Lattice Dynamical Properties of the Rare Earth Aluminum Garnets (RE3Al5O12)

Abstract

This paper reports detailed lattice dynamics studies involving experimental Raman scattering measurements and theoretical rigid ion model calculations of the rare earth aluminum garnets (RE3Al5O12). The studies are fairly involved as these garnets have complex crystal structure with 80 atoms/primitive cell. Our calculations have provided a theoretical understanding of the mode eigenvectors, phonon dispersion relations, density of states, and effective charges of these materials. The calculated Raman mode eigenvectors reveal that they correspond to mixtures of molecular modes of the basic polyhedra, implying thus strongly coupled polyhedra. The assignment of the Raman and infrared active modes has been elucidated and the frequencies of some modes, which do not appear in the vibrational spectrum, have been calculated. Our calculations show a differentiation of the effective charges at the various symmetry sites, which leads to a mostly covalent and to an almost ionic character for the tetrahedral Al–O and the dodecahedral RE–O bonds, respectively. Finally, the dispersion curves along the [100] direction of the Brillouin zone as well as the one and two-phonon density of states have been calculated and discussed.