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Thermal Conductivity Theory , Properties, and Applications

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PREFACE

It has been almost thirty years since a book was published that was entirely dedicated to the theory, description, characterization and measurement of the thermal conductivity of solids. For example, the excellent texts by authors such as Berman1, Tye2 and Carlslaw & Jaeger3 remain as the standards in the field of thermal conductivity. Tremendous e¡orts were expended in the late 1950’s and 1960’s in relation to the measurement and characterization of the thermal conductivity of solid state materials. These e¡orts were made by a generation of scientists, who for the most part are no longer active, and this expertise would be lost to us unless we are aware of the great strides they made during their time.

I became interested in the field of thermal conductivity in the mid 1990’s in relation to my own work on the next generation thermoelectric materials, of which the measurement and understanding of thermal conductivity is an integral part.4 In my search for information, I found that most of the books on the subject of thermal conductivity were out of print. Much of the theory previously formulated by researchers such as Klemens5 and Slack6 contain considerable theoretical insight into understanding thermal conductivity in solids. However, the discovery of new materials over the last several years which possess more complicated crystal structures and thus more complicated phonon scattering mechanisms have brought new challenges to the theory and experimental understanding of these new materials. These include: cage structure materials such as skutterudites and clathrates, metallic glasses, quasicrystals as well as many of new nano-materials which exist today. In addition the development of new materials in the form of thin iflm and superlattice structures are of great theoretical and technological interest. Subsequently, new measurement techniques (such as the 3-! technique) and analytical models to characterize the thermal conductivity in these novel structures were developed. Thus, with the development of many new and novel solid materials and new measurement techniques, it appeared to be time to produce a more current and readily available reference book on the subject of thermal conductivity. Hopefully, this book, Thermal Conductivity-2004: Theory, Properties and Applications, will serve not only as a testament to those researchers of past generations whose great care in experimental design and thought still stands today but it will also describe many of the new developments over the last several years. In addition, this book will serve as an extensive resource to the next generation researchers in the field of thermal conductivity.

TOC

Section 1. - Overview of Thermal Conductivity in Solid Materials

Chapter 1.1 - Theory of Thermal Conductivity (Jihui Yang)
 Introduction 1
 Simple Kinetic Theory 2
 Electronic Thermal Conduction 3
 Lattice Thermal Conductivity 9
 Summary 17
 References 17

Chapter 1.2 - Thermal Conductivity of Metals (Ctirad Uher)
 Introduction 21
 Carriers of Heat in Metals 22
 The Drude Model 24
 Specific Heat of Metals 29
 The Boltzmann Equation 32
 Transport Cofficients 35
 Electrical Conductivity 40
 Electrical Thermal Conductivity 44
 Scattering Processes 46
 Impurity Scattering 46
 Electron-Phonon Scattering 50
 Electron-Electron Scattering 61
 E¡ect of e-e Processes on Electrical Resistivity 64
 E¡ect of e-e Processes on Thermal Resistivity 69
 Lattice Thermal Conductivity 73
 Phonon Thermal Resistivity Limited By Electrons 73
 Other Processes Limiting Phonon Thermal Conductivity in Metals 77
 Thermal Conductivity of Real Metals 79
 Pure Metals 79
 Alloys 86
 Conclusion 87
 References 88

Chapter 1.3 - Thermal Conductivity of Insulators and Glasses
(Vladimir Murashov and Mary Anne White)
 Introduction 93
 Phononic Thermal Conductivity in Simple, Crystalline Insulators 94
 Acoustic Phonons Carry Heat 94
 Temperature-Dependence of  96
 Impurities 97
 More Complex Insulators: The Role of Optic Modes 97
 Molecular and Other Complex Systems 97
 Optic-Acoustic Coupling 99
 Thermal Conductivity of Glasses 100
 Comparison with Crystals 100
 More Detailed Models 100
 The Exception: Recent Amorphous Ice Results 101
 Minimum Thermal Conductivity 101
 Radiation 102
 References 102

Chapter 1.4 - Thermal Conductivity of Semiconductors
(G. S. Nolas and H. J. Goldsmid)
 Introduction 105
 Electronic Thermal Conductivity in Semiconductors 106
 Transport Coe⁄cients for a Single Band 106
 Nondegenerate and Degenerate Approximations 109
 Bipolar Conduction 110
 Separation of Electronic and Lattice Thermal Conductivities 112
 Phonon Scattering in Impure and Imperfect Crystals 114
 Pure Crystals 114
 Scattering of Phonons by Impurities 115
 Boundary Scattering 117
 Prediction of the Lattice Thermal Conductivity 118
 References 120

Chapter 1.5 - Semiconductors and Thermoelectric Materials
(G. S. Nolas, J. Yang, and H. J. Goldsmid)
 Introduction 123
 Established Materials 124
 Bismuth Telluride and Its Alloys 124
 Bismuth and Bismuth-Antimony Alloys 126
 IV-VI Compounds 127
 Silicon, Germanium, and Si-Ge Alloys 128
 Skutterudites 129
 Binary (Uniflled) Skutterudites 130
 E¡ect of Doping on the Co Site 132
 Filled Skutterudites 133
 Clathrates 137
 Half-Heusler Compounds 141
 E¡ect of Annealing 142
 Isoelectronic Alloying on the M and Ni Sites 142
 E¡ect of Grain Size Reduction 144

XVIII CONTENTS
 Novel Chalcogenides and Oxides 145
 Tl9GeTe6 146
 Tl2GeTe5 and Tl2SnTe5 146
 CsBi4Te6 147
 NaCo2O4 147
 Summary 149
 References 149

Chapter 1.6 - Thermal Conductivity of Superlattices (G. D. Mahan)
 Introduction 153
 Parallel to Layers 154
 Perpendicular to Layers 154
 Thermal Boundary Resistance 154
 Multilayer Interference 156
 What is Temperature? 157
 Superlattices with Thick Layers 159
 ‘‘Non-Kapitzic’’ Heat Flow 161
 Analytic Theory 162
 Summary 163
 References 164

Chapter 1.7 - Experimental Studies on Thermal Conductivity of Thin Film and
Superlattices (Bao Yang and Gang Chen)
 Introduction 167
 Thermal Conductivity of Metallic Thin Films 169
 Thermal Conductivity of Dielectric Films 171
 Amorphous SiO2 Thin Films 171
 Thin Film Coatings 173
 Diamond Films 174
 Multilayer Interference 174
 Thermal Conductivity of Semiconductor and Semimetal Thin Films 174
 Silicon Thin Films 175
 Semimetal Thin Films 177
 Semiconductor Superlattices 178
 Conclusions 182
 Acknowledgments 182
 References 182

Section 2 - Measurement Techniques

Chapter 2.1 - Measurement Techniques and Considerations for Determining
Thermal Conductivity of Bulk Materials (Terry M. Tritt and David Weston)
 Introduction 187
 Steady State Method (Absolute Method) 188
 Overview of Heat Loss and Thermal Contact Issues 189
 Heat Loss Terms 191
 The Comparative Technique 193
 The Radial Flow Method 195
 Laser-Flash Di¡usivity 197
 The Pulse-power Method (‘‘Maldonado’’ Technique) 199
 Parallel Thermal Conductance Technique 200
 Z-Meters or Harman Technique 201
 Summary 202
 References 202

Chapter 2.2 - Experimental Techniques for Thin-Film Thermal Conductivity
Characterization (T. Borca-Tasciuc and G. Chen)
 Introduction 205
 Electrical Heating and Sensing 208
 Cross-Plane Thermal Conductivity Measurements of Thin Films 208
 The 3! Method 208
 Steady-State Method 213
 In-Plane Thermal Conductivity Measurements 214
 Membrane Method 216
 Bridge Method 222
 In-Plane Thermal Conductivity Measurement without Substrate Removal 225
 Optical Heating Methods 225
 Time Domain Pump-and-Probe Methods 226
 Frequency-Domain Photothermal and Photoacoustic Methods 230
 Photothermal Re£ectance Method 230
 Photothermal Emission Method 230
 Photothermal Displacement Method 231
 Photothermal Defelection Method (Mirage Method) 231
 Photoacoustic Method 231
 Optical-Electrical Hybrid Methods 232
 Summary 233
 Acknowledgments 234
 References 234

Section 3 - Thermal Properties and Applications of Emerging Materials

Chapter 3.1 - Ceramics and Glasses (Rong Sun and Mary Anne White)
 Introduction 239
 Ceramics 239
 Traditional Materials with High Thermal Conductivity 240
 Aluminum Nitride (AlN) 240
 Silicon Nitride (Si3N4) 243
 Alumina (Al2O3) 244
 Novel Materials with Various Applications 244
 Ceramic Composites 244
 Diamond Film on Aluminum Nitride 244
 Silicon Carbide Fiber-reinforced Ceramic Matrix Composite (SiC-CMC) 244
 Carbon Fiber-incorporated Alumina Ceramics 245
 Ceramic Fibers 245
 Glass-ceramic Superconductor 245
 Other Ceramics 246

XX CONTENTS
Rare-earth Based Ceramics 246
 Magnesium Silicon Nitride (MgSiN2) 247
 Thermoelectric Ceramics 247
 Glasses 248
 Introduction 248
 Chalcogenide Glasses 248
 Other Glasses 249
 Conclusions 250
 References 250

Chapter 3.2 - Thermal Conductivity of Quasicrystalline Materials (A. L. Pope and Terry M. Tritt)
 Introduction 255
 Contributions to Thermal Conductivity 257
 Low-Temperature Thermal Conduction in Quasicrystals 257
 Poor Thermal Conduction in Quasicrystals 258
 Glasslike Plateau in Quasicrystalline Materials 258
 Summary 259
 References 259

Chapter 3.3 - Thermal Properties of Nanomaterials and Nanocomposites (T. Savage and A. M. Rao)
 Nanomaterials 262
 Carbon Nanotubes 262
 Electrical Conductivity,  262
 Thermoelectric Power (TEP) 265
 Thermal Conductivity,  271
 Heat Capacity, C 274
 Nanowires 276
 Electrical Conductivity 276
 Thermoelectric Power 277
 Thermal Conductivity and Heat Capacity 278
 Nanoparticles 278
 Nanocomposites 279
 Electrical Conductivity 279
 Thermal Conductivity 280
 Applications 280
 References 282
Index 285

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