Diffusion and the Kirkendall shift in binary alloys

Manning, J. R.

doi:10.1016/0001-6160(67)90363-x

Cited by 277 publications

(62 citation statements)

References 10 publications

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“…a Al is the activity of Al in Ni 3 Al, S is the vacancy wind factor [64], and the superscript c 0 on X eAl has been dropped as no longer needed. Fortunately, D Ã Ni ,D , and a Al have all been measured at high temperatures (1400-1600 K).…”

Section: The Role Of Concentration-dependent Diffusion In Ni 3 Almentioning

confidence: 99%

Non-integer temporal exponents in trans-interface diffusion-controlled coarsening

Ardell

2016

J Mater Sci

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The kinetics of c 0 -type (Ni 3 X) precipitate growth and solute depletion in Ni-Al, Ni-Ga, Ni-Ge, Ni-Si, Ni-Ti and Ni-Al-Cr alloys is successfully predicted by the trans-interface diffusion-controlled theory of coarsening using non-integer temporal exponents, n, satisfying 2 B n B 3, which are obtained from analyses of particle size distributions (PSDs). The origin of non-integer n is concentrationdependent diffusion through the c/c 0 interface. The literature on diffusion of Al and Ni in Ni 3 Al is specifically examined. It is shown unequivocally that the concentration-dependent diffusion of Al can account semi-quantitatively for the value of n that successfully describes the PSDs and kinetics of coarsening of the c 0 precipitates. There is no need to invoke a particle size-dependent c/c 0 interface width, as was done in prior work. It is argued that existing theory and computational modeling of coarsening in systems with highly disparate diffusion mobilities in both phases do not correctly represent the mobilities in the matrix, precipitate, and interface in Ni-Al alloys. These theories predict temporal exponents satisfying 3 B n B 4, for which there is no experimental support.

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Section: The Role Of Concentration-dependent Diffusion In Ni 3 Almentioning

confidence: 99%

Non-integer temporal exponents in trans-interface diffusion-controlled coarsening

Ardell

2016

J Mater Sci

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“…Manning introduced a correction factor called the vacancy wind effect that describes the effect of vacancy flux on the intrinsic diffusivity of an element and can be expressed [27,30] as where W i and W j are the vacancy wind factors of the species i and j, respectively. We use i for the faster and j for the slower diffusion component in the two different systems.…”

Section: (C) X-ray Diffraction Measurementsmentioning

confidence: 99%

Role of different factors affecting interdiffusion in Cu(Ga) and Cu(Si) solid solutions

et al. 2014

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A detailed diffusion study was carried out on Cu(Ga) and Cu(Si) solid solutions in order to assess the role of different factors in the behaviour of the diffusing components. The faster diffusing species in the two systems, interdiffusion, intrinsic and impurity diffusion coefficients, are determined to facilitate the discussion. It was found that Cu was more mobile in the Cu-Si system, whereas Ga was the faster diffusing species in the Cu-Ga system. In both systems, the interdiffusion coefficients increased with increasing amount of solute (e.g. Si or Ga) in the matrix (Cu). Impurity diffusion coefficients for Si and Ga in Cu, found out by extrapolating interdiffusion coefficient data to zero composition of the solute, were both higher than the Cu tracer diffusion coefficient. These observed trends in diffusion behaviour could be rationalized by considering: (i) formation energies and concentration of vacancies, (ii) elastic moduli (indicating bond strengths) of the elements and (iii) the interaction parameters and the related thermodynamic factors. In summary, we have shown here that all the factors introduced in this paper should be considered simultaneously to understand interdiffusion in solid solutions.

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“…However, they all can be represented by linear lines. Further, as the systems concerned here are assumed as the pseudo-binary solution, the tracer diffusion coefficient for both Re and Ru in Ni 3 Al can be deduced from these lines by considering the Darken-Manning equation 19,20) as follows: The activation energy and the frequency factor for the tracer diffusion of Re and Ru obtained from Arrhenius plot in Fig. 5 is shown in Table 3.…”

Section: Nimentioning

confidence: 99%

Diffusion of Re and Ru in the γ′ Phase of Ni Based Alloys

et al. 2008

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The diffusion of Re and Ru in the 0 -Ni 3 Al phase has been investigated at a range of temperatures 1423-1523 K by using the pseudo-binary diffusion couples. It was found that the concentration gradient of Re appeared to promote the uphill diffusion of Al, whereas that of Ru did not promote the Al uphill diffusion. The cross interdiffusion coefficients ofD D Ni AlRe andD D Ni AlRu were independent of the matrix ordering since they were comparable qualitatively between those in the 0 -Ni 3 Al and in the -Ni phases. The tracer diffusion coefficients for Re and Ru in Ni 3 Al were estimated by extrapolation and the obtained activation energies were consistent with the site preferences of the elements reported in the literature. Further, the results of this work suggest that the diffusion of Ru in Ni 3 Al is mostly governed by the diffusion in Ni sublattice and the diffusion of Re is mainly controlled by the formation of anti-site defects in the Ni sublattice with negligible contribution of the anti-site bridge mechanism.

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Diffusion and the Kirkendall shift in binary alloys

Cited by 277 publications

References 10 publications

Non-integer temporal exponents in trans-interface diffusion-controlled coarsening

Non-integer temporal exponents in trans-interface diffusion-controlled coarsening

Role of different factors affecting interdiffusion in Cu(Ga) and Cu(Si) solid solutions

Diffusion of Re and Ru in the γ′ Phase of Ni Based Alloys

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Diffusion and the Kirkendall shift in binary alloys

Cited by 277 publications

References 10 publications

Non-integer temporal exponents in trans-interface diffusion-controlled coarsening

Non-integer temporal exponents in trans-interface diffusion-controlled coarsening

Role of different factors affecting interdiffusion in Cu(Ga) and Cu(Si) solid solutions

Diffusion of Re and Ru in the &gamma;&prime; Phase of Ni Based Alloys

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Diffusion of Re and Ru in the γ′ Phase of Ni Based Alloys