Phonon Conductivity

The conduction of heat through dielectric solids such as ceramics can happen in two ways  

By the movement of thermal energy units called phonons 

In this equation, c(co) is the specific heat per frequency and l(co) is the attenuation length for the waves. It is the phonon-phonon interaction that 

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It can be observed that these thermal conductances G(7) are typical of phonon conduction between two solids at very low temperature, as already reported [45], The value of the heat capacity was calculated from equation C = r G, where the thermal time constant r is obtained from the fit to the exponential relaxation of the wafer temperature. 

This competition between electrons and the heat carriers in the lattice (phonons) is the key factor in determining not only whether a material is a good heat conductor or not, but also the temperature dependence of thermal conductivity. In fact, Eq. (4.40) can be written for either thermal conduction via electrons, k, or thermal conduction via phonons, kp, where the mean free path corresponds to either electrons or phonons, respectively. For pure metals, kg/kp 30, so that electronic conduction dominates. This is because the mean free path for electrons is 10 to 100 times higher than that of phonons, which more than compensates for the fact that C <, is only 10% of the total heat capacity at normal temperatures. In disordered metallic mixtures, such as alloys, the disorder limits the mean free path of both the electrons and the phonons, such that the two modes of thermal conductivity are more similar, and kg/kp 3. Similarly, in semiconductors, the density of free electrons is so low that heat transport by phonon conduction dominates. 

The discussion of the previous section would also lead us to believe that since most ceramics are poor electrical conductors (with a few notable exceptions) due to a lack of free electrons, electronic conduction would be negligible compared to lattice, or phonon, conduction. This is indeed the case, and we will see that structural effects such as complexity, defects, and impurity atoms have a profound effect on thermal conductivity due to phonon mean free path, even if heat capacity is relatively unchanged. 

Finally, the thermal conductivities of U-ZrHi 6o and U-ZrHi 90 by phonon conduction (/Ip), plotted as (A, O) in Figs. 5 (a) and (b), were determined by subtracting /Lc from /L. At lower temperatures, the contribution by the phonons was greater than that by the electrons, while both electrons and phonons play an important role in the thermal conductivity above 500 K. 

Heat is transferred through slags by a variety of mechanisms which include convection, radiation and various thermal conduction processes, viz. thermal ("phonon") conductivity, (k ), electronic conductivity (kg ) and radiation conductivity (k ). Methods for estimating the various physical properties involved in these processes are considered below. 

Materials of which compositions are isotopically controlled are expected to show improved physical and nuclear properties which can not be attained by usual combinations of elements[l]. Natural silicon is composed of three stable isotopes such as 2 Si, "Si and "Si. If the purified Si is obtained, high thermal conductivity of silicon and its compounds is achievable because of suppressing isotope scattering against phonon conduction. 

Thermal energy is transported by two mechanisms in solids—electronic conduction and lattice or phonon conduction. An electrical analog for thermal conduction is shown in Fig. 2 [% The total thermal conductivity. A, is the sum of the electronic term and the lattice term. For pure metals and dilute alloys, thermal conduction is dominated by the electronic term, while for heavily alloyed metals, the phonon contribution is appreciable. 

Thermal conductivity. Phonon conductivity is most efficient in simple crystal structures formed by small atoms. 

Debye (in 1914) applied Eq, 34.15 to phonon conduction to describe thermal conductivity in dielectric solids. Then C is the heat capacity of the phonons, v is the phonon velocity, and / is the phonon mean free path. 

Phonon conduction in ceramics is very different from that found in metals where the free electrons are the source of the thermal conductivity. The mobility of phonons is... 

Given the close structural and chemical similarities between the MAX and their corresponding MX phases, it is not surprising (as discussed above) that these two classes of compounds share some common attributes and properties. For example, they are both metal-like conductors dominated by d-d bonding their phonon conductivities are both susceptible to the presence of vacancies and the TCEs of the ternaries track those of the binaries, to name a few. 

Figure 4.3 Thermal conductivity components of titanium carbide as a function of temperature k, = electron conductivity, k = phonon conductivity.

In fluids, the atoms and molecules may themselves migrate and set up convection currents or flow. Radiative heat transfer, on the other hand, requires no medium for transport. Thermal energy is carried with light-wave packets, called photons, and heats up the body when the body absorbs the photons. Whereas the phonon conductivity dominates heat transfer in the glassy state, transfer of heat in molten glass tanks is mostly due to radiative transfer and to some extent by convective and conductive transfer. 

Phonon Conductivity in Single-Phase Crystalline Ceramics... 

Both structure and composition affect phonon conductivity in singlephase crystalline ceramics. Complex structures scatter lattice waves to a greater extent. Hence, thermal conductivity is lower in those structures. For example, magnesium aluminate spinel, consisting of two oxides, has a lower thermal conductivity than the single oxides alumina or magnesia. 

The effects of impurities and solid solutions on phonon conductivity in single-phase crystalline ceramics are discussed next. Impurities and solute atoms tend to decrease thermal conductivity. These increase the phonon scattering by way of differences in mass, binding force, and elastic strain field. As the temperature is raised, the scattering increases at low temperatures. At temperatures greater than about half the Debye temperature, it becomes independent of temperature. This is because the average wavelength at these temperatures becomes comparable with or less than the point imperfection. 

Lattice vibrational energy transport, also known as phonon conduction, occurs in all solids—dielectrics and metals. In nonmetallic crystals and some intermetallic compounds, the principal mechanism of heat conduction is by... 

The high thermal conductivities for relatively pme metals are due to the large numbers of free electrons and the efficiency with which these electrons transport thermal energy. By way of contrast, ceramics and polymers are poor thermal conductors because free-electron concentrations are low and phonon conduction predominates. 

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