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Diffusion profiles associated with the onsager matrix in non-equilibrium A-A∗-vacancy and A-B-vacancy solutions

✍ Scribed by J.S. Kirkaldy; D.J. Young; J.E. Lane


Publisher
Elsevier Science
Year
1987
Weight
723 KB
Volume
35
Category
Article
ISSN
0001-6160

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✦ Synopsis


A new derivation of the Onsager matrix is presented based on diffusion correlation effects in a non local equilibrium ternary solution of conserved vacancies with a binary isotope mixture. In this calculation, we proceed deductively, thus avoiding the strong construction of Howard and Lidiard which conjectures a non-equilibrium diffusion thought experiment at a constant isotopic ratio and subjects the result to local equilibrium constraints, thereby generating a phenomenological proof of Onsager Reciprocity for A-A*-vacancy solutions. By contrast, we introduce correlation cross-effects, together with detailed balance, within a strict non local equilibrium structure, and from this derive a symmetric Onsager matrix for the A-A*-V case identical to that of Howard and Lidiard. Solutions of the cor~s~nding Fick equations-are for the first time evaluated and profiles presented for infinite diffusion couples. These solutions demonstrate that the eigen-values of the diffusion matrix are Dv and DX<tD,, so that profiles in infinite diffusion couples are generally very steep near the origin. Furthermore, each isotope flows down the other's gradient (positive off-diagonal D-coefficients). For the more general A-B-V case, Manning's approximate generalization of the Howard-Lidiard L-matrix in a conserved vacancy interpretation is expressed as a Fickian D-matrix which has the eigenvalues 1, = Dv = D/Xvf and A2 = 02 Dg/D where b is the average tracer coefficient. The corresponding diffusion profiles illustrate q~ntitatively the nature of the vacancy pump in a countercurrent A-B experiment.


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