1、Ch1 Points defectsCh1 Points defects1.1 1.1 空位及间隙原子几何组态空位及间隙原子几何组态1.2 1.2 点缺点形成能点缺点形成能1.3 1.3 点缺点热平衡浓度点缺点热平衡浓度1.4 1.4 点缺点运动点缺点运动1/751Classification of Point defectsTwo point defects are intrinsic to the material,meaning that they form spontaneously in the lattice without any external intervention.Th
2、ese 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
3、;that is in an interstice.The qualification“self”indicates that the interstitial atom is the same type as the normal lattice atoms.2/752The 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,usu
4、ally 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 a
5、toms 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.3/753Self interstitialsAside from their identit
6、ies 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 d
7、umbbell-shaped pair.This configuration is also called a split interstitial.The orientation of the dumbbell and the distancebetween the two atoms are determined by the condition that potential energy of the lattice be a minimum.4/754Interstitial impuritiesThe small interstitial impurity atoms,on the
8、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 i
9、nterstices 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.5/7556/756点缺点对材料性能影响点缺点对材料性能影响材料材料退火退火均匀化均匀化热处理热处理沉淀析出沉淀析出蠕变蠕变 等借助等借助空位在点阵中运输空位在点阵中运输7/7571.11.1空位及间隙原子几何组态空位及间隙
10、原子几何组态一、空位一、空位二、间隙原子二、间隙原子8/758一、一、VacanciesA 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 wi
11、th a point in the crystal9/759一、空位一、空位1.形成形成 从晶体正常点阵上抽去一个原子，失去了原子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这个位置就是空位空位。（空位集合可形成更复杂。（空位集合可形成更复杂点缺点）点缺点）2.空位几何组态空位几何组态（1）单空位）单空位A A （2）空位对）空位对B B10/7510（3）三空位）三空位（b）（4）空位四面体）空位四面体（c）（5）空位片）空位片（空位在某结晶学面上聚集）（空位在某结晶学面上聚集）11/7511A schematic drawing of various crystal lattice
12、 defects e)Precipitate of impurity atoms,f)Vacancy type dislocation loop,g)Interstitial type dislocation loop,h)Substitutional impurity atomc)Self interstitial atom d)Vacancy a)Interstitial impurity atom,b)Edge dislocation,空位片空位片12/7512二、二、InterstitialsPreviously we discussed small tetrahedral and o
13、ctahedral 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 energy13/7513Frenkel DefectsOften a vacancy and interstitial occur to
14、gether-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 sample14/7514二、间隙原子二、间隙原子1.形成形成在点阵间隙挤进了一个原子在点阵间隙挤进了一个原子(同类同类oror异类，本身异类，本身oror外来外来)=间隙原子间隙原子 2.间隙原子几何
15、组态间隙原子几何组态(1)体心组态体心组态 球对称性畸变球对称性畸变15/7515(2)哑铃组态哑铃组态(对分间隙组态对分间隙组态)能量略低于体心组态能量略低于体心组态四方畸变四方畸变 方向畸变方向畸变 (六种可能方位六种可能方位,在一定条在一定条件下件下,能够从一个取向转变成另一个取向能够从一个取向转变成另一个取向)16/7516(3)挤列组态挤列组态(高能离子辐射条件下产生高能离子辐射条件下产生)当当传传递递能能量量较较低低时时,沿沿点点阵阵密密排排方方向向一一列列原原子子发发生生连连续续碰碰撞撞,每每个个原原子子都都沿沿密密排排方方向向运运动动,结结果果使使n+1个个原原子占有正常情况下
16、子占有正常情况下n个原子位置个原子位置.17/7517(4)夫伦克耳对夫伦克耳对辐辐照照时时,形形成成间间隙隙原原子子与与原原点点阵阵位位置置空空位位一一起起组组成成了了夫伦克耳对夫伦克耳对18/7518夫伦克耳对形成过程夫伦克耳对形成过程19/751920/752021/752122/752223/7523经理论计算和实际证实经理论计算和实际证实,哑铃组态哑铃组态能量最低能量最低,是平衡组态是平衡组态.24/7524ImpuritiesPreparing pure crystals is extremely difficult-often foreign atoms enter the st
17、ructure and substitute for“native”atoms-often by contamination from containerThis 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.25/7525SiliconSilicon is a group IV e
18、lement 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.TThis is known as the intrinsic effect in semiconductors26/7526Doped SiliconIf we take a group V element(e.g.As)and substitute(at low
19、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 semicondu
20、ctor27/7527Doped SiliconIf we take a group III element(e.g.B)and substitute(at low levels)for Si there is a positive hole and no conduction electronBoron 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 semicond
21、uctor and because the hole is positive this is a p-type semiconductor28/7528The band pictureRed=filled energy states,light blue=empty,white=forbidden(energy gap)Green dotted=donor states,blue dotted=acceptor statesBottom band=valence band,top band=conduction band.Points to note:Energy gap is big(3eV
22、)in an insulator,1eV in a semiconductor29/7529Band Structure.A summary of the band structures of metals,semi-conductors and insulators is given below30/75301.2 1.2 点缺点形成能点缺点形成能一、形成能一、形成能二、形成能大小二、形成能大小三、主要结论三、主要结论31/7531一、一、The formation energy of point defect in elemental crystals空空位位形形成成能能:在在晶晶体体内内
23、取取出出一一个个原原子子（或或离离子子）放放到到晶体表面台阶上晶体表面台阶上(这么不改变晶体表面能这么不改变晶体表面能)所需要能量所需要能量.32/7532一、一、The formation energy of point defect in elemental crystals间间隙隙原原子子形形成成能能:从从晶晶体体表表面面台台阶阶上上取取出出一一个个原原子子,挤进晶体原子间隙中所需能量挤进晶体原子间隙中所需能量.33/7533Point Defects in Ionic CrystalsSelf interstitials and vacancies occur naturally in
24、 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 negativel
25、y 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.34/7534The Schottky defectPoint defects in an MX-type ionic crystal35
26、/7535The Frenkel defect.Point defects in an MX-type ionic crystal36/7536二、形成能大小二、形成能大小我们能够对我们能够对空位形成能空位形成能作一个简单预计：构想晶体为作一个简单预计：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（个键（FCC配位数为配位数为12），而在表面台阶处置放一个原子，），而在表面台阶处置放一个原子，要形成六个键。所以净效应为要形成六个键。所以净效应为割断六个键，应和晶体结合能割断六个键，应和晶体结合能（即升华能）相等（
27、即升华能）相等。这么预计显然是粗略，没有考虑到金属。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，特征，以及周围空位原子位移。更准确计算，表面空位形成表面空位形成能大约只为结合能能大约只为结合能1/2到到1/4。但空位结合能与形成能之间有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：亲密关系这一点是符合试验事实：结合能愈大，熔点愈高，结合能愈大，熔点愈高，则空位形成能也愈大。则空位形成能也愈大。37/7537二、形成能大小二、形成能大小理论计算试验测定38/7538二、形成能大小二、形成能大小试验测定能。能。39/7539试验测定试验测定40/754041
28、/7541试验测定42/7542VacanciesVacancies 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 EV is the energ
29、y of vacancy formation and kB is Boltzmanns constant.Applies to pairs also.43/7543DiffusionSimilary,the diffusion coefficient,D,is given by:where ED is the energy of diffusion and DO is a diffusion constant specific to the element.Strictly this applies only to self-diffusion,that is diffusion in an
30、elemental substance.44/7544QuenchingNon-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 incr
31、ease in resistance at low temperature after quenching from the temperature T.45/7545Usesso:y =c +mxEV can be obtained from a graph of lnR against(1/T)46/7546Example-Gold47/7547三、主要结论三、主要结论Q形形越大越大，形成点缺点越困难；形成点缺点越困难；Q间间隙隙比比Q空空位位大大3-4倍倍，所所以以常常见见点点缺缺点点是是空空位位；如如Cu：Q间隙间隙=4ev,Q空位空位=1ev c=Aexp(Qf/kT)在在Fcc结构
32、中结构中，哑铃组态能最低哑铃组态能最低，是最稳定组是最稳定组态态。48/75481.31.3点缺点热平衡浓度点缺点热平衡浓度一、点缺点形成一、点缺点形成二、二、点缺点是热力平衡缺点点缺点是热力平衡缺点 三、三、点缺点对物理性能影响点缺点对物理性能影响 四、四、点缺点产生、消除与检测点缺点产生、消除与检测 49/7549一、点缺点形成一、点缺点形成热激活造成热激活造成(能量彼此起伏能量彼此起伏)50/7550二、二、点缺点是热力学平衡缺点点缺点是热力学平衡缺点 It is well known that the criterion of chemical equilibrium is the m
33、inimization of the Gibbs free energy of the system at constant temperature and pressure.51/7551The 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 conce
34、ntration,Xv.From this relationship,the equilibrium vacancy concentration,Xve is shown to be that which results in the minimum free energy.52/7552Having looked at the general relationship between Xv and G,the module goes on to look in more detail at the underlying theory.The free energy term G is fir
35、st 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.53/7553Enthalpy of vacancy formation,HThis is the change in enthalpy resulting from the addition of vacancies an
36、d arises from the increase in internal energy caused by breaking interatomic bands(i.e.removing atoms).By making the reasonable assumption that the Xv is low,such that vacancy-vacancy interactions can be ignored,it is shown that H is proportional to Xv,according to the equation:(2)Hv is the molar en
37、thalpy of vacancy formation.54/755455/7555Entropy of vacancy formation,SThis 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 fur
38、ther detail.It is shown that thermal entropy can be given by:56/7556 (3)where Sv 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 ent
39、ropy as a function of vacancy concentration is derived:(4)57/755758/755859/7559C=Aexp(-E/kT)设设N个点阵位置晶体中有个点阵位置晶体中有n个空位时，其系统自由能改变为：个空位时，其系统自由能改变为：F FnE-TSnE-TS C=Aexp(-E/kT)60/7560C=Aexp(-E/kT)在在一一定定温温度度下下，有有一一定定热热力力学学平平衡衡浓浓度度(CT.)是点缺点区分于其它缺点主要特征是点缺点区分于其它缺点主要特征；影响影响C最主要原因最主要原因:Q与与T；结合能绝对值越大结合能绝对值越大，温度
40、越低温度越低，空位结合成空位结合成空位正确倾向愈加显著。空位正确倾向愈加显著。61/756162/7562三、三、点缺点对物理性能影响点缺点对物理性能影响 63/756364/7564四、四、点缺点产生、消除与检测点缺点产生、消除与检测 1.点缺点产生点缺点产生2.点缺点降低或消除点缺点降低或消除3.点缺点检测点缺点检测65/75651.点缺点产生点缺点产生淬火淬火：淬火时，高温下平衡空位来不及消除或扩散到表面，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，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
41、空位。成为空位过饱和状态，淬火产生过饱和空位。冷加工冷加工：T形变T再,金属中产生金属中产生（1）大量位错）大量位错（2）空位和间隙原子（后者易被位错俘获）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。所以冷加工主要产生为位错和空位。辐照辐照：会产生夫伦克耳对，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，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：金属材料发生一些特殊效应，如：电离引发发烧电离引发发烧；蜕变使单晶体沿某结晶学方向伸长或收缩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离位产生大量非
42、平衡点缺点。66/756667/75672.点缺点降低或消除点缺点降低或消除退火处理退火处理淬火后淬火后温度不温度不太低或太低或淬火后淬火后在稍高在稍高温度下温度下放置，放置，这时空这时空位还有位还有较大运较大运动能力，动能力，能够观能够观察到随察到随放置时放置时间延长，间延长，空位浓空位浓度逐步度逐步降低。降低。68/7568辐照回复辐照回复5个阶段个阶段：相邻空位与间隙原子结合：相邻空位与间隙原子结合夫伦克耳对湮灭夫伦克耳对湮灭R R附加附加：R R附加附加（间隙原子从陷井中脱出引发）（间隙原子从陷井中脱出引发）:间隙原子向空位扩散，但空位不一定是间隙原子向空位扩散，但空位不一定是夫伦克耳
43、对中空位夫伦克耳对中空位：单空位运动单空位运动：稀疏区及空位聚集体消失（材料力性完全恢复到辐照前）：稀疏区及空位聚集体消失（材料力性完全恢复到辐照前）69/75693.点缺点检测点缺点检测（1 1）点点缺缺点点产产生生附附加加电电阻阻大大小小与与点点缺缺点点浓浓度度正正比比。即即 R附加C点=Aexp(-Uf/kT)R附加可作为C点标志。测R附加T T关系。关系。（2）R附加T T曲线测量曲线测量 直接在各高温下测直接在各高温下测R样品淬火，保留过饱和空位，室温下测样品淬火，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场离子显微镜技术直接观察 表层中空位：直接观察表层中空位：直接观
44、察体内空位：低温蒸发，使表面层逐层脱去。体内空位：低温蒸发，使表面层逐层脱去。70/75701.41.4点缺点运动点缺点运动一、一、空位运动与鞍点组态空位运动与鞍点组态 二、二、间隙原子运动方式间隙原子运动方式 三、三、点缺点移动激活能点缺点移动激活能 71/7571一、一、空位运动与鞍点组态空位运动与鞍点组态 当当原原子子处处于于图图1-7中中C点点位位置置上上时时引引发发点点阵阵畸畸变变较较大大，因因而而能能量量较高，被称为较高，被称为鞍点组态鞍点组态。空位移动激活能空位移动激活能U Um m=E=E鞍点鞍点-E E正常组态正常组态72/7572二、二、间隙原子运动方式间隙原子运动方式 直
45、接式（主要）；直接式（主要）；间隙式；间隙式；对分式。对分式。73/7573三、三、点缺点移动激活能点缺点移动激活能U Um m 1.点缺点不是静止点缺点不是静止,而是在热激活作用下作无规则布朗运动而是在热激活作用下作无规则布朗运动：组成宏观扩散基础组成宏观扩散基础a.同类相遇同类相遇复合体复合体 b.异类相遇异类相遇互毁（即点缺点回复）互毁（即点缺点回复）点缺点在作不规则布朗运动时点缺点在作不规则布朗运动时,碰到了如自由表面、晶界、位碰到了如自由表面、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。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自扩散决定于空位浓度C C空空和空位跃迁频率和空位跃迁频率空空 U U点自扩散激活能点自扩散激活能=U U空位形成空位形成+U U空位移动空位移动 空位空位=AzAz0 0exp(-Uexp(-Um m/kT)/kT)A:1-10 A:1-10与移动激活熵与移动激活熵S Sm m相关相关;Z:Z:配位数配位数;0 0:原子振动频率原子振动频率;U Um m:空位移动激活能空位移动激活能74/7574点缺点移动激活能试验值点缺点移动激活能试验值75/7575
