ExamplesforMatSc503test2

# ExamplesforMatSc503test2 - Examples for MatSc503 Example 1...

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Examples for MatSc503 Example 1: Consider a diffusion couple, A 2 O 3 -B 2 O 3 and assume that the diffusivities of cations, A and B, are much higher than that of oxygen, derive the expression for the interdiffusion (or chemical diffusion) coefficient in terms of the diffusivities of the cations, A and B. (You may assume that A 2 O 3 and B 2 O 3 form ideal solid solutions). Solution: One may assume that the diffusion coefficient of oxygen is zero. In this case, an inert maker placed at the interface of the diffusion-couple will not move at all. The flux for cations, A and B, are given by J A 3 + =− C A 3 + D A 3 + RT d µ A 3 + dx + 3 F d φ dx J B 3 + C B 3 + D B 3 + RT d B 3 + dx + 3 F d dx where C, D, and μ are the concentration, diffusion coefficient and chemical potential of respective ions, F is the Faraday constant and is the electrical potential. In order to satisfy electrical neutrality condition, the total flux of A and B must be zero, i.e., J A 3 + + J B 3 + = 0 From this charge neutrality condition, we can solve for the unknown electrical potential gradient, 3 F d dx C A 3 + D A 3 + d A 3 + dx + C B 3 + D B 3 + d B 3 + dx C A 3 + D A 3 + + C B 3 + D B 3 + Substituting the electrical potential gradient back into the flux equation for A ions, J A 3 + C A 3 + D A 3 + C B 3 + D B 3 + RT C A 3 + D A 3 + + C B 3 + D B 3 + () d A 3 + dx d B 3 + dx Use the Gibbs-Duhem relation to express d B 3 + in terms of d A 3 + , i.e., X A 3 + d A 3 + + X B 3 + d B 3 + = 0 or d B 3 + dx X A 3 + X B 3 + d A 3 + dx

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Now the flux equation for A ions looks like J A 3 + =− C A 3 + D A 3 + C B 3 + D B 3 + RT C A 3 + D A 3 + + C B 3 + D B 3 + () X B 3 + d µ A 3 + dx Express the chemical potential in terms of mole fraction, X, A 3 + = A 3 + o + RT ln X A 3 + J A 3 + C A 3 + D A 3 + C B 3 + D B 3 + C A 3 + D A 3 + + C B 3 + D B 3 + X B 3 + X A 3 + dX A 3 + dx or J A 3 + D A 3 + D B 3 + X A 3 + D A 3 + + X B 3 + D B 3 + dC A 3 + dx Therefore, the chemical diffusion coefficient is ˜ D = D A 3 + D B 3 + X A 3 + D A 3 + + X B 3 + D B 3 + Example 2: Outline the experimental procedures that you may take to measure the grain boundary diffusion coefficient and surface diffusion coeffcient in a given material. Solution Measurement of grain boundary diffusion coefficient: (1) Apply a thin film of tracer to the surface perpendicular to an artificially fabricated grain boundary or to the surface of a polycrystalline material. (2) Anneal the sample at a given temperature. (3) Measure the average concentration, c , of tracer atoms in a series of thin slices cut parallel to the sample surface.
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## This note was uploaded on 01/19/2010 for the course MAT SCI 503 taught by Professor Chen during the Spring '02 term at Penn State.

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ExamplesforMatSc503test2 - Examples for MatSc503 Example 1...

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