Thermoelectric properties of Ga-doped Ba₈Al _x Si _46-x clathrate

Single-crystalline Ba₈Al _x Ga _y Si _46-x-y clathrates were synthesized by the arc melting method and Czochralski method without subsequent treatment, and their thermoelectric properties were compared with those of Ba₈Al _x Ga _y Si_46-x-y and Ba₈Al _x Si _46-x clathrates with almost the same carrier concentration as estimated from the similar Seebeck coefficient and the Zintl concept. The resistivity of Ba_7.8Al_5.3Ga_7.4Si_33.3 was lower than that of Ba_7.9Al_12.6Si_33.4. The specific electrical resistance of Ba_7.9Al_12.6Si _33.4 and Ba_7.8Al_5.3Ga_7.4Si _33.3 was 0.573 mΩ cm and 0.282 mΩ cm at 750 K, respectively. The band structure of Ba₈Al₈Ga ₈Si₃₀ and Ba₈Al₁₆Si₃₀ was estimated by first-principle calculations using density functional theory with the local density approximation. Based on these calculations, it was found that the shape of the bottom of the conduction band for Ba₈Al _x Si_46-x clathrate changed slightly on Ga doping and the radius of curvature of the bottom of the conduction band for Ba₈Al ₈Ga₈Si₃₀ clathrate was lower than that for Ba₈Al₁₆Si₃₀ clathrate. These results indicate that the mobility was enhanced by Ga doping of Ba₈Al _x Si_46-x clathrate. We also synthesized single-crystalline Ga-doped Ba₈Al _x Si_46-x clathrate. The electrical resistivity decreased dramatically due to the single-crystallization because of reduced electron scattering on grain boundaries. These results suggest that Ga doping and single-crystallization are effective for improvement of the thermoelectric properties of Ba₈Al _x Si_46-x clathrate.