Physical Properties of Solid Solutions and Their Changes After Irradiation

E. K. Zavadovskaya

Introduction

Alloys of ionic compounds with various dielectric properties have found broad application in practice. Impurities determine the luminescent properties of crystalline phosphors, alter their radiation resistance, and affect many other structure-sensitive properties. All this gives great importance to the study of the properties of alloys of ionic compounds in general and of solid solutions in particular.

Solid solutions, or isomorphous mixtures, are understood to mean all solid phases of variable component composition formed without violation of homogeneity in small volumes. Solid solutions of alkali-halide compounds are generally assigned to the type of substitutional solutions, in which impurity ions occupy regular lattice sites, replacing a cation or an anion in the basic compound.

The theory of “composition–property” diagrams is based on the principles of continuity and correspondence. N. S. Kurnakov’s principle of correspondence [1] is formulated as follows: “With a continuous change in the parameters determining the state of a system, the properties of its individual phases change continuously, while the properties of the system taken as a whole also change continuously, provided that no new phases arise and old ones do not disappear.” With a continuous change in a property of the system (or in other equilibrium factors), its properties also change continuously; the curves reflecting these relationships are likewise continuous [2]. The principle of correspondence also asserts that “to every complex of phases in equilibrium in a given system there corresponds, on the composition–property diagram, a definite geometric image” [1]. In a crystal lattice it is possible to replace some ions by others having close ionic radii; replacement of ions by others with sharply differing ionic radii is possible with a simultaneous change in the valence and radius of the ion.

For alloys of elements whose lattice energy increases in comparison with the initial metals, a decrease in electrical conductivity and an increase in hardness are observed.

Replacement of atoms of the vertical groups located higher in D. I. Mendeleev’s table by those located lower is accompanied by the formation of allo-

ions with lower lattice energy and, as a consequence, lower stability. Therefore, replacement of calcium by strontium or barium will be accompanied by the formation of compounds of lower stability. Replacement of ions in the direction from bottom to top of the group is accompanied by the formation of more stable compounds.

N. S. Kurnakov established that:

1. The formation of solid solutions or isomorphous mixtures is accompanied by an increase in hardness and in the pressure of extrusion through an orifice.

2. The change in hardness and in the extrusion pressure of a continuous series of solid solutions is represented by a continuous curve possessing a maximum.

3. The hardness of a system formed by a mechanical mixture of components is a linear function of composition [3].

According to Seitz [4], in alkali-halide crystal phosphors the centers of additional absorption and luminescence are activator ions replacing cations at the lattice sites of the host compound. The concept of the formation of regular substitutional solid solutions in crystal phosphors activated by small impurities is in agreement with Vegard’s rule on the linear change of the lattice parameter of crystals with increasing impurity concentration.

The intensity of the long-wavelength bands of activator absorption increases in proportion to the impurity concentration; therefore it is generally accepted that these same impurity ions also form the luminescence centers.

Alloys with long-range order are strengthened in the process of plastic deformation considerably more strongly than in the disordered state [5]. To explain this phenomenon, theories have been proposed which proceed from the assumption that, when long-range order is present in a solid solution, the dislocations in it are combined in pairs of superdislocations. The more rapid strengthening of ordered alloys in comparison with disordered ones is explained by an increase in the total area of antiphase-domain boundaries when they are intersected by gliding dislocations, or by the motion of superdislocations with steps on partial dislocations, and also as a result of an increase in the length of superdislocations during plastic deformation [6].

The structure of crystals of solid solutions of alkali-halide compounds is, according to the data of E. K. Zavadovskaya, M. S. Ivashkina, M. N. Treskina, and A. N. Kislina, defective [7, 8, 9]. The density of the crystals determined from macroscopic measurements is less than the density determined from X-ray scattering.

M. N. Treskina, E. K. Zavadovskaya, and I. Ya. Melik-Gaikazyan, having investigated the change in the density of \(F\)-centers and the density of crystals, concluded that in single crystals of solid solutions there are chiefly Schottky-type defects, which determine their physical properties [10].

Later, Smakula et al. [11] also noted the increased defectiveness of KCl—KBr solid solutions in comparison with the components of the solution. But since the density of \(F\)-centers formed upon irradiation of solid solutions with electrons lies between the values of the \(F\)-center density for the components, the authors believe that the defects in solid solutions are mainly not vacancies, but aggregates of submicroscopic dimensions or cracks. All investigators, except [12], point to the presence of defects in crystals of solid solutions of the KCl—KBr system. The most probable defects in crystals of solid solutions are micropores and the boundaries of mosaic blocks.

Single crystals of solid solutions are grown from the melt and from aqueous solutions. Solid solutions are also prepared by pressing powders at elevated temperature. In the latter case it is not stated that a single crystal is obtained, but a table is given showing the high homogeneity of the solution [13].

KCl and KBr have the same structure. The anion radii differ by less than 8%; therefore these compounds mix well and form homogeneous solid solutions.

From the results of X-ray diffraction it follows that in KCl--KBr crystals the anions are randomly distributed throughout the volume, and their positions do not agree with those theoretically expected. The root-mean-square displacement of the anions reaches \(0.03\ \text{\AA}\), and for the cations \(0.08\ \text{\AA}\).

The anions probably have only local, short-range displacements, whereas the cations have displacements both in the short-range and in the long-range order.

In solid solutions, as more defective crystals with weakened bonding forces, various kinds of changes in the crystals may develop more readily upon interaction with radiation. However, the increase in defectiveness in this case will probably be small in comparison with the defectiveness already present in solid solutions; as a result, the properties of irradiated solid solutions change only slightly at small irradiation doses. In this respect solid solutions may prove stable under their operating conditions when radiation acts upon them. But at high doses, the destruction of solid solutions and their radiolysis will probably begin earlier than in crystals of the components of the solid solutions.

Heat of Formation of Solid Solutions

The magnitude of the heat \(\Delta U_{\mathrm{ss}}\), absorbed or released when one component dissolves in another, called the heat of formation of a solid solution, is determined by

\[ \Delta U_{\mathrm{ss}} = U_{ab} - (N_1 U_a + N_2 U_b), \tag{1} \]

where \(U_{ab}\), \(U_a\), \(U_b\) are the lattice energies of the solid solution and of components \(A\) and \(B\).

In (1), compiled according to the rule of mixtures, the change in the energy of the solid-solution crystal caused by lattice deformation and polarization is not taken into account.

The heat of formation of solid solutions of alkali-halide compounds was calculated under the assumption that the ions occupy positions corresponding to the minimum of the potential energy when they are placed in the lattice [14].

Theories of the crystal lattice of ideal substitutional solid solutions of alkali-halide compounds are being developed by analogy with the Born lattice theory for pure alkali-halide compounds.

In both cases the interaction energy of the particles, which determines the properties of the compounds, is calculated.

In the case of binary solid solutions with a variable cation or anion, a random distribution over the corresponding lattice sites of the substituting component is assumed.

In calculating the interaction energy of ions in solid solutions and the heat of their formation, in contrast to pure crystals, the difference in the masses of the substituting and substituted ion is taken into account; as a consequence, the magnitude of the kinetic energy will be different.

As a result of the change in ionic radii, the anharmonicity of the vibrations and the elastic bonds change, which is accompanied by a change in the potential energy of the system.

According to N. S. Kurnakov [3], the stability of solid solutions of alkali-halide compounds decreases with an increase in their heat of formation.

It was subsequently shown that the physical properties of solid solutions are determined by their heat of formation [14], which in turn is related to the defectiveness of the lattice.

The theory of solid solutions of low concentration was reduced to calculating the heat of formation, in which the discrete ionic structure of the crystals in the immediate vicinity of the dissolved ion was taken into account. These theories were useful for analyzing microscopic properties determined by the quadrupole interaction of the nuclei of the solvent ions in the immediate vicinity of the dissolved ion.

In highly dilute solutions, the interaction of dissolved ions with one another may be neglected.

In [15] the theory of solid solutions NaCl—NaBr is considered. Stable crystal lattices will be those in which the energy caused by the displacement of ions and by polarization is minimal.

The positions of three ions, Na, Cl, Br, displaced relative to the positions of the ions in NaCl, are considered. The entire remaining crystal is regarded as a continuous medium. It is shown that in such a model the displacements of the three ions under consideration are small. The additional energy arising in the lattice upon displacement of the ions also has components: attractive forces, van der Waals forces, and repulsive forces.

The heat of solution is equal to the energy of the dissolved ion in the solvent lattice minus the energy of the dissolved ion in the lattice of the substance being dissolved.

In calculating the components of the ion energy, effects of two types are taken into account: electrostatic polarization of the crystal due to the presence of a multipole moment at the center, arising upon displacement of the ions, and their electronic polarization; and, secondly, the elastic disturbances arising in the rest of the crystal due to the stress around the dissolved ion caused by the displacement of the ions.

When Br is dissolved in the NaCl lattice, the lattice expands owing to the larger value of the ionic radius.

Comparison of the results of the calculation with experimental data encounters difficulties, since the data of different coauthors who measured the heat of solution differ considerably from one another.

Theoretically and experimentally obtained data show that the branches of the curve of the dependence of the heat of formation on composition are asymmetric with respect to the equimolar composition. The heats of solution for the NaCl—NaBr branch are greater than for the NaBr—NaCl branch.

The calculated changes in the lattice parameter, taking into account repulsive forces and polarizability, are in satisfactory agreement with experimental data and Vegard’s additivity rule

\[ a = a_1 + (a_2 - a_1) f, \]

where \(a_1\) and \(a_2\) are the lattice parameters of the components, and \(f\) is the fraction of the dissolved substance. The signs of the change in the lattice parameter indicate expansion of the lattice when \(Br^{-}\) ions, which have a larger ionic radius than \(Cl^{-}\), are dissolved in NaCl, and compression of the NaBr lattice when \(Cl^{-}\) ions are dissolved.

Color Centers in Single Crystals of Solid Solutions

When a solid solution is formed, an isomorphous mixture is obtained, characterized by a single crystal-lattice parameter and by a single absorption line in reflected infrared light [16].

The absorption of X-rays is an additive process and, for solid solutions, is determined by the atomic attenuation coefficients and the density of the given kind of atoms.

Measurements of X-ray attenuation coefficients in solid solutions, carried out by A. D. Shchelokov, confirmed their almost linear variation as a function of composition.

E. K. Zavadovskaya, V. A. Popov, and V. D. Rutsko established the additive change of the mass attenuation coefficient \(\psi/\rho\), cm\(^2\), for \(\beta\)-rays from Tl\({}^{204}\) with change in the composition of single crystals of KCl—KBr solid solutions. The smaller attenuation coefficient was observed for KCl and the largest for KBr.

The defectiveness of single crystals, which varied with composition along a bell-shaped curve with a maximum in the region of equimolar composition, did not affect the value of the mass attenuation coefficient of \(\beta\)-rays.

In the visible part of the absorption spectrum of single crystals of solid solutions, after their irradiation, one \(F\)-band is observed. The position of the maximum of this band, its width, and its height are connected with the composition of the solid solution and the measurement conditions. For KCl—KBr and KCl—PbCl [17, 18], the frequency \(U_{\max}\), corresponding to the position of the absorption maximum, is related to the lattice parameter \(a\) by the condition

\[ U_{\max}\cdot a^2 = \mathrm{const}. \tag{1} \]

This condition, probably, can be fulfilled only in the case when Vegard’s rule is fulfilled, which according to our data is usually not observed.

In irradiated single crystals of the systems KCl—KBr; PbCl—KCl, a \(V\)-band is observed [17].

The half-width of the \(F\)-band varies with composition along a curve with a maximum [16]. To explain the nonlinear change of the half-width of the \(F\)-band with crystal composition, the influence of the surroundings of the center is taken into account; in this case the \(F\)-band turns out to consist of several separate bands.

Data on the type of defects in crystals of solid solutions can be obtained from a study of the density of \(F\)-color centers, which are formed on anion vacancies.

According to E. K. Zavadovskaya and T. S. Frangulyan, the density of centers at room temperature in single crystals of KCl—KBr solid solutions varies additively with composition.

The measurements were carried out on crystals that had received identical absorbed doses under X-ray irradiation, equal to \(4.2\cdot 10^{20}\) eV/cm and \(16.8\cdot 10^{20}\) eV/cm\(^3\), which corresponds to the formation of \(F\)-centers on old vacancies present before irradiation and on new vacancies formed after irradiation.

It follows from these results that the increased defectiveness of single crystals of certain compositions of solid solutions is not determined by anion vacancies, on which the density of \(F\)-centers depends.

As also for pure alkali-halide crystals, the coloring curve of a solid solution at room temperature has two regions—a region of rapid nonlinear growth in center density, associated with the formation of \(F\)-centers from vacancies present in the crystal before irradiation, and a region of slow linear growth in the density of \(F\)-cent…

associated with the formation of \(F\)-centers from vacancies generated by irradiation.

The slope of the second section of the coloration curve decreases with increasing KBr content in the solid solution; for the composition 96 mol% KBr, saturation of the \(F\)-center density was observed [18].

E. K. Zavadovskaya and T. S. Frangulyan studied the stability of \(F\)-centers against optical bleaching under illumination with light from the \(F\)-band and against thermal bleaching during storage in the dark. The measurements were carried out at room temperature.

The greatest instability is exhibited by color centers in crystals of solid solutions with a low content of the second component, which is probably connected with the structural features of the crystals. In crystals with a low content of the second component, the distribution of the impurity is more chaotic and the lattice is more distorted than at the equimolar composition. A more strained system is less stable and decomposes more readily.

The dependence of the concentration of \(F\)-centers (\(n_0\)) on the composition of KCl—KBr solid-solution single crystals irradiated with X-rays, after 12 months of aging at room temperature, reveals two minima, corresponding to small percentage contents of KCl and KBr in the solid solution.

Approximately the same compositions correspond to maxima in the values of the ionic conductivity of the crystals and to maxima in the dislocation density and the greatest defectiveness. The \(F\)-centers in these same crystals proved to be the least stable under thermal bleaching.

For freshly colored single crystals of KCl—KBr solid solutions, no dependence of the concentration of \(F\)-centers on the dislocation density was observed.

At room temperature, KBr and KJ have limited solubility, which becomes complete at a temperature somewhat below the melting point.

In crystals colored in potassium vapor at high temperature and then rapidly cooled to room temperature, it was possible to preserve solid solutions even for compositions metastable at room temperatures [19].

Measurements of the \(F\)-band were carried out at room temperature \(298 \pm 2^\circ\mathrm{K}\) and at the boiling point of liquid nitrogen \(97 \pm 4^\circ\mathrm{K}\). The density of \(F\)-centers reached \(2 \cdot 10^{16}\ \mathrm{cm}^{-3}\). At temperatures of \(-97^\circ\mathrm{K}\), the existence of the solid solution was not specially investigated. Aging of the solid solution and a decrease in the density of anion vacancies lowered the concentration of \(F\)-centers. The position of the maximum of the absorption band shifts nonlinearly toward larger wavenumbers of wavelengths with increasing KBr content in KJ. In the region of equal contents of the components, there is a considerable departure from the additivity condition both at room temperature and at the boiling point of liquid nitrogen.

The half-width of the absorption band has a maximum in the region of equal contents of the components at room temperature and at 70 mol% KBr in KJ for the temperature of liquid nitrogen.

No general regularities with respect to the formation of color centers and their stability in solid solutions of alkali-halide salts can be established, since a complete investigation has not yet been carried out for alkali-halide solid-solution systems differing in their stability.

Electrical Conductivity and Dielectric Losses in Crystals of Solid Solutions

Our studies have shown that solid solutions of alkali-halide compounds, although they are substitutional solutions, as N. S. Kurnakov believed, nevertheless have significant deviations and structural disturbances, including vacancies.

As is known, the presence of vacancies can be determined from electrical-conductivity measurements; therefore a considerable number of studies have been devoted to measuring the electrical conductivity of solid solutions. By measuring the total electrical conductivity, or by the method of electron spin resonance, the amount of impurity is determined, for example, in crystals of the solid solutions KCl—Sr, NaCl—Mg, LiF—Na.

The formation of color centers at the corresponding high dose rate may occur both at vacancies already present in the crystals and at new ones formed in the course of irradiation. The primary processes in the initial rapid stage of coloration under the action of x-rays, in pure crystals or in crystals with heterovalent and homovalent impurities, consist in the formation of color centers by capture of positive holes, with the subsequent appearance of negative vacancies. Partially dissolved impurities and the corresponding substructure of precipitates and dislocations play an equally important role in the second, slow stage of coloration by x-rays at room temperature [20].

The study of color centers in solid solutions, in addition to being of independent interest, is essential in investigations of the electrical conductivity of solid solutions and of their defectiveness.

E. K. Zavadovskaya, V. A. Popov, and V. D. Ruchkov measured the temperature dependence of the electrical conductivity of crystals of solid solutions of the KCl—KBr system in the temperature range from 29 to 200°C.

Depending on composition, the electrical conductivity of the crystals at temperatures of 22°C and 111°C varies along a curve with a maximum in the region of the equimolar composition.

The electrical conductivity of unirradiated crystals of solid solutions and of the initial components at a temperature of 22°C is lower than the electrical conductivity of crystals irradiated with protons, \(6 \cdot 10^{14}\) protons/cm\(^{-2}\), with an energy of 4.4 MeV. At a temperature of 111°C, the electrical conductivity of unirradiated crystals increases, compared with the electrical conductivity at 22°C, by four and a half orders of magnitude for KCl and by four orders of magnitude for solid solutions of equimolar composition.

The electrical conductivity of proton-irradiated crystals, upon transition to a temperature of 111°C, increases by three and a half orders of magnitude for KCl and by a little more than three orders of magnitude for the equimolar composition.

As a result, the electrical conductivity of unirradiated crystals of all compositions at 111°C proves to be greater than the electrical conductivity of proton-irradiated crystals.

Proton irradiation causes the appearance of defects in KCl and KBr crystals, as well as in their solid solutions, and the occurrence of a break in the linear course of the temperature dependence of the logarithm of the electrical conductivity.

As a result of the appearance of the indicated break, the dependence \(\ln \sigma = f(t)\) for irradiated and unirradiated specimens intersects, and there is a twofold influence of preliminary proton irradiation of specimens on the electrical conductivity in the region of room and elevated temperatures.

The fracture temperature in the linear dependence \(\ln\sigma = f(t)\) for solid solutions after their irradiation, and the activation energy for electrical conductivity for irradiated and unirradiated crystals, are presented in Table 1.

Table 1

According to V. V. Kushpalenko, the electrical conductivity of crystals of NaCl—KCl solid solutions after X-ray irradiation decreases relatively more strongly than for pure crystals.

The solid solution 12% KCl—88% NaCl decomposes at room temperature, which is accompanied by an increase in electrical conductivity. Irradiation of the decomposed solid solution does not change its electrical conductivity.

After X-ray irradiation the electrical conductivity of KCl crystals decreased, while that of KBr increased. It is probable, therefore, that in crystals of solid solutions with a predominant KCl content a decrease in electrical conductivity was observed, while in crystals with a predominant KBr content an increase in electrical conductivity was observed. These phenomena were especially clearly observed after large doses. In the linear dependence \(\ln\sigma = f(t)\) there is a bend. The temperature at which this bend in the dependence occurs and annealing of defects begins, as well as the temperature of complete annealing, shifts with increasing dose toward higher temperatures. For single crystals of solid solutions of the KCl—KBr and KCl—NaCl\({}^{[[unclear: superscript reference]]}\) systems, it decreases with increasing X-ray irradiation dose and, after a certain dose, reaches saturation.

The activation energy for electrical conductivity in solid solutions is greater than for the pure components. The electrical conductivity of solid solutions is also greater than the electrical conductivity of the components. Consequently, the electrical conductivity of solid solutions increases owing to a considerable increase in the pre-exponential factor compared with the initial components. The pre-exponential factor increases in proportion to the concentration of current carriers and to the length of their path. The concentration of charges in single crystals of solid solutions increases as a result of the increase in their defectiveness.

According to [21], the pre-exponential factor in the expression for electrical conductivity \(\sigma_0 = N \dfrac{\nu a^2}{KT}\), where \(N\) is the number of ions in \(1\ \mathrm{cm}^3\), \(a\) is the lattice parameter, and \(\nu\) is the frequency of jumps of ions from one site to another. According to these data, the jump frequency \(\nu\) in solid solutions increases significantly.

According to K. A. Vodop’yanov and G. P. Patakhova, for single crystals of solid solutions of the systems RbCl—KCl, NaCl—NaBr, KI—KBr, the dielectric losses at high frequency, \(\lambda = 30 \div 600\) m, at room temperature have a maximum in the region of equimolar compositions. With a decrease in the melting temperature of the single crystals and a decrease in the stability of the compound, the loss angle increases.

Microhardness and Other Properties of Solid Solutions

In crystals of solid solutions, considerable internal stresses arise, causing changes in their mechanical properties and cracking.

The broadening of exciton bands, measured from the shift of the ultraviolet absorption edge, was greatest for the composition KCl—KBr \(= 2 : 1\). It is possible that this indicates the presence of short-range order in KCl—KBr crystals. Microhardness, dislocation density, electric strength, and heat of formation are nonadditive characteristics of composition for single crystals of solid solutions of the KCl—KBr system, with a maximum of the characteristic in the region of the equimolar composition.

The microhardness of single crystals of solid solutions of the KCl—KBr system, depending on composition, changes along a curve with a maximum at the equimolar composition.

After irradiation with protons, \(7.6 \cdot 10^{14}\) protons/cm\(^2\) with energy 4.8 MeV, the microhardness of crystals of all compositions increases.

For pure KCl and KBr crystals, the increase in microhardness is approximately 50%, respectively, while for crystals of equimolar composition it is 27%.

E. K. Zavadovskaya and V. V. Kutsepalenko observed an increase in microhardness and a decrease in the length of the rays of dislocation etch figures around the indenter in pure crystals after their irradiation with \(\gamma\)-rays from Co\(^{60}\), X-rays, and electrons.

Irradiation of single crystals of solid solutions KCl—KBr and NaCl—KCl is accompanied by an increase in their microhardness and a decrease in the length of the rays of etch figures. These changes are smaller than the changes of the same quantities for pure crystals. No change in the yield limit of crystals of solid solutions after their irradiation with neutrons, \(10^{11}\) cm\(^{-2}\), and with X-rays at doses up to \(10^4\) roentgens was observed.

A. A. Botaki studied the dependence of Young’s modulus on the composition of solid solutions by an ultrasonic method. The dependence of Young’s modulus on the composition of solid solutions has the form of negative nonadditivity for solid solutions of the KCl—KBr and NaCl—NaBr systems, with a minimum occurring in the region of compositions close to equimolar. The greatest decreases in the value of Young’s modulus are observed for the NaCl—NaBr system, which is distinguished by a higher heat of formation and lower stability.

Breakdown Voltage of Single Crystals of Solid Solutions

Electrical breakdown of alkali-halide crystals is an electronic process. According to the ideas of A. A. Vorob’ev and G. A. Vorob’ev, in thick layers breakdown occurs as a result of impact ioni-

…ionization, initiated by a single electron, and in very thin crystals it is a multi-avalanche process.

For the development of impact ionization and an electron avalanche, the medium in which this process, preceding breakdown, develops is essential. Disturbance of the regularity of the crystal lattice by the introduction of dissolved ions, the subsequent decomposition of the solid solution and precipitation of phases, and the appearance of block boundaries disturb the regularity of the structure, increase the thermal resistance to phonon motion, and reduce the speed of sound.

In our earlier works it was suggested that disturbance of the lattice regularity can substantially hinder the motion of low-energy electrons, prevent their accumulation of the energy necessary for impact ionization, and impede the development of prebreakdown phenomena.

Decomposing solid solutions, in which various degrees of disturbance of the homogeneity of the structure and continuity of transitions are possible, are of great scientific interest for studying the conditions of electron motion. Studies of the electric strength of single crystals of solid solutions, carried out earlier by Hippel, A. M. Trubitsyn, and L. N. Kislina, were conducted under different conditions, which makes comparison and analysis of their results difficult.

Hippel broke down, at constant voltage, single crystals of solid solutions of the KCl—KBr system; with an increase in content up to 20 mol% KBr the strength increases. With a further increase in the KBr content (20–80%), the breakdown voltage changes irregularly along a broken line. This course of the dependence is possibly determined by the decomposition of the solid solutions.

A. M. Trubitsyn and A. N. Kislina, in order to normalize the conditions, annealed KCl—KBr single crystals before breakdown for 4 hours at a temperature 60–100°C below the melting temperature.

The breakdown voltage measured at the front of a single pulse for annealed and unannealed crystals varied along a curve with a minimum in the region of the equimolar composition.

When measuring the breakdown voltage of single crystals of other systems as well, no general regularities in the change of strength with composition were established.

In the experiments of G. A. Vorob'ev, E. K. Zavadovskaya, and T. Kocherbaev, attention was paid to normalizing the experimental conditions and normalizing the specimens. The specimens were annealed for 10 hours at a temperature equal to 75% of the melting temperature. The specimen thickness was 0.1 mm.

For specimens prepared from a single block, microhardness, the breakdown voltage at the front of a single pulse of duration \(4 \cdot 10^{-6}\) sec, density, and so forth were measured.

The totality of the measurements makes it possible to draw a conclusion about the state of decomposition of the solid solution and about certain other physical properties of the crystals being broken down.

The breakdown voltage for unannealed specimens was measured 2–3 days after their growth and, for annealed specimens, after 5–6 days.

The chemical composition of the specimen was determined by potentiometric titration.

The breakdown voltage for unannealed specimens of the KCl—KBr systems at low contents of 10–20% of the second component is considerably lower than the breakdown voltage of the components.

The lowest breakdown voltage is exhibited by single crystals of the compositions 14 mol% KBr in KCl and 18% KCl in KBr. With a further increase in the content of the second component, the breakdown voltage also increases, reaching a maximum in the region of 30–40% KBr in KCl.

The observed correlation between electrical strength, block structure, and dislocation density in solid-solution crystals appears to be of substantial importance. Dislocations are a geometrical violation of the homogeneity of a crystal of unchanged chemical composition. T. Kocherbaev, comparing the composition dependence of the dislocation density measured by M. N. Treskina with the breakdown voltage of crystals of the same composition, came to the conclusion that disruption of the geometrical regularity of the structure reduces electrical strength, whereas the introduction of impurities forming a solid solution increases electrical strength.

This regularity must be verified on the same crystals.

At present it is still not possible to draw reliable conclusions regarding the dependence of the breakdown voltage of solid-solution single crystals on composition, since this dependence is complicated by the influence of the state of the macrostructure, dislocations, mosaicity, and other factors affecting the breakdown voltage that were not taken into account in the measurements performed.

According to Kocherbaev, the change in the defectiveness of solid solutions that occurs in them as a result of storage of the specimens (for 5 months) and irradiation with protons in doses from \(1 \cdot 10^{14}\) protons/cm\(^2\) to \(6 \cdot 10^{14}\) protons/cm\(^2\) causes a decrease in the electrical strength of KCl and KBr crystals and their solid solutions. The decrease in electrical strength as a result of aging of the specimens amounts to from 5% to 12%, relative to fresh specimens, depending on their composition. The smallest change in electrical strength is observed for the equimolar composition.

The decrease in electrical strength after irradiation with protons is, for KCl crystals, 49.8%; for KBr, 58%; and for the solid solution 30 mol% KBr in KCl, 58%. The data presented may for the time being be regarded as approximate with respect to numerical values. We note the existence of a decrease in electrical strength occurring in alkali-halide crystals and their solid solutions after irradiation with protons. The investigations are continuing.

General conclusions on the regularities of solid solutions of alkali-halide compounds

1. Depending on the composition of the solid solution of alkali-halide compounds in a stable state, the following in some cases vary along a curve with a maximum: heat of formation, flow pressure, microhardness, width of the \(F\)-absorption band, electrical conductivity, electrical strength, and dielectric losses.

2. Deviations from the indicated concentration dependences of various characteristics are often observed; these are probably partly associated with insufficiently firmly established experimental conditions and with the strong dependence of the characteristics on the state of decomposition of the solid solution.

3. Some properties of solid-solution crystals vary approximately additively and linearly with the composition of the solid solutions. These include: refractive index, X-ray attenuation coefficient, \(\beta\)-radiation, and lattice parameter.

1. The properties of crystals of solid solutions change upon aging. The rate of aging is determined by the conditions and the heat of solution, which is a measure of the stability of the solid solution. The most rapid aging and heat release occur during the first two months of storage of the crystal at room temperature.

2. Some physical properties of single crystals of solid solutions are determined by the heat absorbed during their formation. As the heat absorbed in the formation of a solid solution decreases, its stability against decomposition, its electrical and mechanical strength, melting point, and thermal conductivity increase; its hardness, coefficient of thermal expansion, and deviation from the additive value of the density and molecular concentration decrease. For characteristics of solid solutions whose magnitude varies with composition according to a curve with a maximum, the greatest changes occur at equimolar compositions, during the formation of which the greatest amount of heat is stored.

The heat of formation increases with increasing defectiveness of the lattice, in which energy is stored during the formation of the solid solution.

1. The lattice structure of single crystals of solid solutions is characterized by a chaotic distribution of dissolved ions, the presence of defects of the type of interstitial ions, vacancies (Ya. I. Frenkel defects), pores, blocks, and dislocations.

The density of defects that decrease the density of the crystal is maximal for equimolar compositions. The dislocation density varies along a complex curve with maxima in the region of low concentrations and a diffuse minimum in the region of the equimolar composition.

1. The theory of solid solutions is constructed on the model of the theory of ionic lattices for determining the main characteristic of the change in the potential energy of the system upon formation of a stable solid solution, characterized by a minimum of interaction energy. The theory of thermal conductivity, thermal expansion of crystals, and so forth is constructed separately.

2. Upon irradiation of solid solutions, radiation damage arises in them, in which energy is stored. Since the structure of solid solutions has defects and the system already contains excess stored energy, the relative change in the density of stored energy in crystals of solid solutions will be smaller than in crystals of the components, and, correspondingly, the change in the properties of crystals of solid solutions determined by the magnitude of the energy stored during irradiation will be smaller than for crystals of the components.

Significant difficulties in establishing the regularities of changes in the properties of solid solutions are the insufficient degree of purification of the starting materials, the uncertainty of the chemical composition of the crystals, and the high sensitivity of the properties of crystals of solid solutions to the presence of multivalent ions. All this makes it difficult to compare research results. It is necessary to standardize the study of the properties of crystals of solid solutions and to have specimens of the required high chemical purity.

Measurements should be made of the properties of crystals that have received the same absorbed dose of the given radiation or have the same density of color centers, at identical \(T/\theta\), where \(T\) is the temperature of the experiment and \(\Theta\) is the Debye temperature, or \(T/T_{\text{pl}}\), \(T_{\text{pl}}\) is the melting temperature.

In recent years interest has increased in the study of the properties of solid solutions of alkali-halide compounds. Works are appearing on the study of

to the investigation of certain properties. All these studies have substantial shortcomings, since they consider solid solutions under the conditions of the investigation as not decomposing and not changing their properties. Meanwhile, as can be shown, the compositions often studied under experimental conditions either decomposed or aged, which was not taken into account in the investigations.

In experiments with alloys of alkali-halide compounds, one should draw upon the extensive practice of investigating the properties of metal alloys, in which the kinetics of properties and processes is taken into account.

Let us recall that the theory of metallic alloys and refractory ceramics began with the study of the properties of alloys of alkali-halide compounds.

It is now appropriate to use the richer practice of the theory of metallic alloys for developing the theory of alloys of alkali-halide compounds.

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