The Relationship between Correlation Factor and Isotope Effect of Diffusion in Crystals

Mehrer, H.; Seeger, A.; Steiner, Emilie

doi:10.1002/pssb.2220730110

Cited by 24 publications

(5 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As a consequence of (3.lb) their probabilities of occurrence satisfy c, = c2 = f. AB. Hence, divacancy diffusion parallel to the hexagonal c-axis provides an example for a diffusion mechanism with more than one tracer jump frequency where the correlation factor component satisfies condition (1.3), as already mentioned in [2]. We may therefore conclude that the correlation factor provides Numerical values of the Pk.…”

Section: Correlation Factor and Isotope Effect For Diffusion Parallelsupporting

confidence: 60%

“…However, an upper limit E&(max) for the isotope effect parameter can be obtained numerically as outlined in [2]. It is shown in Pig.…”

Section: Correlation Factor and Isotope Effect For Diffusion Perpendimentioning

confidence: 99%

“…This non-randomness may be taken into account in the present case by the tensor components f*,lI and fT) 1 of the correlation factor. Hence we may write [ 2 ] DT. II = fT,llDII , As a result of correlation effects the isotope effect in diffusion is reduced.…”

Section: Introductionmentioning

confidence: 99%

“…II = fT,llDII , As a result of correlation effects the isotope effect in diffusion is reduced. An appropriate measure is the tensor of the isotope effect parameter for two isotopes tc and ( 3 [ 2 ] . I t s components parallel and perpendicular to the c-axis are defined (l.2a) (1.2b)…”

Section: Introductionmentioning

confidence: 99%

“…When (2.3) is violated the correlation factor constitutes no longer an upper limit for the isotope effect parameter component. Starting from (1.2) and using (1.4), an upper limit can be calculated in a way outlined in [ 2 ] .…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Correlation Factors and Isotope Effect for Self‐Diffusion by Mono‐ and Divacancies in H.C.P. Crystals

Steiner¹,

Mehrer²,

Seeger³

1976

Physica Status Solidi (b)

Self Cite

View full text Add to dashboard Cite

The tensor components of the Bardeen-Herring correlation factor for a divacancy mechanism of self-diffusion in an h.c.p. crystal are calculated and compared with Mullen's results on the monovacancy mechanism. The relationship between the correlation factors and the isotope effect parameters is discussed, in the monovacancy case making use of the work of Batra. For moaovacalzcy diffusion parallel to the c-direction the correlation factor provides an upper limit for the isotope effect parameter, whereas for diffusion perpendicular to the c-axis the isotope effect parameter can be slightly larger than the correlation factor. For the divacancy case it is demonstrated analytically that the correlation factor parallel to the c-axis provides an upper limit for the isotope effect parameter in this direction.Numerica1 calculations show that the upper limit of the isotope effect parameter perpendicular to the c-axis exceeds the correlation factor at most by a few per cent.Die Tensorkomponenten des Bardeen-Herringschen-Korrelationsfaktors fur einen Doppelleerstellenmechanismus der Selbstdiffusion in einer hexagonalen Kugelpackung werden berechnet und mit Mullens Ergebnissen fur den Einfachleerstellenmechanismus verglichen. Die Beziehung zwischen den Korrelationsfaktoren und den Isotopieeffektparame$ern wird diskutiert, wobei im Einfachleerstellenfall von den Ergebnissen Batras Gebrauch gemacht wird. Bei der Einfachleerstellendiffusion stellt der Korrelationsfaktor parallel zur c-Achse eine obere Grenze fur den Isotopieeffektparameter dar, wohingegen bei Diffusion senkrecht zur c-Achse der Isotopieeffektparameter etwas groDer sein kann als der Korrelationsfaktor. Im Doppelleerstellenfall wird analytisch nachgewiesen, da13 der Korrelationsfaktor parallel zur c-Achse eine obere Grenze fur den Isotopieeffektparameter in dieser Richtung darstellt. Numerische Rechnungen zeigen, daD die obere Grenze fur den Isotopieeffektparameter senkrecht zur c-Achse den Korrelationsfaktor maximal um einige Prozent ubersteigt.

show abstract

Section: Correlation Factor and Isotope Effect For Diffusion Parallelsupporting

confidence: 60%

“…However, an upper limit E&(max) for the isotope effect parameter can be obtained numerically as outlined in [2]. It is shown in Pig.…”

Section: Correlation Factor and Isotope Effect For Diffusion Perpendimentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Correlation Factors and Isotope Effect for Self‐Diffusion by Mono‐ and Divacancies in H.C.P. Crystals

Steiner¹,

Mehrer²,

Seeger³

1976

Physica Status Solidi (b)

Self Cite

View full text Add to dashboard Cite

show abstract

A novel method for the direct determination of the activation enthalpy in tracer diffusion studies with applications to “low”-temperature self-diffusion in silver

Maier

Mehrer

Bihr

1978

Phys. Stat. Sol. (a)

Self Cite

View full text Add to dashboard Cite

A method is described for the direct determination of the activation energy of diffusion. It avoids the depth calibration of the penetration curves and is therefore particularly appropriate for tracer diffusion studies using microsectioning. The technique requires two radio isotopes of the same element which are diffused into the specimen during two diffusion anneals at nearby temperatures. Its application to self‐diffusion in silver at “low” temperatures using the isotope pair 105Ag and 110mAg gives an activation energy of (1.73 ± 0.06) eV which agrees within the limits of error with the value deduced from the temperature dependence of the diffusion coefficient. It pertains to the monovacancy mechanism which is the only contribution to volume diffusion in silver at low enough temperatures.

show abstract

On the mass dependence of the energy factor ΔK of the isotope effect for impurity diffusion in copper

Eckseler

Herzig

1978

Physica Status Solidi (b)

View full text Add to dashboard Cite

Using diffusion and isotope effect measurements of Au and Co in Cu a lower limit of the correlation factor of impurity diffusion as well as the corresponding limits of the kinetic energy factor AK are calculated from Manning's jump frequency model of vacancies near impurity atoms. The results show that a variation in impurity mass by a factor of three does not change AK for impurity diffusion significantly. For Au and CO in Cu AK is found to be about the same as for self-diffusion in copper. This result allows to estimate the jump frequency ratios and the corresponding vacancy flow factors. Aus

show abstract

The Relationship between Correlation Factor and Isotope Effect of Diffusion in Crystals

Cited by 24 publications

References 34 publications

Correlation Factors and Isotope Effect for Self‐Diffusion by Mono‐ and Divacancies in H.C.P. Crystals

Correlation Factors and Isotope Effect for Self‐Diffusion by Mono‐ and Divacancies in H.C.P. Crystals

A novel method for the direct determination of the activation enthalpy in tracer diffusion studies with applications to “low”-temperature self-diffusion in silver

On the mass dependence of the energy factor ΔK of the isotope effect for impurity diffusion in copper

Contact Info

Product

Resources

About