Phonon spectra in the Frolich approach-application to the transition metals

Abstract

The first part of this paper is devoted to the self-consistent calculation of the phonon spectra for metals whose band structure can be represented by the tight-binding approximation. Firstly the authors take into account the displacement of the tight-binding basis orbitals and obtain self-consistent expressions for the electronic density and potential changes induced by the atomic displacements: they discuss the relation between the Frolich and the Bloch approaches and show that a reasonable approximation allows the Frolich result to be obtained from the Bloch method. Finally the authors obtain simple self-consistent expressions for the electron-phonon matrix elements and for the dynamical matrix. In the second part they apply the previous formal theory to the transition metals. The authors assumed that the band structure can be approximated by a tight-binding nearly free electron model and show-as previously stated by other authors-that the main role of the 'sp' electrons is to screen the interaction between 'd' electrons. The physical meaning of some approximations which must be used in a practical calculation is discussed and the self-consistent expressions of the elastic constants are derived.