Molecular refraction in the Earth's mantle

Abstract

The Drude law (molecular refraction) for the temperature radiation in a monoatomic model of the Earth's mantle is derived. The considerations are based on the Lorentz electron theory of solids. The characteristic frequency (or eigenfrequency) of independent electron oscillators (in energy units, ħω) is identified with the band gapEG of a solid. The only assumption is that solid material related to the Earth's mantle has the mean atomic weight 〈A〉≈21 g/mole, and its energy gap (EG) is about 9 eV. In this case the value of molecular refraction (in cm3/g) is (n2−1)/ρ=0.516≈0.52, where ρ andn are the density and the refractive index at wavelength λD=0.5893 μm (‘sodium light’), respectively. The average molecular refraction of important silicate and oxide minerals with 〈A〉≈21, obtained byAnderson andSchreiber (1965) from laboratory data, is\({{(\bar n^2 - 1)} \mathord{\left/ {\vphantom {{(\bar n^2 - 1)} \rho }} \right. \kern-\nulldelimiterspace} \rho } \approx 0.52\), where\(\bar n\) denotes the mean arithmetic value calculated from three principal refractive indices of crystal. For the rock-forming minerals with 19≤〈A〉<24 g/mole the new relation\({{(\bar n^2 - 1)} \mathord{\left/ {\vphantom {{(\bar n^2 - 1)} \rho }} \right. \kern-\nulldelimiterspace} \rho } \approx 0.54\) was found byAnderson (1975).