Determination of interatomic interactions in complex ionic crystals from structural and lattice-dynamical data

Abstract

Structural and lattice-dynamical data contain a large amount of information about the interactions in ionic or partially ionic crystals with complex structures. As the complexity of the structure increases, i.e., as the number of ions per unit cell, $n$, becomes large, these become even richer sources of information. These data already exist for a large number of materials, but only recently has it been systematically used to determine interactions in very complex ($n>\mathrm{}20\mathrm{}$) crystals. Very good agreement with experiment was obtained using the rigid-ion approximation with adjustable charges. The object of this paper is to provide the reader with an essentially self-contained treatment of the statics and dynamics of rigid-ion crystals and show how the experimental data may be effectively used to determine the interactions. For very complex crystals the model is primarily determined from the structural data alone using static-equilibrium conditions. This is fortunate since the static-equilibrium conditions are relatively easy to solve compared to the dynamical problem. Methods for making the most of the structural data are discussed. Lattice dynamics in the rigid-ion approximation and the transformation to symmetry coordinates are reviewed. Rotational invariance is shown to be a consequence of the static-equilibrium conditions. Practical considerations which arise in solving the dynamical problem are discussed.