ch2位錯-2.2 位錯的幾何性質(zhì)

1、1Ch2 Ch2 位錯位錯2.1 2.1 位錯理論的產(chǎn)生位錯理論的產(chǎn)生2.2 2.2 位錯的幾何性質(zhì)位錯的幾何性質(zhì)2.3 2.3 位錯的彈性性質(zhì)位錯的彈性性質(zhì)2.4 2.4 位錯與晶體缺陷的相互作用位錯與晶體缺陷的相互作用2.5 2.5 位錯的動力學(xué)性質(zhì)位錯的動力學(xué)性質(zhì)2.6 2.6 實際晶體中的位錯實際晶體中的位錯22.1 2.1 位錯理論的產(chǎn)生位錯理論的產(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、晶體的理論切變強度四、晶體的理論切變強度五、位錯理論的產(chǎn)生五、位錯理論的產(chǎn)生六、位錯的基本知識六、位錯的基本

2、知識32.2 2.2 位錯的幾何性質(zhì)位錯的幾何性質(zhì)一、位錯的幾何模型一、位錯的幾何模型二、柏格斯矢量二、柏格斯矢量三、位錯的運動三、位錯的運動四、位錯環(huán)及其運動四、位錯環(huán)及其運動五、位錯與晶體的塑性變形五、位錯與晶體的塑性變形六、割階六、割階4一、位錯的幾何模型一、位錯的幾何模型 l、2兩列原子已兩列原子已完成了滑移完成了滑移,3、4、5各列原子雖各列原子雖開始滑移開始滑移,但還但還未達(dá)到平衡位置未達(dá)到平衡位置,6、7、8各列各列尚未滑移尚未滑移.這樣這樣,滑移面便分為已滑移面便分為已滑移區(qū)和未滑移區(qū)滑移區(qū)和未滑移區(qū).已滑移區(qū)與末滑移區(qū)的界限已滑移區(qū)與末滑移區(qū)的界限(3、4、5列列),即即定義

3、為定義為位錯位錯.位錯是線缺陷位錯是線缺陷,位錯線上成列的原子發(fā)生了有規(guī)則位錯線上成列的原子發(fā)生了有規(guī)則的錯排的錯排. 位位錯錯與與滑滑移移5位錯的類型位錯的類型1.1.刃型位錯：多余半原子面刃口（正、負(fù)）刃型位錯：多余半原子面刃口（正、負(fù)） 位錯線垂直位錯線垂直b b2.2.螺型位錯：螺旋面軸線（左、右）螺型位錯：螺旋面軸線（左、右） 位錯線平行位錯線平行b b3.3.混合位錯：介于以上兩者混合位錯：介于以上兩者6刃型位錯刃型位錯刃型位錯的基本結(jié)構(gòu)特點刃型位錯的基本結(jié)構(gòu)特點, ,就是它的就是它的位錯線位錯線是是多余半多余半原子面與滑移面的交線原子面與滑移面的交線. .但是但是位錯線位錯線不只

4、是一列原子不只是一列原子, ,而是以而是以EFEF線為中心的一個管道線為中心的一個管道, ,其直徑一般為其直徑一般為3 34 4個個原子間距原子間距. .在此范圍內(nèi)在此范圍內(nèi), ,原子發(fā)生嚴(yán)重的錯排原子發(fā)生嚴(yán)重的錯排. .7在滑移面上部在滑移面上部, ,位錯線周圍的原子因受到位錯線周圍的原子因受到壓應(yīng)力壓應(yīng)力而而向外偏離于平衡位置向外偏離于平衡位置; ;在滑移面下部在滑移面下部, ,位錯線周圍的位錯線周圍的原子因受原子因受拉應(yīng)力拉應(yīng)力也偏離平衡位置也偏離平衡位置. .8刃型位錯的幾何特征刃型位錯的幾何特征(1)(1)刃位錯線與其滑移矢量刃位錯線與其滑移矢量b b垂直垂直. .刃位錯只有唯一的滑

5、移面刃位錯只有唯一的滑移面, ,但但多余半原子面末端可以是任意形狀多余半原子面末端可以是任意形狀, ,故刃位錯線可以為任意故刃位錯線可以為任意形狀的曲線形狀的曲線, ,如下圖所示如下圖所示; ;(2)(2)刃位錯可以人為地分為正和負(fù)兩種刃位錯可以人為地分為正和負(fù)兩種. .當(dāng)晶體倒置時當(dāng)晶體倒置時, ,晶體中晶體中刃位錯的正負(fù)符號隨之顛倒刃位錯的正負(fù)符號隨之顛倒; ;(3)(3)當(dāng)刃位錯滑出晶體表面時當(dāng)刃位錯滑出晶體表面時, ,只在不垂直于位錯線的晶體表面只在不垂直于位錯線的晶體表面上出現(xiàn)滑移臺階上出現(xiàn)滑移臺階; ;(4)(4)刃位錯周圍產(chǎn)生了刃位錯周圍產(chǎn)生了體應(yīng)變體應(yīng)變與與切應(yīng)變切應(yīng)變. .9

6、10Screw dislocation Now we go on and learn a new thing: There is a second basic type of dislocation, called screw dislocation. Its atomistic representation is somewhat more difficult to draw - but a Burgers circuit is still possible: You notice that for no particularly good reason here we chose to g

7、o clock-wise.11If you imagine a walk along the non-closed Burges circuit which you keep continuing round and round, it becomes obvious how a screw dislocation got its name. q It also should be clear by now how Burgers circuits are done. 12螺型位錯螺型位錯 ABCDABCD為為滑移面滑移面, ,EFEF以右為已滑移區(qū)以右為已滑移區(qū), ,EFEF以左為未滑移區(qū)以

8、左為未滑移區(qū), ,它們分界的地方就是它們分界的地方就是位錯線位錯線. .這種位錯是由上下兩部這種位錯是由上下兩部分晶體相對旋轉(zhuǎn)而形成的分晶體相對旋轉(zhuǎn)而形成的, ,所以叫所以叫螺型位錯螺型位錯. .螺型位錯螺型位錯也是也是一個半徑大約為一個半徑大約為3-43-4個原子間距的管道個原子間距的管道. .13 圖圖2-42-4表明了表明了BCBC、EFEF間間, ,上、下兩個原子面上的原子相互錯動上、下兩個原子面上的原子相互錯動的情況的情況. .EFEF與與BCBC之間即之間即位錯線區(qū)位錯線區(qū), ,OOOO可以看作是可以看作是位錯中心位錯中心. .螺螺型位錯形成以后型位錯形成以后, ,所有原來所有原來

9、與位錯線相垂直的晶面與位錯線相垂直的晶面, ,都將由都將由平平面面變成以位錯線為中心軸的變成以位錯線為中心軸的螺旋面螺旋面, ,如圖如圖2-52-5所示所示. .1415螺型位錯的幾何特征螺型位錯的幾何特征(1)(1)螺位錯線與其沿路矢量螺位錯線與其沿路矢量b b平行平行, ,故故純螺位錯只能是直線純螺位錯只能是直線; ;(2)(2)包含有螺位錯線的面必然包含滑移矢量包含有螺位錯線的面必然包含滑移矢量b.b.因此因此, ,對于連續(xù)介對于連續(xù)介質(zhì)質(zhì), ,螺位錯可以有無窮多個滑移面螺位錯可以有無窮多個滑移面. .但是但是, ,在晶體中滑移面只在晶體中滑移面只能在晶體的密排面上進(jìn)行能在晶體的密排面上

10、進(jìn)行, ,故晶體中的故晶體中的螺位錯只有有限個滑螺位錯只有有限個滑移面移面; ;(3)(3)根據(jù)螺蜷面的不同根據(jù)螺蜷面的不同, ,螺位錯可分右和左兩種螺位錯可分右和左兩種, ,左螺和右螺左螺和右螺不不會因為晶體位置的顛倒而改變會因為晶體位置的顛倒而改變; ;(4)(4)當(dāng)螺位錯滑出晶體時當(dāng)螺位錯滑出晶體時, ,只只在不平行于位錯線的晶體表面出現(xiàn)在不平行于位錯線的晶體表面出現(xiàn)滑移臺階滑移臺階; ;(5)(5)螺位錯沒有多余半原子面螺位錯沒有多余半原子面, ,它周圍它周圍只引起切應(yīng)變而無體應(yīng)變只引起切應(yīng)變而無體應(yīng)變. .16 汽相或溶液中生長出的晶體表面臺階汽相或溶液中生長出的晶體表面臺階( (即

11、螺位錯即螺位錯):):如如果有一條螺位錯線在晶體表面露頭果有一條螺位錯線在晶體表面露頭, ,在露頭處的晶面在露頭處的晶面上必然形成上必然形成一個臺階一個臺階, ,這個臺階不會因復(fù)蓋了一層原這個臺階不會因復(fù)蓋了一層原子而消失子而消失, ,這樣這樣, ,螺位錯露頭處就為晶體生長提供了有螺位錯露頭處就為晶體生長提供了有利條件利條件, ,使之能在過飽和度不高使之能在過飽和度不高( (只有只有1%,1%,根據(jù)理論計根據(jù)理論計算應(yīng)高達(dá)算應(yīng)高達(dá)50%)50%)的蒸汽壓下或溶液中連續(xù)不斷地生長的蒸汽壓下或溶液中連續(xù)不斷地生長. .1718We already know enough by now, to de

12、duce some elementary properties of dislocations which must be generally valid1. A dislocation is one-dimensional defect because the lattice is only disturbed along the dislocation line (apart from small elastic deformations which we do not count as defects farther away from the core). The dislocatio

13、n line thus can be described at any point by a line vector t(x,y,z). 2. In the dislocation core the bonds between atoms are not in an equilibrium configuration, i.e. at their minimum enthalpy value ,H; they are heavily distorted. The dislocation thus must possess energy (per unit of length) and entr

14、opy,S.193. Dislocations move under the influence of external forces which cause internal stress in a crystal. The area swept by the movement defines a plane, the glide plane, which always (by definition) contains the dislocation line vector. 4. The movement of a dislocation moves the whole crystal o

15、n one side of the glide plane relative to the other side. 5. (Edge) dislocations could (in principle) be generated by the agglomeration of point defects: self-interstitial on the extra half-plane, or vacancies on the missing half-plane.20Now we will turn to a more formal description of dislocations

16、that will include all possible cases, not just the extreme cases of pure edge or screw dislocations.21Mixed dislocation除除刃型位錯刃型位錯和和螺型位錯螺型位錯之外之外, ,還有一種形式更為普遍還有一種形式更為普遍的位錯的位錯, ,其滑移矢量既不平行于也不垂直于位錯線其滑移矢量既不平行于也不垂直于位錯線, ,而與位錯線相交成任意角度而與位錯線相交成任意角度, ,這種位錯即為這種位錯即為混合位錯混合位錯. .2223Volterra Construction and Conseq

17、uencesWe now generalize the present view of dislocations as follows:q 1. Dislocation lines may be arbitrarily curved - never mind that we cannot, at the present, easily imagine the atomic picture to that.q 2. All lattice vectors can be Burgers vectors, and as we will see later, even vectors that are

18、 not lattice vectors are possible. A general definition that encloses all cases is needed.24 In 1907,Volterra, coming from the mechanics of the continuum (even crystals havent been discovered yet), had defined all possible basic deformation cases of a continuum (including crystals) and in those elem

19、entary deformation cases the basic definition for dislocations was already contained!q The following shows Volterra basic deformation modes - three can be seen to produce edge dislocations in crystals, one generates a screw dislocation.25Volterras TubesHow can we obtain an arbitrary deformation of a

20、n arbitrary body by just repeating and combining some basic deformation procedures? The illustrations shows Volterras answer to this question: Take a cylinder of a material, cut it along some wall, shift the surfaces of the cut in all ways that - after welding the walls together again (including tak

21、ing out or adding material) - will lead to different deformation states. qAs Volterra showed, there is a limited and rather small number of possible independent cuts + shifts. All other cuts plus some deformation can always be expressed as a linear superposition of the elementary cuts.26qHere are th

22、e elementary cuts. The first one just shows the cut, the next three ones correspond to dislocations - i.e. a real dislocation produces exactly the strain field generated by the cut and shift procedure. 27q The last three cuts corresponds to special defects called disclinations旋轉(zhuǎn)位錯，向錯旋轉(zhuǎn)位錯，向錯 that are

23、 more elementary than dislocations, but are not observed in real crystals (except, maybe, in grain boundaries and liquid crystal). They do however, appear in two-dimensional lattices, e.g. in the flux-line lattice of a superconductor.28How to define dislocations in a very general way by Volterra kni

24、fe Volterras insight gives us the tool to define dislocations in a very general way. We use the Volterra knife which has the property that you can make any conceivable cut into a crystal with ease (in your mind). So lets produce dislocations with the Volterra knife:291. Make a cut, any cut, into the

25、 crystal using the Volterra knife. The cut does not have to be on a flat plane (the picture shows a flat cut just because it is easier to draw). The cut is by necessity completely contained within a closed line, the red cut line (most of it on the outside of the crystal). That part of the cut line t

26、hat is inside the crystal will define the line vector t of the dislocation to be formed.302. Move the two parts of the crystal separated by the cut relative to each other by a translation vector of the lattice; allowing elastic deformation of the lattice in the general area of the dislocation line.

27、q The translation vector chosen will be the Burgers vector b of the dislocation to be formed. The sign will depend on the convention used. Shown are movements leading to an edge dislocations (left) and a screw dislocation (right).31q It will always be necessary for obvious reasons if your chosen tra

28、nslation vector has a component perpendicular to the plane of the cut. q Shown is the case where you have to fill in material - always preserving the structure of the crystal that was cut, of course.q Left: After cut and movement. Right: After filling up the gap with crystal material3. Fill in mater

29、ial or take some out, if necessary.32q Since the displacement vector was a translation vector of the lattice, the surfaces will fit together perfectly everywhere - except in the region around the dislocation line defined as by the cut line. A one-dimensional defect was produced, defined by the cut l

30、ine (= line vector t of the dislocation) and the displacement vector which we call Burgers vector b. q It is rather obvious (but not yet proven) that the Burgers vector defined in this way is identical to the one defined before. This will become totally clear in the following paragraphs.4. Restore t

31、he crystal by welding together the surfaces of the cut. 33From the Voltaterra construction of a dislocation, we can not only obtain the simple edge and screw dislocation that we already know, but any dislocation. Moreover, from the Volterra construction we can immediately deduce a new list with more

32、 properties of dislocations:More properties of dislocations341. The Burgers vector for a given dislocation is always the same, i.e. it does not change with coordinates, because there is only one displacement for every cut. On the other hand, the line vector may be different at every point because we

33、 can make the cut as complicated as we like.2. Edge- and screw dislocations (with an angle of 90 or 0, resp., between the Burgers- and the line vector) are just special cases of the general case of a mixed dislocation with has an arbitrary angle between b and t that may even change along the disloca

34、tion line. The illustration shows the case of a curved dislocation that changes from a pure edge dislcation to a pure screw dislocation.35 We are looking at the plane of the cut (sort of a semicircle centeredin the lower left corner). Blue circles denote atoms just below,red circles atoms just above

35、 the cut. Up on the right the dislocation isa pure edge dislocation, on the lower left it is pure screw. In between it is mixed. In the next page this dislocation is shown moving in ananimated illustration.36The picture is animated the dislocation can be seen as it moves out of the crystal, thus rev

36、ersing the cut-and-displace procedure that created it. 373. The Burgers vector must be independent from the precise way the Burgers circuit is done since the Volterra construction does not contain any specific rules for a circuit. This is easy to see, of course:Two arbitrary alternative Burgers circ

37、uits. The colors serve to make it easierto keep track of the steps384. A dislocation cannot end in the interior of an otherwise perfect crystal (try to make a cut that ends internally with your Volterra knife), but only at a crystal surface an internal surface or interface (e.g. a grain boundary) a

38、dislocation knot on itself - forming a dislocation loop. 395. If you do not have to add matter or to take matter away (i.e. involve interstitial or vacancies), the Burgers vector b must be in the plane of the cut which has two consequences: The cut plane must be planar; it is defined by the line vec

39、tor and the Burgers vector. The cut plane is the glide plane of the dislocation; only in this plane can it move without the help of interstitials or vacancies. 40 The glide plane is thus the plane spread out by the Burgers vector b and the line vector t.6. Plastic deformation is promoted by the move

40、ment of dislocations in glide planes. This is easy to see: Extending your cut produces more deformation and this is identical to moving the dislocation! 7. The magnitude of b (= b) is a measure for the strength of the dislocation, or the amount of elastic deformation in the core of the dislocation.

41、A not so obvious, but very important consequence of the Voltaterra definition is 8. At a dislocation knot the sum of all Burgers vectors is zero, Sb = 0, provided all line vectors point into the knot or out of it. A dislocation knot is simply a point where three or more dislocations meet. A knot can

42、 be constructed with the Volterra knife as shown below.41 Statement 8. can be proved in two ways: Doing Burgers circuits or using the Voltaterra construction twice. At the same time we prove the equivalence of obtaining b from a Burgers circuit or from a Voltaterra construction.q Lets look at a disl

43、ocation knot formed by three arbitrary dislocations and do the Burgers circuit - always taking the direction of the Burgers circuit from a right hand rule42q Lets look at a dislocation knot formed by three arbitrary dislocations and do the Burgers circuit - always taking the direction of the Burgers

44、 circuit from a right hand ruleq Since the sum of the two individual circuits must give the same result as the single big circuit, it follows:b1 = b2 + b3 q Or, more generally, after reorienting all t -vectors so that they point into the knot: Si bi = 0 43 Now lets look at the same situation in the

45、Voltaterra construction:q We make a first cut with a Burgers vector b1 (the green one in the illustration below). q Now we make a second cut in the same plane that extends partially beyond the first one with Burgers vector b2 (the red line). We have three different kinds of boundary lines: red and g

46、reen where the cut lines are distinguishable, and black where they are on top of each other. And we have also produced a dislocation knot!44q Obviously the displacement vector for the black line, which is the Burgers vector of that dislocation, must be the sum of the two Burgers vectors defined by t

47、he two cuts: b = b1 + b2. So we get the same result, because our line vectors all had the same flow direction (which, in this case, is actually tied to which part of the crystal we move and which one we keep at rest).45 If we produce a dislocation knot by two cuts that are not coplanar but keep the

48、Burgers vector on the cut plane, we produce a knot between dislocations that do not have the same glide plane. As an immediate consequence we realize that this knot might be immobile - it cannot move. q A simple example is shown below (consider that the Burgers vector of the red dislocation may have

49、 a glide plane different from the two cut planes because it is given by the (vector) sum of the two original Burgers vectors!).46 We can now draw some conclusion about how dislocations must behave in circumstances not so easy to see directly:q Lets look at the glide plane of a dislocation loop. We c

50、an easily produce a loop with the Volterra knife by keeping the cut totally inside the crystal (with a real knife that could not be done). In the example the dislocation is an edge dislocationq The glide plane; always defined by Burges and line vector, becomes a glide cylinder! The dislocation loop

51、can move up or down on it, but no lateral movement is possible.47Sign of Burgers and Line VectorsLets look at a dislocation loop in cross-section. After the cut along the red line, the lower half was moved to the right by b. Two edge dislocation are visible if we look at a cross-section taken throug

52、h the middle of the loop. A Burgers circuit now would give Burgers vectors of different signs - or does it?48 We can ask the same question in a different way: From the Volterra construction we know that the Burgers vector - including the sign - must be the same everywhere. But the dislocations shown

53、 in the cross section look reversed - we would certainly assign different signs just looking at the picture. How is this contradiction to be solved?49Solution to Exercise The problem is solved easily by doing one simple thing: Look at the dislocation loop from aboveq After assigning a direction of t

54、, it is defined for the whole loop. At the places where we took the cross-section, it is actually the sign of t that is reversed! The Burgers vector thus must be the other way around if it is to be constant for the local t. It is important to realize that we only can be unambiguous if we know that w

55、e are looking at one and the same 同一個同一個dislocation. The cross-section by itself does not tell us that fact; it just as well could show two unconnected single dislocations. In this case we would assign Burgers vectors with different signs because we automatically would take the line direction to be

56、the same.50二、二、Burgers vector b(一一)確定柏氏矢量確定柏氏矢量b b的方法的方法(二二)柏氏矢量柏氏矢量b b的物理意義的物理意義(三三)柏氏矢量柏氏矢量b b的守恒性的守恒性(四四)柏氏矢量柏氏矢量b b的表示方法的表示方法51二、二、How to seek out Burgers vector bNow we add a new property. The fundamental quantity defining an arbitrary dislocation is its Burgers vector b. Its atomistic definiti

57、on follows from a Burgers circuit around the dislocation in the real crystal which is illustrated below52q Left picture: Make a closed circuit that encloses the dislocation from lattice point to lattice point (later from atom to atom). You obtain a closed chain of the base vectors which define the l

58、attice. q Right picture: Make exactly the same chain of base vectors in a perfect reference lattice. It will not close. q The special vector needed for closing the circuit in the reference crystal is by definition the Burgers vector b.53 But beware! As always with conventions, you may pick the sign

59、of theBurgers vector at will. q In the version given here (which is the usual definition), the closed circuit is around the dislocation, the Burgers vector then appears in the reference crystal. q You could, of course, use a closed circuit in the reference crystal and define the Burgers vector aroun

60、d the dislocation. You also have to define if you go clock-wise or counter clock-wise around your circle. You will always get the same vector, but the sign will be different! And the sign is very important for calculations! So whatever you do, stay consistent!.54(一一)確定柏氏矢量確定柏氏矢量b b的方法的方法1.規(guī)定位錯線的正向規(guī)定