Impurity-vacancy Binding Energy Research Articles

First-principles analysis of solute diffusion in dilute bcc Fe- X alloys

The diffusivities of substitutional impurity elements in iron have been computed with ab inito electronic density functional techniques, using exchange-correlation functional PW91. Excess entropies and the attempt frequency for a jump were determined by calculating phonon frequencies in the harmonic approximation. The influence of the degree of spontaneous magnetization on diffusivity is taken into account by means of the Girifalco model. The activation energy for diffusion has been determined by computing the vacancy formation energy, impurity-vacancy binding energies, migration barrier energies, and the effective energy associated with correlation of vacancy-mediated jump. For each type of impurity atom these contributions have been evaluated and analyzed up to and including the fifth nearest-neighbor shell of the impurity atom. It is found that impurities that have a low migration energy tend to have high effective energy associated with vacancy migration correlation, and vice versa, so that the total diffusion activation energies for all impurities are surprisingly close to each other. The strong effect of vacancy migration correlation is found to be associated with the high migration energy for iron self-diffusion, so that movement of vacancies through the iron bulk is in all cases, except cobalt, the limiting factor for impurity diffusion. The diffusivities calculated with the PW91 functional show good agreement with most of the experimental data for a wide range of elements.

First-principles study of vacancy-assisted impurity diffusion in ZnO

Group-III elements act as donors in ZnO when incorporated on the Zn site. Their incorporation and behavior upon annealing is governed by diffusion, which proceeds mainly through a vacancy-assisted process. We report first-principles calculations for the migration of Al, Ga, and In donors in ZnO, based on density functional theory using a hybrid functional. From the calculated migration barriers and formation energies, we determine diffusion activation energies and estimate annealing temperatures. Impurity-vacancy binding energies and migration barriers decrease from Al to In. Activation energies for vacancy-assisted diffusion are lowest for In and highest for Al.

Chemical diffusion of niobium in nickel

Although impurity diffusion values are of great interest in developing nickel base super alloys, limited data in 4d-transition elements are available. This paper reports on niobium diffusion data in nickel in the temperature range between 1200 and 1500 K, obtained by using an electron probe microanalyser. The temperature dependence of the diffusion coefficient, D Nb, can be expressed by the following Arrhenius relation, D Nb = 1.0 −0.48 +0.87 × 1- −6 exp[−(202.59 ± 4.71 kJ/mol)/RT] m 2/s. These studies have shown that the niobium diffusivity is nearly one order of magnitude higher than the self diffusivity in nickel. The large difference between the activation energy values ( ΔQ = − 78.31 kJ/mol) indicates a rather high impurity-vacancy binding energy.

Demixing of doped oxides: influence of defect interactions

We analyze the demixing behavior of heterovalent doped transition metal oxides, (A, B)O, in an applied oxygen potential gradient, using a defect model for the doped oxide and the five-frequency model for impurity diffusion. Experimental results for the demixing of Ga-doped cobalt oxide, (Co1−xGax)O, where the dopant becomes enriched on the low-oxygen-potential si de, yield in combination with cation tracer diffusion coefficients of Co and Ga an impurity-vacancy binding energy of about 0.4 eV and a ratio of the non-diagonal and the diagonal coefficients in the Onsager transport matrix LCoGa/LGaGa=−1.6.

Ion mixing and thermochemical properties of tracers in Ag

Very thin films of Ni, Ta, W, Pb, and Bi in a Ag matrix were irradiated at 77 K with 330 keV Kr ions at doses from 3 to 7×1015 ions/cm2 and analyzed at room temperature by backscattering of 1.9 MeV He+. The measured mixing efficiencies, Dt/φFD, for the various tracers correlate with their respective tracer impurity diffusion coefficients and impurity-vacancy binding energies in Ag. The results concur with previous ones with a Cu matrix and further support the idea that the parameters that are important for thermal diffusion are also important for ion mixing in a thermal spike.

Influence of thermochemical properties on ion mixing of markers in Cu and β-Zr at 77 K with Kr

Ion mixing of Nb, Ru, Ag, In, Sb, Hf, Pt, Au, and Bi markers in a Cu matrix and of Ti, Cr, Fe, Co, Ni, Cu, Hf, W, and Au markers in a β-Zr matrix has been studied by irradiation with 750 keV Kr+ ions of doses from 5 × 1015 to 2 × 1016/cm2= at 77 K. Cu and β-Zr have quite different atomic properties and impurities in them also behave quite differently. Thus, through a systematic investigation, the influence of parameters and mechanisms on ion mixing is clarified. The mixing was analyzed in situ, using 1.8 and 1.9 MeV He ion backscattering spectrometry. The overall mixing efficiency, Dt/φFD, is significantly higher in Cu than in β-Zr. This difference is explained in terms of the thermal spike mechanism in these matrices. In Cu, the mixing efficiencies correlate with impurity tracer diffusivities and impurity-vacancy binding energies for the marker atoms in Cu. Vacancies apparently play a major role during thermal spike mixing in Cu. In β-Zr, the markers that are likely to dissolve substitutionally in the matrix, have slightly higher mixing efficiencies than the markers that are likely to dissolve interstitially. The results are interpreted with the diffusion properties of these impurities in β-Zr.

Ion mixing and thermochemical properties of markers in Cu

Markers of Nb, Ru, Ag, In, Sb, Hf, Pt, Au, and Bi in Cu were mixed by irradiation with 750 keV Kr at 77 K and analyzed in situ by backscattering of 1.9 MeV He+. Cu with Pt and Au markers were also irradiated and analyzed at 7 K. The results were identical to those obtained at 77 K results. The measured mixing efficienciesDt/oF D , for the various markers correlate with their respective impurity tracer diffusivities and impurity-vacancy binding energies in Cu. The correlation suggests that diffusion by a vacancy mechanism during a thermal spike as an important process in ion mixing of marker atoms in Cu.

Impurity diffusion and vacancy–impurity binding energy associated with elements of the second transition series in niobium and molybdenum

Abstract Impurity diffusion of ruthenium and palladium in niobium has been studied by radioactive–tracer and electron–microprobe techniques. The results show that the impurity diffusion coefficients are a little higher than the self–diffusion coefficients. Analysis of data for impurity diffusion in niobium and molybdenum shows the following features : (i) the difference Δ Q between activation energies for impurity diffusion and self–diffusion is proportional to Δ Z, the difference of charge between the substitutional d impurity and the matrix ionic cores, when Δ Z is small; (ii) Δ Q is positive for the diffusion in noibium of an impurity at the right of niobium in the periodic table with small ΔZ, and for the diffusion in molybdenum of an impurity at the left of molybdenum; (iii) feature (i) breaks down for |Δ Z| higher than 2. These different points can be qualitatively explained if Δ Q is approximately given by the impurity–vacancy binding energy Δ E. This impurity–vacancy binding energy is estimated in the generalized double–scattering scheme of Gautier, Moraitis and Farlebas (1976).

Isotope effect for diffusion of zinc and copper in aluminum

The isotope effect for the diffusion of copper in aluminum is 0.81 +- 0.05 at 656.9 /sup 0/C and 0.89 +- 0.05 at 584.7 /sup 0/C. The isotope effect for the diffusion of zinc in aluminum increases from approx. 0.35 at 415 /sup 0/C to approx. 0.6 at 654 /sup 0/C with a temperature dependence of 0.1 eV. These results and earlier diffusion data indicate that the impurity-vacancy binding energy is small in aluminum, but they do not resolve the controversy concerning the extent of the divacancy contribution to self-diffusion in aluminum.

Calculation of clustering effects on impurity-vacancy binding energies in aluminum

Calculation of clustering effects on impurity-vacancy binding energies in aluminum

Molybdenyl centers in NH4Cl single crystals

Molybdenyl centers are studied in single crystals of NH4Cl using a set of correlated experimental techniques like EPR, optical absorption, infrared absorption, conductivity, and dielectric loss. EPR studies on NH4Cl single crystals doped with (MoOCl5)2− are made over a wide temperature range. At room temperature the resonance due to even isotopes of Mo and the hyperfine interaction due to the odd isotopes are observed. At 77 K the ligand hyperfine interaction due to 35,37Cl is also observed. The spectra are analyzed using a suitable spin Hamiltonian. An LCAO–MO method is used to interpret all the results. In the optical absorption spectra the bands corresponding to the d–d transitions and charge transfer transitions are observed. Spin–orbit coupling constant is estimated using the EPR and optical results. Molecular orbital parameters are calculated taking into account the spin–orbit effects of the ligands also. The calculated bonding coefficients are correlated with the EPR results and the nature of binding in these complexes is discussed. The spin density on the ligand orbitals is estimated using the results of the ligand hyperfine interactions. The Mo–O stretching frequencies are observed in the infrared absorption spectrum. The evidence for the existence of the bound cation vacancies comes from the conductivity and dielectric loss experiments. The impurity–vacancy binding energy is also estimated.

Impurity-vacancy and vacancy-vacancy binding energies in α-iron

Abstract The impurity-vacancy and the vacancy-vacancy binding energies in α-iron are estimated in a simple electronic model. The band structure of the pure metal is described by a hybridized tight binding nearly free electron (TB-NFE) model adjusted to a self-consistent KKR calculation. Results of the vacancy-vacancy binding energy are compared with previous calculations. It is shown that the impurity-vacancy binding energy is an important part of ΔQ, the difference between the activation energies for impurity diffusion and for self-diffusion. An attempt is made to understand the influence of the magnetic properties upon the binding energies.

Impurity-vacancy binding energy in transition metals

The impurity-vacancy binding energy is calculated using a tight binding scheme. The displaced charge is determined in the Hartree-Fock Slater approximation in order to take into account the presence of ferromagnetism at the end of the first transition series. Friedel's rule is introduced for self-consistency up to the first nearest neighbors of the vacancy. A direct comparison with the experimental data is difficult but the electronic part of the binding energy is a small part of ΔQ, the difference between the activation energies for self-diffusion and impurity diffusion.

Interatomic Potentials and Defect Energetics in Dilute Alloys

Effective interatomic potentials for impurities in aluminum have been constructed according to pseudopotential theory. Based on a local model potential, impurity valence and size factors are defined and their effects on the potential discussed. With these potentials, detailed calculations based on a Green's function lattice statics method are made for the impurity-vacancy binding energy and the difference in diffusion activation energies for an impurity and a host atom. Within the range of valence and size factors studied, it is found that the binding energy is generally small and depends primarily on the valence rather than the size, whereas the migration energy shows larger increases with both valence and size factors. Contributions from the lattice relaxation energies are important, particularly for impurity migration. The results can account satisfactorilfyo r the experimental data of nontransition-metal impurities, but lesss o for the noble-metal impurities. Dielectric screeningof the ion by the conduction electrons is important in determining the potential and must be properly accounted for in calculations of the energetics for impurities.

Impurity-vacancy binding energy in transition metals : C. Demangeat Electronique des Solides (E.R.A. N°100) Universite Louis Pasteur 4, rue Blaise Pascal 67000 Strasbourg, France

Impurity-vacancy binding energy in transition metals : C. Demangeat Electronique des Solides (E.R.A. N°100) Universite Louis Pasteur 4, rue Blaise Pascal 67000 Strasbourg, France

Antimony Centres in Potassium Halides

AbstractAntimony doped potassium halide crystals give one optical absorption band at 205 nm in KCl, 215 nm in KBr, and 243 nm in KI at RT. These bands are ascribed to the divalent state of antimony. Correlated EPR studies show that the paramagnetic antimony (Sb2+) state is associated with a vacancy in the second neighbour position. Experiments have also been performed on the conductivity and dielectric loss. The impurity–vacancy binding energy is found to be ≈ 0.30 eV in these crystals.

Relationships between the impurity-vacancy binding energy and the core radius, the Debye temperature and the melting temperature in aluminum

The impurity-vacancy binding energy in aluminum was found to be approximately related to the core radius, the Debye temperature and the melting temperature using the pseudopotential method.

Impurity-vacancy binding energy obtained from equilibrium resistivity of Cu-doped Au

Impurity-vacancy binding energy obtained from equilibrium resistivity of Cu-doped Au