the value of the absorbed energy as the ratio of the absorbed dose to the number of retained \(F\)-centers, decreases with increasing lattice energy. The value of the energy of formation of one center, determined in this way, varies within the limits from several eV to \(10^4\) eV for crystals of one and the same composition.

The indicated determinations do not take into account all types of damage and their instability in time, the nonuniform distribution of the density of absorbed energy in the crystal, etc.

After isodose irradiation with X-rays, the density of \(F\)-centers in crystals varies with temperature along a curve with a maximum.

The position \(\lambda\) shifts into the region of higher temperatures in going to crystals with greater lattice energy.

The density of \(F\)-centers at one and the same absorbed dose \(\sim 3 \cdot 10^{19}\) eV/cm\(^3\) and \(T_{\max}\) increase with increasing lattice energy.

The rate of ionic processes in alkali-halide crystals increases with decreasing crystal-lattice energy. In accordance with this, the photo- and thermal stability of \(F\)-centers at the boiling temperature of liquid nitrogen and at room temperature, and at the same number

the incident quanta of bleaching light increase with increasing lattice energy.

Changes in the Physical Properties of Irradiated Crystals

The radiation-induced disturbances that arise after irradiation of crystals change not only the absorption spectra, but also other physical and chemical properties of the crystals.

The degree of change in the properties of irradiated alkali-halide crystals increases with increasing lattice energy.

In experiments by workers in our laboratories, after irradiation of crystals with neutrons, electrons, protons, gamma rays, and x-rays at room temperature, only an increase in microhardness, the elastic limit, and strength was always observed. No decrease in hardness was observed, such as that described by E. L. Andronikashvili, N. G. Politov, M. M. Getia, V. V. Mumladze, and L. F. Vorozheikina.

After isodose irradiation at room temperature, the greater change in properties is observed for crystals with higher lattice energy, which, in accordance with the definitions given above, should be regarded as less radiation-resistant; however, such crystals, according to the accepted definitions, are also more resistant electrically, mechanically, and chemically. This contradiction is a consequence of measuring the characteristics at unequal relative states of vibration of the lattice ions. The contradiction can be eliminated if the measurements are made at identical relative temperatures \(T_{\text{op}}/T_{\text{pl}}\), where \(T_{\text{op}}\) and \(T_{\text{pl}}\) are the experimental and melting temperatures of the crystal.

Dielectric losses in alkali-halide crystals at audio frequencies, in unirradiated and irradiated crystals, depend on the chemical composition. At low temperatures and audio frequencies, relaxation losses predominate, while at high temperatures ohmic losses predominate. In the region where relaxation losses predominate, the loss angle is larger in crystals with lower lattice energy, in which there is a greater possibility of displacement as a result of the lower activation energy of the process. At elevated temperatures, where ohmic losses predominate, \(\operatorname{tg}\delta\) is larger in crystals with higher lattice energy, in which the formation of vacancy aggregates occurs with greater difficulty and a higher density of vacancies, which determine the ionic conductivity, is preserved.

After irradiation of crystals with protons, a thin layer with a high density of defects is formed in the crystals. The penetration depth of protons with an energy of \(4.4\) MeV decreases on going through the potassium series of compounds from crystals with higher lattice energy to crystals with weaker bonding forces between ions and larger ionic radii.

Irradiation of crystals with protons causes a decrease of the relaxation maximum in crystals with higher lattice energy and the appearance of relaxation maxima in crystals with lower lattice energy.

The introduction of divalent impurities of strontium and calcium increases the vacancy density, electrical conductivity, and losses.

At high irradiation doses, enamel-like regions appear on the surface of a crystal with higher lattice energy as a result of the formation of large pores after coagulation of vacancies.

Alkali-halide single crystals of the NaCl type have the highest rate of dissolution in water on the (110) face and the lowest rate of dissolution on the (100) face.

The anisotropy of dissolution of alkali-halide crystals is the greater, the higher the surface energy and the lattice energy of the crystal.

Dissolution of a crystal on the (100) face is determined by a diffusion-kinetic mechanism at relative undersaturations of the solution of less than 0.007; for a KBr crystal, less than 0.011; for a KCl crystal, less than 0.025; for a NaCl crystal, less than 0.030; and for a LiF crystal, less than 1. The indicated limits of solution undersaturation are the higher, the greater the lattice energy of the crystal.

The rates of contact melting of the corresponding faces of alkali-halide crystals stand in the same relation to one another as the rates of dissolution of these faces; i.e., the melting rate of crystals in contact along the (110) face is the greatest, and the smallest in contact along the (100) face.

Irradiation of LiF, NaCl, KCl, and KBr crystals with protons of energy 4.5 MeV (with a dose up to \(10^{19}\) protons/cm\(^2\)) causes an 80% increase in the rate of dissolution of the (100) face of the crystals in the diffusion-kinetic dissolution regime.

At low undersaturations of solutions (for NaCl, 0.007), irradiation of alkali-halide crystals with protons of energy 4.4 MeV and with X-rays of energy 8 keV leads to an increase in the rate of dissolution of crystals along the (100) face, following a parabola as a function of dose and a curve with saturation as a function of the X-ray dose.

The same irradiation dose produces the greatest increase in the dissolution rate in crystals with a higher crystal-lattice energy.

A comparison of the extent to which radiation damage has been studied in metals and in alkali-halide crystals leads to the conclusion that, in the former case, analogous properties—for example, those of mechanically irradiated crystals and their inclination, and others—have been studied more deeply.

Many regularities describing physical microprocesses and macroscopic properties that have been studied in metals can be transferred to alkali-halide crystals. After irradiation of alkali-halide crystals, their mechanical properties change in the same way as after plastic deformation—work hardening. The yield limit, hardness, and brittleness increase; internal stresses and the effects associated with them appear. As in plastic deformation, latent energy is stored in irradiated crystals.

At a temperature far from the recrystallization temperature, neutron irradiation accelerates diffusion. In this temperature interval, the number of new vacancies formed under a given irradiation is comparable with the equilibrium number at the given temperature; therefore irradiation leads to an acceleration of the establishment of equilibrium in the alloy. Thus, superimposed on the diffusion processes accelerated by irradiation is the process of accelerated rearrangement of atoms in the lattice and annealing.

Radiation annealing may occur as a consequence of annihilation of defects or of their absorption by dislocations.

Theoretical calculations lead to the conclusion that in the first case the diffusion rate is expressed by a power-law dependence on the neutron flux with exponent \(+0.5\), while in the second case the dependence should be linear. Experiment confirmed the first hypothesis at high dose rates and a higher rate of defect formation. Consequently, annealing occurs through recombination of defects.

Similar results were obtained when metallic alloys were irradiated with electrons and gamma rays.

In the region of low dose rate and at certain temperatures, the mechanism of vacancy capture by dislocations predominates. Irradiation of metallic alloys accelerates diffusion and the destruction of regions in which order exists, or the precipitation of dissolved substances and the formation of new centers of phase transitions. Do identical defects arise in crystals under irradiation with neutrons, electrons, gamma rays of different energies, etc.? It is usually assumed that they are identical. This answer is based mainly on identical absorption spectra for the different types of radiation and on identical changes in microhardness and certain other properties. In the study of semiconductors, for example indium antimonide of the \(n\)- and \(p\)-types, it has been found that in some temperature regions defects after gamma irradiation anneal out and do not anneal out after irradiation with electrons. This phenomenon may be the result of a difference between the defects formed under irradiation with electrons and with gamma rays.

The explanation of the physical nature of hardening and softening under irradiation, proposed by E. L. Andronikashvili, appears significant: \(F\)-centers decrease hardness, softening the crystal, whereas \(V\)-centers increase hardness and harden the crystal. The microscopic effect of hardening or softening of the crystal depends on the accumulation of \(F\)- or \(V\)-centers.

Under different irradiation conditions the accumulation of \(F\)- and \(V\)-centers proceeds differently.

Different answers are given to the question of the interaction between vacancies and dislocations in alkali-halide crystals.

According to one hypothesis, the intersection of dislocations leads to the formation of vacancies. Another hypothesis explains the formation of dislocations as a condensation of vacancies; a third hypothesis allows for the formation, under neutron irradiation, of dislocation loops, as a result of which vacancies appear.

Since the microscopic processes occurring when single crystals interact with radiation are extremely diverse, a macroscopic approach cannot yet provide a scheme for considering the process of interaction with alkali-halide crystals.

Thermodynamics makes it possible to consider this question from general standpoints, to systematize the available experimental data and the theories of the processes occurring when alkali-halide crystals interact with radiation.

With a decrease in lattice energy, the stored energy and the stability of the radiation damage of \(F\)-centers decrease. The amount of energy absorbed by the crystal increases as the lattice energy decreases. Consequently, radiation-induced changes in the properties of crystals at a fixed temperature are correlated with the stored energy, not with the absorbed or exposure energy.

If tests of radiation resistance are carried out under conditions excluding annealing of radiation defects, then the radiation defects will correspond to the absorbed dose; and the absorbed and stored energies are equal to one another, and are the greater the lower the lattice energy.

Radiation resistance, when determined under comparable conditions in which only irreversible radiation defects occur, will be greater for crystals with higher lattice energy.

Lattice Packing Density and Radiation Damage

The interaction of radiation with a body is determined by the magnitude of the surface density of matter, in g·cm\(^{-2}\). The density of electrons and ions in crystals and the dimensions of the latter determine the probability of their collisions with bombarding particles of high energies, while the free volume in the lattice and the size of the ion determine the possibility of displacement of an ion from a lattice site into an interstice.

Stable radiation damage to the lattice, which determines changes in the physical properties of crystals, is formed as a result of the displacement of ions into interstices, predominantly under the action of energetic ions whose energy exceeds the lattice energy.

S. V. Starodubtsev drew attention to the fact that radiation damage in solids is caused almost entirely by secondary electrons or recoil atoms with energies of the order of 100 eV, for any value of the energy of the primary particles.

Under the action of electrons or ions with comparatively low energies \(10^2\)—\(10^5\) eV, one can obtain the same effects as under the action of high-energy particles. The difference will lie in the depth of penetration of the primary particles and in the development of radiation damage at a greater depth.

If phenomena are studied in a thin surface layer, then the basic radiation disturbances will be the same under irradiation by particles of high and low energies, and the difference will be only in the depth of penetration of the damage.

S. V. Starodubtsev’s proposal to study the radiation resistance of materials by irradiating them with comparable absorbed doses of fluxes of slow particles—electrons, protons, or ions of elements entering into the composition of the target—deserves great attention, in view of its practical advantages while at the same time providing the necessary scientific results.

S. V. Starodubtsev and A. E. Kiv showed that the effectiveness of destruction of the crystal lattice increases when the radiation energy is lowered, although the cross section for elastic displacements, as a rule, decreases in this case.

The formation of defects in crystals is observed at radiation energies below the threshold. To explain these phenomena, Varley proposed the hypothesis of the formation of radiation defects of the lattice after excitation and ionization of anions. Ionization processes of defect formation are of primary importance for dielectric crystals because of their low conductivity \(\sigma\) and the long relaxation time of the nonequilibrium charge distribution, which is determined by the condition \(\tau = \varepsilon/\sigma\), where \(\varepsilon\) is the dielectric permittivity.

S. V. Starodubtsev and A. E. Kiv came to the conclusion that ionization of atomic electron shells in valence crystals can play a major role in defect formation, since as a result of multiple ionization an atom may find itself, for a time greater than \(\tau\), above a potential barrier. Such an atom can move into an interstice.

Multiple ionization of an atom is possible under the action of electrons with energies \(10^4 \div 10^5\) eV, when electrons are knocked out of the \(K\)-shells and subsequent transitions occur as a result of the Auger effect. Calculations show that the change in the potential energy of an atom under multiple ionization may exceed 10 eV. In addition, after the emission of electrons in the Auger effect, the atom receives a recoil energy of several eV. As a result of multiple ionization and the emission of Auger electrons, the atom receives an impulse exceeding the binding energy and leaves the lattice site.

S. V. Starodubtsev and A. E. Kiv consider the Varley mechanism in ionic crystals as a special case of the phenomenon described by them. During the motion of a fast particle, its slowing in the crystal is due to inelastic collisions with atoms. Usually, for ionization, an energy on the order of \(A\) keV is required, where \(A\) is the mass number. When the energy decreases so much that it is insufficient for excitation of atoms, the principal losses will be due to elastic collisions, as a result of which an ion can leave its site. The anisotropy of the crystal leads to the liberated ion producing disturbances along certain crystallographic directions. Investigations have led to the conclusion that the geometrical characteristics of a crystal substantially affect their radiation resistance. Therefore, under isodose irradiation, crystals with a lower packing density are damaged to a greater extent; this density can be characterized by the dimensions of the crystal particles and by the interstitial distances.

Stett, studying by X-ray methods the distortions of the structure of various crystals under bombardment by \(\alpha\)-particles, showed that the distortions of the structure are the smaller, the greater the packing density.

It is known that a dose of fast neutrons of \(10^{20}\ \text{n}/\text{cm}^{2}\) transforms crystalline quartz into amorphous quartz. Coesite—a polymorphic modification of quartz, differing from \(\alpha\)-quartz by denser packing—does not become disordered even at a larger dose.

Rubin and Click showed that the energy efficiency of formation of a single \(F\)-center at the temperature of liquid helium is determined by the parameter \(S_A/D\), where \(S_A\) is the distance between neighboring ions along \([110]\) and \(D\) is the diameter of the halogen atom.

The damages are oriented along the most densely packed crystallographic directions, owing to the greater probability of collisions.

The stability of hole centers against jumps is determined by the degree of overlap of the electron shells of the anions along the \([110]\) axis, which can also be characterized by the parameter \(S_A\).

In considering the dynamics of radiation damage, it is necessary to take into account the free volumes in the lattice and the effective cross sections of the processes.

In the theory of focusing collisions in a lattice, it is assumed that in directions with dense packing of atoms, conditions are created for preferential motion of displaced atoms. The elastic displacement of atoms depends on long-range order in the lattice and is determined by the structural features of the body.

With a greater packing density of materials and a decrease in free volume, the energy required to displace an ion from a site into an interstice increases, cascades of knocked-out atoms decrease, and the configuration of the distribution of point defects changes.

Conclusion

Irradiation of ionic crystals is accompanied by an increase in the free energy of the system, through which one can describe the mechanical and electrical characteristics of irradiated specimens and the temperature dependence of their properties.

An energetic description of the properties of irradiated crystals has certain positive aspects, but up to the present time has not yet become widespread. A decrease in the bond energy of alkali-halide compounds

and, accordingly, a decrease in the fraction of the chemical bond of the ionic type is accompanied by a decrease in the resistance of crystals to external influences, and by a decrease in the activation energy of thermal microdefects.

Processes in the crystal lattice associated with the displacement of particles and vacancies and with the formation of various kinds of damage are unambiguously determined by the lattice energy. Color centers in a crystal have the greater stability, the greater the binding energy between the particles. Under isodose irradiation with X-rays filtered from the soft component at room temperature, the concentration of color centers is greatest in crystals with higher lattice energy.

In crystals with higher bond energy fewer color centers are formed, but fewer of them are also destroyed; therefore, when the dependence of the concentration of color centers on irradiation time is recorded, after prolonged irradiation a higher concentration of color centers is found in crystals with higher lattice energy. Color centers in crystals with lower lattice energy are less stable. The rate of decay of \(F\)-centers decreases as the temperature is lowered. Therefore saturation of the density of \(F\)-centers at low temperatures occurs after more prolonged irradiation.

As the temperature of the experiment is lowered, the concentration of color centers in crystals changes along a curve with a maximum.

The concentration of color centers in crystals is determined by the energy of the quanta and by the density of vacancies in the crystal, and by the change in this density during irradiation as a result of the formation of new vacancies and the destruction of \(F\)-centers. Both of the latter processes are associated with the forces of interaction in the lattice. The activation energy for vacancy formation increases with increasing lattice energy.

For the same exposure dose or absorbed dose, in crystals with higher lattice energy at room temperature an equilibrium density of color centers is preserved.

The number of radiation damages in a crystal is determined by its properties and by the absorbed radiation energy.

Radiation-induced changes in the properties of a crystal are characterized by the stored energy, which is less than the absorbed energy, since during annealing of damage part of the absorbed energy is dissipated, which is favored by the higher thermal conductivity and lower heat capacity of crystals with lower lattice energy.

The fraction of stored energy retained depends on the chemical composition and on the conditions under which the crystal is found.

Crystals with a larger total atomic number of the elements forming the compounds and with lower lattice energy, under isodose irradiation, absorb more energy but store less energy than crystals with higher lattice energy.

The absorbed energy is stored in traps of various depths. As the lattice energy decreases, the fraction of shallow traps increases. The energy stored in shallow traps is dissipated in the crystal by means of thermal fluctuations.

The radiation-chemical action is determined per 100 eV of absorbed energy. In the radiation physics of ionic compounds, evaluation of the effect is more complicated.

Residual changes in the properties of ionic crystals are characterized by stored energy. The absorbed energy could probably characterize the change in physical properties at the moment of irradiation. The energy stored in NaCl irradiated with \(Co^{60}\) radiation at room temperature

at a temperature 200 times exceeds the energy stored during plastic deformation of a specimen destroyed by compression.

The large magnitude of the energy stored in an irradiated specimen causes a large change in its properties. As the energy of ionic bonding increases, the energy capacity of the crystal increases, as does the stored free energy that can be concentrated in a given compound under specified conditions.

An increase in free energy weakens the crystal. Substances with high lattice energy, capable of retaining accumulated energy during plastic deformation or irradiation, can be used as memory elements for the actions that caused in them an increase in free energy.

In determining characteristics and quantities in different temperature regions, the thermal expansion of irradiated crystals is not taken into account—or, speaking more generally, the equation of state of the crystal. It is known from lattice theory that in different temperature regions, for crystals with different ratios of cation and anion masses, changes in the vibrational spectrum and in the binding energy occur differently and are not analogous to one another. Without taking the equations of state into account, and without reducing to definite conditions, as is done, for example, in the theory of lattice vibrations and the theory of heat capacity, there is hardly any basis for comparing the characteristics of crystals measured at different temperatures and pressures.

When radiation falls on the surface of a body, partial refraction of the flux and partial reflection of it occur. At the point of incidence, the temperature rises owing to absorption of the radiation. At the point of incidence a high pressure also develops, the action of which may cause a change in the physical properties of crystals. This circumstance has not yet received attention.

It is time to define the subject matter and method of radiation physics. Until now, the main content of work in the field of the interaction of radiation with a solid has been radiation damage and radiation-induced changes in the properties of the body. The kinetics of radiation damage and the kinetics of changes in properties under irradiation have either not been investigated or have been investigated little.

The analysis of various processes in alkali-halide crystals carried out in this article, using the concept of lattice energy, has made it possible to consider them in a unified way, has helped to clarify the contradictions that had arisen, and to draw interesting scientific and practical conclusions.

The materials presented for alkali-halide crystals apply to some extent to ionic crystals with Coulomb bonding that consist of more complex ions or of compounds of elements of other groups of D. I. Mendeleev’s periodic table.

REFERENCES

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