Neutron and nuclear inelastic scattering study of the Einstein oscillators in Ba-, Sr-, and Eu-filled germanium clathrates

Abstract

Inelastic neutron scattering measurements on ${\mathrm{Ba}}_{8}{\mathrm{Ga}}_{16}{\mathrm{Ge}}_{30}$ and ${\mathrm{Sr}}_{8}{\mathrm{Ga}}_{16}{\mathrm{Ge}}_{30}$ indicate the presence of soft local modes with Einstein oscillator energies of $4.9\ifmmode\pm\else\textpm\fi{}0.1$ and $4.4\ifmmode\pm\else\textpm\fi{}0.1\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$, modes which are associated with the lowest ``rattling'' mode of the Ba(B) and Sr(B) guests, respectively. Nuclear inelastic scattering measurements on ${\mathrm{Eu}}_{8}{\mathrm{Ga}}_{16}{\mathrm{Ge}}_{30}$ yield Einstein oscillator energies of between $3.0\ifmmode\pm\else\textpm\fi{}0.3$ and $7.5\ifmmode\pm\else\textpm\fi{}1.2\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$ for the different modes of the Eu guests. Further, the resonant character of the measurements on ${\mathrm{Eu}}_{8}{\mathrm{Ga}}_{16}{\mathrm{Ge}}_{30}$ reveals, without question, that neither of the Eu guests exhibit any vibrational modes above $9\phantom{\rule{0.3em}{0ex}}\mathrm{meV}$.