Optical Properties of Nickel and Tungsten and Their Interpretation According to Drude's Formula

Abstract

New optical data are reported for nickel at 88\ifmmode^\circ\else\textdegree\fi{}, 298\ifmmode^\circ\else\textdegree\fi{}, and 473\ifmmode^\circ\else\textdegree\fi{}K and for tungsten at 298\ifmmode^\circ\else\textdegree\fi{}, 1100\ifmmode^\circ\else\textdegree\fi{}, and 1600\ifmmode^\circ\else\textdegree\fi{}K in the wavelength range 0.365 to 2.65 microns. These data are shown to depend on wavelength in a way which is in good quantitative agreement with a formula initially proposed by Drude. By attributing different terms in Drude's equation to the motion of different classes of free and bound electrons, one may conclude that several classes of each are present in both metals. Each class of free electrons accounts for a portion of the dc conductivity and has its own characteristic relaxation time or wavelength. From this analysis it appears that most of the dc conductivity may be attributed to one class of free electrons, although optical properties are strongly influenced by other classes as well. In both metals the characteristic wavelength ${\ensuremath{\lambda}}_{r1}$ of the first class of free electrons proves to be proportional to the corresponding conductivity ${\ensuremath{\sigma}}_{1}$ at different temperatures. In nickel the constant ratio $\frac{{\ensuremath{\sigma}}_{1}}{{\ensuremath{\lambda}}_{r1}}$ accounts for the low temperature coefficient of optical properties throughout the visible and near infrared range. In tungsten this constant ratio contributes to the existence of the $x$-point or cross-over wavelength in the spectral emissivity. It is shown that the anomalous skin effect may not be a significant factor in the measured optical properties of a metal like nickel in the range of wavelength where these properties have only a small temperature coefficient.