Low-temperature x-ray crystal structure analysis of the cage-structured compounds MBe13(M=La,Sm,and U)

Abstract

The beryllides $M{\mathrm{Be}}_{13}\phantom{\rule{4pt}{0ex}}(M$ = rare earths and actinides) crystallize in a ${\mathrm{NaZn}}_{13}$-type cubic structure, which can be categorized as a cage-structured compound. In this study, powder x-ray diffraction measurements have been performed on ${\mathrm{LaBe}}_{13},{\mathrm{SmBe}}_{13}$, and ${\mathrm{UBe}}_{13}$ in the temperature range between 7 and 300 K in order to investigate their crystallographic characteristics systematically. They keep the ${\mathrm{NaZn}}_{13}$-type cubic structure down to the lowest temperature. We estimated their Debye temperature to be 600--750 K from analyses of the temperature dependence of a lattice parameter, being in good agreement with the values reported previously. Rietveld refinements on the obtained powder patterns revealed that the $M$ atom in the $8a$ site is located in an almost ideal snub cube formed by $24{\mathrm{Be}}^{\mathrm{II}}$ atoms in the $96i$ site, whose caged structure is unchanged even at the low temperatures. In addition, it is argued from the temperature variation of an isotropic mean-square displacement parameter that the $M{\mathrm{Be}}_{13}$ compounds commonly have a low-energy phonon mode, which can be described by a model assuming an Einstein oscillation of the $M$ atom with a characteristic temperature of $\ensuremath{\sim}160$ K.