材料科学基础
Fundamental of Materials
Prof,Tian Min Bo
Tel,62795426, 62772851
E-mail,tmb@mail.tsinghua.edu.cn
Department of Material Science and Engineering
Tsinghua University,Beijing 100084
Lesson twenty-eight
§ 6.5 concentration dependence of D,
Matano method
? Ⅰ.D -C dependence
? Ⅱ.Matano method
? ?1)( xCDxtC ???????
? ?20f o r 0f o r0at
2
1
??
???
xCC
xCCt
)(CDD ?
? ?3L e t tx??
? ?4)2(dd)2(dd tCtt xCtC ??? ??????
? ? ? ? )dd(dd1dd21in4p u t ??? CDttCt ?－
）（
??
?
??
?
?
?
d
d
d
d1
)
d
d1
(
d
d
)(
d
d1
d
d
C
tx
C
t
D
x
C
D
x
C
tx
C
x
C
?
?
?
???
?
?
?
?
?
?
?
??
?
?
t
1
?? ?? CCCC CDC 11 )dd(dd21 ??
?????????? CC
C
CxCxtD
1
ddd21
For points in C-x curve,t = const
?? ?? CCCC xCDtCxt 11 )dd(dd121
CCC
C
C x
CD
x
CD
x
CDCx
t ??
?
??
??
??
?
??
??
??
?
??
??? ?
d
d
d
d
d
dd
2
1
1
1
利用边界方法
=0
M0 0 Mx
1C
2C
1A
B
A
Cx
C
???
?
???
?
Md
d
MCC ?
Mxx ?
0d2
1 M
??CC Cx
?????????? CC
C
CxCxtCD
1
ddd21)( MM
§ 6.6 Kirkendall effect and Partial
diffusion coefficients
? Ⅰ.K -experimental results:
1,The markers move toward brass slice.
2,s h i f t,kltkl ???
Kirkendall–Smigelskas
? 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 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
? Ⅲ.Partial diffusion coefficients.
referred to the fixed interface
)2(
)1(
vC
x
C
D
x
C
DJ
vC
x
C
D
x
C
DJ
B
B
B
B
B
A
A
A
A
A
?
?
?
??
?
?
??
?
?
?
??
?
?
??
)3(xCDvCxCD ABAB ???????
x
C
x
C
CC
BA
BA
?
?
??
?
?
?
??? c o n s t,??
? ? ? ?4
22d
d
t
l
t
k
t
l ??????
BA
A
A
BA
B
B CC
CN
CC
CN
????
? ?53,1f r o m ABBA NDNDD ??
NA,NB, mole fraction
t
l
t
bvtbl
22
??????
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
Examples and Discussions
Exercise
Thank you !
28
Fundamental of Materials
Prof,Tian Min Bo
Tel,62795426, 62772851
E-mail,tmb@mail.tsinghua.edu.cn
Department of Material Science and Engineering
Tsinghua University,Beijing 100084
Lesson twenty-eight
§ 6.5 concentration dependence of D,
Matano method
? Ⅰ.D -C dependence
? Ⅱ.Matano method
? ?1)( xCDxtC ???????
? ?20f o r 0f o r0at
2
1
??
???
xCC
xCCt
)(CDD ?
? ?3L e t tx??
? ?4)2(dd)2(dd tCtt xCtC ??? ??????
? ? ? ? )dd(dd1dd21in4p u t ??? CDttCt ?－
）（
??
?
??
?
?
?
d
d
d
d1
)
d
d1
(
d
d
)(
d
d1
d
d
C
tx
C
t
D
x
C
D
x
C
tx
C
x
C
?
?
?
???
?
?
?
?
?
?
?
??
?
?
t
1
?? ?? CCCC CDC 11 )dd(dd21 ??
?????????? CC
C
CxCxtD
1
ddd21
For points in C-x curve,t = const
?? ?? CCCC xCDtCxt 11 )dd(dd121
CCC
C
C x
CD
x
CD
x
CDCx
t ??
?
??
??
??
?
??
??
??
?
??
??? ?
d
d
d
d
d
dd
2
1
1
1
利用边界方法
=0
M0 0 Mx
1C
2C
1A
B
A
Cx
C
???
?
???
?
Md
d
MCC ?
Mxx ?
0d2
1 M
??CC Cx
?????????? CC
C
CxCxtCD
1
ddd21)( MM
§ 6.6 Kirkendall effect and Partial
diffusion coefficients
? Ⅰ.K -experimental results:
1,The markers move toward brass slice.
2,s h i f t,kltkl ???
Kirkendall–Smigelskas
? 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 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
? Ⅲ.Partial diffusion coefficients.
referred to the fixed interface
)2(
)1(
vC
x
C
D
x
C
DJ
vC
x
C
D
x
C
DJ
B
B
B
B
B
A
A
A
A
A
?
?
?
??
?
?
??
?
?
?
??
?
?
??
)3(xCDvCxCD ABAB ???????
x
C
x
C
CC
BA
BA
?
?
??
?
?
?
??? c o n s t,??
? ? ? ?4
22d
d
t
l
t
k
t
l ??????
BA
A
A
BA
B
B CC
CN
CC
CN
????
? ?53,1f r o m ABBA NDNDD ??
NA,NB, mole fraction
t
l
t
bvtbl
22
??????
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
Examples and Discussions
Exercise
Thank you !
28
