**Related Resources: Heat Transfer**

### Thermal Conductivity Theory , Properties, and Applications

White Papers, Engineering Documents & Specifications

Engineering Heat Transfer

Thermal Conductivity Theory, Properties, and Applications

This resource requires a *Premium Membership*

Open: Thermal Conductivity Theory, Properties, and Applications

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 These e¡orts were made by a generation of scientists, who for the most part are no longer active, and this expertise would be lost to us unless we are aware of the great strides they made during their time.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