Lattice of Shell-Model Atoms

Abstract

In this section the equations of equilibrium are derived for a monatomic, one-dimensional lattice of the Cochran type [13] based on the Dick-Overhauser [12] shell-model of the atom: a core, comprising the nucleus and inner electrons, surrounded by a shell of outer electrons. The polarization is proportional to the relative displacement of the core and shell of the atom. In addition to this intra-atomic interaction, account is taken of interatomic interactions between core and core, core and shell and shell and shell of nearest neighbor atoms. It is shown that the equations of the lattice have, as their continuum limit, the equations of the augmented theory, including the contribution of the polarization gradient to the stored energy, rather than the classical theory of elastic dielectrics. The additional effects associated with the new constants b₁₁ and d₁₁ stem primarily from the shell-shell interaction. This interaction is known to be important in the matching of lattice dispersion relations to neutron diffraction dispersion data at short wave lengths [14,15].