K and Ba distribution in the structures of the clathrate compounds K_xBa_16−x(Ga,Sn)₁₃₆(x= 0.8, 4.4, and 12.9) and K_xBa_8−x(Ga,Sn)₄₆(x= 0.3)

Abstract

Studies of the K–Ba–Ga–Sn system produced the clathrate compounds K 0.8(2) Ba 15.2(2) Ga 31.0(5) Sn 105.0(5) [ a = 17.0178 (4) Å], K 4.3(3) Ba 11.7(3) Ga 27.4(4) Sn 108.6(4) [ a = 17.0709 (6) Å] and K 12.9(2) Ba 3.1(2) Ga 19.5(4) Sn 116.5(4) [ a = 17.1946 (8) Å], with the type-II structure (cubic, space group Fd \overline{3} m ), and K 7.7(1) Ba 0.3(1) Ga 8.3(4) Sn 37.7(4) [ a = 11.9447 (4) Å], with the type-I structure (cubic, space group Pm \overline{3} n ). For the type-II structures, only the smaller (Ga,Sn) 24 pentagonal dodecahedral cages are filled, while the (Ga,Sn) 28 hexakaidecahedral cages remain empty. The unit-cell volume is directly correlated with the K:Ba ratio, since an increasing amount of monovalent K occupying the cages causes a decreasing substitution of the smaller Ga in the framework. All three formulae have an electron count that is in good agreement with the Zintl–Klemm rules. For the type-I compound, all framework sites are occupied by a mixture of Ga and Sn atoms, with Ga showing a preference for Wyckoff site 6 c . The (Ga,Sn) 20 pentagonal dodecahedral cages are occupied by statistically disordered K and Ba atoms, while the (Ga,Sn) 24 tetrakaidecahedral cages encapsulate only K atoms. Large anisotropic displacement parameters for K in the latter cages suggest an off-centering of the guest atoms.