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An improved procedure for determining grain boundary diffusion coefficients from averaged concentration profiles
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10.1063/1.2887993
/content/aip/journal/jap/103/6/10.1063/1.2887993
http://aip.metastore.ingenta.com/content/aip/journal/jap/103/6/10.1063/1.2887993

Figures

Image of FIG. 1.
FIG. 1.

Variation of the errors in determining with time ( was obtained by using Le Claire’s relation): (a) , , (b) , . Errors were estimated according to .

Image of FIG. 2.
FIG. 2.

Variation of the derivative with obtained for (a) and (b) .

Image of FIG. 3.
FIG. 3.

(a) Variation of the derivative as a function of calculated by using a modified Whipple’s solution (see text) for different ratios at (b) Variation of the derivatives with for at different diffusion times (Whipple’s original solution). Le Claire’s constant is also indicated. The dashed curves were obtained for increased sample length and indicate problems related to a finite length.

Image of FIG. 4.
FIG. 4.

Errors in determining calculated by using improved derivatives ( and ) in Le Claire’s original expression [Eq. (7)].

Image of FIG. 5.
FIG. 5.

The maxima of the dependences plotted against the dimensionless parameter for different ratios .

Image of FIG. 6.
FIG. 6.

Variation of the modulus of the maximum of (in ) with for different . The result is shown on a logarithmic scale.

Tables

Generic image for table
Table I.

A comparison of the derivatives at the maximum found by using calculated dependences (true) and Eq. (9) for .

Generic image for table
Table II.

The values of the slope for various .

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/content/aip/journal/jap/103/6/10.1063/1.2887993
2008-03-26
2014-04-24
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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: An improved procedure for determining grain boundary diffusion coefficients from averaged concentration profiles
http://aip.metastore.ingenta.com/content/aip/journal/jap/103/6/10.1063/1.2887993
10.1063/1.2887993
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