Lattice-dynamical study of layered silicates

Using a phenomenological bond-stretching and bond-bending (Keating) force-constant model, we calculate the lattice dynamics of a layered silicate (clay) similar to many naturally occurring trioctahedral 2:1 phyllosilicate minerals. These materials can be intercalated with guest species and provide a somewhat complementary system to graphite intercalated compounds. Using simplified models, we derive approximate formulas for the low-frequency q^=0 modes in terms of the intercalant-basal-plane force constants, allowing these quantities to be determined through experimental measurements. Extending the calculations of previous investigators to nonzero wave vector, we present phonon dispersion curves both within and perpendicular to the clay layer, and explain many of the features with the model system introduced for the zone-center modes. Finally, we discuss the elastic properties of these materials, with particular emphasis on the quadratic dispersion characteristic of layered systems.