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ENGR 240 - 9.19.07

ENGR 240 - 9.19.07 - ENGR 240 Non steady state diffusion o...

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ENGR 240 – September 19, 2007 Non steady state diffusion o Fick’s Second Law ∂c/∂t = D(∂ 2 c/∂x 2 ) Boundary conditions At t = 0, C = C 0 (0 ≤ x ≤ ∞) For t > 0, C = C s (at x = 0) C = C 0 (at x = ∞) Solving this you get o (C x – C 0 )/(C s – C 0 ) = 1 – erf(x/(2√(Δt)) o erf = error function erf is an integrated Gaussian distribution (Bell curve) book gives values for erf(z) as z = x/2√(Δt) o if we want some concentration, c 1 (c 1 – c 0 )/(c s – c 0 ) = constant o x/2√(Δt) = constant o Practical Ways to use this **** x 2 /D m 2 /(m 2 /s) s (diffusion time scale) Practical Diffusion Examples o Carburization Diffuse carbon into the surface of steel to make it harder and more abrasion resistant o Toyota Process Expose steel to molten salt both at high temperature and with Ti, Nb, V, Cr to form carbides Diffusion Paths o Bulk material (bulk diffusion) Slow but speeds up at high temperature Here bulk diffusion dominates o Grain Boundary Diffusion
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