Golden ratio of the r+/r- for the structure-selectivity in the thermoelectric BaZn2-xCdxSb2 system

A total of five Zintl phase compounds in the solid-solution BaZn _2-xCd _xSb ₂ (0.10(2) ≤ x ≤ 2) system have been successfully synthesized by the molten Pb-flux method. Both powder X-ray and single-crystal X-ray diffraction analyses proved that the title compounds displayed the phase transition between the BaCu ₂S ₂-type phase (space group Pnma, Z = 4) and the CaAl ₂Si ₂-type phase (space group P 3 ¯ m 1 , Z = 1) depending on the Zn/Cd mixed ratio. Furthermore, this kind of structure selectivity was dictated by the radius ratio criterion between the cationic and the anionic elements ( r ₊/ r _–): three Zn-rich compounds with the r ₊/ r _– > 1 (BaZn _1.90(1)Cd _0.10Sb ₂, BaZn _1.75(2)Cd _0.25Sb ₂, and BaZn _1.62(2)Cd _0.38Sb ₂) preferred to adopt the BaCu ₂S ₂-type phase, while two Cd-rich compounds with the r ₊/ r _{– ≤} 1 (BaZn _0.16(2)Cd _1.84Sb ₂ and BaCd ₂Sb ₂) preferred to crystallize in the trigonal CaAl ₂Si ₂-type phase. A series of TB-LMTO calculations using the two hypothetical models: BaZn _1.5Cd _0.5Sb ₂ and BaZn _0.5Cd _1.5Sb ₂ , proved that a resonance peak in the density of states of BaZn _1.5Cd _0.5Sb ₂ implied the enhanced Seebeck coefficient of the three Zn-rich compounds, and the reduction of band gap observed in a band structure of BaZn _0.5Cd _1.5Sb ₂ influenced the electrical conductivity of the Cd-rich BaZn _0.16(2)Cd _1.84Sb ₂ . Temperature-dependent thermoelectric property measurements showed the maximum ZT of 0.54 for the quaternary BaZn _1.62(2)Cd _0.38Sb ₂, which should mainly be attributed to the reduced κ _tot due to the Zn and Cd disordering in the anionic frameworks.