Thermal conductivity energy concept

The transport of thermal energy can be broken down into one or more of three mechanisms conduction--heat transfer via atomic vibrations in solids or kinetic interaction amongst atoms in gases1 convection - - heat rapidly removed from a surface by a mobile fluid or gas and radiation—heat transferred through a vacuum by electromagnetic waves. The discussion will begin with brief explanations of each. These concepts are important background in the optical measurement of temperature (optical pyrometry) and in experimental measurement of the thermally conductive behavior of materials. 

Thermal conductivity is the most difficult quantity to understand in terms of the electronic structure. Thermal energy can be stored in vibrational normal modes of the crystal, and one can transport thermal energy through the lattice of ions. These concepts seem to be macroscopic. Therefore, one can set up suitable wave packets to treat thermal conductivity as quantized matter. In particular, electron plus induced lattice polarization can be defined as polarons. For conduction electrons, the electrical conductivity and the thermal conductivity were first observed by Wiedemann and Franz as indicated in the following equation ... 

Slack [25] and Cahill et al. [26] explored the theoretical limits on k for solids within a phonon model of heat transport. Their work utilized the concept of the minimum thermal conductivity, Kj n- At this minimum value the mean free path for all heat carrying phonons in a material approaches the phonon wavelengths [25]. In this limit, the material behaves as an Einstein solid in which energy transport occurs via a random walk of energy transfer between localized vibrations in the solid. Experimentally, K an is often comparable to the value in the amorphous state of the same composition. In principle jc in can be achieved by the introduction of one or more phonon scattering mechanisms that reduce the phonon mean free path to its minimum value over a broad range of frequencies, and therefore reduces Kl over a broad range of temperatures. In practice, there are relatively few crystalline compounds for which this limit is approached. 

The classical approach of conduction does not include the above time lag concept or the wavelike response. It expects a delta function-like response of temperature without any time lag with respect to the applied heat pulse. In the classical approach, we use phenomenological models which do not require any knowledge of the mechanism of energy transport or the microstructure of the solids. Fourier s law of heat conduction uses thermal conductivity as a material property which is a function of temperature. This thermal conductivity depends on the microstructure of the solids, which the thermal conductivity data does not show. For example, thermal conductivity of diamond can span an order of magnitude depending on the type of microstructure obtained by chemical vapor deposition. Thermal conductivity of natural... 

In this chapter, we briefly describe fundamental concepts of heat transfer. We begin in Section 20.1 with a description of heat conduction. We base this description on three key points Fourier s law for conduction, energy transport through a thin film, and energy transport in a semi-infinite slab. In Section 20.2, we discuss energy conservation equations that are general forms of the first law of thermodynamics. In Section 20.3, we analyze interfacial heat transfer in terms of heat transfer coefficients, and in Section 20.4, we discuss numerical values of thermal conductivities, thermal diffusivities, and heat transfer coefficients. 

Localized states in the bulk of a semiconductor that have energies within the bandgap are known to capture mobile carriers from the conduction and valence bands.— The bulk reaction rate is determined by the product of the carrier density, density of empty states, the thermal velocity of the carriers and the cross-section for carrier capture. These same concepts are applied to reactions at semic ijiductor surfaces that have localized energy levels within the bandgap.— In that case the electron flux to the surface, F, reacting with a surface state is given by... 

It is the Peierl s instability that is believed to be responsible for the fact that most CPs in their neutral state are insulators or, at best, weak semiconductors. Hence, there is enough of an energy separation between the conduction and valence bands that thermal energy alone is insufficient to excite electrons across the band gap. To explain the conductive properties of these polymers, several concepts from band theory and solid state physics have been adopted. For electrical conductivity to occur, an electron must have a vacant place (a hole) to move to and occupy. When bands are completely filled or empty, conduction can not occur. Metals are highly conductive because they possess unfilled bands. Semiconductors possess an energy gap small enough that thermal excitation of electrons from the valence to the conduction bands is sufficient for conductivity however, the band gap in insulators is too large for thermal excitation of an electron accross the band gap. 

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