A semiphenomenological theory is proposed for the calculation of the frequency and temperature dependences of the optical properties of polyvalent metals. Utilizing the concept of parallel bands, the transverse optical conductivity is decomposed into a nearly-free-electron part and in an interband part. The theory needs only one fitting parameter, the unknown electron-electron scattering frequency above the Fermi energy. The complete set of optical quantities is calculated for aluminium for a large frequency range (0.01-50 eV) and from T=300 to 2000 K.
Generalizing the Drude conductivity and using experimental data for the complex refractive index or for the complex dielectric function an expression is derived for the determination of the frequency-dependent electron mass, defined as the optical mass. Values for the optical mass are calculated for 27 metals, including in a few both the solid phase and the liquid phase. Additionally, a new formula for the estimation of the polarizability of metals is given and evaluated for 15 metals. Good agreement between existing published literature values and our calculation is found for the optical mass in the zero-frequency limit as well as for the polarizability.
The knowledge of the temperature dependence of the thermal conductivity is necessary in many aspects. It is required, for example, as an important input parameter for the calculation of temperature distributions in metals after interaction with laser pulses. Although extensive compilations exist on this subject they may be of limited value because the data were obtained under steady state conditions where the electrons and phonons are described by a single common temperature. At short laser pulses, however, the electron and phonon subsystems are not in local thermal equilibrium and have to be characterized by different temperatures. It is shown that the validity of the often used linear dependence of the thermal conductivity on the electron temperature is limited to some few thousand kelvin and becomes definitely wrong at higher temperatures. A formula including the thermoelectric effects is derived that is valid throughout the whole temperature range as well as for the case of local thermal equilibrium and nonequilibrium.
Recently we proposed a semiphenomenological theory for the calculation of the optical properties of polyvalent metals. In this paper, we apply it to the heavy metal lead and show that, in contrast to the preceding paper, no fitting parameter is basically necessary. The general agreement between experimental results and theoretical curves is satisfactory for all properties in both the solid and the liquid state. The optical properties in the liquid state are more similar to those of the solid state than to those of a free-electron system and therefore cannot be described by a simple Drude model.
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