Lattice dynamics of lead

Abstract

Abstract Dispersion relation v ( q ) of frequency vs.wave number vector for lead are theoretically calculated by extending the Hartree–Fock method for electron–phonon interaction, taking the band structure of lead into account. The shift of electron density accompanying the lattice vibration is shown to be divided into two parts, one of which arises from the intraband transitions of electrons in partially filled bands, and the other from the interband transitions of electrons in partially as well as fully filled bands. The former is shown to play the role of free electrons in the screening effect, while the latter behave like an ion core. Thus, effective matrix elements for electron–phonon interactions and dispersion relations v ( q ) are formulated for multivalent metals. The v ( q ) for lead are hence worked out assuming simplified band structure for lead and compared with observation by B rockhouse et al. The Kohn anomalies in v ( q ) as observed by B rockhouse et al. are also discussed in the light of the present theory.