Study of interaction forces and phonons in some spinels and mixed systems

Abstract

A detailed study of zone centre phonons in mixed spinel structure compounds is presented, using an angular force constant model considering interatomic interactions up to third neighbours only. For the first time the dynamical matrix for spinel structure compounds AB 2X 4 of the order of 42 × 42 has been solved analytically at the zone centre. Using these analytical expressions and the measured zone centre frequencies, the evaluation of the force constants has been carried out first in the case of CdCr 2S 4, CdCr 2Se 4 and ZnCr 2S 4. It has been found that the second neighbour interatomic interaction between B-X atoms is more significant than the first neighbour interaction between A-X atoms in these normal spinels. The physical aspects for the same are discussed. The computed phonon frequencies of CdCr 2S 4, CdCr 2Se 4 and ZnCr 2S 4 at the zone centre agree well with the Raman and the infrared measurements. Finally, the analysis is carried out to study the zone centre phonons in mixed crystals of these spinels.