结构不完整性

1、3.2. 缺陷化学基础缺陷化学基础 3.3. 本征缺陷本征缺陷 (热缺陷热缺陷) 3.4. 非本征缺陷（杂质缺陷）非本征缺陷（杂质缺陷）3.5. 固溶体固溶体3.6. 晶体中电子结构与缺陷晶体中电子结构与缺陷3.7. 线缺陷：位错线缺陷：位错l缺陷决定众多的固体物理和工程现象: 电子、离子电导、半导体现象、敏感现象、 机械性能、烧结、扩散、晶界现象l控制和消除缺陷 【缺陷分类【缺陷分类】偏离偏离理想理想晶体晶体0 0维维: : 点缺陷点缺陷1 1维维: : 线缺陷线缺陷2 2维维: :面缺陷面缺陷3 3维缺陷维缺陷原子缺陷原子缺陷电子缺陷电子缺陷: 能级跃迁能级跃迁本征缺陷本征缺陷: : 热缺

2、陷热缺陷非本征缺陷非本征缺陷: :杂质缺陷杂质缺陷( (固溶体固溶体) )非化学计量缺陷非化学计量缺陷韧形位错韧形位错固溶体固溶体多晶多晶(陶瓷陶瓷)非晶态非晶态表面界面表面界面晶界晶界表面表面纳米粉体纳米粉体纳米结构纳米结构螺旋位错螺旋位错晶粒晶粒主体符号: 原子离子: Al、Mg、 空位Vacancy: V 电子electron: e 孔穴hole: h位置符号: 晶格中原有的位置: 原有晶格为Al 原有晶格间位置: interstitial sites i 电荷符号: 带正电: , 带负电: 电中性: x 注意: 缺陷电荷为相对电荷reletive charge, 相对原有晶格而言正常晶

3、格: null or nil (非缺陷晶格) AlViMg【K-V符号符号】Kroger-Vinkern Notation主体主体电荷电荷位置位置AlMgl位置比例不变（但总量可变）：位置比例不变（但总量可变）：Al2O3: 2 : 3l电荷、质量平衡电荷、质量平衡l电荷、质量不变电荷、质量不变 例例: Al2O3 加入加入 MgOl浓度符号浓度符号: e n h p【缺陷反应式【缺陷反应式】Defect reaction equations? 完全由热运动所致, 在绝对零度以上, 任何晶体中都必然产生。对于一定的晶体，热缺陷的浓度是温度的单值函数。热缺陷的基本类型 Intrinsic poi

4、nt defectsVacancyFrenkelIntersticialcyDi-vacancySchottkySchottky 缺陷:l可能出现的其他情况TiO2(one titanium vacancy and two oxygen vacancies)Al2O3 (a quintuplet) l晶格数发生变化: BaTiO3Flenkel缺陷:晶格数不发生变化【热缺陷浓度】Concentration of Defect)2()2(kTHkTgeeNn总粒子数总粒子数缺陷数缺陷数讨论： 低温时：kT 缺陷浓度急剧升高, 对研究烧结、扩散、快离子导体有重要意义注意：此处是指平衡浓度平衡浓度生

5、成能生成能本征缺陷浓度与温度及生成能之间的关系本征缺陷浓度与温度及生成能之间的关系 对于一定的物质其热缺陷生成能为常数对于一定的物质其热缺陷生成能为常数, , 故缺陷故缺陷浓度单随温度的变化呈指数变化浓度单随温度的变化呈指数变化. .无法人为控制无法人为控制.l同价杂质同价杂质 Iso-solutes incorporation 特点特点: 无电荷变化无电荷变化 l异价杂质异价杂质 Aliovalent solutes 特点特点: 涉及涉及电价补偿3.4. 非本征缺陷非本征缺陷Extrinsic defects【杂质缺陷杂质缺陷】impurity defect注意注意两种不同的电价补偿机理:

6、l离子补偿l电子补偿上两种情况可由第三式表示内在关联上两种情况可由第三式表示内在关联:“宾宾” foreign“主主” host【氧化还原缺陷】2【非化学计量化合物】 Non-stoichiometric compound Defect structure of Fe1-xO: Nonstoichiometry【】ixOYOOrZSZrO 32)(22ioYOOrZSZrO 32)(22 263)(2YxoYVOZrSZrO密密度度Experiment shows that addition of ZrO2 to Y2O3 leads to formation of interstitial

7、anionsZrO2Y2O3重要的固体电解质材料重要的固体电解质材料复习复习CH4fcc lattice + 复习复习a1a2a1,a2 为该元晶格的为该元晶格的基矢基矢Rn为为格矢量格矢量Rn复习复习复习复习复习复习 = e i (k . r - t)i =-1 , r : 位矢位矢 position vectork: 波矢波矢,就是波数就是波数 （ k = 2） 波的一般表达式：波的一般表达式：复习复习二维二维WS胞及胞及Brillouin Zone补充补充aa2baa一维倒格子及一维倒格子及Brilloin 区正格子正格子倒格子倒格子Brilloin Zonekox复习复习复习复习复习复

8、习化学键复习复习金属金属特性金属特性: :自由电子在离子实自由电子在离子实(ion core)(ion core)之间之间几乎不受约束几乎不受约束自由电子气模型自由电子气模型: (1900: (1900年年) ) 电子完全自由电子完全自由, ,犹如理想气体分子犹如理想气体分子, ,被表面势场约束在金属内部被表面势场约束在金属内部. .电子的电子的能量是纯动能的能量是纯动能的. . “Electron gas in box”“Electron gas in box”离子实离子实复习复习自由电子气模型的说明自由电子气模型的说明:l该经典模型至今依然有效该经典模型至今依然有效l理论解释理论解释: 库

9、伦以外还有量子效应的附加排斥力库伦以外还有量子效应的附加排斥力VR, 所以净力很小所以净力很小 Vc + VR = Vpseudo 赝势赝势 存在如图势能与动能的关系存在如图势能与动能的关系 由于由于Pauli exclusive priciple: 每个电子有每个电子有11 的的“势力范围势力范围”，称为，称为Fermi Hole 复习复习电子所电子所“看到看到”的势场的势场电子速度电子速度晶体中离子实周围势场及电子速度变化关系晶体中离子实周围势场及电子速度变化关系复习复习EFEFT=0kT0kEE复习复习EFEFEFf(E)EFf(E)1/211)(/ )(kTEEFeEf费米能级与费米能

10、级与费费-狄分布狄分布的关系的关系Fermi-Dirac Distribution：T=0kT0k结论：结论：1. 费米能级处电子存在的几率为费米能级处电子存在的几率为1/2。 2. 费米能级不随温度改变。费米能级不随温度改变。EE复复习习温度对电子F-D分布的影响：高温时还原成玻耳兹曼经典分布复习复习The Brillouin zone and Fermi surface of copper复习复习)(2222222dzddyddxd)()()()4(2rErrVmhPlank 常数电子质量电子质量电子状态函数电子状态函数, 即波形即波形. :电子分布概率密度电子分布概率密度电子量子电子量子

11、化能量化能量电子所受电子所受势场势场2)(r复习复习)()()()4(2rErrVmh0)(rV对于晶体对于晶体: : 欲解欲解LLWhy?)()(nRrVrV重要推论重要推论:晶体中电子所受的势场V(r)具有与其晶格相同的周期.故, 晶体中的Rn?)()()()4(2rErRrVmhnabRn复习复习与晶格周期性相同的势场与晶格周期性相同的势场复习复习【】)()()()4(2rErRrVmhn)()(ruRru)()(ruerrk il当势场V(r)具有晶格周期性时, 波动方程的解具 有如下形式和性质:其中:u(r r)具有与晶格相同的周期,即:rk ie其中 为一平面波(正弦波)复习复习)

12、(ru)()(ruerrk irk ie无势场无势场晶格势场晶格势场复习复习复习复习内层电子的能级内层电子的能级保持不变保持不变价电子的能级价电子的能级变为能带变为能带复习复习一维周期性势场周期性势场内形成的住波Potential EnergyaIon coreProbability densityStanding wave 1Standing wave 2复习复习)()()()4(2rErRrVmhn/a/akkEgEnergyEnergy无势场时自由电子无势场时自由电子一维周期性势场一维周期性势场下形成能隙下形成能隙Eg解解 表明表明:晶格内会产生能隙晶格内会产生能隙. aThe stan

13、ding wave 2 piles up electrons around the positive ion cores, which means that the average potential energy will be lower than for a free traveling wave (constant probability density). The potential energy corresponding to standing wave 1 will have higher potential energy than a free traveling wave,

14、 since it piles up electrons between the ion cores (not compensated by positive ions). The energy difference between the standing waves is the origin to the energy gap Eg. The band diagram of Si, e.g., then assumes its standard form: 复习复习复习复习GaAs三维能带构造三维能带构造复习复习【电导与【电导与载流子浓度决定物质的电导特性载流子浓度决定物质的电导特性复习

15、复习【价带【导带【满带空带【禁带禁带的宽度，又称能隙能隙 band gap能带基本术语【金属、绝缘体、半导体能带结构比较金属金属价带未满，电子价带未满，电子无须跃过禁带可无须跃过禁带可直接参与电导。直接参与电导。价带价带导带导带Eg导带导带Eg导带导带价带价带价价带带绝缘体绝缘体价带满价带满, 禁带很禁带很宽宽,电子很难进入电子很难进入导带。导带。半导体半导体价带虽满价带虽满, 但禁但禁带带较窄较窄, 一部分电子一部分电子可以跳入导带可以跳入导带半导体能带宽度半导体能带宽度0.1-2eV【Fermi energy, or Fermi level, EF and its meaningEF费米能

16、级费米能级(EF)是晶体中电子能量高低的基本指示标尺, 晶体的能带结构与EF密不可分。研究的重点是EF附近的能带结构。远离费米能级的能带或能级无实际意义。EFEFT=0KT0K本征半导体能带结构本征半导体能带结构价带价带导带导带Eg禁带禁带【本征缺陷浓度本征缺陷浓度 =电子浓度电子浓度=空穴浓度空穴浓度 ni = ne = nh11)(/ )(kTEEFeEfEF纯锗是本征半导体纯锗是本征半导体, 其载流子浓度随其载流子浓度随温度指数变化温度指数变化典型的半导体材料禁带宽度典型的半导体材料禁带宽度n-type extrinsic semiconductors and the band mode

17、lP5价磷掺杂于价磷掺杂于4价硅中形成价硅中形成 施主能级施主能级, 产成产成n半导体半导体EFp-type extrinsic semiconductors and the band modelAlAl3价铝掺杂于价铝掺杂于4价硅中形成受主能级价硅中形成受主能级, 产成产成P半导体半导体 韧形位错 edge dislocation 螺旋位错 screw dislocation特点： 1. 非平衡缺陷 2. 位错单位均为一个格矢，即b (Burgers Vector)韧形位错 edge dislocationEdge dislocation (line defect)位错的移动：滑移螺旋位错

18、screw dislocationScrew dislocation (line defect)Dislocation formation by shear晶界示意晶界示意三维晶界：类似肥皂泡三维晶界：类似肥皂泡二维二维孪晶界孪晶界小角度晶界小角度晶界高分辨率点电镜：螺旋位错和小角度晶界高分辨率点电镜：螺旋位错和小角度晶界1HRTEM of Screw Dislocations in a Small Angle Grain Boundary Valence Electron Energy Loss Study of Fe doped SrTiO3 and a S13 Boundary: Ele

19、ctronic Structure and Dispersion Forces Fe 掺杂掺杂SrTiO3晶界及其电子结构（势垒）变化2The grains of this hypereutectoid iron-carbon alloy are packed in a similar way to the bubbles in the previous photographs. 1STEM micrographs of the LaAl - Si3N4 sample showing the four interfaces, a) IF 1 to IF 3 and b) IF 4 where

20、SR-VEEL spectrum images were acquired. 1 nm thick Yb-Si-O-N amorphous phase special grain boundary G. Drai and M. Komac, Analytical Electron Microscopy of the Grain Boundaries in Si3N4- Yb2O3 Ceramics, Electron Microscopy, Vol. 1 (Inter- disciplinary Developments and Tools), Edts. B. Jouffrey and C.

21、 Colliex, Les Editions de Physique, p. 685, 1994晶界相界：玻璃相晶界相界：玻璃相固相焼結結果。 複数固相含系焼結過程示。材料焼結幾多物質移動過程絡合複雑現象、様物質移動機構取込本手法、複雑組織形成過程表現可能。 晶界的形成：晶界的形成：计算机模拟的计算机模拟的固相烧结过程固相烧结过程液相焼結結果。 液相含系焼結時起組織形成過程示。液相固相濡性液相介物質移動、緻密化挙動焼結後粒成長挙動多大影響及。 晶界的形成：晶界的形成：计算机模拟的计算机模拟的液相烧结过程液相烧结过程三次元計算格子用複相組織 (固相+液相) 粒成長例。 (a)固相液相、(b)(a

22、)液相取除部分示。、実材料三次元的広複雑組織中、固相連続性持明確捉可能。 晶界的形成：晶界的形成：计算机模拟的计算机模拟的固、液相共存固、液相共存Application of lateral bias and in-situ imaging increases the range of possibilities provided by scanning probe microscopy tenfold. Shown below is surface topography and surface potential for grounded, forward and reverse biase

23、d ZnO varistor surface. Surface topography shows a number of pores and dust particles. Grain boundaries can be detected as small grooves due to preferential grain boundary polishing. Potential image of the grounded surface exhibits a number of potential depressions associated with second phase inclu

24、sions. Application of lateral bias results in the development of potential barriers at the grain boundaries due to the lower resistivity of grain boundary region compared to the grain bulk. Upon switching the lateral bias contrast inverts. Analysis of the grain boundary potential drop dependence on

25、external bias allows transport characteristics of grain boundary to be reconstructed. ZnO变阻器晶界：变阻器晶界： 晶界势垒随变压晶界势垒随变压变化情况变化情况【Tea Break】 de Broglie & Nobel Prizede Broglie1892: born in France 1910: graduated with an arts degree (majored in history)1914: World War I, serving in the army （at the Ei

26、ffel Tower）1920: resuming studying theoretical physics 1924: doctoral thesis on theory of matter waves 1929: awarded with Nobel prize Background1900: Planck “quantum”nhrpM2nhE hhp1905: Einstein “photon”1907: Bohr H atom structure1918 Noble Prize1921 Noble Prize1975 Noble PrizePlanck 常数常数n=1, 2, 3, 频

27、率电子角动量动量波尔量子化条件波尔量子化条件:电子只能在特定能级电子只能在特定能级问题：Why?rhHow de Broglie won Nobel Prize直觉一：Einstein光波光子（photon) 或许：原子中的电子 电子波？直觉二：如果电子是波，它在原子中必定是住波推导推导：是住波 2r = n 又 p = h / (Einstein) 2r = n h / p 得到r p = h/2 nnhrpM2Bohr的的量子化条件量子化条件!Nobel Prize 如此简单！如此简单！# de Broglie 的电子波理论使SchrdingerSchrdinger & de Br

28、oglie波动方程成为可能!住波住波 standing waveA standing wave results from the interference of two or more waves along the same medium. These positions standing still are called nodes. Nodes are the result of the meeting of a crest with a trough. Schrdinger & de Broglie From 1921 he studied atomic structure,

29、then in 1924 he began to study quantum statistics. Soon after this he read de Broglies thesis which became a turning point in the direction of his research and had a major influence on his thinking. On 3 November 1925 Schrdinger wrote to Einstein:- “A few days ago I read with great interest the inge

30、nious thesis of Louis de Broglie, which I finally got hold of. .” On 16 November, in another letter, Schrdinger wrote:- “I have been intensely concerned these days with Louis de Broglies ingenious theory. It is extraordinarily exciting, but still has some very grave difficulties.” One week later Sch

31、rdinger gave a seminar on de Broglies work and a member of the audience, a student of Sommerfelds, suggested that there should be a wave equation. Within a few weeks Schrdinger had found his wave equation. The work was indeed received with great acclaim. Planck described it as:- “. epoch-making work

32、.” 【Tea Break】 Measuring the circle of the earth with a stick about experiment 历史上十大著名实验1 Youngs double-slit experiment applied to the interference of single electrons 2 Galileos experiment on falling bodies (1600s) 3 Millikans oil-drop experiment (1910s) 4 Newtons decomposition of sunlight with a p

33、rism (1665-1666) 5 Youngs light-interference experiment (1801) 6 Cavendishs torsion-bar experiment (1798) 7 Eratosthenes measurement of the Earths circumference (3rd century BC) 8 Galileos experiments with rolling balls down inclined planes (1600s) 9 Rutherfords discovery of the nucleus (1911) 10 Fo

34、ucaults pendulum (1851) 米利肯（米利肯（Millikan）的电子电量测定实验装置的电子电量测定实验装置What Millikan did was to put a charge on a tiny drop of oil, and measure how strong an applied electric field had to be in order to stop the oil drop from falling. Since he was able to work out the mass of the oil drop, and he could calc

35、ulate the force of gravity on one drop, he could then determine the electric charge that the drop must have. By varying the charge on different drops, he noticed that the charge was always a multiple of -1.6 x 10 -19 C, the charge on a single electron. This meant that it was electrons carrying this

36、unit charge.xOiAlAlxOAlOxOAlOMgMgMgOVOMgMgOVOMgMgO3232333222 MgO-FeO完全固溶相图Al2O3-Cr2O3完全固溶相图A-B有限固溶相图BaTiO3-CaTiO3有限固溶相图a1a2a1,a2 为该元晶格的为该元晶格的基矢基矢Rn为格矢量为格矢量RnPhotoconduction effect (a) and Luminescence (b)(a)(b)Line Line & Tow-Dimension DefectsDislocations Linear defects (defined by Burgers vecto

37、r)Edge dislocation Crystal contains an extra half plane of atoms Burgers vector perpendicular to dislocation lineScrew dislocation Atoms of one side of crystal displaced with respect to atoms on other side in part of crystal Burgers vector parallel to dislocation lineMixed dislocation burgers vectors at arbitrary