Phonon Energy Storage, Transport and Transformation Kinetics

Abstract

Heat transfer by lattice (phonon) conduction is proportional to the lattice thermal conductivity tensor K p (W/m-K), i.e., q k = − K p ∇ T (the Fourier law, Table 1.1), and sensible heat storage is determined by the phonon (lattice) specific heat capacity c v,p (J/kg-K). The specific heat capacity is also given per unit volume(J/m 3 -K), or per atom(J/K). Phonons participate in many thermal energy conversion phenomena, including laser cooling of solids, discussed in Chapter 7 [ s i − j (W/m3) in Table 1.1]. In this chapter, we examine how the atomic structure of a solid influences c v,p , K p , and s i− 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.