Philip Hofmann studied physics at the Free University, Berlin and did his PhD research at the Fritz-Haber-Institute of the Max Planck Society, also in Berlin. He stayed at the Oak Ridge National Laboratory, USA, as a Feodor Lynen Fellow of the Alexander von Humboldt Foundation. In 1998, he moved to Aarhus University, Denmark, where he is a professor at the Department of Physics and Astronomy.

• Preface to the First Edition xiPreface to the Second Edition xiiiPreface to the Third Edition xvPhysical Constants and Energy Equivalents xvii1 Crystal Structures 11.1 General Description of Crystal Structures 21.2 Some Important Crystal Structures 31.2.1 Cubic Structures 41.2.2 Close-Packed Structures 51.2.3 Structures of Covalently Bonded Solids 61.3 Crystal Structure Determination 71.3.1 X-Ray Diffraction 71.3.1.1 Bragg Theory 71.3.1.2 Lattice Planes and Miller Indices 81.3.1.3 General Diffraction Theory 91.3.1.4 The Reciprocal Lattice 111.3.1.5 The Meaning of the Reciprocal Lattice 121.3.1.6 X-Ray Diffraction from Periodic Structures 141.3.1.7 The Ewald Construction 151.3.1.8 Relation Between Bragg and Laue Theory 161.3.2 Other Methods for Structure Determination 171.3.3 Inelastic Scattering 171.4 Further Reading 171.5 Discussion and Problems 18Discussion 18Basic Concepts 18Problems 202 Bonding in Solids 232.1 Attractive and Repulsive Forces 232.2 Ionic Bonding 242.3 Covalent Bonding 252.4 Metallic Bonding 322.5 Hydrogen Bonding 332.6 Van der Waals Bonding 332.7 Further Reading 342.8 Discussion and Problems 34Discussion 34Basic Concepts 35Problems 353 Mechanical Properties 373.1 Elastic Deformation 393.1.1 Macroscopic Picture 393.1.1.1 Elastic Constants 393.1.1.2 Poisson’s Ratio 403.1.1.3 Relation Between Elastic Constants 403.1.2 Microscopic Picture 413.2 Plastic Deformation 433.2.1 Estimate of the Yield Stress 433.2.2 Point Defects and Dislocations 453.2.3 The Role of Defects in Plastic Deformation 453.3 Fracture 473.4 Further Reading 483.5 Discussion and Problems 48Discussion 48Basic Concepts 49Problems 494 Thermal Properties of the Lattice 514.1 Lattice Vibrations 514.1.1 A Simple Harmonic Oscillator 514.1.2 An Infinite Chain of Atoms 524.1.2.1 One Atom Per Unit Cell 524.1.2.2 The First Brillouin Zone 554.1.2.3 Two Atoms per Unit Cell 564.1.3 A Finite Chain of Atoms 584.1.4 Quantized Vibrations, Phonons 594.1.5 Three-Dimensional Solids 614.1.5.1 Generalization to Three Dimensions 614.1.5.2 Estimate of the Vibrational Frequencies from the Elastic Constants 634.2 Heat Capacity of the Lattice 644.2.1 Classical Theory and Experimental Results 654.2.2 Einstein Model 664.2.3 Debye Model 684.3 Thermal Conductivity 714.4 Thermal Expansion 744.5 Allotropic Phase Transitions and Melting 75References 784.6 Further Reading 784.7 Discussion and Problems 78Discussion 78Basic Concepts 79Problems 815 Electronic Properties of Metals: Classical Approach 855.1 Basic Assumptions of the Drude Model 855.2 Results from the Drude Model 875.2.1 dc Electrical Conductivity 875.2.2 Hall Effect 895.2.3 Optical Reflectivity of Metals 905.2.4 The Wiedemann–Franz Law 935.3 Shortcomings of the Drude Model 935.4 Further Reading 945.5 Discussion and Problems 95Discussion 95Basic Concepts 95Problems 966 Electronic Properties of Solids: Quantum Mechanical Approach 996.1 The Idea of Energy Bands 1006.2 The Free Electron Model 1036.2.1 The Quantum-Mechanical Eigenstates 1036.2.2 Electronic Heat Capacity 1076.2.3 The Wiedemann–Franz Law 1086.2.4 Screening 1086.3 The General Form of the Electronic States 1116.4 Nearly-Free Electron Model: Band Formation 1146.5 Tight-binding Model 1196.6 Energy Bands in Real Solids 1246.7 Transport Properties 1306.8 Brief Review of Some Key Ideas 134References 1356.9 Further Reading 1356.10 Discussion and Problems 136Discussion 136Basic Concepts 137Problems 1407 Semiconductors 1457.1 Intrinsic Semiconductors 1467.1.1 Temperature Dependence of the Carrier Density 1487.2 Doped Semiconductors 1537.2.1 n and p Doping 1537.2.2 Carrier Density 1557.3 Conductivity of Semiconductors 1577.4 Semiconductor Devices 1587.4.1 The pn Junction 1587.4.2 Transistors 1637.4.3 Optoelectronic Devices 1657.5 Further Reading 1687.6 Discussion and Problems 169Discussion 169Basic Concepts 170Problems 1728 Magnetism 1758.1 Macroscopic Description 1758.2 Quantum-Mechanical Description of Magnetism 1778.3 Paramagnetism and Diamagnetism in Atoms 1798.4 Weak Magnetism in Solids 1828.4.1 Diamagnetic Contributions 1838.4.1.1 Contribution from the Atoms 1838.4.1.2 Contribution from the Free Electrons 1838.4.2 Paramagnetic Contributions 1838.4.2.1 Curie Paramagnetism 1848.4.2.2 Pauli Paramagnetism 1858.5 Magnetic Ordering 1878.5.1 Magnetic Ordering and the Exchange Interaction 1878.5.2 Magnetic Ordering for Localized Spins 1898.5.3 Magnetic Ordering in a Band Picture 1938.5.4 Ferromagnetic Domains 1958.5.5 Hysteresis 196Reference 1988.6 Further Reading 1988.7 Discussion and Problems 199Discussion 199Basic Concepts 200Problems 2019 Dielectrics 2039.1 Macroscopic Description 2039.2 Microscopic Polarization 2059.3 The Local Field 2079.4 Frequency Dependence of the Dielectric Constant 2089.4.1 Excitation of Lattice Vibrations 2089.4.2 Electronic Transitions 2129.5 Other Effects 2139.5.1 Impurities in Dielectrics 2139.5.2 Ferroelectricity 2149.5.3 Piezoelectricity 2159.5.4 Dielectric Breakdown 2169.6 Further Reading 2169.7 Discussion and Problems 216Discussion 216Basic Concepts 217Problems 21810 Superconductivity 22110.1 Basic Experimental Facts 22210.1.1 Zero Resistivity 22210.1.2 The Meissner Effect 22510.1.3 The Isotope Effect 22710.2 Some Theoretical Aspects 22710.2.1 Phenomenological Theory 22710.2.2 Microscopic BCS Theory 23010.3 Experimental Detection of the Gap 23610.4 Coherence of the Superconducting State 23810.5 Type-I and Type-II Superconductors 23910.6 High-Temperature Superconductivity 24210.7 Concluding Remarks 243References 24410.8 Further Reading 24410.9 Discussion and Problems 244Discussion 244Basic Concepts 245Problems 24611 Finite Solids and Nanostructures 24911.1 Quantum Confinement 25011.2 Surfaces and Interfaces 25211.3 Magnetism on the Nanoscale 25511.4 Further Reading 25611.5 Discussion and Problems 257Discussion 257Basic Concepts 257Problems 257Appendix A 259A.1 Explicit Forms of Vector Operations 259A.2 Differential Form of the Maxwell Equations 260A.3 Maxwell Equations in Matter 261Appendix B 263B.1 Solutions to Basic Concepts Questions 263Index 265

Philip Hofmann studied physics at the Free University, Berlin and did his PhD research at the Fritz-Haber-Institute of the Max Planck Society, also in Berlin. He stayed at the Oak Ridge National Laboratory, USA, as a Feodor Lynen Fellow of the Alexander von Humboldt Foundation. In 1998, he moved to Aarhus University, Denmark, where he is a professor at the Department of Physics and Astronomy.

• Preface to the First Edition xiPreface to the Second Edition xiiiPreface to the Third Edition xvPhysical Constants and Energy Equivalents xvii1 Crystal Structures 11.1 General Description of Crystal Structures 21.2 Some Important Crystal Structures 31.2.1 Cubic Structures 41.2.2 Close-Packed Structures 51.2.3 Structures of Covalently Bonded Solids 61.3 Crystal Structure Determination 71.3.1 X-Ray Diffraction 71.3.1.1 Bragg Theory 71.3.1.2 Lattice Planes and Miller Indices 81.3.1.3 General Diffraction Theory 91.3.1.4 The Reciprocal Lattice 111.3.1.5 The Meaning of the Reciprocal Lattice 121.3.1.6 X-Ray Diffraction from Periodic Structures 141.3.1.7 The Ewald Construction 151.3.1.8 Relation Between Bragg and Laue Theory 161.3.2 Other Methods for Structure Determination 171.3.3 Inelastic Scattering 171.4 Further Reading 171.5 Discussion and Problems 18Discussion 18Basic Concepts 18Problems 202 Bonding in Solids 232.1 Attractive and Repulsive Forces 232.2 Ionic Bonding 242.3 Covalent Bonding 252.4 Metallic Bonding 322.5 Hydrogen Bonding 332.6 Van der Waals Bonding 332.7 Further Reading 342.8 Discussion and Problems 34Discussion 34Basic Concepts 35Problems 353 Mechanical Properties 373.1 Elastic Deformation 393.1.1 Macroscopic Picture 393.1.1.1 Elastic Constants 393.1.1.2 Poisson’s Ratio 403.1.1.3 Relation Between Elastic Constants 403.1.2 Microscopic Picture 413.2 Plastic Deformation 433.2.1 Estimate of the Yield Stress 433.2.2 Point Defects and Dislocations 453.2.3 The Role of Defects in Plastic Deformation 453.3 Fracture 473.4 Further Reading 483.5 Discussion and Problems 48Discussion 48Basic Concepts 49Problems 494 Thermal Properties of the Lattice 514.1 Lattice Vibrations 514.1.1 A Simple Harmonic Oscillator 514.1.2 An Infinite Chain of Atoms 524.1.2.1 One Atom Per Unit Cell 524.1.2.2 The First Brillouin Zone 554.1.2.3 Two Atoms per Unit Cell 564.1.3 A Finite Chain of Atoms 584.1.4 Quantized Vibrations, Phonons 594.1.5 Three-Dimensional Solids 614.1.5.1 Generalization to Three Dimensions 614.1.5.2 Estimate of the Vibrational Frequencies from the Elastic Constants 634.2 Heat Capacity of the Lattice 644.2.1 Classical Theory and Experimental Results 654.2.2 Einstein Model 664.2.3 Debye Model 684.3 Thermal Conductivity 714.4 Thermal Expansion 744.5 Allotropic Phase Transitions and Melting 75References 784.6 Further Reading 784.7 Discussion and Problems 78Discussion 78Basic Concepts 79Problems 815 Electronic Properties of Metals: Classical Approach 855.1 Basic Assumptions of the Drude Model 855.2 Results from the Drude Model 875.2.1 dc Electrical Conductivity 875.2.2 Hall Effect 895.2.3 Optical Reflectivity of Metals 905.2.4 The Wiedemann–Franz Law 935.3 Shortcomings of the Drude Model 935.4 Further Reading 945.5 Discussion and Problems 95Discussion 95Basic Concepts 95Problems 966 Electronic Properties of Solids: Quantum Mechanical Approach 996.1 The Idea of Energy Bands 1006.2 The Free Electron Model 1036.2.1 The Quantum-Mechanical Eigenstates 1036.2.2 Electronic Heat Capacity 1076.2.3 The Wiedemann–Franz Law 1086.2.4 Screening 1086.3 The General Form of the Electronic States 1116.4 Nearly-Free Electron Model: Band Formation 1146.5 Tight-binding Model 1196.6 Energy Bands in Real Solids 1246.7 Transport Properties 1306.8 Brief Review of Some Key Ideas 134References 1356.9 Further Reading 1356.10 Discussion and Problems 136Discussion 136Basic Concepts 137Problems 1407 Semiconductors 1457.1 Intrinsic Semiconductors 1467.1.1 Temperature Dependence of the Carrier Density 1487.2 Doped Semiconductors 1537.2.1 n and p Doping 1537.2.2 Carrier Density 1557.3 Conductivity of Semiconductors 1577.4 Semiconductor Devices 1587.4.1 The pn Junction 1587.4.2 Transistors 1637.4.3 Optoelectronic Devices 1657.5 Further Reading 1687.6 Discussion and Problems 169Discussion 169Basic Concepts 170Problems 1728 Magnetism 1758.1 Macroscopic Description 1758.2 Quantum-Mechanical Description of Magnetism 1778.3 Paramagnetism and Diamagnetism in Atoms 1798.4 Weak Magnetism in Solids 1828.4.1 Diamagnetic Contributions 1838.4.1.1 Contribution from the Atoms 1838.4.1.2 Contribution from the Free Electrons 1838.4.2 Paramagnetic Contributions 1838.4.2.1 Curie Paramagnetism 1848.4.2.2 Pauli Paramagnetism 1858.5 Magnetic Ordering 1878.5.1 Magnetic Ordering and the Exchange Interaction 1878.5.2 Magnetic Ordering for Localized Spins 1898.5.3 Magnetic Ordering in a Band Picture 1938.5.4 Ferromagnetic Domains 1958.5.5 Hysteresis 196Reference 1988.6 Further Reading 1988.7 Discussion and Problems 199Discussion 199Basic Concepts 200Problems 2019 Dielectrics 2039.1 Macroscopic Description 2039.2 Microscopic Polarization 2059.3 The Local Field 2079.4 Frequency Dependence of the Dielectric Constant 2089.4.1 Excitation of Lattice Vibrations 2089.4.2 Electronic Transitions 2129.5 Other Effects 2139.5.1 Impurities in Dielectrics 2139.5.2 Ferroelectricity 2149.5.3 Piezoelectricity 2159.5.4 Dielectric Breakdown 2169.6 Further Reading 2169.7 Discussion and Problems 216Discussion 216Basic Concepts 217Problems 21810 Superconductivity 22110.1 Basic Experimental Facts 22210.1.1 Zero Resistivity 22210.1.2 The Meissner Effect 22510.1.3 The Isotope Effect 22710.2 Some Theoretical Aspects 22710.2.1 Phenomenological Theory 22710.2.2 Microscopic BCS Theory 23010.3 Experimental Detection of the Gap 23610.4 Coherence of the Superconducting State 23810.5 Type-I and Type-II Superconductors 23910.6 High-Temperature Superconductivity 24210.7 Concluding Remarks 243References 24410.8 Further Reading 24410.9 Discussion and Problems 244Discussion 244Basic Concepts 245Problems 24611 Finite Solids and Nanostructures 24911.1 Quantum Confinement 25011.2 Surfaces and Interfaces 25211.3 Magnetism on the Nanoscale 25511.4 Further Reading 25611.5 Discussion and Problems 257Discussion 257Basic Concepts 257Problems 257Appendix A 259A.1 Explicit Forms of Vector Operations 259A.2 Differential Form of the Maxwell Equations 260A.3 Maxwell Equations in Matter 261Appendix B 263B.1 Solutions to Basic Concepts Questions 263Index 265

Philip Hofmann studied physics at the Free University, Berlin and did his PhD research at the Fritz-Haber-Institute of the Max Planck Society, also in Berlin. He stayed at the Oak Ridge National Laboratory, USA, as a Feodor Lynen Fellow of the Alexander von Humboldt Foundation. In 1998, he moved to Aarhus University, Denmark, where he is a professor at the Department of Physics and Astronomy.

• Preface to the First Edition xiPreface to the Second Edition xiiiPreface to the Third Edition xvPhysical Constants and Energy Equivalents xvii1 Crystal Structures 11.1 General Description of Crystal Structures 21.2 Some Important Crystal Structures 31.2.1 Cubic Structures 41.2.2 Close-Packed Structures 51.2.3 Structures of Covalently Bonded Solids 61.3 Crystal Structure Determination 71.3.1 X-Ray Diffraction 71.3.1.1 Bragg Theory 71.3.1.2 Lattice Planes and Miller Indices 81.3.1.3 General Diffraction Theory 91.3.1.4 The Reciprocal Lattice 111.3.1.5 The Meaning of the Reciprocal Lattice 121.3.1.6 X-Ray Diffraction from Periodic Structures 141.3.1.7 The Ewald Construction 151.3.1.8 Relation Between Bragg and Laue Theory 161.3.2 Other Methods for Structure Determination 171.3.3 Inelastic Scattering 171.4 Further Reading 171.5 Discussion and Problems 18Discussion 18Basic Concepts 18Problems 202 Bonding in Solids 232.1 Attractive and Repulsive Forces 232.2 Ionic Bonding 242.3 Covalent Bonding 252.4 Metallic Bonding 322.5 Hydrogen Bonding 332.6 Van der Waals Bonding 332.7 Further Reading 342.8 Discussion and Problems 34Discussion 34Basic Concepts 35Problems 353 Mechanical Properties 373.1 Elastic Deformation 393.1.1 Macroscopic Picture 393.1.1.1 Elastic Constants 393.1.1.2 Poisson’s Ratio 403.1.1.3 Relation Between Elastic Constants 403.1.2 Microscopic Picture 413.2 Plastic Deformation 433.2.1 Estimate of the Yield Stress 433.2.2 Point Defects and Dislocations 453.2.3 The Role of Defects in Plastic Deformation 453.3 Fracture 473.4 Further Reading 483.5 Discussion and Problems 48Discussion 48Basic Concepts 49Problems 494 Thermal Properties of the Lattice 514.1 Lattice Vibrations 514.1.1 A Simple Harmonic Oscillator 514.1.2 An Infinite Chain of Atoms 524.1.2.1 One Atom Per Unit Cell 524.1.2.2 The First Brillouin Zone 554.1.2.3 Two Atoms per Unit Cell 564.1.3 A Finite Chain of Atoms 584.1.4 Quantized Vibrations, Phonons 594.1.5 Three-Dimensional Solids 614.1.5.1 Generalization to Three Dimensions 614.1.5.2 Estimate of the Vibrational Frequencies from the Elastic Constants 634.2 Heat Capacity of the Lattice 644.2.1 Classical Theory and Experimental Results 654.2.2 Einstein Model 664.2.3 Debye Model 684.3 Thermal Conductivity 714.4 Thermal Expansion 744.5 Allotropic Phase Transitions and Melting 75References 784.6 Further Reading 784.7 Discussion and Problems 78Discussion 78Basic Concepts 79Problems 815 Electronic Properties of Metals: Classical Approach 855.1 Basic Assumptions of the Drude Model 855.2 Results from the Drude Model 875.2.1 dc Electrical Conductivity 875.2.2 Hall Effect 895.2.3 Optical Reflectivity of Metals 905.2.4 The Wiedemann–Franz Law 935.3 Shortcomings of the Drude Model 935.4 Further Reading 945.5 Discussion and Problems 95Discussion 95Basic Concepts 95Problems 966 Electronic Properties of Solids: Quantum Mechanical Approach 996.1 The Idea of Energy Bands 1006.2 The Free Electron Model 1036.2.1 The Quantum-Mechanical Eigenstates 1036.2.2 Electronic Heat Capacity 1076.2.3 The Wiedemann–Franz Law 1086.2.4 Screening 1086.3 The General Form of the Electronic States 1116.4 Nearly-Free Electron Model: Band Formation 1146.5 Tight-binding Model 1196.6 Energy Bands in Real Solids 1246.7 Transport Properties 1306.8 Brief Review of Some Key Ideas 134References 1356.9 Further Reading 1356.10 Discussion and Problems 136Discussion 136Basic Concepts 137Problems 1407 Semiconductors 1457.1 Intrinsic Semiconductors 1467.1.1 Temperature Dependence of the Carrier Density 1487.2 Doped Semiconductors 1537.2.1 n and p Doping 1537.2.2 Carrier Density 1557.3 Conductivity of Semiconductors 1577.4 Semiconductor Devices 1587.4.1 The pn Junction 1587.4.2 Transistors 1637.4.3 Optoelectronic Devices 1657.5 Further Reading 1687.6 Discussion and Problems 169Discussion 169Basic Concepts 170Problems 1728 Magnetism 1758.1 Macroscopic Description 1758.2 Quantum-Mechanical Description of Magnetism 1778.3 Paramagnetism and Diamagnetism in Atoms 1798.4 Weak Magnetism in Solids 1828.4.1 Diamagnetic Contributions 1838.4.1.1 Contribution from the Atoms 1838.4.1.2 Contribution from the Free Electrons 1838.4.2 Paramagnetic Contributions 1838.4.2.1 Curie Paramagnetism 1848.4.2.2 Pauli Paramagnetism 1858.5 Magnetic Ordering 1878.5.1 Magnetic Ordering and the Exchange Interaction 1878.5.2 Magnetic Ordering for Localized Spins 1898.5.3 Magnetic Ordering in a Band Picture 1938.5.4 Ferromagnetic Domains 1958.5.5 Hysteresis 196Reference 1988.6 Further Reading 1988.7 Discussion and Problems 199Discussion 199Basic Concepts 200Problems 2019 Dielectrics 2039.1 Macroscopic Description 2039.2 Microscopic Polarization 2059.3 The Local Field 2079.4 Frequency Dependence of the Dielectric Constant 2089.4.1 Excitation of Lattice Vibrations 2089.4.2 Electronic Transitions 2129.5 Other Effects 2139.5.1 Impurities in Dielectrics 2139.5.2 Ferroelectricity 2149.5.3 Piezoelectricity 2159.5.4 Dielectric Breakdown 2169.6 Further Reading 2169.7 Discussion and Problems 216Discussion 216Basic Concepts 217Problems 21810 Superconductivity 22110.1 Basic Experimental Facts 22210.1.1 Zero Resistivity 22210.1.2 The Meissner Effect 22510.1.3 The Isotope Effect 22710.2 Some Theoretical Aspects 22710.2.1 Phenomenological Theory 22710.2.2 Microscopic BCS Theory 23010.3 Experimental Detection of the Gap 23610.4 Coherence of the Superconducting State 23810.5 Type-I and Type-II Superconductors 23910.6 High-Temperature Superconductivity 24210.7 Concluding Remarks 243References 24410.8 Further Reading 24410.9 Discussion and Problems 244Discussion 244Basic Concepts 245Problems 24611 Finite Solids and Nanostructures 24911.1 Quantum Confinement 25011.2 Surfaces and Interfaces 25211.3 Magnetism on the Nanoscale 25511.4 Further Reading 25611.5 Discussion and Problems 257Discussion 257Basic Concepts 257Problems 257Appendix A 259A.1 Explicit Forms of Vector Operations 259A.2 Differential Form of the Maxwell Equations 260A.3 Maxwell Equations in Matter 261Appendix B 263B.1 Solutions to Basic Concepts Questions 263Index 265