Activation Energy For Impurity Diffusion Research Articles

High-throughput prediction of activation energy for impurity diffusion in fcc metals of Group I and VIII

We develop a high-throughput calculation method that rigorously mines correlations embodied within experimental data and use it to direct quantum mechanical techniques efficiently toward the diffusion activation predictions and assessments. The new diffusion activation energies data of 298 binary systems, covering six faced-centered cubic (fcc) host metals of Group I (Cu, Ag, Au) and Group VIII (Fe, Co, Ni) and 76 elements of periods of 3, 4, 5 and 6, are predicted in this work. Furthermore, a new analytic expression, derived from data-mining, has been developed, which sheds light on the delicate relationship between diffusion activation energy and materials fundamental properties. The present approach can be extended to study the impurity diffusion in metal alloys of other complex structures where diffusion activation energies are difficult to obtain from first-principles calculation due to the complex diffusion mechanism. The present results could be used to provide useful data for other material simulation techniques such as CALPHAD or facilitate the choice of materials for technological applications.

The "C" Factor in LeClaire's Theory of Solute Impurity Diffusion

The "C" factor for the calculation of the relative activation energy for solute impurity diffusion using LeClaire's theory as modified by Burachynsky and Cahoon has been determined for the diffusion of several solutes in FCC Cu , FCC Fe and BCC Fe. Inclusion of the "C" factor results in good agreement between the calculated and experimental values of relative activation energy for impurity diffusion inn the solvents considered. For positive values of relative valence, Z, the value of C is given by C » 20 Z. For negative values of Z, C » 0.

拡散原子の基礎的性質に基づく銅および銀中の不純物拡散係数の予測

This paper tries to predict diffusion coefficients of impurity atoms in copper and silver from the basic properties of the solute atoms. For this purpose a multiple regression analysis was made on the diffusion data selected from the JST Diffusion Database. The coefficients of determination (R2) for the activation energy of diffusion were 0.71 for Cu solvent and 0.92 for Ag solvent, and those for the frequency factor were 0.27 and 0.77 for Cu and Ag solvents, respectively. The position in the periodic table and the electronegativity of solute atoms were found to be highly significant independent variables. The present model shows an ability comparable to Le Claire’s electrostatic model in prediction of the activation energies for impurity diffusion in Cu and Ag.

A theory for solute impurity diffusion, which considers engel-brewer valences, balancing the fermi energy levels of solvent and solute, and differences in zero point energy

A theory that assumes the Engel-Brewer valence of elements (one for bcc structures, two for cph structures, and three for fcc structures) and considers the effects of balancing the solute and solvent Fermi energy levels and differences in zero point energy between solvent and solute atoms to calculate an “effective” relative valence for solute impurities is presented. The calculated values of relative valence and the experimental values of the differences in diffusional activation energy between solute and solvent atoms, ΔQ, are compared to the values of ΔH2 + ΔE calculated from the Lazarus-LeClaire theory for several solute impurities in ten solvent metals. The calculated results agree very well with the experimental values for the large majority of solutes. The theory presented adequately describes solute impurity diffusion in both α-Fe and γ-Fe, Al, Ni, and the noble metals. In particular, the low activation energies for impurity diffusion of the alkali metals (ground state valence of one) in Al (ground state valence of three) are accounted for by the theory. It is shown that the diffusion of the electronegative solute impurities (Cr, Mn, Fe, and Co) in Al is not anomalous when the relative valence is calculated by the proposed theory. The diffusion of electronegative solute impurities in the noble metals, which has been problematic in the past, is also well described by the proposed theory. The proposed theory introduces a simple method of estimating the effective electron densities of solute impurities and illustrates that the Lazarus-LeClaire theory adequately describes solute impurity diffusion in the ten solvent metals studied. It is expected that more accurate calculations of effective electron density for solute impurities would result in even better agreement between experimental and calculated results.

Empirical Relations Between the Activation Energies for Impurity Diffusion in Molten Iron and its Solid Polymorphic Phases

Empirical Relations Between the Activation Energies for Impurity Diffusion in Molten Iron and its Solid Polymorphic Phases

Self-excited oscillation and non-linear anelasticity of In20 at.% Tl due to transformation twins

Non-linear anelasticity of In20 at.% Tl thermoelastic martensite is studied by measuring self-excited oscillations and resonance curves. The self-excited frequency is of the order of one-tenth of the driving frequency, and thus the fundamental wave is amplitude-modulated by the self-excited oscillation. The modulation frequency depends on temperature and shows a maximum near 5°C. The activation energies estimated are roughly half of the activation energy for impurity diffusion of Tl in In. The experimental results obtained are similar to those of In-19.1 at.% Tl by Wuttig and Lin. The impurity drag effect, as applied to the twin anelasticity in InTl by Wuttig and Lin, and the effects of assumed triangular and rectangular potentials between Tl atom and twin boundary on the temperature dependence of the maximum modulation frequency are discussed.

Heterogeneous ordering in superlattice alloys

Abstract The occurrence of heterogenerous ordering in ordered alloys is investigated by the differential thermal analysis (DTA) of some quenched alloys having L12 and B2 crystal structures. The activation energy for ordering in these alloys is deduced by Kissinger's method from these DTA data. The results are compared with the activation energy for impurity diffusion and the migration energy of vacancies, deduced by a simple calculation given by Srikrishnan and Ficalora. The activation energy for heterogeneous ordering is found to be lower than that for homogeneous ordering. It is also found that the activation energy for the former is in good agreement with the migration energy of vacancies and that for the latter agrees with the activation energy for impurity diffusion. The conditions under which heterogeneous ordering occurs, as previously proposed by the present authors, are shown to be applicable to many other alloys which are known already to exhibit heterogeneous ordering.

Effect of high pressure on interdiffusion in Cu-Zn alloys at temperatures near the melting point

Interdiffusion of copper and zinc alloys of Cu-28.5 at. pct Zn and Cu-4.9 at. pct Zn has been investigated under pressures from 0.101 to 3240 MPa in the temperature range from 1256 to 1377 K. The diffusion coefficients decrease with increasing pressure. The activation energy for impurity diffusion of zinc in copper increases with pressure. The ratio of the activation volume to the molar volume of copper is between 0.75 and 0.90. It is concluded that the impurity diffusion of zinc in copper occurs predominantly by the monovacancy mechanism at temperatures near the melting point of the alloy.

Impurity diffusion constants and vacancy–impurity binding energies in solids

Activation energies for impurity diffusion in solids are discussed. New approaches based on elasticity are outlined to predict values of activation energy from the atomic size, surface energy, and elastic modulus of the matrix and impurity. The activation energy for self-diffusion in the matrix must also be known. It is shown that reasonable agreement between the theoretical and experimental values of activation energy are obtained for copper, aluminium, nickel, and iron matrices. The elastic strain energy model is extended to facilitate predictions of vacancy–impurity binding energies. Again good agreement between experiment and theory is obtained, except in the case of aluminium matrices.MST/211

Impurity diffusion constants and vacancy–impurity binding energies in solids

Activation energies for impurity diffusion in solids are discussed. New approaches based on elasticity are outlined to predict values of activation energy from the atomic size, surface energy, and elastic modulus of the matrix and impurity. The activation energy for self-diffusion in the matrix must also be known. It is shown that reasonable agreement between the theoretical and experimental values of activation energy are obtained for copper, aluminium, nickel, and iron matrices. The elastic strain energy model is extended to facilitate predictions of vacancy–impurity binding energies. Again good agreement between experiment and theory is obtained, except in the case of aluminium matrices.MST/211

Cation impurity diffusion in CoO and NiO

Impurity diffusion of 59Fe, 54Mn, 46Sc, 88Y, 95Zr and 95Nb in both CoO and NiO, and of 22Na in CoO has been measured as a function of temperature (1000–1600° C) in air by the tracer-sectioning technique. It has been shown that the larger ions diffuse more rapidly and have a smaller activation energy than do smaller ions for transition-metal impurity ions having the same valence. The absolute values of the divalent-impurity diffusion coefficients in CoO and NiO are comparable to the self-diffusion coefficients of Co and Ni, respectively. The diffusion coefficients of the bivalent impurity ions are smaller than those of the divalent impurity ions in these oxides. The activation energies for impurity diffusion in CoO and NiO are discussed in terms of the ionic size and the charge state of the diffusing ions.

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).

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.

Dissolution Kinetics of Precipitates of Divalent Cadmium in Sodium Chloride Studied by means of Ionic Thermoconductivity

In OH− “free” system the isothermal time evolution of the solution process of I.V . (impurity‐vacancy) dipoles to achieve the thermodynamical equilibrium was studied by means of the I.T.C. (ionic thermoconductivity) method in the annealing temperature range from 323° to 423 °K. Two stages were found, both described by a monomolecular first order kinetics. The early fast stage and the subsequent slow one are characterized by activation energies of and , comparable with the activation energy for impurity diffusion, and pre‐exponential frequency factors . The sources of I.V . dipoles in the two stages were tentatively identified with dipolar precipitates responsible for the additional peaks in I.T.C. spectrum. The energy required to decompose one kind of the above microprecipitates is close to the solution energy of I.V . dipoles. The role of preannealing on thermodynamical equilibrium value ns and on the solution kinetics was also analyzed.

Negative temperature dependence of the activation energy for impurity diffusion in metals

Negative temperature dependence of the activation energy for impurity diffusion in metals

On the theory of impurity diffusion in metals

Abstract The theory of diffusion proposed by Lazarus (1954), in which attention was directed to the effects on diffusion properties of the electrostatic interaction between an impurity and a vacancy, is re-examined and a model proposed which, in particular, allows a more direct estimation of the difference in the activation energies for jumps of an impurity atom and a solvent atom. This difference is simply related to the electrostatic interaction between the excess charge Ze of the impurity and the two half-vacancies which flank it at the saddle point. Calculated values of the difference between an observed activation energy for impurity diffusion and that for self-diffusion of the (noble metal) solvent turn out to be in good agreement with experiment. As in the original treatment by Lazarus, the effective charge difference between solute and solvent ions is a central parameter of the model and magnetic properties are invoked to suggest values for this in cases where the solute is a transition metal. The contribution from the temperature dependence of the correlation factors, which is also estimated from the model, appears to be considerable and may be connected with the difference often observed between activation energies for diffusion directly measured and those obtained indirectly, for example, by internal friction measurements. Estimates also are made, with satisfactory results, of the correlation factors and the effects of a solute on the solvent diffusion rates. The ratios of the vibrational frequencies of solute and solvent are inferred from the model and their order of magnitude shown to be consistent with the expected effect of the electrostatic interaction between vacancy and solute.