位错理论

Dislocations in Nickel （TEM ）
Dislocation Tangles
位错缠结
A crack in Si (Dark line) emits a number of dislocations on thermal cycling. The dislocations were formed to relieve thermal stresses.
Mixed Dislocation 混合位错
柏氏矢量的确定 （1）包含位错线做一封闭回路－柏氏回 （2） 将同样的回路置于完整晶体中－不能 闭合 （3） 补一矢量（终点指向起点）使回路闭 合－柏氏矢量
BURGER’S VECTOR 柏氏矢量 Edge dislocation Screw dislocation
1.3 位错的原子模型及柏氏矢量
Edge Dislocation 刃型位错
Contains an additional plane of atoms which extends indefinitely along the crystal
多余原子面
From A. G. Guy, Elements of Physical Metallurgy, Addison-Wesley Publishing Co., Inc., Reading, Mass., 1959.
Q ND = D÷ ÷ exp kT N
Self Diffusion Via Vacancy Mechanism
点缺陷对晶体性能的影响
间隙原子－体积膨胀1~2个原子体积 空位－体积膨胀0.5个原子体积 屈服强度↑ 对扩散、高温形变和热处理等过程均有重 要影响
面缺陷 plane defect
Juan Villegas, Ph.D. thesis (UConn MSE)
线缺陷 line defect
刃型位错 Edge dislocation 螺型位错 Screw dislocation 混合位错 Mixed dislocation
1.2 位错概念的引入
1934
解释实测的晶体临界切应力值与理论计 算值相差千倍以上的问题
Variation in Grain Boundary Energy With Misorientation for Copper. 晶界能～角度
0.6 0.5 0.4 0.3 0.2 0.1 0 0 10 20 30
Degrees
E ne rgy (J/m2)
40
50
60
相界面
两个不同相之间的界面 － 共格界面 －半共格界面 －非共格界面 弹性能 与 界面能？
Burger’s vector
Burger’s vector
Dislocation line
Dislocation line: into page
Edge dislocation: Burger’s vector perpendicular to dislocation line Screw dislocation: Burger’s vector parallel to dislocation line Mixed dislocation: Orientation of Burger’s vector with respect to dislocation changes with position
Screw Dislocation 螺型位错
Mixed Dislocation 混合位错
Screw Dislocation
Edge Dislocation
Has both edge and screw character.
From J.F. Shackelford, Introduction to Material Science for Engineers, MacMillan Publishing Co, New York, NY, 1985
特性
（1） 满足右螺旋规则时，柏氏矢量与柏氏回路路 径无关 － 唯一性 （2） 用柏氏回路求得的柏氏矢量为回路中包围的 所有位错柏氏矢量的总和（矢量和） －可加性 （3） 同一位错，柏氏矢量处处相同－ 同一性
位错密度
单位体积中位错的总长度：
L ρ = , cm / cm 3 V
将位错线看作于垂直某一平面的直位错线
No. of potential Temperature defect sites. Boltzmann's constant (1.38 x 10-23 J/atom K) (8.62 x 10-5 eV/atom K) Each lattice site is a potential vacancy site
晶界特点
1） 晶界—畸变—晶界能—向低能量状态转化— 晶粒长大、晶界变直—晶界面积减小； 2） 阻碍位错运动— σb↑ —细晶强化； 3） 位错、空位等缺陷多—晶界扩散速度高； 4） 晶界能量高、结构复杂—容易满足固态相变 的条件——固态相变首先发生地； 5） 化学稳定性差—晶界容易受腐蚀； 6） 微量元素、杂质富集
Edge Dislocation 刃型位错
Screw Dislocation 螺型位错
Spiral Stacking of crystal planes. The direction of motion is perpendicular to the shearing stress.
From J.F. Shackelford, Introduction to Material Science for Engineers, MacMillan Publishing Co, New York, NY, 1985
小角度晶界 low angle grain boundary 大角度晶界 high angle grain boundary 相界面 interphase boundary
小角度晶界特点
*θ<10° 由位错构成 *位错密度↑— 位向差↑—晶格畸变↑—晶界 能↑
大角度晶界
θ>10°
小角度晶界 类型
Point Defects 点缺陷
Substitutional atom 替换原子
Vacancy 空位
Selfinterstitial atom
Interstitial atom 间隙原子
空位平衡浓度
Equilibrium concentration varies with temperature! How? No. of defects Formation energy
Point Defects in a Single Crystal Lattice
Extra atom
Missing atom
Foreign atom
Extra atom
Schematic illustration of types of defects in a single-crystal lattice: self-interstitial, vacancy, interstitial, and substitutional.
理想晶体的临界切应力
G τm = 2π
实际晶体的逐步滑移
- Effect of dislocations in the lattice structure under stress In the series of diagrams, the movement of the dislocation allows deformation to occur under a lower stress than in a perfect lattice
nL n ρ=Etching to Reveal Dislocation Motion
Movement of dislocations in LiF. “A” are sessile dislocations & “B” are glissile dislocations. When a stress is applied the glissile dislocation slides, hence, when it is etched again it leaves a new trace where as the old trace gets wider, but not deeper. Sessile dislocations do not move and the etch pits get deeper and wider on repeated etching.
晶界处新晶粒
晶界与亚晶界
新晶粒与位错
Laminar structure 片层状组织
High resolution TEM 高分辨电子显微镜 成百上千个原子 成百上千个原子单个原子排列
ELECTRON MICROSCOPY
[110] [001] advancing twin
Nickel alloy
（1）对称倾侧晶界相邻晶粒各转θ/2同号刃 位错垂直排列 （2）不对称倾侧晶界相互垂直的两组刃位错 垂直排列
Low Angle Grain Boundary －小角晶界
GRAIN BOUNDARIES
Schematic
晶界
grain boundaries
Adapted from Fig. 4.7, Callister 6e.
1.位错理论基础
1.1 晶体缺陷概论
晶体中的缺陷 缺陷： 缺陷 原子排列偏离完整性的区域 点缺陷－在三个方向上尺寸都很小 线缺陷－在二个方向上尺寸很小 面缺陷－在一个方向上尺寸很小
点缺陷 point defects
空位 vacancy 间隙原子 interstitial atom 杂质原子 impurity atom