Vacancy models for concentrated binary alloys—I short-range ordered and clustered alloys

The activation energies for diffusion in transition metals is correlated against the localized d electron population. The d electron population is determined by the Engel-Brewer theory. A quasichemical model of a binary solid solution is used to determine the distribution of atoms and vacancies. The use of this model enables one to determine the average number of bonds affected by the formation of a vacancy and the jumping of an atom into the vacancy. The activation energy is considered to consist of energies of vacancy formation and atom migration. The correlative curve and an empirical ratio is used to separate the activation energies into the above two parts. Finally the results of the quasichemical model and the correlation are combined. The calculated activation energies of impurity atoms in pure metals and of self diffusion in binary alloys (Co -Ni, Fe-Ti, Fe-Cr and Fe-V) are compared with experimental results.DIFFUSION coefficients of substitutional impurities in pure metals and alloys are commonly determined by thin-film tracer techniques. When a vacancy mechanism is the principal diffusion mechanism, the selfdiffusion coefficient is determined by the frequency at which an atom will jump into a vacancy neighboring its site and by the probability that a given neighboring site is vacant. It is clear that the energy barriers involved arise from the perturbation of the lattice interactions in an otherwise perfect solid. The quasi chemical model considers the interactions among the ion cores and the electron clouds as bonds and therefore lends itself to an accurate description of the lattice interactions in transition metals. The activation energy required for the atom jump frequency (EJ) and the energy for the formation of the vacancy (BV) arise mainly from the perturbation of the nearest neighbor bonds. With this approach, the problem in metallic solutions reduces to one of describing the distribution of atoms in the solid solution and evaluating the energies of the different bonds and their contribution to E.1 and Ev by some empirical correlation. A similar attempt' is based on the use of melting points, heats of sublimation and shear moduli to evaluate the vacancy formation and migration energies. The advantage of using bonding electrons as the parameter for determining the above energies will be discussed in the conclusion of this paper. I. DISCUSSION i) Description of the ProblemThe two quantities to be evaluated are: a) the energetics of vacancy formation at a particular site in the lattice. b) the energy involved in the jumping of a particular neighboring atom into this vacant site.Darken2 showed that the diffusion coefficient of an atom in a multicomponent system is related to its mobility and the compositional variation of the activity coefficient. Further Pines and Smushkov 3 showed the compositional dependence of the self diffusivity to be V. SRIKRISHNAN and P. J. FICALORA are Graduate Student and Associate Professor, respectively,where DZ d(c) and DZ d (l) refer to the self diffusion coefficients...

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“…DA = tracer D 0 . exp (-Ev II /RT) • exp (-EÁ /RT) [ 9 ] Ef arise from all AB bonds, since A is so dilute that all nearest neighbors are B atoms.…”

Section: Iv) Determination Of Activation Energiesmentioning

confidence: 99%

“…The diffusivity is then given by Eq. [9]. In such a dilute solution one expects the energy for jumping to be due to the existence of A -B bonds and the energy for vacancy formation to be the same as that of the pure matrix.…”

Section: Iv) Determination Of Activation Energiesmentioning

confidence: 99%

Diffusion in transition metals and alloys

Srikrishnan

Ficalora

1975

Metall Trans A

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“…For the case of a random solution the probability of a lattice point being occupied by A ( A * i p and i p are the un-normalized and normalized probabilities respectively that atom i will occupy the lattice point. ij p is the probability that atom j will acquire atom i as a neighbor and depends on alloy composition, temperature and ε ∆ [6]. Black and gray atoms are A and B respectively.…”

Section: Random and Non-random Population Of A Simulation Cellmentioning

confidence: 99%

Passivation in Non-Random Solid-Solution Alloys

Artymowicz

Sieradzki²,

Newman

2013

ECS Trans.

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Results from large-cell Monte Carlo renormalization group calculations for the effects of ordering and clustering on site percolation thresholds in bcc alloys are presented. The results demonstrate that for the case of relatively small positive heats of mixing (0.015 eV/atom), the site percolation threshold is lowered from its conventional value of ~0.25 to 0.16. Conversely, for a small negative heat of mixing (-0.015 eV/atom), the threshold increases to ~0.30. The implications of these results on corrosion/passivation in the context of the integrity of materials for nuclear power systems are indicated.

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Kinetics of Order–Disorder Transformation in Alloys under Electron Irradiation

Banerjee

Urban

1984

Phys. Stat. Sol. (a)

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A simple kinetic model is presented which describes the order–disorder reaction under irradiation. The model is based on the Bragg‐Williams approximation. It is assumed that radiation‐induced disordering is opposed by radiation‐enhanced reordering. The ordering process is modeled by a chemical reaction whose elementary step occurs via vacancy jumps. The activation energy of such jumps is a linear function of the degree of order. Compared to the value in disordered material it is higher for a jump contributing to disordering and lower in the opposite case. A set of rate equations is derived which allow to calculate the steady‐state vacancy concentrations as a function of the degree of order. The treatment is given in general form applicable to alloys with B2, LI2, and D1a, structure. Details are worked out numerically for B2 and D1a alloys. The results for D1a are compared with those of recent experiments on Ni4Mo.

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Vacancy models for concentrated binary alloys—I short-range ordered and clustered alloys

Cited by 22 publications

References 4 publications

Diffusion in transition metals and alloys

Diffusion in transition metals and alloys

Passivation in Non-Random Solid-Solution Alloys

Kinetics of Order–Disorder Transformation in Alloys under Electron Irradiation

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