Lattice dynamics at zero wave vector and elastic constants of spinel in the rigid ion approximation

Abstract

The long wavelength limit of the optical frequencies and of the microscopic Grueneisen parameters, the elastic constants and their first and second pressure derivatives are calculated for the spinel structure from a modified rigid ion model. The model includes Coulomb, first and second neighbor two-body central force interaction, and the three-body central force interaction of Basu and Sengupta for the tetrahedral and octahedral cation-anion units. Application to Al 2MgO 4 is made on the basis of (a) a rigid ion model and (b) the above modified rigid ion model with the three-body forces included for the MgO 4 tetrahedra. In addition to two parameters which are determined by the equilibrium conditions the models contain three and four parameters, respectively, which are fitted to experimental values of one Raman and two i.r. frequencies and, for model (b), to one elastic constant. Good to fair agreement with experimental data of the remaining optical frequencies, elastic constants and their first pressure derivatives and the macroscopic Grüneisen parameter is obtained. Both models results in new assignments for the Raman and i.r. active modes.