Velocity-density systematics: Derivation from Debye theory and the effect of ionic size

Simple approximations for the lattice vibrational spectrum allow the regularities of velocity-density plots with structure and composition to be semiquantitatively explained from a simple and unified point of view. It is possible to explicitly separate paths of constant mean atomic weight A where velocities change because of compression or phase changes from paths of constant crystallographic structure where the mean atomic weight is changed. One can approximate the hydrodynamic velocity υϕ along the path of constant crystallographic structure by the formula ∂ ln υϕ/∂ ln ρ = − ½[1−(∂ ln VM/∂ ln A)]−1, where ρ is the density and VM is the molar volume.