chap6_5

chap6_5 - 材材材材材材 Fundamental of Materials Prof:...

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Unformatted text preview: 材材材材材材 Fundamental of Materials Prof: Tian Min Bo Prof: Tian Tel: 62795426 材 62772851 E-mail: tmb@mail.tsinghua.edu.cn tmb@mail.tsinghua.edu.cn Department of Material Science and Engineering Tsinghua University. Beijing 100084 Lesson twenty­eight §6.5 concentration dependence of D. Matano method Matano Ⅰ.D-C dependence Ⅱ.Matano method ∂C ∂ ∂C = (D ) ∂t ∂x ∂x (1) D = D(C ) at t = 0 C = C1 C = C2 for x > 0 for x < 0 ( 2) x Let λ = t ( 3) ∂C dC x dC λ = (− )= (− ) ∂t dλ 2t t dλ 2t ( 4) ∂C dC ∂λ 1 dC 1 = ⋅ = ∂x dλ ∂x t dλ 材t ∂ ∂C d 1 dC ∂λ 1 d dC (D )= (D ⋅ )⋅ = 材 材 ∂x ∂x dλ t dλ ∂x t dλ dλ put ( 4) in (1) ­ λ dC 1 d dC = (D ) 2t dλ t dt dλ C 1C dC − ∫C λdC =∫C d ( D ) 1 21 dλ For points in C-x curve, t = const 11 − 2t 1 − 2t dC ∫C1 xdC = t ∫C1 d( D dx ) C C dC dC dC ∫C1 xdC =D dx − D dx = D dx C C1 C C 材材材材材材 =0 1 dx C ∴ D = − ∫C xdC 2t dC C 1 x → xM C2 ∫C 1 xM dC = 0 1 dxM C ∴ D(C ) = − ∫C xM dC 2t dC C 1 dC dx M C C2 A1 A C1 C = CM B 0M 0 xM §6.6 Kirkendall effect and Partial diffusion coefficients coefficients Ⅰ.K-experimental results: 1. The markers move toward brass slice. 2. ∆l = k t Kirkendall–Smigelskas ∆l : k shift Ⅱ.K-effect: .K-effect: In substitutional solid solutions, the markers placed on original interface move parabolically with time toward the zinc-rich zone. toward This phenomenon is called K-effect The meaning of K-effect: The a. Denied the diffusion mechanism about transposition b. Proved the vacancy mechanism c. Partial diffusion coefficients is different d. Built relationship between micro and macro e. Universality Accessary effect: Accessary Superfluous vacancy Ⅲ.Partial diffusion coefficients. referred to the fixed interface referred ∂C A ∂C A J A = −D = − DA + C Av ∂x ∂x ∂C B ∂C B J B = −D = − DB + CB v ∂x ∂x (1) ( 2) C A + C B = ρ = const. ∂C A ∂C B ⇒ =− ∂x ∂x ∂C A ∂C A ∴ DB + CBv = D ∂x ∂x (3) d( ∆l ) k ∆l ν= = = dt 2 t 2t from 1, 3 D = D A N B + DB N A ( 4) ( 5) NA, NB : mole fraction CB NB = C A + CB CA NA = C A + CB ∆l ∆l = b t ⇒ v = = 2 t 2t b 材 l 材材材 t 材材材材 v 材材材材材材材材 D 材 材 D 材 v 材材材材材 DA 材 DB Examples and Discussions Examples Exercise Exercise Thank you ! Thank you ! 28 ...
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