Abstract
It is shown empirically that the force constant $k=m{\ensuremath{\omega}}^{2}$ of transverse optical vibrations in dielectric solids depends strongly on the fraction of covalent bonding $C=1\ensuremath{-}i$ between neighboring atoms, where $i$ is the fraction of ionic character in the bond. For solids in the heavy isoelectronic series (e.g., the mixed series of Si-Ge, the Ge series, the mixed series of Ge-$\ensuremath{\alpha}$-Sn, and the $\ensuremath{\alpha}$-Sn-series), where the internuclear distances are kept nearly constant within the same isoelectronic series, $k$ depends solely on $C$ and is approximately proportional to ${C}^{n}$ with $1<n<2$. The covalent dependence of the force constant may be interpreted in terms of Pauling's theory of the chemical bond or parameters in the shell model of lattice vibration.
Published Version
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