Structure and physical properties of type-I clathrate solid-solution ${\mathrm{Ba}}_8{\mathrm{Pt}}_x{\mathrm{Ge}}_{46-x-y}{◻}_y$ $(◻=\text{vacancy})$

Formation, crystal chemistry, and physical properties were investigated for the solid-solution ${\mathrm{Ba}}_8{\mathrm{Pt}}_x{\mathrm{Ge}}_{46-x-y}{◻}_y$ ($◻$ is a vacancy) deriving from binary clathrate ${\mathrm{Ba}}_8{\mathrm{Ge}}_{43}{◻}_3$ with a solubility limit of $\sim 3.5$ Pt atoms/f.u. at $T=800°\mathrm{C}$. Structural investigations throughout the homogeneity region confirm isotypism with the cubic primitive clathrate type-I structure (space group type $Pm\overline{3}n$) and lattice parameters ranging from $a=1.0657\left(2\right)\mathrm{nm}$ for ${\mathrm{Ba}}_8{\mathrm{Ge}}_{43}{◻}_3$ to $a=1.0752\left(2\right)\mathrm{nm}$ for ${\mathrm{Ba}}_8{\mathrm{Pt}}_{3.5}{\mathrm{Ge}}_{41.5}{◻}_{1.0}$. Phase relations for the region concerning the clathrate solution were derived at subsolidus temperatures as well as at $800°\mathrm{C}$. Transport properties evidence electrons as the majority charge carriers in the system with a slight dependency on the Pt content. The system is located close to a semiconducting regime with a gap in the electronic density of states of a few thousand K. No low temperature maximum is obvious from thermal conductivity which is dominated by the lattice contribution. Thermal conductivity furthermore documents a high efficiency of phonon scattering on vacancies.

Figure 1

(Color online) Lattice parameters vs Pt content for ${\mathrm{Ba}}_8{\mathrm{Pt}}_x{\mathrm{Ge}}_{46-x-y}{◻}_y$ alloys. The dashed line denotes the solubility limit of Pt at $T=800°\mathrm{C}$.

Figure 2

(Color online) (a) Defect concentration $y$ vs Pt content $x$; dependences of deficiency from $M$ content $(M=\mathrm{Pt},\mathrm{Pd},\mathrm{Zn},\mathrm{Cd})$ in ${\mathrm{Ba}}_8{\mathrm{Pt}}_x{\mathrm{Ge}}_{46-x-y}{◻}_y$ are compared for two boundary models for the incorporation of $M$ atoms in the lattice of ${\mathrm{Ba}}_8{\mathrm{Ge}}_{43}{◻}_3$; (b) the $6d$ site preference for ${\mathrm{Ba}}_8{\mathrm{Pt}}_x{\mathrm{Ge}}_{46-x-y}{◻}_y$.

Figure 3

Partial isothermal section at $T=800°\mathrm{C}$ for the region $\mathrm{Ge}\text{−}\mathrm{Pt}\mathrm{Ge}\text{−}\mathrm{Ba}{\mathrm{Ge}}_2$.

Figure 4

(Color online) Temperature displacement parameters of ${\mathrm{Ba}}_8{\mathrm{Pt}}_{2.7}{\mathrm{Ge}}_{41.7}{◻}_{1.6}$ vs temperature. M1 denotes a random mixture of [0.442 $\mathrm{Pt}+0.302\left(5\right)$ $\mathrm{Ge}+0.256$ vacancy] as shown in Fig. 2.

Figure 5

(Color online) (a) Energy dependent reflectivity of ${\mathrm{Ba}}_8{\mathrm{Pt}}_x{\mathrm{Ge}}_{46-x-y}{◻}_y$ for $x=2.7$ and 3.3 measured at room temperature. The thin solid lines are least-squares fits. (b) Optical conductivity of ${\mathrm{Ba}}_8{\mathrm{Pt}}_x{\mathrm{Ge}}_{46-x-y}{◻}_y$ for $x=2.7$ and 3.3 as obtained by spectroscopic ellipsometry and KK analysis at room temperature.

Figure 6

(Color online) Temperature dependent resistivity $\rho$ of various concentrations of ${\mathrm{Ba}}_8{\mathrm{Pt}}_x{\mathrm{Ge}}_{46-x-y}{◻}_y$, plotted in a normalized representation (a) and on an absolute scale (b). The solid lines are least-squares fits as explained in the text.

Figure 7

(Color online) Lattice (${\lambda }_{\mathit{ph}}$, filled and semifilled symbols) and electronic (${\lambda }_e$, short- and long-dashed lines) thermal conductivities of ${\mathrm{Ba}}_8{\mathrm{Pt}}_{2.7}{\mathrm{Ge}}_{41.8}{◻}_{1.5}$ and ${\mathrm{Ba}}_8{\mathrm{Pt}}_{3.3}{\mathrm{Ge}}_{41.6}{◻}_{1.1}$. The data corresponding to the filled symbols are derived from those with semifilled symbols by subtracting a radiation-loss term proportional to $T^3$. The solid lines are least-squares fits according to Eq. (2). The dashed dotted line corresponds to the upper border of the theoretical lower limit of the lattice thermal conductivity.

Figure 8

(Color online) Temperature dependent thermopower $S\left(T\right)$ for various concentrations of ${\mathrm{Ba}}_8{\mathrm{Pt}}_x{\mathrm{Ge}}_{46-x-y}{◻}_y$; $x=2.0$, $x=2.7$, and $x=3.3$. The sample with $x=3.3$ was measured in an extended temperature range.