点击下载

advertisement
Chapter 4 Imperfections in Crystal
4.1 Point defects and Equilibrium concentration
4.2 Impurity atoms
4.3 Origin and Concept of dislocations
~ Linear defects
4.4 Burgers vectors and movement of dislocation
4.5 Elastics properties of dislocation
4.6 Formation and proliferations of dislocation
4.7 Dislocations in real crystal
4.8 Dislocation reaction
4.9 Outer surface
4.10 Grain boundaries and sub-grain boundaries
4.11 Phase boundaries
Lan Yu
4.1 点缺陷的形成和平衡浓度
4.2 杂质原子
4.3 位错理论的提出和基本概念
4.4 伯氏矢量 位错的运动 位错的基本性质
4.5 位错的弹性性质
4.6 位错的起源与增殖
4.7 实际晶体中的位错
4.8 位错反应
4.9 外表面 晶体外形与表面微观形貌 表面驰豫与重构
4.10 晶界、亚晶界、孪晶界
4.11 相界
Lan Yu
Imperfections in Crystal
Ideal or perfect crystal:the arrangements of atoms that can
regularly and repetitively fill space
Real or defective crystal: A very tiny fraction of the atom
sites, often less than one in a million, the atoms arrangement is
not perfect.~ discrepancy structure
According to dimension, types:




Lan Yu
point defect: vacancies, interstitial atoms, impurity atoms
line defect: dislocation
planar defect: stacking fault
volume defect: mosaic structure

晶体缺陷:实际晶体中存在原子排列偏离理想状态的
不完整区域。

按晶体缺陷的几何特征,分为:点缺陷、线缺陷(位
错)、面缺陷和体缺陷。
即按照晶体缺陷在空间所占的维度,分为
零维、一维、二维和三维缺陷。

晶体缺陷赋予材料丰富内容
Lan Yu
晶体缺陷(晶格的不完整性):晶体中任何对完整周期性
结构的偏离就是晶体的缺陷。
结构缺陷:
没有杂质的具有理想的化学配比的晶体
中的缺陷,如空位,填隙原子,位错。
晶体的缺陷
化学缺陷:
由于掺入杂质或同位素,或者化学配比偏
离理想情况的化合物晶体中的缺陷,如杂
质,色心等。
Lan Yu
4.3 Origin and Concept of dislocations
~ Linear defects 位错~线缺陷
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,which is called atoms misfit.
So dislocation is a linear imperfection.
在三维空间的一个方向上的尺寸很大(晶粒数量级101nm~102um),
另外两个方向上的尺寸很小(原子尺寸大小~Å)的晶体缺陷。周期性遭
受破坏的区域形成一条线。
晶体中的位错:
刃型位错
螺型位错
混合型位错
Lan Yu
Dislocation
edge dislocation
screw dislocation
mixed dislocation



The dislocation can’t be seen by eyes.
How did people originally realise the dislocation?
What is dislocation?
Ⅰ. Origin of dislocation theory
位错学说的产生
Clue
1905, Vito Volterra originally developed the theory about dislocation.
The crystal plastic deformations had been experimentally studied.
1926, Professor Sir Frederick Charles Frank calculated theoretical
shearing strength of crystal according the crystal sliding mode
Theoretical shearing strength of crystal:
m 
G
2
估算一般金属:
τm=103~105MPa
实际金属单晶:
1~10MPa
理论剪切强度与实际值相差3-4个量级

b
S.P.
a
x
’
’
x
=b
Lan Yu
   m sin 2x
Assuming
b
x: displacement of atoms 原子位移
For small x:

2x
m b
x
 Gr  G ( )
a
G
G b
~
m 
( )
2
2 a
 .m ~ 103  104 MPa
 C ~ 1MPa
Development of dislocation theory
The shearing force required to deform a crystal solidcan be a facter of
about 103-104 smaller than the theoretical shearing force. The dramatic
discrepancy was solved by assumed presence of lattice defects called
Dislocation.
1934,Orowam,Taylor and Polanyi independently applied the concept of
edge dislocations.
1939, Burgers described the lattice distortion associated with a dislocation
by the so-called Burgers vector.
1947, Cottrell suggested the interaction between the dislocation and solute
Atoms~ Cottrell atmosphere.
1950, mechanism of Frank-Read Source has been applied.
1956, the first observations of edge dislocation by TEM (transmission
electron microscope) were published.
1934年,泰勒、波朗依、奥罗万几乎同时提出位错的概念。
1939年,柏格斯提出用柏氏矢量表征位错。
1947年,柯垂耳提出溶质原子与位错的交互作用。
1950年,弗兰克和瑞德同时提出位错增殖机制。
之后,用TEM直接观察到了晶体中的位错。
蠕虫蠕动机制
A extra half-plane has been inserted from the crystal top and
terminated in crystal. EF is called the dislocation line.
Regions of compression and tensionaround an edge dislocation
EF:位错线
Lan Yu
Ⅱ. Edge dislocation 刃位错
Lan Yu
()

Lan Yu
( )
G
H
D
A
E
Extra half-plane:EFGH
Dislocation line: EF
Sliding plane: ABCD
F
B
C
Characters of edge dislocation
刃型位错的特征:
1) 刃型位错是由一个多余半原子面所组成的线缺陷;
2) 位错滑移矢量(柏氏向量)垂直于位错线,而且滑移面是位错线和滑移
矢量所构成的唯一平面;
3) 位错的滑移运动是通过滑移面上方的原子面相对于下方的原子面移
动一个滑移矢量来实现的;
4) 刃型位错线的形状可以是直线、折线和曲线;
5) 晶体中产生刃型位错时,其周围的点阵发生弹性畸变,使晶体处于
受力状态,既有正应变,又有切应变。
Ⅲ. Screw dislocation
错
螺位
The upper front region of the crystal is shifted one atomic
distance to the back relative to the bottom portion.~ distortion
Dislocation line BC
(a)
(b)
右螺位错


b


L
左螺位错




L
Characters of screw dislocation
螺型位错的特征:
1) 螺型位错是由原子错排呈轴线对称的一种线缺陷 ;
2) 螺型位错线与滑移矢量平行,因此,位错线只能是直线;
3) 螺型位错线的滑移方向与晶体滑移方向、应力矢量方向互相垂直;
4) 位错线与滑移矢量同方向的为右螺型位错;为此系与滑移矢量异向
的为左螺型位错。
Ⅳ. Mixed dislocation
混合型位错
混合位错
a) 晶体的局部滑移; b) 混合位错的原子组态
Ⅴ. Burgers vectors 柏氏矢量
1. Burgers loops
Edge dislocation
柏氏回路
先确定位错的方向(一般规定位错线垂直纸面时,由纸面向外为正),按右手
法则做柏氏回路,右手大拇指指位错正方向,回路方向按右手螺旋方向确定。
Burgers loops: MNOPQ
2. Burgers vector 柏氏矢量:b
N
O
N
O
Q
Q
P
b=QM,终点-起点
M
P
M
刃型位错柏氏矢量的确定 柏氏矢量b=QM
(a) 有位错的晶体 (b) 完整晶体
位错线⊥b
Screw dislocation
柏氏矢量b=QM
螺型位错柏氏矢量的确定
(a) 有位错的晶体 (b) 完整晶体
位错线∥b
4.守恒性
若干位错线交于一点,
流入节点的位错线的柏氏矢量和=流出节点的位错线的柏氏矢量和
Ⅵ. Dislocation density 位错密度
Total dislocation length per unit volume-Number of
dislocations intersecting unit area of a random section.

单位体积中位错的总长度:  L , cm / cm 3
V
将位错线看作于垂直某一平面的直位错线
nL n


AL A
Examples:
Carefully solidified metal: 103 mm-2.
Heavy deformed metals: 109 – 1010 mm-2.
Heat treated metals: 105 – 106 mm-2.
Ceramic materials: 102 – 104 mm-2.
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。
Download