The Free Electron Contribution

The thermal conductivity of a metal or alloy consists of two components, a phonon contribution (a phonon is a quantum of acoustic energy, which possesses wave-particle duality), Kph, and an electronic contribution (free electrons moving through the crystal also carry thermal energy), k i- In pure metals, Xei is the dominant contribution to the total thermal conduction. This free electron contribution to the thermal conductivity is given by the gas-kinetic formula as  

The fact that the thermal conductivity in a pure metal is dominated by the free electron contribution was Ulustrated in 1853 by Gustav Wiedemann (1826-1899) and Rudolf Franz (1827-1902), who showed that Xei and the electrical conductivity, (Tei, are proportionally related (Wiedemann and Franz, 1853). A few years later Danish physicist Ludvig Lorenz (1829-1891) realized that this ratio scaled hnearly with the 

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The free-electron contribution to the dielectric function in Fig. 9A2b is obtained from the Drude theory with parameters determined from the low-... 

The calculated extinction spectrum of a polydispersion of small aluminum spheres (mean radius 0.01 jam, fractional standard deviation 0.15) is shown in Fig. 11.4 both scales are logarithmic. In some ways spectral extinction by metallic particles is less interesting than that by insulating particles, such as those discussed in the preceding two sections. The free-electron contribution to absorption in metals, which dominates other absorption bands, extends from radio to far-ultraviolet frequencies. Hence, extinction features in the transparent region of insulating particles, such as ripple and interference structure, are suppressed in metallic particles because of their inherent opacity. But extinction by metallic particles is not without its interesting aspects. 

Ey stands for the free-electron contribution, which can be described in a classical way by the Drude model [9] ... 

If one considers heat transfer in a temperature range high enough for ionization to occur, one might be tempted to expect a strong increase of the heat transfer coefficient because the free electrons contribute strongly to the thermal conductivity, as they do in a metal. 

The first example concerns the ER effect, an effect which is always present in optical studies of electrode surfaces but which was first recognised using reflectance spectroscopy. It arises from the fact that, even in the absence of any surface reaction, there is a layer at the electrode surface (typically less than 0.1 nm thick) that does not have the same optical properties as the bulk electrode, and that the optical properties of this layer are potential dependent. There are now several theories to account for the ER effect the simplest, and one that accounts fairly well for the behaviour observed at noble metal electrodes, is due to McIntyre Aspnes [23]. It assumes that the optical properties of the metal can be split into two contributions, one from bound electrons and the other from free electrons. Whilst the bound electron contribution is assumed to be independent of the electrode potential, the free electron contribution changes with the surface charge density, and thus the potential. For normal incidence it is shown that... 

It is clear from Figure 27.5, that the contribution of free electrons and the core electrons to the annihilation process are well resolved. The inverted parabolas represent the free electrons contributing to annihilation process, while the broad Gaussian curves represent the contribution of the core electrons. 

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