Heat transfer physics

Cover......Page 1
Half-title......Page 3
Title......Page 5
Copyright......Page 6
Contents......Page 9
Preface......Page 19
Acknowledgments......Page 23
1 Introduction and Preliminaries......Page 25
1.1.1 Phonon......Page 27
1.1.2 Electron (and Hole)......Page 31
1.1.4 Photon......Page 32
1.2 Combinatorial Probabilities and Energy Distribution Functions......Page 33
1.3 Particles, Waves, Wave Packets and Quasi-Particles......Page 35
1.4 A History of Contributions Toward Heat Transfer Physics......Page 37
1.5.1 Boltzmann and Planck Constants......Page 39
1.5.2 Atomic Units and Fine-Structure Scales......Page 40
1.6 Principal Carriers: Concentration, Energy, Kinetics and Speed......Page 42
1.6.1 Principal Energy Carriers Concentration......Page 43
1.6.2 Principal Carrier Energy......Page 44
1.6.4 Principal Carrier Speed......Page 46
1.7 Periodic Table of Elements......Page 47
1.8 Heat Transfer Physics: Atomic-Level Energy Kinetics......Page 50
1.9 Ab Initio/MD/BTE/Macroscopic Treatments......Page 56
1.10 Scope......Page 58
1.11 Problems......Page 60
2.1 Interatomic Forces and Potential Wells......Page 63
2.1.2 Intermolecular Forces......Page 65
2.1.3 Kinetic and Potential Energies and Potential Wells......Page 66
2.2.1 Atomic and Molecular Electron Orbitals......Page 71
2.2.2 Ab Initio Computation of Interatomic Potentials......Page 73
2.2.3 Potential Models......Page 77
2.2.4 Examples of Atomic Bond Length and Energy......Page 81
2.3.2 Thermodynamic Relations......Page 86
2.4.1 Classical and Quantum Hamiltonians......Page 89
2.4.3 Ergodic Hypothesis in Theoretical Statistical Mechanics......Page 91
2.5.1 Ensemble and Descretization of Governing Equations......Page 92
(B) Ensemble-Averaged Energy......Page 93
(C) Computational Classical Particle Dynamics......Page 94
(D) Descretization Verlet Algorithm for MD Computation......Page 95
2.5.2 A Molecular Dynamics Simulation Case Study......Page 96
2.5.3 L–J MD Scales in Classical Harmonic Oscillator......Page 99
2.5.4 L–J Potential Phase Transformations......Page 102
2.5.5 Atomic Displacement in Solids and Quantum Effects......Page 103
2.6 Schrodinger Equation and Quantum Energy States......Page 105
2.6.1 Time-Dependent Schrodinger Equation and Wave Vector......Page 106
2.6.3 Quantum-Mechanics Formalism, Bra–Ket and Matrix Element......Page 109
2.6.4 Quantum Mechanical, Harmonic Oscillator......Page 110
2.6.5 Periodic, Free Electron (Gas) Model for Metals......Page 114
2.6.6 Electron Orbitals in Hydrogenlike Atoms......Page 118
2.6.7 Perturbation and Numerical Solutions to Schrodinger Equation......Page 120
2.7 Problems......Page 124
3 Carrier Energy Transport and Transformation Theories......Page 128
3.1.2 A Simple Derivation of BTE......Page 129
3.1.3 In- and Out-Scattering......Page 131
3.1.4 Relaxation-Time Approximation and Transport Properties......Page 133
3.1.5 Boltzmann Transport Scales......Page 136
3.1.7 Moments of BTE......Page 137
3.1.8 Numerical Solution to BTE......Page 138
3.2.1 Elastic and Inelastic Scattering......Page 139
3.2.2 Phonon Interaction and Transition Rates......Page 140
3.2.3 Electron (and Hole) Interaction and Transition Rates......Page 141
3.2.4 Fluid Particle Interaction and Transition Rates......Page 144
3.3.1 Maxwell Equations......Page 145
3.3.2 Electromagnetic Wave Equation......Page 147
3.3.3 EM Wave and Photon Energy......Page 150
3.3.4 Electric Dipole Emission, Absorption and Scattering of EM Waves......Page 151
3.3.5 Dielectric Function and Dielectric Heating......Page 153
3.3.6 Electrical Resistance and Joule Heating......Page 157
3.4 Onsager Transport Coefficients......Page 158
3.5.1 Langevin Particle Dynamics Equation......Page 159
3.5.2 Fokker–Planck Particle Conservation Equation......Page 160
3.6 Fluctuation–Dissipation and Green–Kubo Transport Theory......Page 161
3.7 Macroscopic Fluid Dynamics Equations......Page 164
3.9 Macroscopic Scales......Page 167
3.10 Problems......Page 168
4.1 Phonon Dispersion in One-Dimensional Harmonic Lattice Vibration......Page 178
4.2 Phonon Density of States and Phonon Speeds......Page 185
4.2.1 Phonon DOS for One-Dimensional Lattice and van Hove Singularities......Page 186
4.2.2 Debye and Other Phonon DOS Models......Page 187
4.3.1 Reciprocal Lattice......Page 190
4.3.2 Brillouin Zone......Page 192
4.3.3 Primitive Cell and Its Basis: Number of Phonon Branches......Page 193
4.4 Normal Modes and Dynamical Matrix......Page 194
4.5 Quantum Theory of Lattice Vibration......Page 197
4.6 Examples of Phonon Dispersion and DOS......Page 200
4.7.1 Specific Heat Capacity......Page 203
(A) Group Velocity from Directional Spring Constant......Page 208
(C) Nearest-Neighbor SC Structures......Page 209
4.8 Atomic Displacement in Lattice Vibration......Page 210
4.9.1 Single-Mode Relaxation Time......Page 213
4.9.2 Callaway Phonon Conductivity Model from BTE......Page 214
4.9.4 Relaxation-Time Models......Page 217
(B) Impurity Scattering......Page 220
(C) Phonon–Phonon Scattering......Page 221
(D) Electron Scattering......Page 223
(G) Temperature Dependence of Phonon Conductivity......Page 224
(A) Debye Model......Page 225
(B) Holland Model......Page 226
(E) BZBC Model......Page 227
4.9.6 Comparison of Dispersion Models......Page 228
(A) Role of Dispersion Model......Page 229
(C) Transverse and Longitudinal Phonon Contributions......Page 231
4.10 Einstein and Cahill–Pohl Minimum Phonon Conductivities......Page 233
4.11 Material Metrics of High-T Phonon Conductivity......Page 234
4.11.1 Derivation of Slack Relation......Page 235
4.11.2 Force-Constant Combinative Rule for Arbitrary Pair-Bond......Page 237
4.11.3 Evaluation of Sound Velocity and Debye Temperature......Page 243
4.11.4 Prediction of Gruneisen Parameter......Page 246
4.11.5 Prediction of Thermal Conductivity......Page 251
4.12 High-T Phonon Conductivity Decomposition: Acoustic Phonons......Page 256
4.12.1 Heat Current Autocorrelation Function......Page 257
4.12.2 Phonon Conductivity Decomposition......Page 259
4.12.3 Comparison with Experiment......Page 261
4.13 High-T Phonon Conductivity Decomposition: Optical Phonons......Page 262
4.14 Quantum Corrections to MD/G-K Predictions......Page 264
4.15 Phonon Conductivity from BTE: Variational Method......Page 268
4.17 Phonon Boundary Resistance......Page 271
4.18 Absorption of Ultrasound Waves in Solids......Page 276
4.19.1 Finite-Size Effect on Phonon Conductivity......Page 277
4.19.2 Superlattice Phonon Conductivity......Page 278
4.19.3 Phonon Density of States of Nanoparticles......Page 280
(A) Nanoparticle Atomic Structure and MD......Page 281
(B) Simulation Results and Analysis......Page 283
(C) Dp for Nanoparticles......Page 284
4.19.4 Phonon Conductivity Rectification in Anisotropic One-Dimensional Systems......Page 287
4.20 Problems......Page 288
5 Electron Energy Storage, Transport and Transformation Kinetics......Page 304
5.1 Schrodinger Equation for Periodic-Potential Band Structure......Page 306
5.2 Electron Band Structure in One-Dimensional Ionic Lattice......Page 308
5.3 Three-Dimensional Bands Using Tight-Binding Approximation......Page 311
5.3.1 General LCAO......Page 312
5.3.2 Example of Tight-Binding Approximation: FCC s Orbital......Page 313
5.4 Electron Band Structure for Semiconductors and Effective Mass......Page 316
5.5 Ab Initio Computation of Electron Band Structure......Page 319
5.6 Periodic Electron Gas Model for Metals......Page 321
5.7 Electron–Hole Density of States for Semiconductors......Page 323
5.8 Specific Heat Capacity of Conduction Electrons......Page 327
5.9 Electron BTE for Semiconductors: Thermoelectric Force......Page 329
5.10 Electron Relaxation Time and Fermi Golden Rule......Page 330
5.11 Average Relaxation Time…......Page 333
5.12 Thermoelectric Transport Tensors for Power-Law…......Page 337
5.13.1 Seebeck, Peltier, and Thomson Coefficients, and Electrical and Thermal Conductivities......Page 341
5.13.2 Electron Mean Free Path for Metals......Page 343
5.15 Electron–Phonon Relaxation Times in Semiconductors......Page 344
5.15.1 Electron–Phonon Wave Function......Page 345
5.15.2 Rate of Acoustic-Phonon Scattering of Electrons......Page 347
(A) Nonpolar Optical Phonons......Page 350
5.15.4 Summary of Electron-Scattering Mechanisms and Relaxation-Time Relations......Page 353
5.16.1 Structural Defects in Crystalline Solids......Page 354
5.16.2 Metals......Page 355
5.16.3 Semiconductors......Page 358
5.16.4 TE Figure of Merit Ze......Page 365
5.17.1 TE Transport Tensors and Variable Chemical Potential......Page 370
5.17.2 Introduction to BoltzTraP......Page 371
5.17.3 Relaxation Times Based on Kane Band Model......Page 373
(A) Scattering by Deformation Potential of Acoustic Phonons…......Page 375
(C) Scattering by Polar-Optical Phonons…......Page 376
5.17.4 Predicted Seebeck Coefficient and Electrical Conductivity......Page 377
5.17.5 Electrical and Phonon Thermal Conductivities......Page 381
(B) Phonon Thermal Conductivity......Page 382
5.18.1 Derivations......Page 385
5.18.2 Phonon Modal Energy Equations......Page 388
5.18.3 Summary of Conservation (Electrohydrodynamic) Equations......Page 389
5.19 Cooling Length in Electron–Phonon Local Thermal Nonequilibrium......Page 390
5.20 Electronic Energy States of Ions in Crystals......Page 393
5.21 Electronic Energy States of Gases......Page 397
5.22 Size Effects......Page 400
5.22.1 Quantum Well for Improved TE ZeT......Page 401
5.22.2 Reduced Electron–Phonon Scattering Rate Quantum Wells......Page 403
5.23 Problems......Page 405
6 Fluid Particle Energy Storage, Transport and Transformation Kinetics......Page 415
6.1 Fluid Particle Quantum Energy States and Partition Functions......Page 416
6.1.1 Translational Energy and Partition Function......Page 417
6.1.2 Vibrational Energy and Partition Function......Page 418
6.1.3 Rotational Energy and Partition Function......Page 419
6.1.4 Electronic Energy and Partition Function......Page 420
6.2 Ideal-Gas Specific Heat Capacity......Page 421
6.3 Dense-Fluid Specific Heat Capacity: van der Waals Model......Page 424
6.4.1 Interparticle Collisions......Page 427
6.4.2 Equilibrium Distribution Function for Translational Energy......Page 429
6.5 Ideal-Gas Binary Collision Rate and Relaxation Time......Page 432
6.6 Ideal-Gas Mean Free Path and Viscosity......Page 435
6.7 Theoretical Maximum Evaporation–Condensation Heat Transfer Rate......Page 436
6.8 Ideal-Gas Thermal Conductivity from BTE......Page 438
6.8.2 Thermal Conductivity......Page 439
6.9 Liquid Thermal Conductivity from Mean Free Path......Page 443
6.10.1 Langevin Derivation of Brownian Diffusion......Page 445
6.10.2 Effective Fluid Thermal Conductivity......Page 447
6.11.1 Fluid Flow Regimes......Page 448
6.11.2 Knudson-Flow-Regime Surface Accommodation Coefficients......Page 450
6.11.3 Slip Coefficients in Transitional-Flow Regime......Page 452
6.11.4 Solid Particle Thermophoresis in Gases......Page 454
6.11.5 Physical Adsorption and Desorption......Page 455
6.11.6 Disjoining Pressure in Ultrathin-Liquid Films......Page 458
6.12 Turbulent-Flow Structure and Boundary-Layer Transport......Page 459
6.12.1 Turbulent Kinetic Energy Spectrum for Homogeneous Turbulence......Page 461
6.12.3 Boundary-Layer Turbulent Mixing Length and Thermal Conductivity......Page 464
6.12.4 Spatial Variation of Boundary-Layer Turbulent Mixing Length......Page 465
6.13 Thermal Plasmas......Page 467
6.13.1 Free Electron Density and Plasma Thermal Conductivity......Page 468
6.13.2 Thermal Nonequilibrium Plasma Energy Equation......Page 472
6.13.4 Kinetics of Energy Exchange Between Electrons and Heavier Species......Page 473
6.14.1 Gas Thermal Conductivity in Narrow Gaps......Page 474
6.14.2 Thermal Creep (Slip) Flow in Narrow Gaps......Page 476
6.15 Problems......Page 479
7 Photon Energy Storage, Transport and Transformation Kinetics......Page 485
7.1 Quasi-Particle Treatment: Photon Gas and Blackbody Radiation......Page 489
7.2.2 Classical EM Wave Near-Field Thermal Emission......Page 492
7.3.1 Hamiltonians of Radiation Field......Page 495
7.3.2 Photon-Matter Interactions......Page 498
7.4.1 Einstein Population Rate Equation......Page 500
7.4.2 Einstein Coefficients for Equilibrium Thermal Source......Page 502
7.4.3 Spontaneous Versus Stimulated Emissions in Thermal Cavity......Page 503
7.4.4 Spectral Absorption Coefficient......Page 504
7.5 Particle Treatment: Photon BTE......Page 506
7.5.1 Absorption Coefficient and Relation between Photon Absorption and Emission......Page 507
7.5.2 Photon–Free Electron Scattering Rate......Page 509
7.6.1 General Form of ERT......Page 512
7.6.2 Optically Thick Limit and Radiant Conductivity......Page 514
7.7 Wave Treatment: Field Enhancement and Photon Localization......Page 516
7.7.1 Photon Localization in One-Dimensional Multilayer......Page 517
7.7.2 Coherence and Electric Field Enhancement......Page 520
(A) One-Dimensional Multilayer Geometry......Page 521
(B) Two-Dimensional Geometry......Page 522
(A) Formulation and Two-Flux Approximation......Page 523
7.8.1 Photon Absorption in Solids......Page 526
7.8.2 Photon Absorption in Gases......Page 530
7.9.1 Emission Mechanisms......Page 535
7.9.2 Reciprocity between Spectral Photon Absorption and Emission for Multiple-Level Electronic Systems......Page 536
7.10 Spectral Surface Emissivity......Page 538
7.11 Radiative and Nonradiative Decays......Page 540
7.12.1 Laser Cooling of Ion-Doped Solids......Page 545
7.12.2 Laser Cooling Efficiency......Page 548
7.12.3 Photon–Electron–Phonon Transition Rate Using Weak Coupling Approximation......Page 550
(A) Acoustic Phonons......Page 551
(B) Optical Phonons......Page 554
7.12.4 Time Scales for Laser Cooling of Solids (Weak Couplings)......Page 555
7.12.5 Optimal Host Material......Page 559
(A) Photon–Electron Coupling (Transition Dipole Moment)......Page 562
(B) Strong Electron–Vibration Coupling (Electron–Phonon Wave Function)......Page 565
7.13.1 Molecular-Gas Lasers......Page 570
7.13.2 Laser Cooling of Atomic Gases......Page 576
7.14 Photovoltaic Solar Cell: Reducing Phonon Emission......Page 579
7.14.1 Single-Bandgap Ideal Solar PV Efficiency......Page 581
7.14.2 Multiple-Bandgap Ideal Solar PV Efficiency......Page 583
7.14.3 Semiempirical Solar PV Efficiency......Page 586
7.15.1 Enhanced Near-Field Radiative Heat Transfer......Page 588
7.15.2 Photon Energy Confinement by Near-Field Optical Microscopy......Page 591
7.16 Problems......Page 592
Appendix A Tables of Properties and Universal Constants......Page 603
B.1 Perturbation Energy Equation and Fourier Transform......Page 610
B.2 Taylor Series Expansion and Ensemble Averaging......Page 611
B.3 Thermal Conductivity Tensor......Page 615
B.4 Physical Interpretation of Heat Current Vector Autocorrelation......Page 617
C.1 Einstein Thermal Conductivity......Page 618
C.2 Cahill–Pohl Thermal Conductivity......Page 623
Appendix D Derivation of Phonon Boundary Resistance......Page 625
D.1.1 Transmission Probability for Diffuse Scattering......Page 626
D.1.2 Net Heat Flow for Diffuse Scattering......Page 627
D.2.1 Transmission Probability for Specular Scattering......Page 628
E.1 Time-Dependent Perturbation......Page 631
E.2 Transition Rate......Page 633
E.3 Example: Photoelectric Transition Rate for Hydrogen......Page 635
E.4 Examples of Perturbation Hamiltonian......Page 637
F.1 Partition Functions......Page 638
F.3 Bose–Einstein Distribution Function…......Page 640
F.5 Comparison Among Fermion, Boson, and M–B Particles......Page 641
Nomenclature......Page 643
Abbreviations......Page 649
Glossary......Page 651
Bibliography......Page 663
Index......Page 679