Lattice dynamics calculations of the phonon spectra and thermodynamic properties of the aluminosilicate garnets pyrope, grossular, and spessartineM3Al2Si3O12(M=Mg,Ca, and Mn)

Abstract

This paper reports lattice dynamics calculations of various microscopic and macroscopic phonon properties of the aluminosilicate garnets pyrope, grossular, and spessartine (given by ${M}_{3}{\mathrm{Al}}_{2}{\mathrm{Si}}_{3}{\mathrm{O}}_{12},$ where $M=\mathrm{Mg},$ Ca, and Mn, respectively) using a transferable interatomic potential based on a shell model. These studies are fairly involved as these garnets have complex crystal structures with 80 atoms/primitive cell. The calculations have provided a theoretical understanding of the elastic constants, equation of state, phonon dispersion relations, and density of states of these materials. The computed density of states is used to derive various macroscopic thermodynamic quantities like the specific heat, thermal expansion, and mean-square atomic displacements. The computed phonon dispersion relations and total and partial densities of states have been particularly useful in interpreting the inelastic neutron-scattering data reported in the literature and the calculated results are found to be in good agreement with available experimental data. These studies have enabled a microscopic understanding of the variations in the phonon spectra of these materials and their manifestations in various macroscopic thermodynamic properties.