1971/02/15 by S. H. Wemple, M. DiDomenico · 5 citations
Physics and Astronomy · Chemistry · Materials Science · #Spectroscopy and Quantum Chemical Studies #Electrochemical Analysis and Applications #Solid-state spectroscopy and crystallography
paper · doi:10.1103/physrevb.3.1338
Refractive-index dispersion data below the interband absorption edge in more than 100 widely different solids and liquids are analyzed using a single-effective-oscillator fit of the form n2\ensuremath-1=\fracEdE0(E02\ensuremath-\ensuremathℏ2\ensuremathω2), where \ensuremathℏ\ensuremathω is the photon energy, E0 is the single oscillator energy, and Ed is the dispersion energy. The parameter Ed, which is a measure of the strength of interband optical transitions, is found to obey the simple empirical relationship Ed=\ensuremathβNcZaNe, where Nc is the coordination number of the cation nearest neighbor to the anion, Za is the formal chemical valency of the anion, Ne is the effective number of valence electrons per anion (usually Ne=8), and \ensuremathβ is essentially two-valued, taking on the "ionic" value \ensuremathβi=0.26\ifmmode±\else\textpm\fi0.04 eV for halides and most oxides, and the "covalent" value \ensuremathβc=0.37\ifmmode±\else\textpm\fi0.05 eV for the tetrahedrally bonded ANB^8\ensuremath-N zinc-blende- and diamond-type structures, as well as for scheelite-structure oxides and some iodates and carbonates. Wurtzite-structure crystals form a transitional group between ionic and covalent crystal classes. Experimentally, it is also found that Ed does not depend significantly on either the bandgap or the volume density of valence electrons. The experimental results are related to the fundamental \ensuremathε2 spectrum via appropriately defined moment integrals. It is found, using relationships between moment integrals, that for a particularly simple choice of a model \ensuremathε2 spectrum, viz., constant optical-frequency conductivity with high- and low-frequency cutoffs, the bandgap parameter Ea in the high-frequency sum rule introduced by Hopfield provides the connection between the single-oscillator parameters (E0,Ed) and the Phillips static-dielectric-constant parameters (Eg,\ensuremathℏ\ensuremathωp), i.e., (\ensuremathℏ\ensuremathωp)2=EaEd and Eg2=EaE0. Finally, it is suggested that the observed dependence of Ed on coordination number and valency implies that an understanding of refractive-index behavior may lie in a localized molecular theory of optical transitions.