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 thirty
§ 6.8 Diffusion Mechanism
? Ⅰ.Flick's law in microscopic form
1,One dimensional diffusion.
Γ, probability of atom jumping to nearest position
??
1?
,jump frequency period?
?? 221112 2121 nJnJ ??
??
??
1
1 nC?
22
2
1
2
1 aD ??? ???
)(21 2121121 nnJJJ ???? ?
x
CCCCCJ
d
d
2
1)(
2
1)(
2
1 2212
211 ??????? ??
?????
simple cubic:
2,Two dimensional diffusion.
3,Three dimensional diffusion.
2
4
1 aD ??
FCC( ):Fe??
22
12
1)
2(12
4 aaD ?? ??
122
6
1 aD ??
4,For diffusion of interstitial atoms in BCC
22 aD ????? ?????
For tetrahedral interstitial
For octahedral interstitial
4
1???
4
0???
22
24
1
)
2
(
6
1
26
1
a
a
D
a
??
??
???
???
? Ⅱ.Diffusion Mechanisms
1,Direct exchange of neighboring atoms.
Atom must acquire additional energy,called the
activation energy,before they jump from normal
state to activated state (the saddle point).
This mechanism seems to be unrealistic for large
??G
??G
?????? ??????????? STVPESTHG
2,Interstitial mechanism to be effective for
diffusion in interstitial sol.sol.
3,Vacancy mechanism.
Atoms jump directly in to nearby vacant site,being
small.
Different kind of atoms has different (chemical) affinity
for vacancy.
??G
? Ⅲ.Calculation of D
1.
2.
2aD ???
))(e x p ()e x p ( **2*2 RTSTHaRTGaD oo ????????? ????
)e x p ()e x p ( **2 RTHRSa o ????? ??
)(e x p *21 RTGPP o ??? ???
321 PPP??
P1,probability of atom acquiring additional ??G
RTGeP
*
1
???
o
vP ?
?? ??? ?
21
2
v i b r a t i o nofe n c ye i g e n f r e q u:o?
RT
G v
eP
??
?3
RT
H
RT
H
R
S
o
RT
G
o
RT
GG
o
eD
ee
ee
v
?
??
???
?
???
?
?
???
?
?
???
?
)(
)(
**
RT
HH
R
SS
o
vv eeaD )(2 ** ??????? ?? ??
0D
f a c t o rf r e q u e n c y:
e n e r g ya c t i v a t i o n:
0
**
D
H
HHHSSS vv
?
??????????
§ 6.9 Empirical rule for diffusion
Factors influencing diffusion
1,Temperature and the diffusion coefficient
RTQo eDD ??
D, The activation energy for diffusion of species under
consideration.
R, The gas constant
T, The absolute temperature
D0, The pre-exponential term
2,Composition
3,Size
? ??? ??? ?aQQ o
4,Grain size,Defects
5,Cold wording or irradiation
a,Accelerate diffusion
b,Up-hill diffusion may take place
s u r f.b.gvol DDD ????
6,Structure,
a,D in closed packed structures is smaller than in,open”
structures.
b,Diffusion is anisotropy in crystals other than cubic.
7,Third elements.
a,No effect.
b,Accelerate by forming fine grains or causing lattice
distortion.
c,Retard by forming compound.
d,Curious effect.
8,For self-diffusion
)m e l t i n gofh e a tl a t e n t(5.16
)p o i n tm e l t i n g(36
m
m
LQ
TQ
?
?
Example
Design an iron membrane that will allow no more than 1% of
the nitrogen to be lost through the membrane each hour,while
allowing 90% of the hydrogen to pass through the membrane
per hour.
The total number of nitrogen atoms in the container is:
a t o m sN10343.35103)4/()105.0( 2020 ?????? ?
a t o m sN100098.0
3600/10343.351hp e rl o s sa t o m sN
18
20
??
??? ）％（
Then:
scm
a t o m sN1000 1 39.0
)cm3)(
4
(
1000 9 8.0
2
18
2
18
?
???? ?J
)e x p ( RTQDD o ???
s
cm
1064.3)4654.9e x p(0047.0
973987.1
300,18
e x p0047.0
2
7
N
??????
?
?
?
?
?
?
?
?
??? D
)( xcDJ ????? ? ?
cm0128.0
1000139.0
)1050101)(1064.3(
/ 18
18187
?
?
?????
??????
?
JcDx
(minimum thickness of the membrane)
a t o m sH100 0 8 8.0
3 6 0 0/10343.3590hp e rl o s sa t o m sH
20
20
??
??? ）％（
scm
a t o m sH101 2 5.0
2
18
???J
s
cm1086.1
973987.1
600,3e x p0 0 1 2.0 24
H
????
?
?
??
?
?
???? D
cm0 7 2 9.0/ ?????? JcDx (maximum thickness)
So iron membrane between 0.0128 and 0.0729 cm
Examples and Discussions
Exercise
Thank you !
30