Strong renormalization of Ba vibrations in thermoelectric type-IX clathrate Ba24Ge100

Abstract

We report a combined experimental and theoretical study of the lattice dynamics of the type IX clathrate ${\mathrm{Ba}}_{24}{\mathrm{Ge}}_{100}$ by inelastic neutron scattering (INS) experiments and density functional theory (DFT) calculations. We observe low-energy optical modes at $\ensuremath{\sim}2--3\phantom{\rule{0.16em}{0ex}}\mathrm{meV}$ due to the motion of the heavy Ba atoms along the high-symmetry axis and the largest dimension of the open Ge@20 cages present in the compound. Even though the phonon participation ratio indicates that these low-energy modes are localized, their $Q$ dependence shows that the dynamics of the Ba guests are correlated. We observe a strong change in the spectral weight of these modes when the compound undergoes a temperature-induced structural transformation in the temperature range 190--230 K. In the high-temperature phase, the low-energy optical modes show high intensities in the INS data and frequencies rather insensitive to temperature changes up to \ensuremath{\sim}550 K. In the low-temperature structural modification, the low-energy mode intensities are strongly depleted and apparently shifted to higher energies; this behavior is in line with an off-centering of the Ba atoms at low temperatures. Our DFT calculations successfully approximate the essential features in the dynamics of the high-temperature ${\mathrm{Ba}}_{24}{\mathrm{Ge}}_{100}$ structure.