Physics, Optics, and Spectroscopy of Materials

ISBN-13: 9781119768739 / Angielski / Twarda / 2022 / 544 str.

Zeev Burshtein

Spis treści

Introduction XIII1 Electromagnetic Radiation/Matter Interaction - A Classical Approach 11.1 Electromagnetic Radiation by Atoms and Molecules 11.2 Spectral Line Widths 51.2.1 Natural Width 51.2.2 Doppler Broadening 71.2.3 Additional Broadening Mechanisms 91.3 Electromagnetic Radiation Absorption by Atoms and Molecules 101.4 Radiation Scattering by Atoms and Molecules 141.5 Reminder: Multipole Moments Expansion 18Exercises for Chapter 1 202 Electromagnetic Radiation/Matter Interaction - A Semi-Quantum Approach 212.1 A Reminder of Perturbation Theory 212.1.1 Static Perturbation Theory 212.1.2 Time-Dependent Perturbation Theory 232.2 A Reminder of Planck's Black-Body Radiation 262.3 An Atom or Molecule in an Electromagnetic Radiation Field 282.4 Stimulated Emission and Einstein's Coefficients 302.5 Radiation Absorption and Amplification in Matter 322.6 Black Body Radiation - Continuation and Completion 36Exercises for Chapter 2 393 The Hydrogen Atom - Electrostatic Attraction Approximation 413.1 De Broglie Waves and Schrödinger's Equation 413.2 Differential Operators and Physical Quantities 443.3 Schrödinger Equation Solution for Hydrogen and Hydrogen-Like Atoms 453.4 Physical Meanings of Schrödinger Equation Solutions for Hydrogen-Like Atoms 553.5 Spectroscopy of Hydrogen and Hydrogen-Like Atoms 603.6 Selection Rules 61Exercises for Chapter 3 644 Hydrogen Atom - Corrections to the Electrostatic Attraction Approximation 674.1 Angular Momentum and the Orbital Quantum Number 674.2 Mechanical Relativistic Correction to the Eigenenergies of the Hydrogen Atom 714.3 Electron Spinning 724.3.1 Infinitesimal Rotations and the Angular Momentum Operator 734.3.2 Generalization of the Angular Momentum Concept 754.3.2.1 Basis Functions Properties 754.3.2.2 Eigenvalues of the J 2 Operator 764.3.2.3 Matrix Elements of Angular Momentum Operators 774.3.2.4 Electron Spin 774.4 Combining Orbital Angular Momentum and Spin 804.5 Gyromagnetic Ratio and Spin/Orbit Coupling 824.5.1 The Gyromagnetic Ratio 824.5.2 Spin/Orbit Interaction 834.5.2.1 Electric Dipole of a Moving Magnetic Dipole 834.5.2.2 Thomas Precession 844.5.2.3 Total Spin/Orbit Coupling 854.5.3 Summed Energy Spectrum Correction 854.6 Landé Factor 864.7 Lamb Shift 874.8 Selection Rules and Transition Probabilities 914.9 Static External Magnetic and Electric Fields: Zeeman and Stark Effects 954.9.1 Zeeman Splitting 954.9.1.1 Weak Magnetic Field 954.9.1.2 Strong Magnetic Field 974.9.2 Stark Splitting 984.9.2.1 Ground State; First-Order Perturbation Theory 984.9.2.2 Ground State; Second-Order Perturbation Theory 984.9.2.3 First Excited State; First-Order Perturbation Theory 1014.10 The Fine Structure 1034.10.1 Isotope Shifting 1034.10.2 Nuclear Magnetic Shifting 1044.10.3 Nuclear Quadrupole Shifting 1044.11 Appendix: Clebsch-Gordan Coefficients for Coupling of Two Angular Momentums 104Exercises for Chapter 4 1045 Many-Electron Atoms 1075.1 Preamble 1075.2 Helium-Like Atoms 1075.2.1 Zero-Order Approximation under the Independent Electron Model 1085.2.2 First-Order Correction and the Effective Screening Idea 1095.2.3 Exchange Symmetry 1115.2.4 Helium Energy Level Scheme 1145.3 Bosons, Fermions, and Pauli Exclusion Principle 1155.3.1 Harmonic Oscillator 1155.3.1.1 Hamiltonian and Creation and Destruction Operators 1155.3.1.2 Energy Levels Scheme of the Harmonic Oscillator 1175.3.1.3 Eigenfunctions of the Harmonic Oscillator 1175.3.1.4 Bosons 1195.3.2 Angular Momentum 1195.3.2.1 Annihilation, Creation, and Occupation Operators 1195.3.2.2 Pauli Exclusion Principle 1215.4 Electronic Structure of Many-Electron Atoms 1225.4.1 Slater Determinant 1225.4.2 Electron Configuration and the Shell Structure 1225.4.3 Electronic Configuration and Chemical Stability 1245.4.4 Spin/Orbit Coupling and Term Determination 1255.5 Excited-States Structure in Many-Electron Atoms 1335.5.1 States Structure of Single Valence Atoms 1335.5.2 States Structure of Two-Valence Atoms 1355.5.3 Classical Approximations 138Exercises for Chapter 5 1396 Electron Orbits in Molecules 1416.1 Preamble 1416.2 The Hydrogen Molecule Ion 1426.2.1 The Hamiltonian of the Hydrogen Molecule Ion 1426.2.2 A Qualitative Approach to Solution Using a Linear Combination of Atomic Orbitals 1436.2.3 Energy States Calculation by LCAO Method 1456.2.4 Improvements in the LCAO Method 1496.2.5 Optical Transition Probabilities 1496.3 Molecular Electronic Angular Momentum 1506.3.1 Eigenfunctions of L 2 and L 2 Z in a Lone Atom 1506.3.2 Orbital Angular Momentum of an Independent Electron in a Molecule 1526.3.3 Electronic Spin in a Diatomic Molecule 1536.4 Many-Electron Homonuclear Diatomic Molecules 1536.5 Many-Electron Heteronuclear Diatomic Molecules 1586.6 Multiatomic Molecules 1606.6.1 Nonconjugated Molecules 1616.6.2 Conjugated Molecules 1666.7 Appendix: Calculation of an Infinitesimal Volume Element in Elliptic Coordinates 170Exercises for Chapter 6 1727 Molecular (Especially Diatomic) Internal Oscillations 1737.1 Preamble 1737.2 The Born-Oppenheimer Approximation 1737.3 Vibrational and Rotational Modes of Diatomic Molecules 1767.3.1 Empiric Analytic Potential 1767.3.2 Molecular Vibrational Modes 1777.3.3 Molecular Rotational Modes 1787.3.4 Molecular Vibrational/Rotational Modes 1807.3.5 Transition Probabilities and Selection Rules 1827.4 Vibrational/Rotational Absorption Spectra 1857.4.1 Pure Rotational Transitions 1857.4.2 Temperature Dependence of Pure Rotational Transitions 1857.4.3 Mixed Vibration/Rotation Transitions 1887.5 Electronic Transitions and the Franck-Condon Principle 1897.5.1 General Considerations 1897.5.2 Selection Rules for Electronic Transitions 1907.5.3 Temperature Dependence of the Electronic Transitions Spectrum 1927.5.4 The Franck-Condon Principle 1937.5.5 Fluorescence and Stokes-Shift 1957.5.6 Selection Rules for Electronic Transitions Including Vibrations and Rotations 197Exercises for Chapter 7 1998 Internal Oscillations of Polyatomic Molecules 2018.1 Preamble 2018.2 Zero-Order Mechanical Energy Approximation of a Polyatomic Molecule 2018.3 Molecular Vibrational Modes 2048.4 Vibrational Energy Scheme 2078.5 Rayleigh and Raman Scattering 2078.5.1 General Rayleigh Scattering by Molecules 2078.5.2 Raman Scattering 2128.6 Point Symmetry 2158.7 Group Representations, Characters, and Reduction Equation 2208.8 Similarity Classes, Irreducible Representations, and Character Tables 2218.9 Selection Rules for Electric Dipole Absorption and Raman Scattering 2238.10 Method for Calculation and Description of Molecular Vibrational Species 2258.11 Examples of Molecular Vibrational Symmetry Species 2278.11.1 The Ammonia NH 3 Molecule 2278.11.2 The Ethylene C 2 H 4 Molecule 2288.11.3 The Carbon Tetrachloride CCl 4 Molecule 2308.12 Point Groups, Character Tables, and Selection Rules 2328.12.1 The C p group 232Exercises for Chapter 8 2419 Crystalline Solids 2459.1 Preamble 2459.2 Periodic Crystals 2459.3 Lattice-Vector and Lattice-Plane Orientations 2519.4 The Reciprocal Lattice 2519.5 Internal Crystalline Oscillations 2529.5.1 Introduction 2529.5.2 Hamiltonian and Dynamic Equations 2539.5.3 Allowed Wave-Number States and Their Density 2559.5.4 Dispersion Curves 2579.5.4.1 Acoustic Modes 2599.5.4.2 Optical Oscillation Modes 2649.5.5 Theoretical Dispersion Curve Calculations - A Basic Approach 2729.5.6 Dispersion Curves and Specific Heats 2739.6 Appendix: Intermediate Calculation for Justifying Eq. (9.11) 274Exercises for Chapter 9 27510 Dielectric Crystalline Solids 27710.1 Light Propagation in a Dielectric Medium 27710.2 Light Transition from Vacuum into a Dielectric Medium 28310.3 Kramers-Kronig Relations 28610.4 A Microscopic Model of the Dielectric Function 28910.5 A Reminder: Gradient, Divergence, Rotor, and the Cauchy Equation 29710.5.1 Gradient, Divergence, and Rotor 29710.5.2 Cauchy's Equation 298Exercises for Chapter 10 29911 Crystalline Oscillation Species 30111.1 Introduction 30111.2 Crystalline Sites 30111.3 Tabulation Method 30211.4 Calculation of Crystalline Oscillation Species - An Example 30511.5 Tabulation of Crystalline Space Group Properties 310Exercises for Chapter 11 34612 Atoms and Ions in Crystalline Sites 34712.1 Introduction 34712.2 Energy States of Alkali and Alkali-Like Atoms 34712.3 Energy States of Many-Electron Atoms and Ions 34912.4 Dopant Atoms or Ions in Crystalline Sites 36212.4.1 The Full Rotation Group and its Representations 36312.4.2 A Hydrogen-Like Atom in a Crystalline Perturbation Field 36612.4.3 Example: States Splitting in a Cubic Perturbation Field 36812.4.4 Tanabe-Sugano Diagrams 37312.5 Transition Probabilities and Selection Rules 37412.6 Spectroscopic Examples 37512.7 Appendix: An Integral Over Three Multiplied Spherical Harmonics 378Exercises for Chapter 12 37913 Non-Radiative and Mixed Decay Transitions 38113.1 Non-Radiative Transitions Between Close Electronic States 38113.1.1 Debye Approximation of Phonon Dispersion Curves 38113.1.2 Non-Radiative Transitions Between Very Close Electronic States 38213.1.3 Non-Radiative Transitions Between Close Electronic States 38613.2 Radiative Transition Lifetime and Optical Absorption and Emission Spectra 38913.3 Multi-Phonon Non-Radiative Transitions 39513.3.1 Principles and Methods in Experimental Measurement of Non-Radiative Lifetimes 39513.3.2 Theoretical Calculation of the Non-Radiative Lifetime 396Exercises for Chapter 13 40614 Basic Acquaintance with the Laser and Its Components 40714.1 General Description 40714.2 The Optical Cavity 40814.3 The Prism 40914.3.1 A Prism Minimum Deviation Arrangement 41014.3.2 Light Dispersion in a Prism 41214.3.3 Prism Wavelength Resolution 41214.4 Reflection Grating 41414.4.1 Light Diffraction Off a Reflection Grating 41414.4.2 Wavelength Resolution of a Reflection Grating 41614.5 Fabry-Pérot Etalon 41714.5.1 General Description and Fundamental Terms 41714.5.2 The Etalon as an Optical Filter 41914.5.3 The Etalon as a Spectrometer 42114.5.3.1 A Solid Etalon 42114.5.3.2 A Scanning Etalon 42214.5.4 Etalon Transmission of Incoherent Light 42314.6 Brewster Window and a Brewster Plate 42314.6.1 Snell's Law and Fresnel Equations 42314.6.2 Achieving Polarized Laser Emission 42814.7 Loss Presentation in a Laser Cavity 429Exercises for Chapter 14 43015 Transverse Optical Modes and Crystal Optics 43115.1 Preamble 43115.2 Transverse Single-Mode Gaussian Beam 43215.3 Transverse Multi-Mode Beams 43515.4 Selecting a Transverse Mode for a Laser Output 43715.5 Lens Crossing of a Single-Mode Transverse Gaussian Beam 43715.6 Multi-Mode Transverse Gaussian Beams 43915.7 Crystal Optics 44015.7.1 General Description 44015.7.2 Uniaxial Crystals 44115.7.3 Walk-Off 44215.8 Retardation Plates 443Exercises for Chapter 15 44516 Pulsed High Power Lasers 44716.1 Introduction 44716.2 Passive Q-Switching Using a Saturable Light Absorber 44716.2.1 Saturable Absorbers 44716.2.1.1 Slow Saturable Absorber 44916.2.1.2 Fast Saturable Absorber 45016.2.1.3 Examples 45116.2.2 Q-Switching Using a Saturable Absorber 45516.3 Active Q-Switching Using Electrooptic Crystals 45616.3.1 The Electrooptic Effect 45616.3.2 Q-Switching Using an Electrooptic Crystal 46116.4 Mode-Locking 462Exercises for Chapter 16 46617 Frequency Conversions of Laser Beams 46917.1 Non-Linear Crystals 46917.2 Electromagnetic Wave Propagation in a Non-Linear Crystal 47517.2.1 Maxwell's Equations 47517.2.2 Overlapping Beams of Different Frequencies Propagating in the Same Direction 47617.2.3 Frequency Doubling 47717.3 Optical Parametric Oscillations 48317.3.1 Forced Parametric Oscillations 48317.3.2 Optical Parametric Amplification 48517.3.3 Optical Parametric Oscillations Based Laser 48817.4 A Reminder: Hyperbolic "Trigonometric" Functions 490Exercises for Chapter 7 49018 Examples of Various Laser Systems 49318.1 Introduction 49318.2 Helium-Neon Laser 49318.3 Copper Vapor Laser 49618.4 Hydrogen Fluoride Chemical Laser 49918.5 Neodymium-YAG Laser 50318.6 Dye Lasers 50618.7 Diode Lasers 510Exercises for Chapter 18 515Appendix A Greek alphabet and phonetic names 517Appendix B Table of physical constants 519Appendix C Dirac delta function 521Appendix D Literature references for further reading 523Index 525

O autorze

Zeev Burshtein, Ph.D., is a retiree of the Nuclear Research Center, Negev (NRCN). He currently teaches and instructs graduate and Ph.D. students in the Materials Engineering department, Ben-Gurion University, Be'er Sheva, Israel. He served as chief advisor of the Israeli Minister of Science and Technology, has authored and co-authored 90 papers in the areas covered by this book, over 30 proprietary scientific and technical reports of the NRCN, and (along with others) registered 7 patents in the field of x-ray technology.