Dilute Fcc Alloys Research Articles

Formation of Point Defects in Dilute FCC Alloys

Using pseudopotential approach, vacancy formation energy , different non-split interstitial formation energies and binding energy for the vacancy-impurity pair and that for interstitial impurity over host have been calculated in some cubic fcc metal systems, viz. copper, silver, gold and lead using Ashcroft's potential and Taylor's exchange and correlation function with standard (AT) and fitted to (ATF) and also Heine-Abarenkov’s model potential and same exchange and correlations (HAT). It is difficult to have a universal value for all types of atomic property calculations. The results show that ATF and HAT combinations are better in comparison to AT. Also, the substitutional impurity adjacent to a vacancy is found to be more loosely bound than the interstitial impurity in fcc metals.

Enhancement of solute self-diffusion in fcc alloys

Using a new simulation approach to the calculation of correlation factors in very dilute solutions, the present paper reports on results of the first calculations of the first and second solute enhancement factors for solute self-diffusion in the fourteen-frequency model postulated by Bocquet for describing the diffusion kinetics of paired and unpaired solute atoms in dilute fcc alloys. Bocquet's assumption that correlation effects do not contribute to solute self-diffusion enhancement is shown to have a fairly limited range of validity. Specifically, it is shown that this assumption is reasonable when the solvent–vacancy exchange frequency far from the solute is high compared with the others or when all of the solute–vacancy exchange frequencies are small compared with the others. The assumption is also reasonable when the vacancy is not attracted to the solute atoms and when the vacancy does not often alternate between two solute atoms. The present study would strongly suggest that many of the ratios of exchange frequencies that have been determined from experimental data on the basis of this assumption are likely to be in error.

On Vacancy Concentrations in Dilute FCC Alloys

Berces and Kovacs [1] have estimated the vacancy concentrations cv(x) in dilute alloys taking into account V-iX complexes with i impurity atoms X in nearest-neighbour (NN) distance of the vacancy V and NN X-X interactions. The obtained approximation is based on the statistical arrangement of the impurity atoms in NN distance of the vacancy. In thermodynamical equilibrium a redistribution of the impurity atoms has to be taken into consideration. This means that e.g. for attractive V-X interaction and repulsive X-X interaction arrangements with smaller numbers of impurity atoms in NN distance are preferred. In the present study the correct solution for the Gibbs free energy of vacancy formation for V-iX complexes is derived. The improved model is compared with experimental data of cv(x) obtained with the aid of differential dilatometric investigations on dilute fcc alloys [2].

Computer simulation of solute-enhanced diffusion kinetics in dilute fcc alloys

This paper describes a Monte Carlo study of the linear enhancement factor for the solvent tracer diffusivity in dilute fcc alloys. The model used is the well-known five-frequency model with isolated solute atoms. It is shown that the analytical treatments by Howard and Manning and by Ishioka and Koiwa have major shortcomings in their handling of correlation effects for certain combinations of the atom-vacancy exchange frequencies. Many of the values of the exchange frequency ratios that have been determined from experiment by way of these treatments are probably in some error.

Self-diffusion and solute diffusion in alloys under irradiation: Influence of ballistic jumps

We have studied the influence of ballistic jumps on thermal and total diffusion of solvent and solute atoms in dilute fcc alloys under irradiation. For the diffusion components that result from vacancy migration, we introduce generalized five-frequency models, and show that ballistic jumps produce decorrelation effects that have a moderate impact on self-diffusion but that can enhance or suppress solute diffusion by several orders of magnitude. These could lead to new irradiation-induced transformations, especially in the case of subthreshold irradiation conditions. We also show that the mutual influence of thermal and ballistic jumps results in a nonadditivity of partial diffusion coefficients: the total diffusion coefficient under irradiation may be less than the sum of the thermal and ballistic diffusion coefficients. These predictions are confirmed by kinetic Monte Carlo simulations. Finally, it is shown that the method introduced here can be extended to take into account the effect of ballistic jumps on the diffusion of dumbbell interstitials in dilute alloys.

Diffusion and Vacancy Impurity Interaction in Dilute fcc Alloys

Diffusion and Vacancy Impurity Interaction in Dilute fcc Alloys

Linear response theory of correlation effects in anisothermal atomic transport in crystals

Linear response formulae are derived for the phenomenological coefficients for matter transport in a system characterised by a set of jump probabilities. The expressions for the isothermal transport coefficients are the same as those originally derived by Allnatt (1981-82) but the expressions for the anisothermal transport coefficients are different. The details of the derivation differ somewhat from those of the earlier work and are clearer and technically more satisfactory. The matrix method developed by Okamura and Allnatt (1983) for calculations of the isothermal transport coefficients in dilute binary alloys is extended to the anisothermal coefficients. As an example, new exact formulae for the terms in these coefficients which are of first order in the concentrations of paired and unpaired defects are calculated for the five-frequency model of the vacancy mechanism in a dilute FCC alloy. The results reduce to earlier less exact expressions in the appropriate limit.

Comment on 'Calculation of the free enthalpy of binding of impurity-vacancy in FCC very dilute alloys'

For original paper see ibid., vol.12, p.L67 (1982). A recent letter claimed that the three-jump frequency ratios W2/W1, W3/W1 and W4/W0 for the standard five-frequency model for dilute FCC alloys contained all the thermodynamic information on these alloys, namely the value of the binding enthalpy of an impurity-vacancy pair. The authors show that this conclusion is erroneous since it rests on an incorrect sampling procedure along the chain of the microscopic configurations through which a given alloy evolves with time.

Calculation of the free enthalpy of binding of impurity-vacancy in FCC very dilute alloys

A method is developed to obtain values for the free enthalpy of binding of a vacancy to an impurity in very dilute FCC alloys. On the basis of the five-jump frequency model a computer simulation of the diffusion process is carried out using Monte-Carlo methods. This simulation method is then applied to some copper alloys from which experimental values are well known.

Phenomenological coefficients for matter transport by vacancies from linear response theory: I. Derivation of Manning's equations for the impurity correlation factor

Liner response formulae for the phenomenological coefficients LAA, LAB, and LBB for matter transport by vacancies are calculated exactly for the five-frequency model of a very dilute FCC alloy of solute B in solvent A. The method reduces each formula to a set of random walk problems in the homogeneous system, and these are solved by Green function methods. In this paper the results for LBB are shown to be the same as that obtained by Manning in 1964 using the method of equivalent vacancy distributions. The key steps are noted and used in the following paper to calculate LAB and LAA.

Phenomenological coefficients for matter transport by vacancies from linear response theory: II. Completion of the five-frequency model

For pt.I see ibid., vol.14, p.5453 (1981). Linear response formulae for the phenomenological coefficients LAB and LAA for matter transport by vacancies are calculated exactly for the five-frequency model of a very dilute FCC alloy of solute B in solvent A. The Green function method used is a straightforward application of the method developed in the preceding paper for LBB. In the latter case the results are the same as those obtained by Manning in 1964 through the method of equivalent vacancy distributions.

Self-Diffusion in Dilute fcc-Alloys. Comparison of Recalculated Enhancement Factors with Theory

Self-Diffusion in Dilute fcc-Alloys. Comparison of Recalculated Enhancement Factors with Theory

Phonon self-energy in some symmetry directions of a dilute fcc alloy

We study the dynamical quantities that describe the one-phonon approximation to the coherent response of a dilute fcc alloy in a neutron scattering experiment. We allow for a mass change at the impurity site and also consider the changes in the central force constants connecting the defect to its first neighbors. We make use of previously derived relations among the various relevant lattice Green's functions, to obtain simple analytic expressions for some dynamical quantities of the impure system, which are directly related to neutron scattering experiments. As well as simplifying some of the earlier results of Lakatos and Krumhansl, we also provide some new results for the phonon self-energy and shift. We briefly apply our results to study some available experimental data on Cu-Au alloys, and comment on the difficulty of allowing for volume changes that occur on alloying.

Kinetics of Solute-Enhanced Diffusion in Dilute Face-Centered-Cubic Alloys

A theory of the effect of solutes on solvent self-diffusion in dilute fcc alloys is given, based on the model of nearest-neighbor interactions between solute impurities and vacancies. The parameters of the theory are the four vacancy-jump frequencies in the neighborhood of an impurity and the vacancy-jump frequency in the pure crystal. No assumptions are made about the relative magnitudes of these frequencies. This distinguishes the present theory from previous theories based on the same model. The theory is used to deduce for each of nine dilute Ag-based alloys sets of jump-frequency ratios (and corresponding impurity correlation factors) that are consistent with measured values of the solute enhancement coefficient and of the impurity diffusion coefficient. The desirability of isotope-effect measurements to determine the impurity correlation factors is emphasized.