Structure and thermoelectric properties of the new quaternary bismuth selenides A_1-xM_4-xBi_11+xSe₂₁ (A = K and Rb and Cs; M = Sn and Pb) members of the grand homologous series k_m(M₆Se₈)_m(M_5+nSe _9+n)

Several members of the new family A_1-xM_4-xBi_11+xSe₂₁ (A = K, Rb, Cs; M = Sn, Pb) were prepared by direct combination of A₂Se, Bi₂Se₃, Sn (or Pb), and Se at 800°C. The single-crystal structures of K_0.54Sn_3.54Bi_11.46Se₂₁,K _1.46 Pb_3.08Bi_11.46Se₂₁, Rb_0.69Pb_3.69Bi_11.31Se_21,, and Cs_0.65Pb_3.65Bi_11.35Se₂₁ were determined. The compounds A_1-xM_4-xBi_11+x Se₂₁ crystallize in a new structure type with the monoclinic space group C2/m, in which building units of the Bi₂Te₃ and NaCl structure type join to give rise to a novel kind of three-dimensional anionic framework with alkali-ion-filled tunnels. The building units are assembled from distorted, edge-sharing (Bi,Sn)Se₆ octahedra. Bi and Sn/Pb atoms are disordered over the metal sites of the chalcogenide network, while the alkali site is not fully occupied. A grand homologous series K_m(M₆Se₈)_m(M_5+nSe _9+n) has been identified of which the compounds A_1-x M_4-xBi_11+xSe₂₁ are members. We discuss here the crystal structure, charge-transport properties, and very low thermal conductivity of A_1-xM_4-xBi_11+xSe₂₁.