Complex vibrations in arsenide skutterudites and oxyskutterudites

Abstract

The local structure of two skutterudite families---$\mathrm{Ce}{M}_{4}{\mathrm{As}}_{12}$ ($M=\mathrm{Fe}$, Ru, Os) and $Ln{\mathrm{Cu}}_{3}{\mathrm{Ru}}_{4}{\mathrm{O}}_{12}$ ($Ln=\mathrm{La}$, Pr, and Nd)---have been studied using the extended x-ray absorption fine structure (EXAFS) technique with a focus on the lattice vibrations about the rare-earth ``rattler atoms'' and the extent to which these vibrations can be considered local modes, with the rattler vibrating inside a nearly rigid cage. X-ray absorption data at all the metal edges were collected over a temperature range of 4 to 300 K and analyzed using standard procedures. The pair distances from EXAFS results agree quite well with the average structure obtained from diffraction. The cage structure is formed by the $M$ and As atoms in $\mathrm{Ce}{M}_{4}{\mathrm{As}}_{12}$ and by Cu, O, and Ru atoms in $Ln{\mathrm{Cu}}_{3}{\mathrm{Ru}}_{4}{\mathrm{O}}_{12}$. Although some of the bonds within the cage are quite stiff (correlated Debye temperatures, ${\ensuremath{\theta}}_{\mathrm{cD}}$, are $\ensuremath{\sim}500$ K for $\mathrm{Ce}{M}_{4}{\mathrm{As}}_{12}$ and above 800 K for $Ln{\mathrm{Cu}}_{3}{\mathrm{Ru}}_{4}{\mathrm{O}}_{12}$), we show that the structure is not completely rigid. For the rattler atom the nearest-neighbor pairs have a relatively low Einstein temperature, ${\ensuremath{\theta}}_{\mathrm{E}}:\ensuremath{\sim}100--120$ K for Ce-As and $\ensuremath{\sim}130$ K for $Ln\text{\ensuremath{-}}\mathrm{O}$. Surprisingly, the behaviors of the second-neighbor pairs are quite different: for $\mathrm{Ce}{M}_{4}{\mathrm{As}}_{12}$ the second-neighbor pairs $(\mathrm{Ce}\text{\ensuremath{-}}M)$ have a weaker bond while for $Ln{\mathrm{Cu}}_{3}{\mathrm{Ru}}_{4}{\mathrm{O}}_{12}$ the $Ln\text{\ensuremath{-}}\mathrm{Ru}$ second-neighbor pair has a stiffer effective spring constant than the first-neighbor pair. In addition, we show that the ${\mathrm{As}}_{4}$ or ${\mathrm{CuO}}_{4}$ rings are relatively rigid units and that their vibrations are anisotropic within these cubic structures, with stiff restoring forces perpendicular to the rings and much weaker restoring forces in directions parallel to the rings. Consequently vibrations of the rings may also act as ``rattlers'' and help suppress thermal conductivity. In general neither the rigid-cage approximation nor the simple reduced-mass approximation are sufficient for describing rattler behavior.