Crystal structures, atomic vibration, and disorder of the type-I thermoelectric clathratesBa8Ga16Si30,Ba8Ga16Ge30,Ba8In16Ge30, andSr8Ga16Ge30

Abstract

Temperature dependent synchrotron powder diffraction and single crystal neutron diffraction data are used for probing the vibrational states and disorder in type I clathrates ${\mathrm{Ba}}_{8}{\mathrm{Ga}}_{16}{\mathrm{Si}}_{30}$, ${\mathrm{Ba}}_{8}{\mathrm{Ga}}_{16}{\mathrm{Ge}}_{30}$, ${\mathrm{Ba}}_{8}{\mathrm{In}}_{16}{\mathrm{Ge}}_{30}$, and ${\mathrm{Sr}}_{8}{\mathrm{Ga}}_{16}{\mathrm{Ge}}_{30}$. If an empirical disorder term is included, the temperature dependence of the atomic displacement factors (ADPs) of the framework and guest atoms can be described by a Debye and Einstein model, respectively. None of the guest atoms in the large cages are located in the center and the vibrational frequencies $({\ensuremath{\theta}}_{\mathrm{E}})$ are of the order $80\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ or larger for all structures, in good agreement with theoretical predictions. Even though the Sr ADPs are larger than the Ba ADPs in all the clathrates, the data show that ${\ensuremath{\theta}}_{\mathrm{E}}$ of Sr in ${\mathrm{Sr}}_{8}{\mathrm{Ga}}_{16}{\mathrm{Ge}}_{30}$ is larger than for the Ba atoms. This is due to stronger guest-host chemical bonding in ${\mathrm{Sr}}_{8}{\mathrm{Ga}}_{16}{\mathrm{Ge}}_{30}$. Since ${\ensuremath{\theta}}_{\mathrm{E}}$ of Sr has been reported to be much smaller in the literature we have also measured the specific heat of ${\mathrm{Sr}}_{8}{\mathrm{Ga}}_{16}{\mathrm{Ge}}_{30}$ with ${\mathrm{Ba}}_{8}{\mathrm{Ga}}_{16}{\mathrm{Ge}}_{30}$ as a reference. It is found that localized excitations with a characteristic energy of approximately $35\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ exist in both compounds, however, the total number of states is too low to be associated with either tunneling states or localized vibration of each of the guest atoms.