ExamplesforMatSc503test2

ExamplesforMatSc503test2 - Examples for MatSc503 Example 1...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
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.
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Page1 / 8

ExamplesforMatSc503test2 - Examples for MatSc503 Example 1...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online