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 eighteen
§ 5.3 Origin of Concept for
Dislocation
Discrepancies between theory and practice
in Deformation.
1,Morphology of the surface in deformation.
2,The great difference between theoretical and actual
strength of single crystals ( ).
c?? ???
?=b
x
?’
b
a
?
?’
S.P,x
x,displacement of atoms
For small x:
)( axGGr ??
)(2m abG?? ?? ～ ?2G
M P a1M P a1010 C43m,?? ?～ ～
s inA s s u m in g m?? ?bx?2
m?? ? b
x?2
§ 5.4 What’s Dislocation
? Ⅰ.By local slip
According to the relative orientation of the slip direction
and the line of demarcation between slipped and
unslipped zones,the follows types of dislocation can be
formed.
1,edge dislocation
2,screw dislocation
3,mixed dislocation
? ???
? ? ?? ? ?
? ? ? ??
??
? ?
?? ??
??
? ?
??
??
??
??
?
??
??
?
??
??
?
?
W
1,Edge dislocation
（ ?） （ ）?
2,Screw dislocation
3,Mixed dislocation
Dislocation is a long tubular transition zone from
slipped to unslipped zones,Within this zone,
atoms on opposite sides of the slip plane do not
fit.
( This is called atoms misfit)
So dislocation is a line imperfection.
Screw dislocation
right-handed dislocation
left-handed dislocation
? Ⅱ.Local cut and displacement
1,Make a cut through part of the crystal
2,Let both sides of the cut displace with
respect to each other,the displacement
vector being,
3,Fill in or take off the atoms to make the
crystal structure unchanged.
b?
§ 5.5 Burgers Circuit and Burgers
Vector
? Ⅰ.Burgers Circuit.
1,Read method
Burgers Circuit is made up of atom to atom
steps along closely-packed direction,this circuit
satisfies the following two conditions:
① It must pass through good materials.
② It should close in ideally perfect crystal
If the Burgers Circuit does not close,then it
must contain dislocation and the closure
failure is called the Burgers Vector
000 ??? ??? iii zyx
2,Frank method
? Ⅱ.The meaning of,
1,Determination
The vector required to complete the loop and return us
to our starting point is the Burgers Vector,
b?
b?
① For fissile dislocation,is slip vector.
② is also the sum of the elastic deformation
around dislocation.
③ is a measure of the elastic energy
associated with the dislocation.
b?
b?
b?
2,Physical meaning:
3,Description
Characterization of dislocations by and,b? l?
positive negative
b?
l?
b?
l?
right-handed left-handed
b?
b?
Edge dislocations Screw dislocations
? Ⅲ.Description of dislocation by
and
For edge dislocation
directs to that part of crystal which contains extra-
half plane.
For screw dislocation:
b?
bl ?? ?
bl ???
∥ - —— left-handed screwl? b?
∥ —— right-handed screwl? b?
l?
? Ⅳ.Conservation of
1,is unique for single dislocation line,either
straight or curved,and single loop.
2,Kirchhoff’s law holds for branching dislocation.
b?
231213
o u tin
bbb
bb
???
??
???
???
b?
O
I
II
III
1b
?
2b
?
3b
?
1b
? 2b?
3b
?
b?
Examples and Discussions
1,位错线从晶体表面入出，封闭环。
2,一个圆形位错环，柏氏矢量垂直于表面。讨论
3,晶体中的环代表什么
4,单晶体中的位错环运动到表面。晶体外形发生什
么变化。
Exercise
Thank you !
18
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 eighteen
§ 5.3 Origin of Concept for
Dislocation
Discrepancies between theory and practice
in Deformation.
1,Morphology of the surface in deformation.
2,The great difference between theoretical and actual
strength of single crystals ( ).
c?? ???
?=b
x
?’
b
a
?
?’
S.P,x
x,displacement of atoms
For small x:
)( axGGr ??
)(2m abG?? ?? ～ ?2G
M P a1M P a1010 C43m,?? ?～ ～
s inA s s u m in g m?? ?bx?2
m?? ? b
x?2
§ 5.4 What’s Dislocation
? Ⅰ.By local slip
According to the relative orientation of the slip direction
and the line of demarcation between slipped and
unslipped zones,the follows types of dislocation can be
formed.
1,edge dislocation
2,screw dislocation
3,mixed dislocation
? ???
? ? ?? ? ?
? ? ? ??
??
? ?
?? ??
??
? ?
??
??
??
??
?
??
??
?
??
??
?
?
W
1,Edge dislocation
（ ?） （ ）?
2,Screw dislocation
3,Mixed dislocation
Dislocation is a long tubular transition zone from
slipped to unslipped zones,Within this zone,
atoms on opposite sides of the slip plane do not
fit.
( This is called atoms misfit)
So dislocation is a line imperfection.
Screw dislocation
right-handed dislocation
left-handed dislocation
? Ⅱ.Local cut and displacement
1,Make a cut through part of the crystal
2,Let both sides of the cut displace with
respect to each other,the displacement
vector being,
3,Fill in or take off the atoms to make the
crystal structure unchanged.
b?
§ 5.5 Burgers Circuit and Burgers
Vector
? Ⅰ.Burgers Circuit.
1,Read method
Burgers Circuit is made up of atom to atom
steps along closely-packed direction,this circuit
satisfies the following two conditions:
① It must pass through good materials.
② It should close in ideally perfect crystal
If the Burgers Circuit does not close,then it
must contain dislocation and the closure
failure is called the Burgers Vector
000 ??? ??? iii zyx
2,Frank method
? Ⅱ.The meaning of,
1,Determination
The vector required to complete the loop and return us
to our starting point is the Burgers Vector,
b?
b?
① For fissile dislocation,is slip vector.
② is also the sum of the elastic deformation
around dislocation.
③ is a measure of the elastic energy
associated with the dislocation.
b?
b?
b?
2,Physical meaning:
3,Description
Characterization of dislocations by and,b? l?
positive negative
b?
l?
b?
l?
right-handed left-handed
b?
b?
Edge dislocations Screw dislocations
? Ⅲ.Description of dislocation by
and
For edge dislocation
directs to that part of crystal which contains extra-
half plane.
For screw dislocation:
b?
bl ?? ?
bl ???
∥ - —— left-handed screwl? b?
∥ —— right-handed screwl? b?
l?
? Ⅳ.Conservation of
1,is unique for single dislocation line,either
straight or curved,and single loop.
2,Kirchhoff’s law holds for branching dislocation.
b?
231213
o u tin
bbb
bb
???
??
???
???
b?
O
I
II
III
1b
?
2b
?
3b
?
1b
? 2b?
3b
?
b?
Examples and Discussions
1,位错线从晶体表面入出，封闭环。
2,一个圆形位错环，柏氏矢量垂直于表面。讨论
3,晶体中的环代表什么
4,单晶体中的位错环运动到表面。晶体外形发生什
么变化。
Exercise
Thank you !
18
