Tropochemical Cell-Twinning in the New Quaternary Bismuth Selenides K _xSn_6-2xBi_2+xSe₉ and KSn ₅Bi₅Se₁₃

The quaternary K_xSn_6-2xBi_2+xSe ₉ were discovered from reactions involving K₂Se, Bi ₂Se₃, Sn, and Se. The single crystal structures reveal that K_xSn_6-2xBi_2+xSe₉ is isostructural to the mineral heyrovskyite, Pb₆Bi₂S ₉, crystallizing in the space group Cmcm with a = 4.2096(4) Å, b = 14.006(1) Å, and c = 32.451(3) Å while KSn₅Bi ₅Se₁₃ adopts a novel monoclinic structure type (C2/m, a = 13.879(4) Å, b = 4.205(1) Å, c = 23.363(6) Å, β = 99.012(4)°). These compounds formally belong to the lillianite homologous series xPbS·Bi₂S₃, whose characteristic is derivation of the structure by tropochemical cell-twinning on the (311) plane of the NaCl-type lattice with a mirror as twin operation. The structures of K_xSn_6-2xBi_2+xSe₉ and KSn ₅Bi₅Se₁₃ differ in the width of the NaCl-type slabs that form the three-dimensional arrangement. While cell-twinning of 7 octahedra wide slabs results in the heyrovskyite structure, 4 and 5 octahedra wide slabs alternate in the structure of KSn₅Bi₅Se ₁₃. In both structures, the Bi and Sn atoms are extensively disordered over the metal sites. Some physicochemical properties of K _xSn_6-2xBi_2+xSe₉ and KSn ₅Bi₅Se₁₃ are reported.