Covalent Bonding Effect on Optical Phonons—Empirical Relation

It is shown empirically that the force constant k=mω² of transverse optical vibrations in dielectric solids depends strongly on the fraction of covalent bonding C=1-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-α-Sn, and the α-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 Cⁿ 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.