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单击此处编辑母版标题样式,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,*,*,本资料仅供参考，不能作为科学依据。谢谢。本资料仅供参考，不能作为科学依据。本资料仅供参考，不能作为科学依据。谢谢。本资料仅供参考，不能作为科学依据。,Ch1 Points defects,1.1 空位及间隙原子几何组态,1.2 点缺点形成能,1.3 点缺点热平衡浓度,1.4 点缺点运动,1/75,1,Classification of Point defects,Two point defects are intrinsic to the material,meaning that they form spontaneously in the lattice without any external intervention.These two are,the,vacancy,and,the,self-interstitial,shown schematically in a 2-D representation in the following Fig.,The vacancy is simply an atom missing from a lattice site,which would be occupied in a perfect lattice.The self-interstitial is an atom lodged in a position between normal lattice atoms;that is in an interstice.The qualification“self”indicates that the interstitial atom is the same type as the normal lattice atoms.,2/75,2,The two panels in Fig.3.1 show the two basic mechanisms by which a foreign or impurity atom exists in the crystal lattice of a host element.,Large impurity atoms,usually of the same category as the host atoms(e.g.,both metals,as nickel iniron),replace the host atoms on regular lattice positions.These are called,substitutional impurities,.The structure of the lattice is not disturbed,only the identity of the atoms occupying the lattice sites are different.,Small atoms that are also chemically dissimilar from the host atoms occupy interstitial positions and do not appreciably distort the surrounding host crystal.They are termed,interstitial impurities,.Typical examples are carbon in iron and hydrogen in zirconium.,3/75,3,Self interstitials,Aside from their identities relative to the host atoms,the self-interstitial and the interstitial impurity differ in the way that they reside in the lattice.As shown in the Fig.using the,bcc lattice,as an example,the self interstitial,because of its size,displaces a host atom off of its,normal lattice position,creating,a dumbbell-shaped pair,.This,configuration is also called a,split interstitial,.The orientation,of the dumbbell and the distance,between the two atoms are,determined by the condition,that potential energy,of the lattice be a minimum.,4/75,4,Interstitial impurities,The small interstitial impurity atoms,on the other hand,occupy definite sites without significant distortion of the host lattice.These sites are named after the shape of the polyhedron formed by joining the host atoms surrounding the interstitial.The examples shown in the Fig.for the bcc lattice are,octahedral,and,tetrahedral,sites.These two interstices offer the most space for the impurity atom to reside in,but which site is occupied is a sensitive function of,the interaction energy,between the impurity atom and the host atom.,5/75,5,6/75,6,点缺点对材料性能影响,材料,退火,均匀化,热处理,沉淀析出,蠕变,等借助,空位在点阵中运输,7/75,7,1.1空位及间隙原子几何组态,一、空位,二、间隙原子,8/75,8,一、,Vacancies,A vacancy is the absence of an atom in the lattice.,In ionic crystals(e.g NaCl)vacancies occur in pairs(Na+Cl)so that charge balance is maintained.,Also called a Schottky Defect.,Vacancies allow diffusion through the crystal:,Vacancy:,point,defect,-associated with a point in the crystal,9/75,9,一、空位,1.,形成,从晶体正常点阵上抽去一个原子，失去了原子这个位置就是,空位,。（空位集合可形成更复杂点缺点）,2.,空位几何组态,（,1,）单空位,A,（,2,）空位对,B,10/75,10,（,3,）三空位,（,b）,（,4,）空位四面体,（,c）,（5）空位片,（空位在某结晶学面上聚集）,11/75,11,A schematic drawing of various crystal lattice defects,e)Precipitate of impurity atoms,f)Vacancy type dislocation loop,g)Interstitial type dislocation loop,h)Substitutional impurity atom,c)Self interstitial atom d)Vacancy,a)Interstitial impurity atom,b)Edge dislocation,空位片,12/75,12,二、,Interstitials,Previously we discussed small tetrahedral and octahedral interstitial atoms within the close packed structure.,If the interstitial atom is the same size as the close packed atoms,then considerable disruption to the structure occurs.,Again,this is a point defect and requires much energy,13/75,13,Frenkel Defects,Often a vacancy and interstitial occur together-an ion is displaces from its site into an interstitial position.,This is a,Frenkel Defect,(common in e.g.AgCl)and charge balance is maintained.,Frenkel defects can be induced by irradiation of a sample,14/75,14,二、间隙原子,1.,形成,在点阵间隙挤进了一个原子,(同类,or,异类，本身,or,外来),=,间隙原子,2.,间隙原子几何组态,(1),体心组态,球对称性畸变,15/75,15,(2),哑铃组态,(,对分间隙组态,),能量略低于体心组态,四方畸变,方向畸变,(,六种可能方位,在一定条件下,能够从一个取向转变成另一个取向,),16/75,16,(3),挤列组态,(,高能离子辐射条件下产生,),当传递能量较低时,沿点阵,密排方向,一列原子发生连续碰撞,每个原子都沿密排方向运动,结果使,n+1,个原子占有正常情况下,n,个原子位置,.,17/75,17,(4),夫伦克耳对,辐照时,形成间隙原子与原点阵位置空位一起组成了夫伦克耳对,18/75,18,夫伦克耳对形成过程,19/75,19,20/75,20,21/75,21,22/75,22,23/75,23,经理论计算和实际证实,哑铃组态,能量最低,是平衡组态,.,24/75,24,Impurities,Preparing pure crystals is extremely difficult-often foreign atoms enter the structure and substitute for“native”atoms-often by contamination from container,This can have a large effect(either detrimental or beneficial)on the properties of the crystal.We can also add impurities(or dopants)deliberately.,An important example is that of silicon.,25/75,25,Silicon,Silicon is a group IV element and,like carbon,bonds to four nearest neighbours:,At elevated temperatures bonds are broken to produce a(positive)gap-known as a hole-and a conduction electron.,T,This is known as the,intrinsic,effect in semiconductors,26/75,26,Doped Silicon,If we take a group V element(e.g.As)and substitute(at low levels)for Si there is a spare electron for conduction and no positive hole:,This process is known as“doping”.Arsenic acts as an electron,donor,to Si,making it easier to conduct electricity.,Si doped with As is an,extrinsic,semiconductor and because the electron is negative this is an,n-type semiconductor,27/75,27,Doped Silicon,If we take a group III element(e.g.B)and substitute(at low levels)for Si there is a positive hole and no conduction electron,Boron acts as an electron,acceptor,to Si.,Holes can move by diffusion-“hopping”into the hole leaves behind a new hole.,Again this is an,extrinsic,semiconductor and because the hole is positive this is a,p-type,semiconductor,28/75,28,The band picture,Red=filled energy states,light blue=empty,white=forbidden(energy gap),Green dotted=donor states,blue dotted=acceptor states,Bottom band=valence band,top band=conduction band.,Points to note:Energy gap is big(3eV)in an insulator,1eV in a semiconductor,29/75,29,Band Structure.,A summary of the band structures of metals,semi-conductors and insulators is given below,30/75,30,1.2 点缺点形成能,一、形成能,二、形成能大小,三、主要结论,31/75,31,一、,The formation energy of point defect in elemental crystals,空位形成能,:,在晶体内取出一个原子（或离子）放到晶体表面台阶上,(,这么不改变晶体表面能,),所需要能量,.,32/75,32,一、,The formation energy of point defect in elemental crystals,间隙原子形成能,:,从晶体表面台阶上取出一个原子,挤进晶体原子间隙中所需能量,.,33/75,33,Point Defects in Ionic Crystals,Self interstitials and vacancies occur naturally in ionic crystals as well as in elemental solids.However,because the,cations,and,anions,carry electrical charges,vacancy and interstitial formation are not independent processes,.To create a vacancy on the anion sublattice by moving the anion to the surface,for example,would leave the surface negatively charged and the interior around the vacancy with a net positive charge.This violation of,local,electrical neutrality precludes such a process.Similar arguments apply to cation vacancies or self interstitials of either ionic type.,34/75,34,The,Schottky,defect,Point defects in an MX-type ionic crystal,35/75,35,The,Frenkel,defect.,Point defects in an MX-type ionic crystal,36/75,36,二、形成能大小,我们能够对,空位形成能,作一个简单预计：构想晶体为,FCC，,原子间交互作用限于近邻。在晶体内取出一个原子要割断12个键（,FCC,配位数为12），而在表面台阶处置放一个原子，要形成六个键。所以净效应为,割断六个键，应和晶体结合能（即升华能）相等,。这么预计显然是粗略，没有考虑到金属特征，以及周围空位原子位移。更准确计算，,表面空位形成能大约只为结合能1/2到,1/4,。,但空位结合能与形成能之间有亲密关系这一点是符合试验事实：,结合能愈大，熔点愈高，则空位形成能也愈大。,37/75,37,二、形成能大小,理论计算,试验测定,38/75,38,二、形成能大小,试验测定,能。,39/75,39,试验测定,40/75,40,41/75,41,试验测定,42/75,42,Vacancies,Vacancies are not energetically favourable-the number of vacancies increases with temperature(i.e.putting energy into the system),Mathematically,for a crystal containing N atoms,there is an equilibrium number of vacancies,n,at temperature T(in K)given by:,where E,V,is the energy of vacancy formation and k,B,is Boltzmanns constant.Applies to pairs also.,43/75,43,Diffusion,Similary,the diffusion coefficient,D,is given by:,where E,D,is the energy of diffusion and D,O,is a diffusion constant specific to the element.,Strictly this applies only to self-diffusion,that is diffusion in an elemental substance.,44/75,44,Quenching,Non-equilibrium concentrations of vacancies may be obtained by rapidly cooling(quenching)metals from high temperatures.,These defects can cause additional resistivity proportional to the number of defects:,where C is a proportionality constant.,R is the relative increase in resistance at low temperature after quenching from the temperature T.,45/75,45,Uses,so:,y =c +mx,E,V,can be obtained from a graph of ln,R against(1/T),46/75,46,Example-Gold,47/75,47,三、主要结论,Q,形,越大,，,形成点缺点越困难；,Q,间隙,比,Q,空位,大,3-4,倍,，,所以常见点缺点是空位,；如,Cu,：,Q,间隙,=4ev,Q,空位,=1ev,c=Aexp(Q,f,/kT),在,Fcc,结构中,，,哑铃组态能最低,，,是最稳定组态,。,48/75,48,1.3点缺点热平衡浓度,一、点缺点形成,二、,点缺点是热力平衡缺点,三、,点缺点对物理性能影响,四、,点缺点产生、消除与检测,49/75,49,一、点缺点形成,热激活造成,(,能量彼此起伏,),50/75,50,二、,点缺点是热力学平衡缺点,It is well known that the criterion of chemical equilibrium is the minimization of the Gibbs free energy of the system at constant temperature and pressure.,51/75,51,The remainder of the section concentrates on vacancies,and in particular the equilibrium vacancy concentration.Firstly,an overview is given of the variation in free energy of a crystal,G,with vacancy concentration,X,v,.From this relationship,the,equilibrium,vacancy concentration,X,v,e,is shown to be that which results in the minimum free energy.,52/75,52,Having looked at the general relationship between,X,v,and,G,the module goes on to look in more detail at the underlying theory.,The free energy term,G is first rewritten in terms of enthalpy(,H)and entropy(,S)of vacancy formation,using the familiar relationship:,(1),where,T,is the,absolute,temperature.The,H,and,S,terms are each considered in turn.,53/75,53,Enthalpy of vacancy formation,H,This is the change in enthalpy resulting from the addition of vacancies and arises from the increase in,internal,energy caused by breaking interatomic bands(i.e.removing atoms).By making the reasonable assumption that the,X,v,is low,such that vacancy-vacancy interactions can be ignored,it is shown that,H,is proportional to,X,v,according to the equation:,(2),H,v,is the molar enthalpy of vacancy formation.,54/75,54,55/75,55,Entropy of vacancy formation,S,This arises from the increased degree of randomness introduced by the addition of vacancies to a crystal.,S,itself can be separated into 2 components:,Thermal entropy,Configurational entropy.,Each of these terms is explained in further detail.It is shown that thermal entropy can be given by:,56/75,56,(3),where,S,v,is the molar thermal entropy.Special attention is given to the dominant configurational entropy term,and a side-branch takes the user to background information and related exercises.An expression for configurational entropy as a function of vacancy concentration is derived:,(4),57/75,57,58/75,58,59/75,59,C=Aexp(-,E/kT),设,N,个点阵位置晶体中有,n,个空位时，其系统自由能改变为：,FnE-TS,C=Aexp(-,E/kT),60/75,60,C=Aexp(-,E/kT),在一定温度下,，,有一定热力学平衡浓度,(,C,T.,),是点缺点区分于其它缺点主要特征,；,影响,C,最主要原因,:,Q,与,T；,结合能绝对值越大,，,温度越低,，,空位结合成空位正确倾向愈加显著。,61/75,61,62/75,62,三、,点缺点对物理性能影响,63/75,63,64/75,64,四、,点缺点产生、消除与检测,1.点缺点产生,2.点缺点降低或消除,3.点缺点检测,65/75,65,1.点缺点产生,淬火,：,淬火时，高温下平衡空位来不及消除或扩散到表面，绝大部分保留到低温，使低温下空位浓度超出其平衡浓度，成为空位过饱和状态，淬火产生过饱和空位。,冷加工,：,T,形变,T,再,金属中产生,（,1,）大量位错,（,2,）空位和间隙原子（后者易被位错俘获）,所以冷加工主要产生为位错和空位。,辐照,：会产生,夫伦克耳对，,辐照效应：即在高能离子（如中子、电子、质子等）照射下，金属材料发生一些特殊效应，如：,电离引发发烧,；,蜕变使单晶体沿某结晶学方向伸长或收缩,；,离位产生大量非平衡点缺点,。,66/75,66,67/75,67,2.点缺点降低或消除,退火处理,淬火后温度不太低或淬火后在稍高温度下放置，这时空位还有较大运动能力，能够观察到随放置时间延长，空位浓度逐步降低。,68/75,68,辐照回复5个阶段,：相邻空位与间隙原子结合,夫伦克耳对湮灭,R,附加,：,R,附加,（间隙原子从陷井中脱出引发）,:间隙原子向空位扩散，但空位不一定是,夫伦克耳对中空位,：,单空位运动,：稀疏区及空位聚集体消失（材料力性完全恢复到辐照前）,69/75,69,3.点缺点检测,（1）点缺点产生附加电阻大小与点缺点浓度正比。即,R,附加,C,点,=Aexp(-U,f,/kT),R,附加,可作为,C,点,标志。测,R,附加,T,关系。,（2）,R,附加,T,曲线测量,直接在各高温下测,R,样品淬火，保留过饱和空位，室温下测,R,（3）,场离子显微镜技术直接观察,表层中空位：直接观察,体内空位：低温蒸发，使表面层逐层脱去。,70/75,70,1.4点缺点运动,一、,空位运动与鞍点组态,二、,间隙原子运动方式,三、,点缺点移动激活能,71/75,71,一、,空位运动与鞍点组态,当,原子处于图,1,-,7,中,C,点位置上时引发点阵畸变较大，因而能量较高，被称为,鞍点组态,。,空位移动激活能,U,m,=E,鞍点,-,E,正常组态,72/75,72,二、,间隙原子运动方式,直接式（主要）；,间隙式；,对分式。,73/75,73,三、,点缺点移动激活能,U,m,1.,点缺点不是静止,而是在热激活作用下作无规则布朗运动,：,组成宏观扩散基础,a.,同类相遇,复合体,b.,异类相遇,互毁（即点缺点回复）,点缺点在作不规则布朗运动时,碰到了如自由表面、晶界、位错等点缺点漏洞，即消失在漏洞中，引发了点缺点回复。,2.,空位布朗运动所造成原子迁移就是晶体中自扩散,自扩散决定于空位浓度,C,空,和空位跃迁频率,空,U,点自扩散激活能,=,U,空位形成,+,U,空位移动,空位,=,Az,0,exp(-U,m,/kT),A:1-10,与移动激活熵,S,m,相关;,Z:,配位数;,0,:原子振动频率;,U,m,:空位移动激活能,74/75,74,点缺点移动激活能试验值,75/75,75,
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