PROCEEDINGS
OF THE TOMSK ORDER OF THE RED BANNER OF LABOR POLYTECHNIC
INSTITUTE named after S. M. KIROV

Volume 140　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　　1965

CHANGES IN THE PROPERTIES OF IONIC COMPOUNDS

WITH CHANGES IN CHEMICAL BONDS

A. A. VOROB'EV

The theory of the chemical bond shows that in crystals the configuration of the electron shells corresponds to the states \(1S^2\), \(2S^2\), and \(2p^6\) for the Na ion, and to the states \(1S^2\), \(2S^2\), \(2p^6\), \(3S^2\), and \(3p^6\) for the Cl ion.

With a uniform distribution of charges in ions, the interaction energy arising between neighboring ions depends only on the distance between them and is given by Born’s formula. The magnitude of the repulsive force between ions is determined by the distribution and number of electrons in the outer shells of the ions. For \(Na^+\) ions, which have eight electrons in the outer shell, the exponent is larger than for lithium ions, which have only two electrons in the outer shell. Quantum-mechanical corrections to Born’s theory made it possible to take into account the crystal energy at \(^{\circ}K\) and an addition to the energy of cohesion forces, allowing for the van der Waals interaction between ions or atoms of the inert-gas type. For alkali-halide crystals, the increase in the energy of attractive forces due to van der Waals interaction—dipole-dipole and dipole-quadrupole—amounts to several percent of the total lattice energy; for silver halide compounds, owing to their greater polarizability, the increase in the interaction energy is greater and for AgBr reaches 14%.

The correction due to van der Waals interaction forces in the compounds under consideration is greater for heavier elements, which undergo greater polarization.

The correction due to the zero-state energy is large for compounds formed from light elements, for which the frequency of the characteristic Debye vibrations is higher.

Consequently, a change in the chemical composition in the series of alkali-halide compounds is accompanied by a change in the specific role of a certain type of chemical bond in the compound, which is associated with a change in their properties, traced by us experimentally.

The chemical bond in ionic crystals is described theoretically without taking into account its changes upon deviation from the stoichiometric composition of the compound, the presence of impurities, or disruption of the calculated structure. Deviations of a real crystal from the ideal substantially alter

many physical properties of crystals, including structural stability. When impurities are introduced into a crystal, a change in the type of chemical bond is possible, as is observed for semiconductors.

In 1925, Fridericks proposed that compounds in which not all valence electrons are in a bound state have high electrical resistance. He also noted the low electronic conductivity of molecular crystals.

In 1944, Maier drew the following conclusions.

1. The electrical specific conductivity of solid compounds is connected with the mutual arrangement of electrons in the atoms constituting the compound.

2. Semiconductors and insulators are compounds with normal valence. Compounds that do not conform to the valence rule, and compounds with structural deviations from stoichiometry, are metallic conductors.

A decrease in the bond energy in a molecule of alkali-halide compounds, and correspondingly a decrease in the fraction of chemical bonding of the ionic type, is accompanied by a decrease in the stability of the crystals against external influences; this was investigated at the Tomsk Polytechnic Institute.

For a given type of crystal structure of ionic alkali-halide compounds, their physical and chemical properties change systematically when the cation or anion is replaced by another of larger ionic radius.

The energy of the crystal lattice decreases with increasing sum of the atomic numbers of the halide and the alkali metal \((Z = Z_{\mathrm{h}} + Z_{\mathrm{m}})\), approaching, at large \(Z_{\mathrm{k}}\), a constant value.

A change in the energy of the crystal lattice is accompanied by changes in the physical and chemical properties and characteristics of the compounds determined by this quantity. For example, with decreasing lattice energy there decrease the heats of formation of the compound, dissociation, hydration, melting, activation in diffusion, ionic electrical conductivity, dielectric losses, the heat of activation in the formation of ionic vacancies, the melting temperature, and the mechanical and electrical strength of the body; the time for healing defects in the lattice, the temperature of decomposition of vacancy aggregates and defects, and consequently the time and temperature of annealing of crystals, etc., are reduced.

Processes in the crystal lattice associated with the displacement of particles and vacancies and with the formation of various damage centers are determined unambiguously by the lattice energy.

Regular changes in properties are observed for real defective crystals, which is probably a consequence of the dependence of the equilibrium concentration of vacancies, dislocations, and other physical defects of the crystal structure on the composition of the compound and on the conditions in which it is found. In crystals with lower lattice energy, defects form more readily and with lower activation energy, but they also heal more readily. Therefore, after identical treatments, a lower equilibrium concentration of defects will remain in crystals with lower lattice energy. As a result, KJ crystals will have a more perfect structure than LiF crystals. This conclusion is confirmed by many kinetic regularities in the change of properties under action on a crystal, when processes of accumulation and annealing of defects occur simultaneously. Owing to the slow formation, accumulation, and retention of defects, in crystals with higher lattice energy the kinetic curves characterizing changes in the properties of such crystals under external action at first rise slowly,

and then, as defects accumulate, faster. For crystals with low lattice energy the kinetic curves have a different course. In accordance with the rapid increase in the concentration of defects at the beginning of the process, a rapid change in the property and in the corresponding characteristic is observed; then there is a slowing of this growth and saturation, which sets in when the rate of growth of defects becomes equal to the rate of their decay.

In agreement with the proposition stated above concerning the low concentration of defects in crystals with a small binding energy between ions is the well-known fact that in KJ crystals it is difficult to create \(F\)-color centers, since there are few vacancies in them. After the creation in a KJ crystal of vacant anion sites and the coloring of the KJ crystal, the \(F\)-centers in the crystal are rapidly destroyed at room temperature. Defect healing occurs. Therefore, after its bleaching the crystal is again difficult to color. The electronic properties of crystals and their characteristics are in a regular dependence on the lattice energy. The electronic properties can be considered by representing the crystal as a system of interacting ions. In this case the principal filled band of energy levels and the conduction band are associated with a definite state of the ions forming the crystal. To determine the electronic levels in isolated atoms, we take the rest energy of a free electron in vacuum to be zero. The lowest free level of the free ion \(\mathrm{Na}^+\) corresponds to the \(3S\) state, which is located below the zero level by an amount equal to the ionization energy, \(5.12\ \mathrm{eV}\). The highest filled level for the ion \(\mathrm{Cl}^-\) is \(3p\), located below the vacuum level by the amount of the electron affinity energy to the atom \(\mathrm{Cl}^-\), equal to \(-4\ \mathrm{eV}\).

Consequently the free \(3S\) level lies below the occupied \(3p\) electronic level by \(1.12\ \mathrm{eV}\).

As the free \(\mathrm{Na}^+\) and \(\mathrm{Cl}\) approach each other and the energy of the Coulomb interaction increases, the relative position of the energy levels changes, and at some distance between the ions a change occurs in the mutual arrangement of the electronic levels; with a further decrease of the distance between the ions, the occupied upper \(3p\) levels of the \(\mathrm{Cl}^-\) ion are located lower than the free \(3S\) levels of \(\mathrm{Na}^+\).

When the distance between ions reaches a value equal to the lattice period, at which the wave functions of neighboring ions of the same sign overlap, the discrete atomic electronic levels then broaden into bands. The lattice period determines the distance between the bands and the width of the bands. The levels corresponding to pairs of like-named ions overlap, forming an energy band. Thus, the scheme of energy levels for electrons in crystals proves to be connected with the lattice parameter and its energy structure on the one hand, and, on the other, with the electronic structure and the levels of the atom. For example, the lower filled band of the NaCl crystal is connected with the upper filled \(3p\) levels of the \(\mathrm{Cl}^-\) ions, while the free upper energy band of the crystal corresponds to the lower unoccupied \(3S\) levels of the \(\mathrm{Na}^+\) ions.

As a consequence of the foregoing, experimental regularities are observed that describe the connection between electron-hole transitions in alkali-halide crystals and the energetics of the ionic lattice. With decreasing crystal-lattice energy, the width of the forbidden energy gap for electrons in the crystal, \(\Delta E\), decreases; the ...

dielectric constant $\varepsilon$. For alkali-halide crystals with $F$-centers, Mott’s formula $\varepsilon^{-2} \approx \Delta E$, proposed for impurity semiconductors, is approximately satisfied.

The systematic increase of $\varepsilon$ with decreasing $U$ is a consequence of the increase in the polarizability of the anions in going from fluorides to iodides and of the cations in going from lithium to cesium, as well as of the weakening of the Coulomb bonds in the structure and the increase of the van der Waals components of the chemical bonds in these compounds. With the indicated substitutions of the chemical composition of alkali-halide compounds and changes in their chemical bond, their properties vary within the limits from a good dielectric, such as lithium fluoride, stable under normal conditions, to semiconductors, which cesium iodide approaches.

With increasing lattice energy, the refractive index of light and the absorption of radiation in a broad energy range decrease. The position of the short-wavelength edge of the intrinsic absorption band, of the maxima of intrinsic and additive absorption in the infrared, visible, and ultraviolet parts of the spectrum in crystals activated by impurities, shifts toward the short-wavelength part of the spectrum when, in a given series of compounds with an unchanged cation, one passes to crystals with higher lattice energy.

Some physical processes in crystals are not directly connected with the energy of the crystal lattice, for example, the scattering of phonons, photons, and high-energy particles by atoms that form part of the crystal. These processes are determined by the magnitude of the scattering cross section of the centers, the magnitude of the ionic radius, the number of electrons, and so forth. With increasing ionic radii, the scattering of particles, phonons, and photons also increases, and the energy of the crystal lattice decreases. Thus, with decreasing lattice energy, an increase is observed in the absorption of radiation and in the scattering of phonons, and a decrease in the thermal conductivity and the speed of sound in crystals.

The indicated correlation makes it possible to extend to these properties as well the possibility of classifying the properties of ionic structures by means of a single characteristic of the crystal—the energy of the crystal lattice.

The properties of structures with other types of chemical bond can also be classified by means of an energy characteristic. For example, for semiconductors with covalent bonding, a correlation is observed between many properties and the magnitude of the atomization energy or the heat of formation of the compound.

The classification of the properties of polymers, as for crystals, may be based on the magnitude of the bonding forces between the structural units forming the polymer into which it decomposes upon destruction.

An increase in the bond energy between structural elements in glasses is accompanied by an increase in the temperature and heat of glass transition, in the thermal, mechanical, and chemical stability of the glass, and by a decrease in the loss angle and electrical conductivity, with a shift of the region of anomalous dispersion of the dielectric constant and losses to the region of higher temperatures.

The radiation resistance of solids changes with a change in the type of chemical bond. In order of resistance to the action of ionizing radiation, chemical bonds are arranged in the following order: metallic, covalent, ionic, and the least stable, molecular.

When the halide is substituted in the series of alkali-halide compounds in going from fluorine to iodine, the Coulomb component decreases

and the van der Waals component of the lattice energy increases. The accumulated experimental material makes it possible to correctly assess the changes in the properties of compounds as their chemical composition changes, and to approach the consideration of the regularities of chemical bonding in the solid state, which is at present one of the central problems of solid-state physics and chemistry.