Diffusion and Isotope Effects for Diffusion in Transition Metals

Klotsman, S. M.

doi:10.4028/www.scientific.net/ddf.66-69.85

Cited by 3 publications

(6 citation statements)

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“…However, experimental results are difficult to obtain because of the reactivity of W at high diffusion temperatures, and different investigators report widely varying results. [28,42] Also, Klotsman et al [28] use a value of 596.7 kJ/mole for the self-diffusion of W in W as opposed to the calculated value of 560.1 kJ/mole used here. [28,42] Also, Klotsman et al [28] use a value of 596.7 kJ/mole for the self-diffusion of W in W as opposed to the calculated value of 560.1 kJ/mole used here.…”

Section: Diffusion In Tungstenmentioning

confidence: 94%

“…Klotsman, [28] in attempting to rationalize diffusion of solute impurities in Ni, used effective relative valences ranging from Ϫ6 for Ti to ϩ6 for S, based on atomic magnetic moments. Besides the size problem of ions with a relative charge of Ϫ6, a long extrapolation of the curve for ⌬H 2 ϩ ⌬E in Figure 17 shows that the activation energy for diffusion of Ti in Ni would be enormous when, in fact, the experimental value is lower than that for the self-diffusion of Ni.…”

Section: G Diffusion In Nickelmentioning

confidence: 99%

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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

Burachynsky

Cahoon

1997

Metall Mater Trans A

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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, ⌬Q, are compared to the values of ⌬H 2 ϩ ⌬E 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 ␣-Fe and ␥-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.

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Section: Diffusion In Tungstenmentioning

confidence: 94%

Section: G Diffusion In Nickelmentioning

confidence: 99%

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

Burachynsky

Cahoon

1997

Metall Mater Trans A

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“…[6], ⌬Q S is the difference in enthalpies for a vacancysolute atom exchange, , and a vacancy-solvent atom ex-S H 2 change, , plus the difference in enthalpies to form a S H 0 vacancy next to a solute atom, , and that required to form S E 2 a vacancy in the pure solvent, , minus a constant, C S , S E 0 which takes into consideration the possible temperature variation of the solute correlation factor, , which may not be S f 2 a purely geometric factor as is the case for solvent selfdiffusion:…”

Section: A Activation Energymentioning

confidence: 97%

“…''It has become a habitual notion that the diffusion behaviour in normal metals is well described in terms of the simple and physically lucid Lazarus-LeClaire model.'' [6] The LazarusLeClaire model is sound in principle and widely accepted, despite the fact that it only works well for the diffusion of electropositive solutes in the noble metals. The diffusion of electronegative solutes is not described well by the theory, and attempts to apply the theory to other solvent metals, such as Al, ␣-Fe, and ␥ -Fe, have been largely unsuccessful.…”

Section: Introductionmentioning

confidence: 99%

A modified “Hole” theory for solute impurity diffusion in liquid metals

Cahoon

1997

Metall Mater Trans A

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A modified ''hole'' theory for solute impurity diffusion in liquid metals is presented. The theory calculates an ''effective'' valence for the solute impurities by assuming that the bulk valences of the solvent and solute metals are those given by the Engel-Brewer theory (one for bcc structures, two for cph structures, and three for fcc structures). The effects of balancing the Fermi energy level of the solute with that of the solvent and differences in zero point energy are then considered in calculating the effective valence. The effective valence is then used to calculate a value of diffusional activation energy from a modified Lazarus-LeClaire approach. It is shown that the proposed theory works very well for solute impurity diffusion of a number of solutes in Al, Cu, Ga, Ag, Pb, and Sn, but the paucity of diffusion data is a hindrance to development of theoretical models.

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“…The hole theory ignores the energy needed for a diffusing atom to enter a hole. 2,3 Applications of the hole theory [4][5][6][7] have worked well for diffusion of electropositive solutes in noble metals, but not for electronegative solutes. Data for diffusion in metals are important from both practical and theoretical viewpoints.…”

Section: Synopsismentioning

confidence: 99%

Diffusion of oxygen in liquid copper and nickel

Hocking¹

2000

Mineral Processing and Extractive Metallurgy

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Diffusion and Isotope Effects for Diffusion in Transition Metals

Cited by 3 publications

References 0 publications

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 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 modified “Hole” theory for solute impurity diffusion in liquid metals

Diffusion of oxygen in liquid copper and nickel

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