Optical properties of geomaterials: Specific refraction of low-density silica polymorphs

A linear relationship between the refractive index n and the density ? (often called the specific refraction or Gladstone-Dale law) for pure low-density silica polymorphs is derived from simple atomic properties of SiO2 complex. The considerations are based on the Lorentz electron theory of solids. The eigenfrequency ?0 of elementary electron oscillators, in energy units hv0, is identified with the energy gap EG of a low-quartz. The numerical value of specific refraction is 0.212 cm3/g if we assume EG = 10.1 eV and mean atomic weight = 20.03 g/mol. From laboratory data of several porosils (synthetical isotropic SiO2 phases) with ? = 1.760:1.997 g/cm3 and n = 1.376:1.416 we obtain the average value of the specific refraction equal to 0.211+-0.001 cm3/g.