1、1Ch2 位错2.1 位错理论的产生2.2 位错的几何性质2.3 位错的弹性性质2.4 位错与晶体缺陷的相互作用2.5 位错的动力学性质2.6 实际晶体中的位错22.1 位错理论的产生一、晶体的塑性变形方式二、单晶体的塑性变形三、多晶体的塑性变形四、晶体的理论切变强度五、位错理论的产生六、位错的基本知识32.2 位错的几何性质一、位错的几何模型二、柏格斯矢量三、位错的运动四、位错环及其运动五、位错与晶体的塑性变形六、割阶42.3 位错的弹性性质一、弹性连续介质、应力和应变二、刃型位错的应力场三、螺型位错的应力场四、位错的应变能五、位错的受力六、向错七、位错的半点阵模型52.4 2.4 位错与晶
2、体缺陷的相互作用位错与晶体缺陷的相互作用一、位错间的相互作用力一、位错间的相互作用力二、位错与界面的交互作用二、位错与界面的交互作用三、位错与点缺陷的交互作用三、位错与点缺陷的交互作用62.5 2.5 位错的动力学性质位错的动力学性质 位错的动力学位错的动力学是研究位错运动的动力、阻力、是研究位错运动的动力、阻力、速度以及增殖。速度以及增殖。一、位错的萌生一、位错的萌生 二、位错的增殖二、位错的增殖 三、滑移的动力学三、滑移的动力学 四、攀移的动力学四、攀移的动力学 解决这些问题是理解晶体中解决这些问题是理解晶体中位错的来位错的来源源、范性变形的实际过程范性变形的实际过程以及许多以及许多受位错
3、受位错影响的物理性质影响的物理性质的必要前提。的必要前提。7 一、位错的萌生一、位错的萌生（一）位错是热力学不稳定的晶体缺陷（一）位错是热力学不稳定的晶体缺陷（二）位错的均匀形核二）位错的均匀形核（三）位错的不均匀形核（三）位错的不均匀形核（四）晶体中形成位错的三种途径（四）晶体中形成位错的三种途径8（一）位错是热力学不稳定的晶体缺陷（一）位错是热力学不稳定的晶体缺陷前人曾计算过，对于单位长度位错线：熵S2kT/b,应变能EGb2，由于Gb3的典型值为5eV，而kT在300K时为1/40eV，因此位错引起的自由能G0。所以，无应力晶体中热力学稳定的位错密度应为0。然而，除晶须以及精心制备的硅等
4、较大晶体材料等个别例子外，所有晶体中都存在位错。退火晶体中的位错密度约为104mm2，经大量范性变形后增至1089mm2。形变初期，位错运动倾向于在单一相互平行的滑移面内进行，其后在其它滑移系统中继发滑移，不同系统中运动的位错会相互作用，快速增殖导致加工硬化。9（二）位错的均匀形核（二）位错的均匀形核设在某一驱动力F作用下形成半径为R的位错圈：形成能位错圈自身的能量驱动力所作的功 10假设，在无能量涨落时，晶体中要能自发萌生位错圈，则有c/10，这是一个很高的值，接近晶体的理论强度；实际屈服应力/1000，取=2b，则Rc500b，临界形核功Uc650b3,典型金属大约是3KeV。而热涨落的能
5、量大约是1/40eV，故屈服应力下均匀形核显然是不可能的；以上讨论表明，位错萌生是一个相当困难的过程，实际晶体往往借助应力集中产生位错的非均匀萌生。11（三）位错的不均匀形核（三）位错的不均匀形核 在在370370均匀保温，去除与包裹体相关的内应变，最后冷至均匀保温，去除与包裹体相关的内应变，最后冷至2020，形成棱柱位错环，形成棱柱位错环(图中为其侧面图中为其侧面)，它们显然是被玻璃包，它们显然是被玻璃包裹体挤压出来的。位错环轴向平行于裹体挤压出来的。位错环轴向平行于。12一种常见的非均匀位错萌生过程一种常见的非均匀位错萌生过程 棱柱挤压棱柱挤压：当压头很有力地压在晶体的表面时，可以萌生一系
6、列棱柱位错圈而生成压痕。如图高度为nb的坑对应于n个伯格斯矢量为b的棱柱圈，此过程的能量关系为作用于压头的力作用于压头的力P P所作的功所作的功生产棱柱圈的能量生产棱柱圈的能量增加的表面能增加的表面能，即 其中D为压头直径，若D很小，则局部正应力可很大，因而在一般的P值，即可达到萌生位错圈所需要的应力。13141516（四）晶体中形成位错的三种途径（四）晶体中形成位错的三种途径171819202122二、位错的增殖二、位错的增殖（一）弗兰克瑞德源(F-R滑移源)（二）双交滑移位错源（三）攀移位错源（Bardeen-Herring）23Production of DislocationsExam
7、ple:Frank Read Source dislocation pinned at both ends.What is the force on the curved segment causing it to bow out?Line tension T can be equated to energy/unit length.T 1/2 Gb224For curved segmentTotal normal force on segment If in equilibrium with applied stress,ori.e equilibrium radius of curvatu
8、re is controlled by stress.25The Frank Read source expands under the stress,pinned at both ends.When the bowed dislocation line reaches a semicircle it can continue to expand under a diminishing force.There are other sources of dislocation lines:single Frank-Read sources,where the line is pinned onl
9、y at a single source.Intersections with other dislocations jogs increase the length of the line,and may act as Frank Read sources.26（一）弗兰克瑞德源（一）弗兰克瑞德源(F-RF-R源源)双轴F-R源（U形源）单轴F-R源（L形源）27双轴F-R源（U形源）28Generation of dislocations Whereas we now learned a little bit about the complications that may occur w
10、hen dislocations move,we first must have some dislocations before plastic deformation can happen.In other words:We need mechanisms that generate dislocations in the first place!Of course,dislocations can just be generated at the surface of the crystal;the simple pictures showing plastic deformation
11、by an(edge)dislocation mechanism give anidea how this may happen.But more important are mechanisms that generate dislocations in the bulk of acrystal.The most important mechanism is the Frank-Read mechanism shown below.29Frank-Read mechanism We have a segment of dislocation firmly anchored at two po
12、ints(red circles).The force F=b tres is shown by a sequence of arrows 30 The dislocation segment responds to the force by bowing out.If the force is large enough,the critical configuration of a semicircle may be reached.This requires a maximum shear stress oftmax=Gb/R 31 If the shear stress is highe
13、r than Gb/R,the radius of curvature is too small to stop further bowing out.The dislocation is unstable and the following process now proceeds automatically and quickly.32 The two segments shortly before they touch.Since the two line vectors at the point of contact have opposite signs(or,if you only
14、 look at the two parts almost touching:the Burgers vectors have different signs for the same line vectors),the segments in contact will annihilate each other.33 The configuration shown is what you have immediately after contact;it is totally unstable(think of the rubber band model!).It will immediat
15、ely form a straight segment and a nice dislocation loop which will expand under the influence of the resolved shear stress.The regained old segment will immediately start to go through the whole process again,and again,and again,.-as long as the force exists.A whole sequence of nested dislocation lo
16、ops will be produced.34Stable configuration after the process.The loop is free to move,i.e.grow much larger under the applied stress.It will encounter other dislocations,form knots and become part of a network.The next loop will follow and so on-as long as there is enough shear stress.35 The Frank-R
17、ead process,although looking a bit odd,will occur many times under sufficient load.It can produce any density of dislocations in short times,because the newly formed dislocations will move,become anchored at some points,and start to generate Frank-Read loops,too.q Of course,Frank-Read dislocation so
18、urces can also be stopped-e.g.by cutting through the generating dislocation by another dislocation.We thus will have a certain finite dislocation density under certain external conditions.It may,however,depend on many parameters,including the history of the material.q Some kind of Frank-Read mechani
19、sm may also operate from irregularities on the surface(external or internal),an example of such a source is shown in the X-ray topography below.36q It is a result of investigations into wafer bonding,where to Si wafers are placed on top of each other and bonded,so that a single piece of Si results w
20、ith a grain boundary in between.Themottled area in the upper left handcorner shows such a bonded,structure whereas the dark area containing the dislocations as white lines,remained unbonded.q Dislocation were introduced into one of the wafers and one point on the edge of the bonded area acted as a F
21、rank-Read source.The nested series of dislocation loops is splendidly visible.There are also lots of straight dislocations which have moved considerable distances from their point of origin.3738394041F-RF-R源开动的临界切应力源开动的临界切应力q 复习：位错线张力表达式42F-RF-R源开动的临界切应力源开动的临界切应力43The dislocation Frank-Read sourceOn
22、e of the main mechanisms for dislocation multiplication under stress is the Frank-Read mill or Frank-Read source.The operation of a Frank-Read source can be observed on a dislocation segment pinned at its ends.44Two interacting Frank-Read sources When a Frank-Read source interacts with other disloca
23、tions,its critical stress for dislocation multiplication is modified.Interactions between two sources illustrate this property.The critical stress for dislocation multiplication is decreased or increased when two repulsive or attractive dislocations are respectively considered.Two repulsive sourcesT
24、wo attractive sources45 单轴单轴F-R源（源（L形源）形源）464748The dislocation spiral sourceUnder stress,a dislocation segment pined at one end act as a spiral source.Similar features is also observed at the surface of solids during crystal growth.4950（二）双交滑移位错源（二）双交滑移位错源515253（三）攀移位错源（三）攀移位错源（Bardeen-HerringBarde
25、en-Herring）在过饱和点缺陷所造成的渗透力的作用下，位错可以通过攀移进行增殖。图中原位错段AC1B，其b纸面（即多余半原子面），AC1B为其边缘。过饱和点缺陷使AC1B逐步攀移成AC2B，AC3B，最后给出环形原子层或空位层。AC1B又回到原位，继续攀移增殖，形成一叠不断攀移长大的位错环。54Bardeen与Herring曾计算上述过程进行的条件为：55三、滑移的动力学三、滑移的动力学（一）滑移的驱动力（二）滑移的阻力（三）晶体形变速度与位错滑移速度的关系56（一）滑移的驱动力（一）滑移的驱动力作用于位错线上的力F求解：虚功原理外力作的功ldsb虚拟力作的功Flds大小：F=b方向：垂
26、直于位错线，指向未滑移区F作用：驱使位错滑移，克服阻力，产生速度注意：同一下，位错各处F大小一样 F与方向不一定一样57位错受力的一般公式58（二）滑移的阻力（二）滑移的阻力 点阵阻力 即晶格阻力、P-N力，也是基本阻力 其它阻力 1.其它晶体缺陷（点缺陷、其它位错、晶界、相界等）2.第二相粒子 3.位错线张力59位错运动的晶格阻力位错运动的晶格阻力P-NP-N力力60 可见可见：（：（1 1）bb，P-NP-N力力 ，所以，所以b b小的容易滑移小的容易滑移；滑移总是沿密排方向滑移总是沿密排方向。（2 2）aa ，P-NP-N力力 ，密排面的，密排面的aa，所以所以一般滑移沿密排面一般滑移沿
27、密排面61注意事项注意事项P-NP-N力实际反映了结合键力的大小；力实际反映了结合键力的大小；P-NP-N力是位错运动的基本阻力，但不一定是主力是位错运动的基本阻力，但不一定是主要阻力，如要阻力，如fccfcc金属的金属的P-NP-N力很小；力很小；P-NP-N力不能与屈服应力混为一谈，前者是位错力不能与屈服应力混为一谈，前者是位错在理想点阵滑移的临界切应力，后者是塑性变在理想点阵滑移的临界切应力，后者是塑性变形的临界切应力；形的临界切应力；一般螺位错的一般螺位错的P-NP-N力力 刃位错的刃位错的P-NP-N力（因为螺力（因为螺位错的位错的wwo，拉应力，Fe为负，向下攀移；xxFm(攀移所
28、需要的力)，位错才可能在Fe作用下攀移。702.渗透力晶体中的过饱和点缺陷（主要是空位），在位错自应力场作用下，使点缺陷凝聚在位错上，促使位错攀移，好象有力沿攀移方向作用在位错上，称为渗透力Fs(或化学力)。用c0表示空位平衡浓度，c表示上升后的空位浓度，表示伯格斯矢量b与位错线的夹角，则有71723.线张力线张力由上可知，若位错在攀移面内呈弯曲状，曲率半径为r，则其线张力T驱使位错攀移的力FT:FT=T/r单位长度刃位错受的力Fc=Fe+Fs+FT73（二（二）攀移的阻力攀移的阻力攀移是物质输运过程，需要吸收或放出点缺陷（主要是攀移是物质输运过程，需要吸收或放出点缺陷（主要是空位），这就需要
29、能量，从而构成攀移的阻力空位），这就需要能量，从而构成攀移的阻力F Fm m；设单位长度刃位错攀移了设单位长度刃位错攀移了dsds距离，引起体积变化距离，引起体积变化dVdV=b=bdsds1 1，若原子体积若原子体积v vb b3 3，则则dVdV所需点缺陷数所需点缺陷数dNdN=dV/vdV/v=ds/b=ds/b2 2；克服攀移阻力作的功产生克服攀移阻力作的功产生dNdN个点缺陷所需要的能量个点缺陷所需要的能量设点缺陷的形成能为设点缺陷的形成能为U Uf f，则单位长度刃位错攀移阻力则单位长度刃位错攀移阻力F Fm m U Uf fdN/dsdN/ds=U=Uf f/b/b2 2；攀移比
30、滑移困难得多；攀移比滑移困难得多；通常，驱动力通常，驱动力F Fc c远小于攀移阻力远小于攀移阻力F Fm m，因此，位错不能整，因此，位错不能整体攀移，只能通过割阶的攀移（即点缺陷扩散）来实现。体攀移，只能通过割阶的攀移（即点缺陷扩散）来实现。74（三）攀移速度（三）攀移速度由于攀移过程是割阶的形成与移动过程，也是点缺陷(主要是空位)的输运过程，所以攀移速度Vc取决于割阶浓度Cj、割阶移动速度Vj及点缺陷空位扩散速度；对单位长度刃位错，设x为割阶的平均间距，则割阶浓度Cj1/x，因为割阶自位错一端移到另一端，位错攀移距离为b，若割阶移动的平均速度为Vj，则位错攀移速度VcbCjVj。75（三）攀移速度（三）攀移速度若割阶浓度为Cj、割阶移动速度为Vj、位错攀移距离为b，则位错攀移速度VcbCjVj；影响因素：1.割阶浓度为Cj：热平衡时 Uj为割阶形成能；2.割阶移动速度为Vj：取决于割阶与点缺陷的交互作用，点缺陷的扩散速度。一般，Cj未达饱和时，Cj是控制Vc的主要因素；Cj达饱和时，Vj是控制Vc的主要因素；
