衍射物理:John M. Cowley的权威教材

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"Diffraction Physics" 是一本由John M. Cowley编写的关于衍射物理的教材,特别针对透射电子显微镜(Transmission Electron Microscopy, TEM)领域。这本书经历了多次修订和再版,首次出版于1975年,最新的第三修订版发行于1995年。书中涵盖了衍射物理的基础理论、实验技术和应用,是理解TEM技术的重要参考书。 衍射物理是研究光、声波或物质波在遇到障碍物或通过孔径时,其波前发生弯曲、扩散和干涉现象的科学。在TEM中,这个原理被用来观察和分析微小尺度的材料结构,如原子级别的晶体结构。透射电子显微镜利用高能电子束代替光,通过透射和衍射来获取样品内部的详细图像。 John M. Cowley作为TEM领域的先驱者,他的著作深入浅出地介绍了衍射物理的各个方面。教材可能包括了以下知识点: 1. **电磁波的衍射与波动理论**:讲解电磁波的基本性质,包括波长、频率和波前的概念,以及衍射如何由波的干涉产生。 2. **电子光学基础**:解释电子的波动性,电子束的形成,以及电子在电磁场中的传播和聚焦。 3. **布拉格定律**:阐述如何根据晶体的晶格结构预测电子束的衍射模式,以及如何通过衍射图案解析晶体结构。 4. **TEM仪器与操作**:介绍TEM的基本构造,包括电子枪、透镜系统、探测器等,并讲解如何操作和调整显微镜参数。 5. **衍射图案分析**:讨论衍射图案的形成,解析衍射数据以获取材料的晶体学信息,如晶向、晶格参数和缺陷结构。 6. **高分辨TEM(HRTEM)**:介绍HRTEM技术,用于观察原子级别的细节,以及如何解释HRTEM图像。 7. **动力学衍射理论**:探讨电子在晶体中的动态行为,包括电子能量损失谱(EELS)和相位问题。 8. **实际应用**:展示TEM在材料科学、纳米科技、生物科学等领域中的应用实例。 9. **实验技巧与问题**:涵盖实验中可能遇到的问题,如样品制备、电子束损害、信噪比优化等解决方案。 10. **数学工具**:介绍处理衍射数据所需的数学方法,如傅立叶变换和四元数运算。 这本教材不仅适合TEM研究人员和学生,也是材料科学家、物理学家和工程师了解衍射物理和TEM技术的宝贵参考资料。它包含详尽的文献引用和索引,便于读者深入研究和查找相关资料。
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CONTENTS 1 MATHEMATICAL PRELIMINARIES 1.1 Invariants 1 1.2 Some geometrical invariants 2 1.3 Elements of differential geometry 5 1.4 Gaussian coordinates and the invariant line element 7 1.5 Geometry and groups 10 1.6 Vectors 13 1.7 Quaternions 13 1.8 3-vector analysis 16 1.9 Linear algebra and n-vectors 18 1.10 The geometry of vectors 21 1.11 Linear operators and matrices 24 1.12 Rotation operators 25 1.13 Components of a vector under coordinate rotations 27 2 KINEMATICS: THE GEOMETRY OF MOTION 2.1 Velocity and acceleration 33 2.2 Differential equations of kinematics 36 2.3 Velocity in Cartesian and polar coordinates 39 2.4 Acceleration in Cartesian and polar coordinates 41 3 CLASSICAL AND SPECIAL RELATIVITY 3.1 The Galilean transformation 46 3.2 Einstein’s space-time symmetry: the Lorentz transformation 48 3.3 The invariant interval: contravariant and covariant vectors 51 3.4 The group structure of Lorentz transformations 53 3.5 The rotation group 56 3.6 The relativity of simultaneity: time dilation and length contraction 57 3.7 The 4-velocity 61 4 NEWTONIAN DYNAMICS 4.1 The law of inertia 65 4.2 Newton’s laws of motion 67 4.3 Systems of many interacting particles: conservation of linear and angular vii momentum 68 4.4 Work and energy in Newtonian dynamics 74 4.5 Potential energy 76 4.6 Particle interactions 79 4.7 The motion of rigid bodies 84 4.8 Angular velocity and the instantaneous center of rotation 86 4.9 An application of the Newtonian method 88 5 INVARIANCE PRINCIPLES AND CONSERVATION LAWS 5.1 Invariance of the potential under translations and the conservation of linear momentum 94 5.2 Invariance of the potential under rotations and the conservation of angular momentum 94 6 EINSTEINIAN DYNAMICS 6.1 4-momentum and the energy-momentum invariant 97 6.2 The relativistic Doppler shift 98 6.3 Relativistic collisions and the conservation of 4- momentum 99 6.4 Relativistic inelastic collisions 102 6.5 The Mandelstam variables 103 6.6 Positron-electron annihilation-in-flight 106 7 NEWTONIAN GRAVITATION 7.1 Properties of motion along curved paths in the plane 111 7.2 An overview of Newtonian gravitation 113 7.3 Gravitation: an example of a central force 118 7.4 Motion under a central force and the conservation of angular momentum 120 7.5 Kepler’s 2nd law explained 120 7.6 Central orbits 121 7.7 Bound and unbound orbits 126 7.8 The concept of the gravitational field 128 7.9 The gravitational potential 131 8 EINSTEINIAN GRAVITATION: AN INTRODUCTION TO GENERAL RELATIVITY 8.1 The principle of equivalence 136 8.2 Time and length changes in a gravitational field 138 8.3 The Schwarzschild line element 138 8.4 The metric in the presence of matter 141 8.5 The weak field approximation 142 viii 8.6 The refractive index of space-time in the presence of mass 143 8.7 The deflection of light grazing the sun 144 9 AN INTRODUCTION TO THE CALCULUS OF VARIATIONS 9.1 The Euler equation 149 9.2 The Lagrange equations 151 9.3 The Hamilton equations 153 10 CONSERVATION LAWS, AGAIN 10.1 The conservation of mechanical energy 158 10.2 The conservation of linear and angular momentum 158 11 CHAOS 11.1 The general motion of a damped, driven pendulum 161 11.2 The numerical solution of differential equations 163 12 WAVE MOTION 12.1 The basic form of a wave 167 12.2 The general wave equation 170 12.3 The Lorentz invariant phase of a wave and the relativistic Doppler shift 171 12.4 Plane harmonic waves 173 12.5 Spherical waves 174 12.6 The superposition of harmonic waves 176 12.7 Standing waves 177 13 ORTHOGONAL FUNCTIONS AND FOURIER SERIES 13.1 Definitions 179 13.2 Some trigonometric identities and their Fourier series 180 13.3 Determination of the Fourier coefficients of a function 182 13.4 The Fourier series of a periodic saw-tooth waveform 183 APPENDIX A SOLVING ORDINARY DIFFERENTIAL EQUATIONS 187 BIBLIOGRAPHY 198