Zintl behavior and vacancy formation in type-I Ba-Al-Ge clathrates

In a study of type-I ${\text{Ba}}_8{\text{Al}}_x{\text{Ge}}_{46-x}$ clathrates for $4\le x\le 16$, several samples with different stoichiometric compositions were prepared and measured. Here we report wavelength dispersion spectroscopy, powder x-ray diffraction and resistivity measurements, coupled with first-principles calculations. The lattice constant and vacancy count showed linear behavior for low Al content, extrapolating to the values for ${\text{Ba}}_8{\text{Ge}}_{43}$ as $x\to 0$, with the $x=4$ sample exhibiting a superstructure identical to that of ${\text{Ba}}_8{\text{Ge}}_{43}$. In ab initio calculations we identified the most stable configurations and examined energy differences for departures from Zintl behavior. We found the energy barrier for off-Zintl compositions to be relatively low and attributed this to the presence of a pseudogap near the Fermi energy.

Figure 1

Lattice constant as a function of Al doping. Filled circles correspond to our measured samples. Hollow circle is the reported value for ${\text{Ba}}_8{\text{Ge}}_{43}$ (Ref. 18) and hollow triangles correspond to samples measured by Christensen and Iverson (Ref. 11). Lines correspond to linear fits described in text.

Figure 2

(Color online) Number of vacancies as a function of Al doping. Continuous line is a linear fit to the data. Zintl line is also included as a reference. Horizontal and vertical error bars as described in text.

Figure 3

(Color online) Resistivity as a function of temperature for ${\text{Al}}_4$, ${\text{Al}}_8$, and ${\text{Al}}_{16}$. Solid curves: Bloch-Grüneisen fits.

Figure 4

Band structures for (a) ${\text{Ba}}_8{\text{Ge}}_{43}{◻}_3$ and the lowest energy configurations of (b) ${\text{Ba}}_8{\text{Al}}_{15}{\text{Ge}}_{31}$, (c) ${\text{Ba}}_8{\text{Al}}_{14}{\text{Ge}}_{32}$, and (d) ${\text{Ba}}_8{\text{Al}}_{12}{\text{Ge}}_{34}$.

Figure 5

Total calculated density of states for ${\text{Ba}}_8{\text{Ge}}_{43}$. Upper curve is the total DOS including the interstitial contribution. Ba and Ge contributions of atoms are also shown as labeled.

Figure 6

(Color online) Total calculated density of states for ${\text{Ba}}_8{\text{Al}}_{12}{\text{Ge}}_{34}$ in 3-1-8–0 configuration. Upper curve is the total DOS including the interstitial contribution. Ba, Ge, and Al contributions of atoms are also shown as labeled.