清华大学：《材料科学基础》课程教学资源（PPT课件讲稿）Chapter 6. 5 concentration dependence of D

36. 5 concentration dependence of D Matano method ◆|.D- C dependence Matano method CO、aC (D-) at ax ax D= D(C tt=0 for x>o for x<0

§6.5 concentration dependence of D. Matano method ◆ Ⅰ.D-C dependence ◆ Ⅱ.Matano method ( ) (1) x C D t x C     =   (2) for 0 at 0 for 0 2 1 =  = =  C C x t C C x D = D(C)

Let d= ac dC x dc n at dn 2tt dn 2t ac dc an1 dc Oxdλax d 0C、d dC、0λ1ddC D )=(D axax d2 √t d"ax/td2dλ put(4)in(1 2 dc 1 d dc (D 2t da t dt dn

Let (3) t x  = ) (4) 2 ( d d ) 2 ( d d t C t t C x t C    = − = −   ( ) ( ) ) d d ( d 1 d d d 2 put 4 in 1    C D t t C t － = （ ）         d d d 1 d ) d 1 d ( d d ( ) d 1 d d d C x t C t D x C D x C x t C x C =   =       =   =    t 1

do ndc= d(D 2 d For points in C-x curve, t=const 2E减C=Ea 2t rdC dc dc dc D D d 几利用边界方法 0 d D= xdC 2t dc IJci

  − = C C C C C C D 1 1 ) d d d d( 2 1           = − C C C x C C x t D 1 d d d 2 1 For points in C-x curve, t = const   − = C C C C x C x C t D t 1 1 ) d d d d( 1 2 1 C C C C C x C D x C D x C x C D t       =       −       − =  d d d d d d d 2 1 1 1 利用边界方法 =0

x→>XM 2x,dC=0 1( dx D(C)= M xdo 2t dC dc C=CM A 00

0 M 0 x M C1 C2 A1 B A C x C         d M d C = CM x → x M d 0 2 1 M =  C C x C         = − C C C x C C x t D C 1 d d d 2 1 ( ) M M

36.6 Kirkendall effect and Partial d ffus ion coefficients K-exper i mental results 1. The markers move toward brass slice 2. A=kt Al:k shift 0.014 0.012 0.010 0.008 Cu+30%Zn 安0.006 u 0.004 0.002 Kirkendall-Smigelskas

§6.6 Kirkendall effect and Partial diffusion coefficients ◆ Ⅰ.K-experimental results: 1. The markers move toward brass slice. 2. l = k t l : k shift Kirkendall–Smigelskas

.K-e千fect: In substitutional solid solutions, the markers placed on original interface move parabolically with time toward the zinc-rich zone This phenomenon is called K-effect

◆ Ⅱ.K-effect: In substitutional solid solutions, the markers placed on original interface move parabolically with time toward the zinc-rich zone. This phenomenon is called K-effect

The mean ing of K-effect (1 Denied the diffusion mechanism about transposition (2 Proved the vacancy mechanism Partial diffusion coefficients is different 4 Built relationship between micro and macro ⑤ Universality

The meaning of K-effect: ① Denied the diffusion mechanism about transposition ② Proved the vacancy mechanism ③ Partial diffusion coefficients is different ④ Built relationship between micro and macro ⑤ Universality

Accessary effect Superfluous vacancy

Accessary effect: Superfluous vacancy

◆Ⅲ. Partial diffus ion coefficients referred to the fixed interface D - D OCA+CAV 标志物 0 x aC OCB 高熔点A低熔点B D D B CB(2) Ox >0 4+CB=P=const. J aC aC B aC aC B +CBV=D (3) mmmr Ox

◆ Ⅲ.Partial diffusion coefficients. referred to the fixed interface (2) (1) C v x C D x C J D C v x C D x C J D B B B B B A A A A A +   = −   = − +   = −   = − (3) x C C v D x C D A B A B   + =    x C x C C C A B A B   = −     + =  = const

d(△A1)k△l dt2√t from 1, 3 D= DANB+ DBNA N A, NB: mole fraction NB-C+CB c+c B △=bt→y= b△l 2√t2t 测l,记录t,可得到ν,由实验曲线计算D, 由D、v,即可求得D4,DB

( ) (4) d 2 2 d t l t k t l  = =   = A B A A A B B B C C C N C C C N + = + = from 1,3 (5) D = DA NB + DB NA NA , NB : mole fraction t l t b l b t v 2 2   =  = = 测l，记录t，可得到v，由实验曲线计算D， 由D、v，即可求得DA，DB