ch2位錯(cuò)-2.4位錯(cuò)與晶體缺陷作用

1、1Ch2 Ch2 位錯(cuò)位錯(cuò)2.1 2.1 位錯(cuò)理論的產(chǎn)生位錯(cuò)理論的產(chǎn)生2.2 2.2 位錯(cuò)的幾何性質(zhì)位錯(cuò)的幾何性質(zhì)2.3 2.3 位錯(cuò)的彈性性質(zhì)位錯(cuò)的彈性性質(zhì)2.4 2.4 位錯(cuò)與晶體缺陷的位錯(cuò)與晶體缺陷的相互作用相互作用2.5 2.5 位錯(cuò)的動力學(xué)性質(zhì)位錯(cuò)的動力學(xué)性質(zhì)2.6 2.6 實(shí)際晶體中的位錯(cuò)實(shí)際晶體中的位錯(cuò)22.1 2.1 位錯(cuò)理論的產(chǎn)生位錯(cuò)理論的產(chǎn)生一、晶體的塑性變形方式一、晶體的塑性變形方式二、單晶體的塑性變形二、單晶體的塑性變形三、多晶體的塑性變形三、多晶體的塑性變形四、晶體的理論切變強(qiáng)度四、晶體的理論切變強(qiáng)度五、位錯(cuò)理論的產(chǎn)生五、位錯(cuò)理論的產(chǎn)生六、位錯(cuò)的基本知識六、位錯(cuò)的基本

2、知識32.2 2.2 位錯(cuò)的幾何性質(zhì)位錯(cuò)的幾何性質(zhì)一、位錯(cuò)的幾何模型一、位錯(cuò)的幾何模型二、柏格斯矢量二、柏格斯矢量三、位錯(cuò)的運(yùn)動三、位錯(cuò)的運(yùn)動四、位錯(cuò)環(huán)及其運(yùn)動四、位錯(cuò)環(huán)及其運(yùn)動五、位錯(cuò)與晶體的塑性變形五、位錯(cuò)與晶體的塑性變形六、割階六、割階42.3 2.3 位錯(cuò)的彈性性質(zhì)位錯(cuò)的彈性性質(zhì)一、彈性連續(xù)介質(zhì)、應(yīng)力和應(yīng)變一、彈性連續(xù)介質(zhì)、應(yīng)力和應(yīng)變二、刃型位錯(cuò)的應(yīng)力場二、刃型位錯(cuò)的應(yīng)力場三、螺型位錯(cuò)的應(yīng)力場三、螺型位錯(cuò)的應(yīng)力場四、位錯(cuò)的應(yīng)變能四、位錯(cuò)的應(yīng)變能五、位錯(cuò)的受力五、位錯(cuò)的受力六、向錯(cuò)六、向錯(cuò)七、位錯(cuò)的半點(diǎn)陣模型七、位錯(cuò)的半點(diǎn)陣模型52.4 2.4 位錯(cuò)與晶體缺陷的相互作用位錯(cuò)與晶體缺陷的相

3、互作用一、位錯(cuò)間的相互作用力一、位錯(cuò)間的相互作用力二、位錯(cuò)與界面的交互作用二、位錯(cuò)與界面的交互作用三、位錯(cuò)與點(diǎn)缺陷的交互作用三、位錯(cuò)與點(diǎn)缺陷的交互作用6Interactions Between DislocationsWe will first investigate the interaction between two straight and parallel dislocations of the same kind.q If we start with screw dislocations, we have to distinguish the following cases: 7

4、In analogy, we next must consider the interaction of edge dislocations, of edge and screw dislocations and finally of mixed dislocations. q The case of mixed dislocations - the general case - will again be obtained by considering the interaction of the screw- and edge parts separately and then addin

5、g the results. With the formulas for the stress and strain fields of edge and screw dislocations one can calculate the resolved shear stress caused by one dislocation on the glide plane of the other one and get everything from there. But for just obtaining some basic rules, we can do better than tha

6、t. We can classify some basic cases without calculating anything by just examining one obvious rule: q If the superposition of the strain fields of dislocations add up to values of the compressive or tensile strain larger than those of a single dislocations, they will repulse each other. If the comb

7、ined strain field is lower than that of the single dislocation, they will attract each other.8This leads to some simple cases: 1. Arbitrarily curved dislocations with identical b on the same glide plane will always repel each other. 92. Arbitrary dislocations with opposite b vectors on the same glid

8、e plane will attract and annihilate each other Edge dislocations with identical or opposite Burgers vector b on neighboring glide planes may attract or repulse each other, depending on the precise geometry. The blue double arrows in the picture below thus may signify repulsion or attraction.10The ge

9、neral formula for the forces between edge dislocations in the geometry shown above isFx = Gb2 / 2p p(1 n n) x (x2 y2) /(x2 + y2)2 Fy = Gb2 / 2p p(1 n n) y (3x2 + y2) /(x2 + y2)2 q For y = 0, i.e. the same glide plane, we have a 1/x or, more generally a 1/r dependence of the force on the distance r b

10、etween the dislocations.qFor y 0 we find zones of repulsion and attraction. At some specific positions the force is zero - this would be the equilibrium configurations; it is shown below. q The formula for Fy is just given for the sake of completeness. Since the dislocations can not move in y-direct

11、ion, it is of little relevance so far.11The illustration in the link gives a quantitative picture of the forces acting on one dislocation on its glide plane as a function of the distance to another dislocation.12一、位錯(cuò)間的相互作用力一、位錯(cuò)間的相互作用力1314（一）相互平行的兩個(gè)螺位錯(cuò)間的作用力（一）相互平行的兩個(gè)螺位錯(cuò)間的作用力（二）相互平行的兩個(gè)刃位錯(cuò)間的作用力（二）相互平行的

12、兩個(gè)刃位錯(cuò)間的作用力（三）其它情況的位錯(cuò)之間的作用力（三）其它情況的位錯(cuò)之間的作用力（四）位錯(cuò)運(yùn)動的晶格阻力（四）位錯(cuò)運(yùn)動的晶格阻力P-NP-N力力15（一）相互平行的兩個(gè)螺位錯(cuò)間的作用力（一）相互平行的兩個(gè)螺位錯(cuò)間的作用力16上式說明，兩平行螺位錯(cuò)之間只有徑向交互作用徑向交互作用，因而交互作用力是一中心力。（即F=Fz=0,Fr0）17（二）相互平行的兩個(gè)刃位錯(cuò)間的作用力（二）相互平行的兩個(gè)刃位錯(cuò)間的作用力yy 與zz 不考慮，它們對位錯(cuò)運(yùn)動無影響xx 使b2攀移yx使b2滑移18根據(jù)根據(jù)F=bF=b有：有：F Fyx= =yxbb，F(xiàn) Fxx= =xxbb1920212223Forces

13、between Edge Dislocations Shown is the force between edge dislocations of identical and opposite Burgers vectors as a function of their normalized distance.q The distance x between the dislocations is expressed in units of y, the distance of the glide planes.24qThe force changes from repulsive to at

14、tractive or vice verse for a distance x = y; i.e. if the dislocations are at an angle of 45o relative to the glide plane.q The 45o position is a stable equilibrium position for opposite Burgers vectors, because at this position F = 0, and dF/dx 基體原子基體原子R 柯垂耳柯垂耳(Cottrell)處理處理: 假設(shè)假設(shè)(1)晶體為連續(xù)彈性介質(zhì)晶體為連續(xù)彈性

15、介質(zhì);(2)溶質(zhì)原子為剛球溶質(zhì)原子為剛球;(3)溶質(zhì)溶質(zhì)原子引起的點(diǎn)陣畸變是球形對稱畸變原子引起的點(diǎn)陣畸變是球形對稱畸變.則溶質(zhì)原子溶入則溶質(zhì)原子溶入,相當(dāng)于在相當(dāng)于在(r,)處挖一個(gè)處挖一個(gè)R的球形洞的球形洞,再擠入再擠入一個(gè)一個(gè)R的剛球的剛球. 交互作用能交互作用能=剛球擠入過程中反抗位錯(cuò)應(yīng)力場做的功剛球擠入過程中反抗位錯(cuò)應(yīng)力場做的功=位位錯(cuò)應(yīng)力場做的負(fù)功錯(cuò)應(yīng)力場做的負(fù)功由4041溶質(zhì)原子R基體原子R,即4243（二）螺位錯(cuò)與點(diǎn)缺陷的交互作用（二）螺位錯(cuò)與點(diǎn)缺陷的交互作用因?yàn)槁菸诲e(cuò)是純切應(yīng)力場，所以當(dāng)點(diǎn)缺陷引起因?yàn)槁菸诲e(cuò)是純切應(yīng)力場，所以當(dāng)點(diǎn)缺陷引起球球形對稱畸變時(shí)，兩者無交互作用；形對稱

16、畸變時(shí)，兩者無交互作用；若點(diǎn)缺陷引起的是若點(diǎn)缺陷引起的是非球形對稱畸變非球形對稱畸變時(shí)，則溶質(zhì)原時(shí)，則溶質(zhì)原子與位錯(cuò)仍發(fā)生交互作用，結(jié)果使溶質(zhì)原子向位子與位錯(cuò)仍發(fā)生交互作用，結(jié)果使溶質(zhì)原子向位錯(cuò)偏聚，形成溶質(zhì)原子氣團(tuán)；錯(cuò)偏聚，形成溶質(zhì)原子氣團(tuán)；例如，鋼中的例如，鋼中的C、N溶入溶入bcc鐵的八面體間隙時(shí)，鐵的八面體間隙時(shí)，引起非球形對稱畸變（稱為四方畸變），其應(yīng)力引起非球形對稱畸變（稱為四方畸變），其應(yīng)力場既有正應(yīng)力，又有切應(yīng)力，能與位錯(cuò)發(fā)生交互場既有正應(yīng)力，又有切應(yīng)力，能與位錯(cuò)發(fā)生交互作用；作用；螺型位錯(cuò)的純切應(yīng)力場可以等效一個(gè)正應(yīng)力場，螺型位錯(cuò)的純切應(yīng)力場可以等效一個(gè)正應(yīng)力場，使溶質(zhì)原子擇

17、優(yōu)分布，形成使溶質(zhì)原子擇優(yōu)分布，形成史諾克（史諾克（Snock）氣團(tuán)氣團(tuán)，對位錯(cuò)有強(qiáng)烈的釘扎作用。對位錯(cuò)有強(qiáng)烈的釘扎作用。4445（三）關(guān)于空位與位錯(cuò)的作用（三）關(guān)于空位與位錯(cuò)的作用46The fundamental interactions between The fundamental interactions between dislocations and elastic obstaclesdislocations and elastic obstacles The goal of the work is to understand the fundamental interactio

18、ns between dislocations and elastic obstacles. The primary tool that will be used is the in-situ TEM deformation technique. With this technique it is possible to directly observe the interaction between dislocations and elastic obstacles at high spatial resolution. From these observations, the magni

19、tude of the pinning strength, the bypass mechanism, and the process by which dislocation loops are destroyed can be ascertained. Copper was selected simply for ease of comparison with computer simulation studies. In-situ TEM straining specimens of 99.999% pure polycrystalline Cu were cut from 250 mm thick cold rolled strip into 11mm by 2.7 mm pieces. Holes for the straining pins in the stage were drilled in the ends of the tensile bars followed by polishing the surfaces to a 600-grit finish. Samples were then annealed at 750 C in a vacuum furnace for 2 hours and allowed to