Isotope effect in vacancy diffusion

Tharmalingam, K.; Lidiard, A. B.

doi:10.1080/14786435908238264

Cited by 71 publications

(13 citation statements)

References 9 publications

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“…Isotopic fractionation during diffusion in metal has been extensively studied because it is useful in elucidating diffusion mechanisms (e.g., Schoen 1958;Tharmalingam and Lidiard 1959;Mullen 1961). The β-values calculated for diffusion of Fe in pure α (bcc, <910 °C), (fcc, 910 to 1390 °C), δ (bcc 1390 to melting at 1534 °C) iron, pure Fig.…”

Section: Input Parametersmentioning

confidence: 99%

Diffusion‐driven kinetic isotope effect of Fe and Ni during formation of the Widmanstätten pattern

Dauphas

2007

Meteorit & Planetary Scien

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Abstract-Iron meteorites show resolvable Fe and Ni isotopic fractionation between taenite and kamacite. For Toluca (IAB), the isotopic fractionations between the two phases are around +0.1‰/amu for Fe and −0.4‰/amu for Ni. These variations may be due to i) equilibrium fractionation, ii) differences in the diffusivities of the different isotopes, or iii) a combination of both processes. A computer algorithm was developed in order to follow the growth of kamacite out of taenite during the formation of the Widmanstätten pattern as well as calculate the fractionation of Fe and Ni isotopes for a set of cooling rates ranging from 25 to 500 °C/Myr. Using a relative difference in diffusion coefficients of adjacent isotopes of 4‰/amu for Fe and Ni (β = 0.25), the observations made in Toluca can be reproduced for a cooling rate of 50 °C/Myr. This value agrees with earlier cooling rate estimates based on Ni concentration profiles. This supports the idea that the fractionation measured for Fe and Ni in iron meteorites is driven by differences in diffusivities of isotopes. It also supports the validity of the value of 0.25 adopted for β for diffusion of Fe and Ni in Fe-Ni alloy in the temperature range of 400-700 °C.

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Section: Input Parametersmentioning

confidence: 99%

Diffusion‐driven kinetic isotope effect of Fe and Ni during formation of the Widmanstätten pattern

Dauphas

2007

Meteorit & Planetary Scien

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“…Schoen [a] used equation (3) to show that the so-called isotope effect (a and b being isotopes of the same element) is equal to the correlation factor under the condition of a na-l/z mass dependence of jump frequency. However, Tharmalingam and Lidiard [5] argued that this result was obtained by use of the approximate expression (3) and succeeded to prove that the relation is generally valid for all systems having a t least a twofold symmetry around the vacancy-solute jump direction.…”

Section: Introductionmentioning

confidence: 94%

“…Such measurements are indispensible to furnish information about which atomic processes determine the diffusion coefficient of the impurity. Mullen [6] has shown on the basis of Vineyard's theory [7] that, if there is a deviation from a m-*lz mass dependence of jump frequency, one gets E = f A K , ( 5 ) AK being the fraction of the translational kinetic energy carried by the jumping atom (AK = 1 under the condition of a m-ll2 dependence).…”

Section: Introductionmentioning

confidence: 98%

A Simple Straight‐Forward Method to Calculate the Correlation Factor and Its Relation to the Isotope Effect for Impurity Diffusion

Bakker

1970

Physica Status Solidi (b)

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A general formalism is developed by which i t is possible to relate the correlation factor t o the isotope effect and to calculate the correlation factor for impurity diffusion by monovacancies in systems having a t least a twofold symmetry around the vacancy-solute jump direction. However, the formalism can be extended to more complicated systems. Some well known results are deduced easily from a general equation. The case of impurity diffusion in the two-dimensional hexagonal lattice and in the three-dimensional f.c.c. lattice is worked out completely. Es wird ein allgemeiner Formalismus zur Berechnung des Korrelationsfaktors fur dieFremdatomdiffusion durch Einzelleerstellen in Systemen mit wenigstens zweifacher Symmetric um die Leerstellen-Fremdatom-Sprungrichtung entwickelt und der Zusammenhang zwischen Korrelationsfaktor und Isotopieeffekt dargestellt. Eine Erweiterung des Formalismus auf kompliziertere Systeme ist moglich. Aus unserer allgemeinen Gleichung konnen leicht einige bereits bekannte Resultate wiedergewonnen werden. Fur ein zweidimensionales hexagonales Gitter und fur das dreidimensionale k.f.2. Gitter wurde der Formalismus vollstandig ausgearbeitet.

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“…Correlation effects have been shown to cause deviations from the Nernst-Einstein relationship [6], to reduce the isotope effect [7] and to result in a deviation from the Arrhenius temperature dependence of the diffusion coefficient [8].…”

Section: Introductionmentioning

confidence: 99%

A Theoretical Analysis of Cation Diffusion in Potassium Azide

Danemar

Royce

Welch

1974

Physica Status Solidi (b)

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A theoretical analysis has been made of the temperature dependence and anisotropy of the self-diffusion of tracer potassium ions in KN,. A vacancy mechanism is assumed, and the effects of correlation on diffusion are examined. An approximate analytic expression is obtained for the correlation factor, and its validity is determined by comparison with more accurate numerical calculations. The temperature dependence of the elements of the diffusion tensor including correlation is evaluated, making use of theoretical values of the migration energy of cation vacancies, and the role of correlation in determining the crystallographic anisotropy of cation diffusion is discussed. Comparison is made to available experimental data.Es wird die theoretische Analyse der TemperaturabhLngigkeit und Anisotropie der Selbstdiffusion von radioaktiv markierten Kaliumionen in KN, durchgefuhrt. Es wird ein Leerstellenmechanismus angenommen und die Einflusse der Korrelation auf die Diffusion untersucht. Ein geeigneter analytischer Ausdruck fur den Korrelationsfaktor wird erhalten und seine Gultigkeit durch Vergleich mit genaueren numerischen Rechnungen bestimmt. Die Temperaturabhangigkeit der Elemente des Diffusionstensors wird unter EinschluD der Korrelation berechnet, wobei theoretische Werte der Wanderungsenergie der Kationenleerstellen benutzt werden und die Rolle der Korrelation bei der Bestimmung der Kristallanisotropie der Kationendiffusion diskutiert wird. Die Ergebnisse werden mit erhaltlichen experiment ellen Werten verglichen.

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Isotope effect in vacancy diffusion

Cited by 71 publications

References 9 publications

Diffusion‐driven kinetic isotope effect of Fe and Ni during formation of the Widmanstätten pattern

Diffusion‐driven kinetic isotope effect of Fe and Ni during formation of the Widmanstätten pattern

A Simple Straight‐Forward Method to Calculate the Correlation Factor and Its Relation to the Isotope Effect for Impurity Diffusion

A Theoretical Analysis of Cation Diffusion in Potassium Azide

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