Point defect interaction in alkali halide crystals

Abstract

Molecular statics method is used to determine the energy and configuration peculiarities of vacancy-bivacancy interaction in alkali halide crystals. It is shown that high level of local vacancy supersaturation defines the possibility of cluster formation. The study of carrier traps by luminescence methods is used to reveal vacancy clusters.     

Quantum-Size Dependence of the Energy for Vacancy Formation in Charged Small Metal Clusters. Drop Model

Self-consistent computations of the monovacancy formation energy are performed for Na _N , Mg _N , and Al _N (12 < N ≤ 168) spherical clusters in the drop model for stable jelly. Scenarios of the Schottky vacancy formation and “bubble vacancy blowing” are considered. It is shown that the asymptotic behavior of the size dependences of the energy for the vacancy formation by these two mechanisms is different and the difference between the characteristics of a charged and neutral cluster is entirely determined by the difference between the ionization potentials of clusters and the energies of electron attachment to them.     

On the long-lived excited states and the spontaneous tunnel transitions in some positively charged color center systems in alkali halide crystals

A possible energy instability of some color center systems is pointed out, including an anion vacancy (α-center) in alkali halide crystals. When an optical electron passes from an F-aggregate center to an α-center, the system as a whole occupies a lower lying energy level. As an example the probability of the spontaneous radiative tunnel transition M + α → M⁺ + F in a KC1 crystal is calculated.     

Non-spherical contributions to the vacancy formation energy

A linear response formalism is presented which allows the calculation of the non-spherically symmetric (angular momentum index, l ≠ 0) response to a random external charge perturbation when the spherically symmetric response is available. This procedure is applied to the problem of the energy of vacancy formation so that the electron charge depletion in the vicinity of vacancy is taken into account. The non-spherical contribution to the energy formation for the alkali metals is estimated and found to be non-negligible.     

Point Defect Production Under High Internal Stress Without Dislocations in Ni and Cu

Kiritani et al. have observed a large number of small vacancy clusters without dislocations at the tip of torn portions of fcc metals such as Au, Ag, Cu and Ni. Small vacancy clusters, rather than dislocation cell structures, have also been observed after high-speed compressive deformation, suggesting the possibility of plastic deformation without dislocations. In this paper, in order to investigate the mechanism of deformation without dislocations, change in formation energy of point defects under high internal stress was estimated by computer simulation. Elastic deformation up to - 20% strain was found to provide a remarkable lowering of formation energy of point defects. For example, when Ni is subjected to elastic strain, the formation energy of an interstitial atom decreases to 40% that without strain and the formation energy of a vacancy decreases to 51% that without strain. The number of point defects formed under thermal equilibrium during deformation was evaluated. The number was judged to be insufficient for explaining the formation of vacancy clusters as observed in experiments.     

Detection of defects binding free polarons in colored alkali halide crystals

The assumption has been made that defects binding free polarons in colored alkali halide crystals are F'-center, i.e., defects that slow down the motion of dislocations (photoplastic effect). This assumption has been confirmed by the experiments performed in this study. Thus, the anion vacancy in alkali halide crystals at a low temperature can capture three electrons: two electrons at a deep level (F'-center) and one electron in a bound polaron state. This electron is retained due to the energy gain in the interaction of a local deformation of the polaron and a local deformation surrounding the F'-center, despite the presence of the Coulomb repulsion.     

Structure of nano-objects through polarizability and dipole measurements

The electric polarizability and the electric permanent dipole are important quantities for understanding the electronic properties of a cluster. Experimental techniques, the simulations necessary to interpret the experimental results, and a review of measurements on atomic and mixed clusters are presented. For atomic clusters, the polarizability is related to the type of bonding. In simple metal clusters such as alkali clusters, the results are well interpreted by the electron delocalization characteristic of the metallic bonding. In other metal clusters, the polarizability reflects the difficulty of establishing a clear and regular picture of the size evolution of electronic properties. The size evolution observed for covalent and semiconductor clusters is different from the evolution for metal clusters, and the influence of the geometry is preponderant, as demonstrated in the case of fullerenes. For mixed clusters, the measurements of the electric dipole allows one to deduce the charge transfers and the geometric arrangement. This is illustrated in the case of the metal-fullerene system and alkali halide clusters. To cite this article: M. Broyer et al., C. R. Physique 3 (2002) 301–317.     

Ab initio study of the formation of vacancy and hydrogen-vacancy complexes in palladium and its hydride

We report on the results of ab initio calculations of vacancy and hydrogen-vacancy complexes in palladium and palladium hydride. Comparative analysis of the energies of the formation of defect complexes in palladium and its hydride has revealed that the formation of vacancy clusters is easier in the palladium hydride structure. Investigation of hydrogen-vacancy complexes in bulk crystalline palladium has shown that a hydrogen atom and a vacancy interact to form a stable hydrogen-vacancy (H-Vac) defect complex with a binding energy of E _b = ?0.21 eV. To investigate the initial stage in the formation of hydrogen-vacancy complexes (H _n -Vac _m ), we consider the clusterization of defects into clusters containing H-Vac and H₂-Vac complexes as a structural unit. It is found that hydrogen-vacancy complexes form 2D defect structures in palladium in the (100)-type planes.     

Mechanoluminescence response to the plastic flow of coloured alkali halide crystals

The present paper reports the luminescence induced by plastic deformation of coloured alkali halide crystals using pressure steps. When pressure is applied onto a γ-irradiated alkali halide crystal, then initially the mechanoluminescence (ML) intensity increases with time, attains a peak value and later on it decreases with time. The ML of diminished intensity also appears during the release of applied pressure. The intensity I_m corresponding to the peak of ML intensity versus time curve and the total ML intensity I_T increase with increase in value of the applied pressure. The time t_m corresponding to the ML peak slightly decreases with the applied pressure. After t_m, initially the ML intensity decreases at a fast rate and later on it decreases at a slow rate. The decay time of the fast decrease in the ML intensity is equal to the pinning time of dislocations and the decay time for the slow decrease of ML intensity is equal to the diffusion time of holes towards the F-centres. The ML intensity increases with the density of F-centres and it is optimum for a particular temperature of the crystals. The ML spectra of coloured alkali halide crystals are similar to the thermoluminescence and afterglow spectra. The peak ML intensity and the total ML intensity increase drastically with the applied pressure following power law, whereby the pressure dependence of the ML intensity is related to the work-hardening exponent of the crystals. The ML also appears during the release of the applied pressure because of the movement of dislocation segments and movements of dislocation lines blocked under pressed condition. On the basis of the model based on the mechanical interaction between dislocation and F-centres, expressions are derived for the ML intensity, which are able to explain different characteristics of the ML. From the measurements of the plastico ML induced by the application of loads on γ-irradiated alkali halide crystals, the pinning time of dislocations, diffusion time of holes towards F-centres, the energy gap E_a between the bottom of acceptor dislocation band and the energy level of interacting F-centres, and work-hardening exponent of the crystals can be determined. As in the elastic region the strain increases linearly with stress, the ML intensity also increases linearly with stress, however, as in the plastic region, the strain increases drastically with stress and follows power law, the ML intensity also increases drastically with stress and follows power law. Thus, the ML is intimately related to the plastic flow of alkali halide crystals.     

Energy Characteristics of Small Metal Clusters Containing Vacancies

Self-consistent calculations of spatial distributions of electrons, potentials, and energies of dissociation, cohesion, vacancy formation, and electron attachment, as well as the ionization potential of solid Al _N , Na _N clusters (N ≥ 254), and clusters containing a vacancy (N ≥ 12) have been performed using a model of stable jellium. The contribution of a monovacancy to the energy of the cluster, the size dependences of the characteristics, and their asymptotic forms have been considered. The calculations have been performed on the SKIT-3 cluster at the Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine (Rpeak = 7.4 Tflops).     

Slow positron beam study of corrosion-related defects in pure iron

Corrosion-related defects of pure iron were investigated by measuring Doppler broadening energy spectra (DBES) of positron annihilation and positron annihilation lifetime (PAL). Defect profiles of the S-parameter from DBES as a function of positron incident energy up to 30 keV (i.e. ∼1 μm depth) were analyzed. The DBES data show that S-parameter increases as a function of positron incident energy (mean depth) after corrosion, and the increase in the S-parameter is larger near the surface than in the bulk due to corrosion. Furthermore, information on defect size from PAL data as a function of positron incident energy up to 10 keV (i.e. ∼0.2 μm depth) was analyzed. In the two-state trapping model, the lifetime τ₂ = 500 ps is ascribed to annihilation of positrons in voids with a size of the order of nanometer. τ₁, which decreases with depth from the surface to the bulk, is ascribed to the annihilation of positrons in dislocations and three-dimensional vacancy clusters. The corroded samples show a significant increase in τ₁ and the intensity I₂, and near the surface the corroded iron introduces both voids and large-size three-dimensional vacancy clusters. The size of vacancy clusters decreases with depth.     

Dielectric properties of evaporated films

The evidence for vacancy-pair formation in alkali halide crystals is reviewed. Existing information on the dielectric properties and structure of thin films is discussed with a view to using the high defect concentrations in vacuum-deposited films to confirm vacancy-pair orientation effects. Experimental measurements of the dielectric constant and dissipation factor of evaporated films have been made at room temperature over a range of frequencies from 100 c.p.s. to 100 kc/s. Even under vacuum these films show pronounced losses at low frequencies which are attributed to excess vacancy concentrations. Such losses are contrary to the theory of ideal lattices and are not shown by single crystals.

In spite of the excess defect concentrations no evidence of vacancy-pair orientation has been found. Ageing effects have been observed in all cases, the losses decreasing with time as the defect concentration decreases. In the alkali halides the magnitude of the losses depends on the cation mobility but they decrease at a rate determined by the anion mobility. This leads to a proposed dielectric relaxation mechanism in which individual crystallites form the polarizable units, becoming polarized by migration of the cation vacancies towards one end. The losses decrease as the defects are gradually eliminated by simultaneous condensation of positive and negative vacancies at grain boundaries. This is essential to maintain electrical neutrality and the rate is determined by the diffusion of the slower anion vacancies. The measured rates are in agreement with anion activation energies obtained by tracer methods. These results cannot be explained by vacancy-pair formation even if it is assumed that vacancy pairs can form but are incapable of orientation and hence we must conclude that there is little or no vacancy-pair formation.

Measurements at atmospheric pressure show that moisture has a pronounced effect in all cases, producing dielectric losses which completely obscure the vacancy effects. The changes in dielectric properties during and after adsorption cannot be explained as conductivity effects and are in complete opposition to any modification of the Maxwell-Wagner theory. The ageing effects show that after the initial adsorption, the water molecules migrate over crystallite surfaces to positions where they are more strongly bound and contribute to the dielectric polarization by a form of hindered rotation closely analogous to mechanisms proposed for ice. At these equilibrium sites, H-bonds are frequently formed between the adsorbed molecules and the halide ions of the crystal lattice.     

Deformation-induced excitation of the luminescence centres in coloured alkali halide crystals

The present paper reports the deformation-induced excitation of the luminescence centres in coloured alkali halide crystals. The peaks of the mechanoluminescence (ML) in γ-irradiated KCl, KBr, KI, NaCl and LiF crystals lie at 455, 463, 472, 450 and 485 nm, i.e. at 2.71, 2.67, 2.62, 2.75 and 2.56 eV, respectively. From the similarity between the ML spectra and the thermoluminescence (TL) and afterglow spectra, the ML of KCl, KBr, KI, NaCl and LiF crystals can be assigned to the deformation-induced excitation of the halide ions in V₂-centres or any other hole centres. For the deformation-induced excitation of the halide ions in V₂-centres, or in other centres, the following four models may be considered: (i) free electron generation model, (ii) electron–hole recombination model, (iii) dislocation exciton radiative decay model and (iv) dislocation exciton energy transfer model. The dislocation exciton energy transfer model is found to be suitable for the coloured alkali halide crystals. According to the dislocation exciton energy transfer model, during the deformation of solids the moving dislocations capture electrons from the F-centres and then they capture holes from the hole centres and consequently the formation of dislocation excitons takes place. Subsequently, the energy released during the decay of dislocation excitons excites the halide ions of the V₂-centres or any other hole centres and the light emission occurs during the de-excitation of the excited halide ions, which is the characteristic of halide ions. The mechanism of ML in irradiated alkali halide crystals is different from that of the TL in which the electrons released form F-centres due to the thermal vibrations of lattices reach the conduction band and the energy released during the electron–hole recombination excites the halide ions in V₂-centres or in any other hole centres. It is shown that the phenomenon of ML may give important information about the dislocation bands in coloured alkali halide crystals.     

Local structure and lattice dynamics of alkali halide crystals with an anion vacancy

The local structure and vibrations in the region of an anion vacancy are studied using the pair interionic potentials within the shell model for crystals Me ⁺Cl^? (Me ⁺ = Rb⁺, K⁺, Na⁺). The pair potentials are derived from first-principles calculations of different clusters by the Hartree-Fock-Roothaan method with the one-electron states constructed in the form of molecular orbitals as linear combinations of atomic orbitals (MO LCAO). The calculations are performed with the GAMESS program package (US). The correlation corrections are included in the calculations. The validity of the model parameters is verified by comparing the calculated with experimental structural and dynamic properties of ideal alkali halide crystals.     

Ab initio study of formation, migration and binding properties of helium-vacancy clusters in aluminum

Ab initio calculations based on density functional theory have been performed to study the dissolution and migration of helium, and the stability of small helium-vacancy clusters He_nV_m (n, m=0-4) in aluminum. The results indicate that the octahedral configuration is more stable than the tetrahedral. Interstitial helium atoms are predicted to have attractive interactions and jump between two octahedral sites via an intermediate tetrahedral site with low migration energy. The binding energies of an interstitial He atom and an isolated vacancy to a He_nV_m cluster are also obtained from the calculated formation energies of the clusters. We find that the di- and tri-vacancy clusters are not stable, but He atoms can increase the stability of vacancy clusters.     

Hydrogen behavior in Pd0.75Ag0.25H x studied by PAC and PAS

Hydrogen behavior in Pd_0.75Ag_0.25H _x has been investigated by both perturbed angular correlation (PAC) and positron annihilation lifetime spectroscopy (PAS) techniques. The PAC measurements with the ¹¹¹Ag/¹¹¹Cd probe nuclei were conducted at room temperature as a function of the hydrogen concentration x up to 0.35. At x = 0 the probe nuclei experienced no quadrupole perturbation, while a distinct perturbation was observed after hydrogen charging. The quadrupole interaction frequency ω ₁ and its distribution width σ ₁ and relative fraction f₁ all decrease with increasing hydrogen concentration, indicating size growth and concentration reduction of the hydrogen induced vacancy clusters. The measured frequency distribution width σ ₁ reveals hydrogen diffusion. The PAS measurements were also performed at room temperature. The obtained lifetimes and their variation with hydrogen concentration strongly support the PAC results. The experimental results can be explained by the appearance of the β-phase in the Pd_0.75Ag_0.25H _x samples. The α-phase is the major phase in the Pd_0.75Ag_0.25H _x samples. Charging of the hydrogen leads to the formation of the β-phase and the fraction of the β-phase increases with increasing hydrogen concentration. The present PAC and PAS results show that as the fraction of the β-phase increases, hydrogen induced vacancy clusters are formed and become larger and larger, while the cluster density reduces due to the combination of the vacancy clusters into larger size vacancy clusters.     

Relaxation round vacancies in the alkali metals

The long-range ionic displacements round a vacancy are shown to come from both the elastic, long-wavelength, limit and from the Kohn anomaly. The effect of the topology of the Fermi surface is stressed.Attention is then focussed on the alkali metals with almost spherical Fermi surfaces, where it can reasonably be assumed that the elastic displacements dominate. Complete relaxation around a vacancy relates formation energy E_v, bulk modulus B and atomic volume Ω through E_v = αBΩ where α is a constant. The formation volume follows as a balance between a negative harmonic contribution and a positive and larger anharmonic term.     

Formation of an ensemble of nanoclusters under rapid deposition of atoms on a surface

The results of an experimental study of the formation of nanometer-size Au clusters on NaCl(100) and HOPG(0001) surfaces under pulsed laser deposition are presented. No clusters of small sizes (d ≤ 1 nm) have been found in the cluster size distribution. The distribution itself at d < 5 nm has the form of a percolation distribution. It has been established that the perimeter of clusters with sizes d < 5 nm has a fractal structure. The fractal dimension of clusters is different for NaCl(100) and HOPG(0001) surfaces with different symmetries; it decreases with increasing cluster size from D _f ≈ 1.2–1.4 at d ≈ 1.5 nm to D _f ≈ 1 at d ≈ 5 nm. A physical mechanism of nanocluster formation is suggested. Under pulsed laser deposition, the attainable densities of adatoms are close to the percolation threshold in the region of thermodynamically unstable states and many-particle correlation regions are formed in a spatially inhomogeneous adsorbate. Clusters are formed on the surface from many-particle correlation regions in several diffusion jumps. The suggested mechanism allows the fractal dimension of the clusters forming on surfaces with different symmetries, its dependence on cluster size, and the cluster size distribution functions to be calculated.     

Electromigration of Small Vacancy Clusters on the (100) Copper Surface

The electromigration of small vacancy islands on the Cu(100) surface has been studied using the self-learning kinetic Monte Carlo method. The dependence of the drift velocity of vacancy clusters on their size, temperature of the substrate, and magnitude and direction of the electric current density has been obtained. It has been shown that the dependence of the drift velocity of small clusters on their size has a pronounced oscillatory character. These oscillations are due to the difference in the mechanisms of diffusion of “fast” and “slow” clusters. It has been found that events associated with the diffusion of dimers should be taken into account for the correct simulation of the electromigration of vacancy clusters.     

О кИНЕтИкЕ ВНУтРИцЕН тРОВОИ лУМИНЕсцЕНцИ И ЩЕлОЧНОгАлОИДНых кРИстАллОВ, АктИВИРО ВАННых тАллИЕМ

The luminescence decay of some alkali halide crystals activated with thallium was studied experimentally. On the basis of data from the literature and the results of this paper an assumption is made as to the mechanism of activator luminescence of such crystals. The probability of spontaneous transitions and the energy differences between excited levels participating in luminescence were determined from a comparison of the experimental data and the results of calculation.