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Consider a system with components 1, *1, and v

Ji = Lij Fj

Wiki MarkupJ*1C = \ -kT \ [ L11 / C1 - L1*1 / C*1\] d*1 / dx

Mix radioactive atoms with non-radioactive atoms.  There is a different mass.

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Mix in a radioactive component on one side.  There is no gradient in the concentration of species 1.  Use a similar formula to find almost the same expression.unmigrated-wiki-markup

J*1C = \ -kT \ [L11 / C1 - L1*1 / C*1\] dC*1 / dx

J*1C = -*D1 dC11 / dx

The self-diffusivity of 1 in the alloy is termed D1*

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There is local equilibrium, and the Gibbs-Duhem equation allows one to simplify.unmigrated-wiki-markup

J1C = \ -kT \ [ L11 / C1 - L12 / C2 \ ]\[ 1 + d ln gamma / d ln C1 + d ln < omega > / d ln C1 \ ] dC1 / dx

The activity coefficient is gamma and is related to the thermodynamics of the 1-2 solution

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There is a thesis of a study of gold-nickel diffusion.  Show the value of coefficients

unmigrated-wiki-markup\-kT \ [ L11 / C1 - L12 / C2 \ ]\[ 1 + d ln gamma / d ln C1 + d ln <omega> / d ln C1 \ ]

The intrinsic diffusivity is D1.  Everything is concentration dependent.

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Relate the intrinsic diffusivity to the self-diffusivities

Wiki MarkupD1 = \ *D1 \ [ 1 + d ln gamma1 / d ln C1 \ ]

The instrinsic diffusivity describes an interdiffusion process.  There is a correction due to the thermodynamics of the system.  The diffusivities are almost the same.

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 vCV varies across the diffusion zone.

Wiki MarkupJ1v = \ -\[C1 omega1 D2 + C2 omega2 D1\] d C1 / dx

This is a Fick's law type expression.

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Darken equation: links the v-frame and c-frameSummarize

Summary

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V-

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Frame Description

There is a single term Dtilda related to interdiffusivity

Use a fixed frame of reference, which is often the end of samplec

C-

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Frame Description

There are intrinsic diffusivities of D1 and D2 and a local reference frame attached to crystal planes

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