Lattice dynamics of pyrite FeS₂ — polarizable-ion model

Abstract

Lattice dynamical calculations of the pyrite FeS₂ were performed using the polarizable-ion model (PIM) with different sets of short-range force constants. Not until the mean deviations between the observed and the calculated phonon energies become smaller than 3 cm^-1, the true force field can be established. In the case of only slightly greater deviations, the force fields computed differ strongly being without any physical meaning. The results are discussed with respect to the force constants K _i , F _i , and H _i , the effective dynamic charges and polarizabilities of the atoms involved, and the eigenvectors and potential energy distributions of the phonon modes. The most important short-range force constants are K ₁ (Fe-S stretching): 0.5 N cm^-1, K ₂ (internal stretching of the S₂ units): 1.0 N cm^-1, F ₁ (Fe^....Fe stretching): 0.2 N cm^-1, which indicate repulsive interactions of Fe atoms due to the occupied t _2g orbitals despite the relatively large Fe⋯Fe distances of 383 pm, and F ₂ and F ₃ (both intermolecular S₂⋯S₂ interactions): 0.2 N cm^-1. The great TO/LO splittings of some of the IR allowed phonon modes (species F _u) are caused by the large polarizabilities (2.4^.10⁶ and 3.3^.10⁶ pm³) of the atoms involved rather than by their effective charges (Fe: 0.2 e).