Comparison of infrared reflectance spectra of fluoride perovskites

Vibrational frequencies of 11 alkali-metal-fluorides with the cubic perovskite structure were found to relate directly to either the cation mass, reduced mass μ, lattice constant a, or to reduced force constant a ^{-3 2}μ^-1. These simple relationships are used to predict peak positions for missing or inactive modes. Lattice constant has the strongest affect on frequency. If lattice constant is more than 4.1 Å (mostly perovskites with heavy cations), then the infrared (IR) frequencies depend linearly on force constant, with non-parallel slopes. The variation in behavior is consistent with assignments based on symmetry analysis, i.e. from low to high frequency, the IR modes are mainly a translation of the dodecahedral cation, an octahedral bend, and an octahedral stretching motion. If the lattice constant is less than 4.1Å (mostly perovskites with light cations), then IR frequencies depend linearly on force constant and have parallel slopes, indicating that their modes are largely mixed. Force constants in perovskite were found to be slightly lower if the electronic configuration of the octahedral cation is spherical, rather than non-spherical.