Vacancies In Cu Research Articles

Computer Simulation of Formation Energy and Migration Energy of Vacancies under High Strain in Cu

Recently it has been reported that many vacancy clusters are generated at sawtooth-like fractured tips of thin foils. The elastic strain of the torn portion is more than 10% before the fracture, which is expected to cause the generation of many vacancy clusters. In this paper, the formation and migration behaviors of vacancies in Cu under high elastic strain from 10% compression to 20% elongation were studied by computer simulation using the effective medium theory (EMT) potential. The model lattice was elastically deformed along the ‹110› and ‹100› directions. Poisson's ratio was determined to minimize the total energy. After full relaxation of the lattice by the static method (Newton-Raphson method) under fixed boundary conditions, a vacancy was introduced and the change of the total energy (formation energy) was calculated. The migration energy of vacancies was obtained as the total energy difference between the model lattice with an atom at the lattice point and the atom at the saddle point. High strain dependence of these energies is obtained. For example, the formation and the migration energies of vacancies are 1.21 eV and 0.79 eV in the absence of deformation, respectively. The formation energy in the ‹100› deformation is 1.09 eV and 1.13 eV by 10% compression and 10% elongation, respectively. The migration energies and the migration distances vary with the migration direction. For example, the migration energy for the shortest migration distance in the ‹100› deformation is reduced to 0.45 eV and 0.26 eV by 10% compression and 10% elongation, respectively. While that for the longest migration distance increases to 1.29 eV by 10% compression. These results are explained by the configuration of neighboring atoms nearest to the vacancy.

Simulation of vacancy migration energy in Cu under high strain

The activation energy for the migration of vacancies in Cu under high strain was calculated by computer simulation using static methods. The migration energy of vacancies was 0.98 eV in the absence of deformation. It varied with the migration direction and stress direction because the distance between a vacancy and its neighboring atoms changes by deformation. For example, the migration energy for the shortest migration distance was reduced to 9.6 and 39.4% of its initial value by 10% compression and 20% elongation, respectively, while that for the longest migration distance was raised to 171.7 by 20% elongation. If many vacancies are created during high-speed deformation, the lowering of migration energy enables vacancies to escape to sinks such as surfaces, even during the shorter deformation period. The critical strain rate above which the strain rate dependence of vacancy accumulation ceases to exist increases with the lowering of vacancy migration energy.

Defect Physics of CuInSe2 for Photovoltaic Applications Using Extended X-ray Absorption Fine Structure (EXAFS)

AbstractNative point defects in undoped samples of CuInSe2 (CIS) have been identified by a multiple-edge refinement of the extended x-ray absorption fine structure of the copper, indium and selenium absorption edges. Ab initio theoretical models for the pure compound and for various defect structures were constructed and carrier-type statistics were predicted by simultaneously fitting multiple absorption sites to these models. As expected, a model of our measurements based on pure compounds with no defects does not yield a good fit to the data. We find that a best fit requires a significant population of defects. Preliminary quantitative analysis suggests a 15 % vacancy in Cu, a 2-12% population of Cu-Se anti-sites and 15% In-Se anti-sites.

First-principles calculations for vacancy formation energies in Cu and Al; non-local effect beyond the LSDA and lattice distortion

We show ab initio calculations for vacancy formation energies in Cu and Al. The calculations are based on density-functional theory and the full-potential Korringa–Kohn–Rostoker Green's function method for impurities. The non-local effect beyond the local-spin-density approximation (LSDA) for density-functional theory is taken into account within the generalized-gradient approximation (GGA) of Perdew and Wang. The lattice relaxation around a vacancy is also investigated using calculated Hellmann–Feynman forces exerted on atoms in the vicinity of a vacancy. We show that the GGA calculations reproduce very well the experimental values of vacancy formation energies and bulk properties of Cu and Al, as they correct the deficiency of LSDA results (underestimation of equilibrium lattice parameters, overestimation of bulk moduli, and vacancy formation energies). It is also shown that the GGA calculations reduce the LSDA results for the lattice relaxation energy for a vacancy in Cu.

Effect of gamma irradiation damage on the jump rate of vacancies in Cu doped Ni-Zn ferrite

Abstract The system Ni0.65Zn0.35CuxFe2-xO4 (x=0, 0.1, 0.2, 0.3, 0.4 and 0.5) was prepared by the usual ceramic method and the cubic spinel structure was confirmed using X-ray analysis. The electrical conductivity and the number of jump rate of vacancies were determined before and after gamma irradiation of 106 rad. An estimate was carried out to evaluate the number of vacancies in the lattice sites. This number is maximized at x=0.4, leading to a high conductivity at this composition.

Origin of magnetic energy anomalies of 3d systems: a model study

Abstract The magnetic moments and spin-polarizization energies of 3d impurities adjacent to vacancies in Cu are calculated by use of the impurity KKR-Green's function method. The present calculations elucidate the micromechanism of magnetic energy anomalies in the observed cohesive and surface energies of 3d metals.

Thermal analysis of Y1−xCaxBa2Cu3O7−y

TG and DTA analysis of Y1−xCaxBa2Cu3O7−y suggests that the stability of the 123 phase increases with increasing Ca contents. The O(1) in the Cu(1)-O chain is unstable but O(2) and O(3) in Cu(2)-O planes are very stable. There are hardly any oxygen vacancies in the Cu(2)-O plane. The replacement of Y by Ca does not make oxygen vacancies in Cu(2)-O planes but leads to an increase in the oxidation number of copper in Cu(2)-O planes.

Distribution of pinning energies in metal (M) substituted YBa 2Cu 2−xM xO 7−y

Distributions of pinning energies were determined for orthorhombic and tetragonal YBa 2Cu 2.0Fe 0.1O 7−δ samples. Both have nearly the same oxygen content and T c . Although the distribution of the orthorhombic sample is similar to that of none-doped one in a energy range below 40 meV. pinning centers with pinning energies from 20 meV to 40 meV are diminished in the tetragonal sample. The difference in the pinning features is related to the difference in the configuration of oxygen vacancies in Cu(1)−0 planes.

Application of LAPW and Green-function methods to calculation of electronic structure of crystal defects

Calculations based on the Linear Augmented Plane-Wave (LAPW) which was treated by the KKR-Green-function method were performed for the electronic structure of 3d impurities (Sc, Ti, V, Cr, Mn, Fe, Co, Ni) in Cu-matrix as well as for vacancies in Cu and Ni. The results are in good agreement with experiments.

Interaction energies of impurities in Cu and Ni.

We present systematic local-density-functional calculations for the interaction energies of 3d and 4sp impurities (Sc--Br) with vacancies in Cu and Ni crystals. We apply the Kohn-Korringa-Rostoker Green's-function method and evaluate the full anisotropic charge density. The interaction energies are obtained by total-energy calculations and by a newly derived formula based on the Hellmann-Feynman theorem. Both methods agree very well and confirm the experimentally known trends.

Positron annihilation in vacancies: Korringa-Kohn-Rostoker formulation and application to Cu.

We develop a Green's-function formulation of the two-photon momentum density ${\ensuremath{\rho}}_{2\ensuremath{\gamma}}$(p) for a vacancy-trapped positron in a metal within the framework of the Korringa-Kohn-Rostoker (KKR) scheme. This formulation is easily extended to treat disordered alloys. Employing a real-space representation for the electron and positron Green's functions, we express ${\ensuremath{\rho}}_{2\ensuremath{\gamma}}$(p) as a lattice sum, which converges rapidly for a vacancy-trapped positron. Results for a vacancy in Cu are presented; these are the first calculations of ${\ensuremath{\rho}}_{2\ensuremath{\gamma}}$(p) for a vacancy in a d-band metal. It is found that ${\ensuremath{\rho}}_{2\ensuremath{\gamma}}$(p) in the region p\ensuremath{\lesssim}4 mrad is dominated by contributions from the vacancy and the nearest-neighbor (NN) shell. Our considerations indicate that the width and weight of the central peak in ${\ensuremath{\rho}}_{2\ensuremath{\gamma}}$(p) is a sensitive function of the NN-shell composition in metals and alloys.

Conduction-electron scattering from vacancies in copper.

The first experimental results of the anisotropy of the conduction-electron scattering from vacancies in Cu are reported. The method used to study the electron-vacancy scattering rate is magnetic-field-induced surface-state resonance. The results show that the scattering rate in the {110} plane of Cu varies by a factor of 2 over the Fermi surface. It is highest near the 〈100〉 axis and 〈111〉 neck and lowest at the 〈110〉 and 〈112〉 axes. A partial-wave analysis was performed and the Friedel phase shifts determined. This analysis shows the vacancy to have a predominantly sp character. The results for Cu are compared with de Haas--van Alphen data in Au and marked differences are noted. A companion paper analyzes the scattering rates in both Cu and Au with vacancies in terms of the cluster-defect formalism based on the Korringa-Kohn-Rostoker Green's-function method.

Equilibrium vacancies in Cu and Ag alloys with electropositive solutes

Abstract A new method is presented for the calculation of interaction energies of a vacancy-impurity pair and of higher-order complexes from the vacancy formation energy in pure metals and the concentration dependence of the effective formation energy in alloys. In terms of a modified complex model introduced by Berces and Kovacs, changes in the formation entropy of vacancy-impurity complexes compared with that of free vacancies as well as non-random solute distributions around vacancies are taken into account. The treatment is applied to effective vacancy formation energies as a function of alloying in several silver and copper systems with electropositive impurities obtained by resistivity measurements and positron annihilation. Vacancy impurity binding entropies of about k (Boltzmann's constant) are observed. The corresponding binding energies vary from −0·10 to −0·20 eV.

Vacancies in Cu<sub>3</sub>Au and CuAu by Positron Annihilation

Vacancies in Cu<sub>3</sub>Au and CuAu by Positron Annihilation

A Possible Mechanism of Exiton Exchanging Percolated Superconductivity for Oxide Balacuo

The effect of oxygen vacancies in oxide (La1-xBax) CuO4-y (Balacuo) is analyzed. It is pointed out that the vacancies in Cu–O basal plane will break the bonds Cu–O–Cu to delete the hopping between those coppers so that the electrical conduction of Cu–O basal plane would become a bond percolation system where there is an infinite cluster to carry a current and a lot of finite clusters are hung about it. It is favorable to create some mechanism of exchanging exciton so that the transition temperature TC of superconductivity could be increased significently. The comparison with Y1Ba2Cu3O9-y is also discussed briefly.

Electric field gradient for muonium and monovacancies in Cu and Al

The electric field gradient (EFG) and asymmetry parameter (η) at the first nearest neighbour (1NN) site of muonium (μ +) and at the first four NN sites of vacancies in Cu and Al are calculated. The defect induced charge density, used to evaluate the valence effect EFG, is calculated self-consistently in the density functional formalism. The formalism for the size effect EFG for μ + at the octahedral site in the fcc lattice is developed in the elastic continuum model. For both the μ + and the vacancy the components of the strain field tensor are evaluated assuming the lattice of dressed point ions interacting through the screened Coulomb potential. The size effect EFG for μ + is found cylindrically symmetric at the 1NN and 2NN sites. The size effect EFG is found larger than the valence effect EFG at all the NN sites for Cu- and Al-vacancies and the same is obtained at the 1NN site for μ +. The valence effect EFG for an Al-vacancy is found to be relatively larger than for a Cu-vacancy while the contrary is concluded for the μ +. It is noted that η depends upon the relative phases of components of EFG and not on their absolute values independently. The calculated and the experimental values of EFG and η agree reasonably.

Self-consistent calculations for the electronic structure of a vacancy in copper. A solution of the embedding problem

The charge density and the local density of states for a vacancy in Cu and for the first shell of Cu neighbours are calculated by the KKR-Green's function technique. The muffin-tin potentials for the vacancy and the neighbour shell atoms are determined self-consistently in the local density approximation of density functional theory. By the use of the proper host Green's function the embedding of this cluster of 13 perturbed muffin-tins into the infinite array of bulk Cu muffin-tin potentials is described rigorously, thus representing a solution of the embedding problem. The calculations demonstrate a rather large charge transfer of 1.1 electrons from the first neighbour shell to the vacancy.

Lattice Vibrations around a Vacancy in Cubic Crystals

The local vibrational densities of states of the neighbors of a vacancy in α-Fe and Cu were calculated by the recursion method. Resonance mode was found in both cases, but a localized mode occurred at the 1st nearest neighbor site of a vacancy in Cu.

Defect annealing studies on metals by positron annihilation and electrical resitivity measurements

Doppler-broadening positron-annihilation measurements combined with electrical-resistivity measurements were performed on Cu and Al samples, irradiated by high-energy electrons at liquid-helium temperature. A defect-specific parameter $R$ was determined from the shape of the 511-keV annihilation line. The $R$ parameter is found to be independent of the defect concentration $C$ and the positron trapping constant $\ensuremath{\mu}$ within the framework of the two-state trapping model. During isochronal annealing of electron-irradiated copper the line-shape parameter $\ensuremath{\Delta}{I}_{v}$ increases in stage III, whereas the electrical resistivity decreases, indicating a reduction in the Frenkel-defect concentration. These two combined effects and the pronounced steps in the $R$ parameter during stage-III annealing, which are found to be dose independent, signify that radiation-produced vacancies become mobile and coalesce into clusters before they anneal out. The positron trapping constant $\ensuremath{\mu}$ for vacancies in Cu was determined to be $\ensuremath{\mu}=(4.25\ifmmode\times\else\texttimes\fi{}0.8)\ifmmode\times\else\texttimes\fi{}{10}^{14}$ ${\mathrm{sec}}^{\ensuremath{-}1}$. Furthermore, the annealing behavior of copper and aluminum samples, deformed plastically at 77 K and irradiated at 4.2 K by electrons, respectively, is discussed. In both cases no indication for the formation of vacancy agglomerates is found during annealing. The $R$-parameter analysis is also applied to the data for electron-irradiated Mo, as reported by Eldrup et al.

The measurement of the formation energy of a vacancy in Cu by positron annihilation

The temperature dependence of the coincidence counting rates of two annihilation photons was measured for Cu at theta =0. Analysing the results by the trapping model, the formation energy of a vacancy in Cu was determined to be 1.17+or-0.07 eV. This value is in good agreement with that by Simmons and Balluffi (1963).