The F+ center in reactor-irradiated aluminum oxide

A point-ion calculation has been performed for the F⁺ center in α-Al₂O₃ (one electron in an O^2? vacancy). Optical transitions are predicted at 2·26, 3·39 and 5·15 eV. Contact hyperfine interactions with the two nearest pairs of Al³⁺ ions are calculated to be 151 and 39 G. Single crystals of α-Al₂O₃ were reactor-irradiated up to doses of 10²⁰ fast neutrons per cm², and studied by electron spin resonance (ESR). A broad ESR spectrum with 13 resolved components at g=2·0029±0·0005 was interpreted as the interaction of an unpaired electron with two pairs of Al³⁺ nuclei with hyperfine constants of 49·2 and 13·5 G. These values are in the same ratio as the values calculated for the F⁺ center, to which this ESR spectrum is attributed. The discrepancy of a factor of three is typical of point-ion calculations. The optical absorption spectrum for heavily-irradiated samples is not available for comparison with calculated transition energies.     

Magneto-optical spectroscopy and optical detection of EPR spectra of Yb<Superscript>3+</Superscript> paramagnetic centers with cubic symmetry in single crystals <Emphasis Type="Italic">Me</Emphasis>F<Subscript>2</Subscript> (<Emphasis Type="Italic">Me</Emphasis> = Cd,Ca, Pb)

Cubic paramagnetic centers formed by Yb³⁺ impurity ions in fluorite-type crystals MeF₂ (Me = Cd, Ca, Pb) have been investigated using electron paramagnetic resonance, magnetic circular dichroism, magnetic circular polarization of luminescence, Zeeman splitting of optical absorption and luminescence lines, and optical detection of electron paramagnetic resonance. The g factors of the ²Γ₇ state in the excited multiplet ² F _5/2 of Yb³⁺ ions in Me F₂ crystals, the hyperfine interaction constant ¹⁷¹ A (¹⁷¹Yb) for the excited multiplet ² F _5/2 in the CaF₂ crystal, and the energies and symmetry properties of all energy levels of Yb³⁺ ions in MeF₂ crystals are determined. The crystal-field parameters for the crystals under investigation are calculated.     

On the 2<Emphasis Type="Italic">s</Emphasis>-like relaxed excited state of the <Emphasis Type="Italic">F</Emphasis> center in alkali halide crystals

The energy and spectroscopic characteristics of the first excited 2s-like electron state of the F center are presented according to the calculations performed in the framework of the variational model proposed by Gourary and Adrian. The relaxation of the crystal lattice in the vicinity of the excited F center is described. The problem of the spatial propagation of the F center is discussed. The results obtained for the 2p and 2s states of the F center are compared with each other and with the relevant experimental data.     

Accurate core binding energies of ions from Dirac-Fock calculations combined with experimental atomic binding energies

Core binding energies are reported for the singly-charged alkali ions obtained by removing the outer s electron and for the singly-charged halide ions obtained by adding a P_{$\text{3}\text{2}$} electron. The levels studied are Li 1s, Na 1s, K 2p, Rb 3p, Cs 3d, F 1s, Cl 2p, Br 3p and I 3d. The binding energies were obtained by combining DiracF?ock ΔSCF binding-energy shifts between the ions and the corresponding isoelectronic rare gases with experimental rare-gas binding energies, and also by combining the calculated atomīon shifts with experimental atomic binding energies where available. It is shown that the former approach corrects accurately for the correlation energy, which is not included in single-configuration calculations.     

Excited states of a bound polaron

Expressions for the energies of the 3s, 3p and 3d states of a polaron, bound to a positively charged impurity ion in a polar crystal through a Coulomb potential, are obtained in analytic forms using perturbation theory. The values of these energies are calculated in several polar crystals.     

Ultraviolet photoemission study of LiF

Photoemission from evaporated films of LiF were measured at photon energies of 10-27 eV. The photoelectron spectra exhibit features that can be identified as density-of-states structures in the valence and conduction bands of LiF. Regions of high density of states can be seen at ca. 3.3 and 7.8 eV above the vacuum level. The valence-band spectrum shows a doublet structure similar to the calculated density of states for the F^?2p band of LiF. The base width of this structure is found to be 4.6 ± 0.3 eV. The photoelectron spectra for photon energies > 15 eV indicate that the highest occupied states of the F^?2p band are located at 11.8 ± 0.3 eV below the vacuum level. The photoelectron spectra in the exciton region, however, show photo-emission from higher occupied states.     

Diffusion of one- and two-electron vacancy centers in polar crystals

The change in the diffusion barrier for anion vacancies in polar crystals is calculated in the case where one electron (F centers) or two electrons (F′ centers) are captured. The lowest singlet and triplet states are considered for the two-electron system. It is shown that the capture of two electrons on the lowest metastable triplet state (which is possible under nonequilibrium conditions, for example, in the case of either exchange scattering of band electrons or thermal refilling of energy levels) leads to a decrease in the diffusion barrier for the system. However, for the two-electron center in the lowest singlet state, the potential barrier to migration, as a rule, is higher than that for a vacancy without electrons. Calculations are carried out for Gaussian functions with the inclusion of the effects of interelectron correlations and electron-phonon interactions.     

Temperature behavior of the 6.05-eV band in optical absorption spectra of oxygen-deficient corundum

The effect of temperature on the 6.05-eV absorption band in α-Al₂O₃ has been studied in the 80–515 K region. The data obtained are analyzed in terms of a one-coordinate model with strong electron-phonon coupling. This band is shown to be formed by two peaks at 5.91 and 6.22 eV (T=293 K) originating from absorption at the F ⁺ and F centers, respectively. An analysis of the experimental temperature dependences has allowed us to calculate the energies of effective phonons responsible for the broadening and shift of the peaks. The energies calculated agree with the data obtained in other studies and lie in the region of corundum acoustic-vibration frequencies. The Huang-Rhys factors have been evaluated for both centers and found to be close to the estimates made by other authors. The results are discussed in detail and compared with independent data on optical absorption and luminescence of anion centers in colored and irradiated α-Al₂O₃ single crystals.     

Calculation of energies of radiative tunneling transitions between defects in alkali halides

The procedure for calculating the energies of radiative tunneling transition between spatially separated electron and hole centres in ionic crystals based on semiempirical INDO calculation of a pair of close defects and on a further account of electronic polarization of a crystal due to defects has been presented. Pairs of an electron, F, and hole (H, V_k, V₂) centres in KCl and LiF crystals are studied. The influence of close defect interaction and of polarization upon emitted photon energy has also been considered. It is shown that due to polarization this energy varies with a distance between defects in a more complicated way than $\text{e}{}^2\text{?R}$ shown in semiconductors.     

Effect of the electron initial state on the ionization probability at different impact parameters

The probability, W, of ionization of hydrogen-like particles in the 1s- and 2s-states by atomic nuclei has been calculated within the Born approximation at different impact parameters p. Relations between the values of W(p) for the 1s and 2s initial states at the same energies of their binding are compared with the relations between the electron density distributions. Qualitative conclusions are drawn about relative importance of electrons located at different distances from nucleus.     

Relation between orbital binding energies and ionicities in alkali and alkaline earth flourides

The differences between the ionization potentials and binding energies for M^q+ (np⁶), F^?(1 s²), andF^?(2p⁶) orbital electrons, adjusted for the electrostatic self-potentials, in alkali and alkaline earth fluorides have been correlated with ionicites derived from the indices of refraction through optical dispersion theory of Phillips and van Vechten. The differences are linear in ionicities and are related to the covalent energies and the polarizabilities. The gap between the valence band and the Fermi level, determined with X-ray photoelectron spectroscopy, has been compared with the energy in the Phillips-van Vechten model. Whereas the former is a measure of the thermal activation energy for conduction, the latter is determined essentially by the valence electron density, the molar volume, and the polarizability.     

Oscillator strength of electron-type color centers in KCl single crystals irradiated with electrons and protons

The absorption spectra of KCl single crystals irradiated with electrons and protons at energies of 15 and 100 keV and a particle flux ranging from 5×10¹² to 10¹⁵ cm^?2 are investigated. The absorption bands attributed to simple (F, F _a, K) and complex (M, R ₂, R ₄, N) color centers are identified in the spectra. The correlation dependences of the absorption coefficients for M, R ₂, and R ₄ centers on the absorption coefficient of F centers and the correlation dependences of the absorption coefficients for R ₂ and R ₄ centers on the absorption coefficient of M centers are established. The oscillator strengths are calculated for M, R ₂, and R ₄ color centers.     

Lattice dynamics in heavy rare-gas crystals under pressure

The lattice dynamics of compressed rare-gas crystals is theoretically investigated within the ab initio approach in the framework of the Tolpygo model, which explicitly includes the deformation of electron shells in the dipole approximation. The phonon frequencies of compressed rare-gas crystals are calculated with allowance made for the electron-phonon interaction at the mean-value points with the use of the dynamic matrix constructed with the ab initio short-range repulsive potential. The energy of zero-point vibrations and the heat capacity of compressed krypton and xenon face-centered cubic crystals are calculated in the harmonic approximation. The calculated temperature dependences of the specific heat capacity and the Debye temperature are in good agreement with the data available in the literature on the experiment at zero pressure and the results of the calculations within the density-functional theory for all pressures. The quantum effects, in particular, the energies E _zp of zero-point vibrations for krypton and xenon crystals, are investigated at different pressures.     

Elastic properties of heavy rare-gas crystals under pressure in the model of deformable atoms

The quantum-mechanical model of deformable and polarizable atoms has been developed for the purpose of investigating the elastic properties of crystals of rare gases Kr and Xe over a wide range of pressures. The inclusion of the deformable electron shells in the analysis is particularly important for the shear moduli of heavy rare-gas crystals. It has been shown that the observed deviation from the Cauchy relation δ(p) for Kr and Xe cannot be adequately reproduced when considering only the many-body interaction. The individual dependence δ(p) for each of the rare-gas crystals is the result of two competitive interactions, namely, the many-body and electron-phonon interactions, which manifests itself in a quadrupole deformation of the electron shells of the atoms due to displacements of the nuclei. The contributions of these interactions in Kr and Xe are compensated with good accuracy, which provides a weakly pressure-dependent value for the parameter δ. The ab initio calculated dependences δ(p) for the entire series Ne-Xe are in good agreement with the experiment.     

Elastic scattering of electrons by europium and ytterbium atoms

The method of relativistic optical potential is applied to studying elastic scattering of electrons by europium and ytterbium atoms in a wide range of collision energies up to 2 keV. The angular dependences of the scattering differential cross sections and the energy dependences of the scattering integral (total, elastic, momentum transfer, and viscosity) cross sections are calculated in both spin-polarized and spin-unpolarized approximations. It is shown that the spin-polarized approximation should be used to calculate the scattering cross sections at energies below 10 eV for a europium atom. The low-energy scattering of an electron by a europium atom is characterized by P-, D-, and F-wave shape resonances. For an ytterbium atom, the calculated cross sections are in good agreement with available experimental data and with those obtained by calculation in terms of the relativistic convergent close-coupling method.     

Nature of the N b absorption band in LiF crystals

It was found by the methods of optical spectroscopy and X-ray diffraction analysis that the N _b absorption band in LiF crystals is related to the reoriented F ₄ center when all the F centers lie in the (110) plane. These defects are decomposed into F ₂ centers at annealing.     

Photoemission studies of single crystals of titanium carbide

The electron distribution in the valence band from single crystals of titanium carbide has been studied by photoelectron spectroscopy with photon energies h?ω = 16.8, 21.2, 40.8 and 1486.6 eV. The most conspicious feature of the electron distribution curves for TiC is a hybridization between the titanium 3d and carbon 2p states at ca. 3–4-eV binding energy, and a single carbon 2s band at ca. 10 eV. By taking into account the strong symmetry and energy dependence of the photoionization crosssections, as well as the surface sensitivity, we have identified strong emission from a carbon 2p band at ? 2.9-eV energy. Our results are compared with several recent energy band structure calculations and other experimental data. Results from pure titanium, which have been used for reference purposes, are also presented.The valence band from single crystals of titanium carbide have been studied by means of photoelectron spectroscopy, with photon energies ranging from 16.8 to 1486.6 eV.By taking into account effects such as the symmetry and energy dependence of the photoionization cross-sections and surface sensitivity, we have found the valence band of titanium carbide to consist of two peaks. The upper part of the valence band at 3–4 eV below the Fermi level consists of a hybridization between Ti 3d and C 2p states. The C 2p states observed in our spectra were mainly excited from a band about 2.9 eV below the Fermi level. The APW^5–9, MAPW¹⁰ and EPM¹¹ band structure calculations predict a flat band of p-character between the symmetry points X′₄ and K₃, most likely responsible for the majority of C 2p excitations observed. The C 2s states, on the other hand, form a single band centered around ?10.4 eV.The results obtained are consistent with several recent energy band structure calculations^{5–11, 13} that predict a combined bonding of covalent, ionic and metallic nature.     

Efficiency of formation of quasi-metallic defects in alkali-halide crystals

The formation of quasi-metallic defects on the basis of the F _L center (F center with a metal atom) has been investigated with the aim of increasing the efficiency and decreasing the pump threshold of laser elements based on alkali-halide crystals. The regularity of formation of quasi-metallic defects in a number of alkali-halide crystals has been established.     

Polaron theory of the F-F′ conversion in alkali halides

Extending recent suggestions regarding the vibronic properties of F-centers in alkali halides, the following scenario is now proposed of the optical conversion of F-centers into F′-centers: An excited F-center electron, formed by photobleaching in the F-band, passes into a bound polaron state before passing on to an F-center to give rise to an F′-center. The detachment of the electron cloud from the excited F-center involves configurational tunneling in an exothermic process. However, both the tunneling barrier and the electron-transfer expectancy depend drastically on the host material leading to different activation energies and frequency factors of the conversion efficiency in different hosts. The Fcenter-polaron conversion is effected through the strong coupling to at least two modes, one being the LO lattice mode of the crystal. The F to F′ conversion efficiency for various hosts is calculated using a reaction-rate method and found to agree reasonably well with available experimental data.     

F-Zentren und Kolloide in der amorphen,hexagonalen und kubischen Phase von LiJ

By simultaneous evaporation of LiI and Li onto a cooled substrate F centers can be produced in the hexagonal (78 K<T _K <200 K) and amorphous (T _K <78 K) phase of one and the same salt. In both modifications there exist two types of centers F and F^*. The F^* center differs from the cubic F center (T _d -symmetry) by a nearby Frenkel defect. In hexagonal films the normal F band peaks at 2.58 eV, whereas the transitions of the F^* center appear at 2.92 and 2.58 eV too. Polarized irradiation at 20 K causes a dichroic behaviour of the F^* centers. Both types of centers can be transformed into one another photochemically. In the amorphous phase all transitions are shifted to lower energies by about 0.1 eV. After the phase change amorphous→hexagonal the absorption bands shift back by the same amount of energy. AboveT _K =230 K the excess metal forms colloids. The absorption bands are due to colloidal centers embedded in the crystalline material (2.25 eV) and films adsorbed to the crystallites (3.1 eV), respectively. By annealing a particle growth can be observed. After electrolytic colouration cubic single crystals of LiI exhibit an absorption band peaking at 2.36 eV. However, it is not yet sure, if this band is allowed to be ascribed to F centers.