Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgments
- 1 Introduction and Preliminaries
- 2 Molecular Orbitals/Potentials/Dynamics, and Quantum Energy States
- 3 Carrier Energy Transport and Transformation Theories
- 4 Phonon Energy Storage, Transport and Transformation Kinetics
- 5 Electron Energy Storage, Transport and Transformation Kinetics
- 6 Fluid Particle Energy Storage, Transport and Transformation Kinetics
- 7 Photon Energy Storage, Transport and Transformation Kinetics
- APPENDIX A Tables of Properties and Universal Constants
- APPENDIX B Derivation of Green–Kubo Relation
- APPENDIX C Derivation of Minimum Phonon Conductivity Relations
- APPENDIX D Derivation of Phonon Boundary Resistance
- APPENDIX E Derivation of Fermi Golden Rule
- APPENDIX F Derivation of Equilibrium, Particle Probability Distribution Functions
- Nomenclature
- Abbreviations
- Glossary
- Bibliography
- Index
4 - Phonon Energy Storage, Transport and Transformation Kinetics
Published online by Cambridge University Press: 06 July 2010
- Frontmatter
- Contents
- Preface
- Acknowledgments
- 1 Introduction and Preliminaries
- 2 Molecular Orbitals/Potentials/Dynamics, and Quantum Energy States
- 3 Carrier Energy Transport and Transformation Theories
- 4 Phonon Energy Storage, Transport and Transformation Kinetics
- 5 Electron Energy Storage, Transport and Transformation Kinetics
- 6 Fluid Particle Energy Storage, Transport and Transformation Kinetics
- 7 Photon Energy Storage, Transport and Transformation Kinetics
- APPENDIX A Tables of Properties and Universal Constants
- APPENDIX B Derivation of Green–Kubo Relation
- APPENDIX C Derivation of Minimum Phonon Conductivity Relations
- APPENDIX D Derivation of Phonon Boundary Resistance
- APPENDIX E Derivation of Fermi Golden Rule
- APPENDIX F Derivation of Equilibrium, Particle Probability Distribution Functions
- Nomenclature
- Abbreviations
- Glossary
- Bibliography
- Index
Summary
Heat transfer by lattice (phonon) conduction is proportional to the lattice thermal conductivity tensor Kp(W/m-K), i.e., qk = − Kp ∇ T (the Fourier law, Table 1.1), and sensible heat storage is determined by the phonon (lattice) specific heat capacity cv,p(J/kg-K). The specific heat capacity is also given per unit volume(J/m3-K), or per atom(J/K). Phonons participate in many thermal energy conversion phenomena, including laser cooling of solids, discussed in Chapter 7 [si − j(W/m3) in Table 1.1]. In this chapter, we examine how the atomic structure of a solid influences cv,p, Kp, and si− j involving phonons.
Phonons are lattice-thermal-vibration waves that propagate through a crystalline solid. Most lattice vibrations have higher frequencies than audible sound, ultrasound, and even hypersound. Figure 4.1 shows the various sound- and vibrational-wave regimes. A single, constant speed (dispersionless, i.e., having a linear frequency dependence on the wave number) of 103 m/s is used for the sake of illustration. As will be shown, the vibrational waves have different modes, and the propagation speed can be strongly frequency dependent. In this chapter, we begin with lattice vibration and the relation between frequency and wave number (the dispersion relation) for a simple, harmonic, one-dimensional lattice. Then we discuss the quantization of phonons and a general three-dimensional treatment of dispersion. We discuss lattice specific heat capacity and thermal conductivity (from the BTE for phonons), including quantum effects, and discuss the atomic structural metrics of the thermal conductivity at high temperatures.
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- Information
- Heat Transfer Physics , pp. 154 - 279Publisher: Cambridge University PressPrint publication year: 2008