Diffusion in a Chemical Concentration Gradient

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Abstract
The concept of correlated reverse jumps is used to treat correlation effects in a chemical concentration gradient. It is shown that the correlation factor associated with a given atom jump will be very nearly the same as that in a homogeneous alloy having the composition associated with the point midway between the initial and final atom positions for that jump. This is true for either a vacancy or interstitialcy mechanism. With the aid of this result, expressions for the atom flux of a given species and the mean atom displacement of a layer of diffusing atoms are derived from a purely atomistic approach, taking correlation effects into account. These expressions differ from equations obtained by Darken and LeClaire in that they contain extra terms which arise where there is a flow of vacancies or interstitialcies. These extra terms can appreciably increase the predicted Kirkendall shift. They appear as both diagonal and cross terms in the general thermodynamic formulation of the diffusion equations. The method used here to analyze the effect of a chemical concentration gradient can also be used to study the effect of other types of gradients and external driving forces.

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