Barium Triel Mercurides BaMxHg4−x and Ba3MxHg11−x (M = Ga, In, Cd)

The systematic experimental and bond-theoretical study of the phase width of the BaAl₄ structure type in the ternary system BaIn₄–BaHg₄ shows that this structure type is stable up to BaIn_1.7Hg_2.3 (tetragonal, tI10, space group I4/mmm, a = 474.2(3), c = 1228.7(9) pm, R1 = 0.0529). The planar 4⁴ layers (M(2) site) are preferentially formed by In, whereas Hg occupies the tips (M(1) site) of the [M(1)M(2)₄] square pyramids. The layers of the pyramids are connected via short M(1)–M(1) dumbbells (bonds a). The analysis of the calculated band structures of BaIn₂Hg₂ in comparison to BaIn₄ and RbIn₄ shows that contributions of Ba-d states (which are missing for RbIn₄) and Hg-d states (which are missing in the pure indides) are significant. The respective compound with the smaller triel gallium (Hg-richest phase: BaGa_1.9Hg_2.1, tetragonal, oI40, space group I4₁/amd, a = 671.3(2), c = 2220.4(8) pm, Z = 8, R1 = 0.0641) forms a new superstructure of the BaAl₄ structure with a partial ordering of three statistically occupied mixed Ga/Hg positions. The 4⁴ nets are formed by an intermediate proportion of Ga/Hg. The tips of the pyramids are alternately formed by a Ga- and an Hg-rich position leading to smaller and larger bond lengths a' and a'', respectively, between the tip atoms and, consequentely, a puckering of the 4⁴ net. The two Hg-rich 3:11 compounds Ba₃InHg₁₀ and Ba₃CdHg₁₀ (orthorhombic, oI28, space group Immm, a = 513.96(8)/511.50(2), b = 993.8(2)/991.54(3), c = 1500.7(3)/1499.26(5) pm, Z = 2, R1 = 0.0619/0.0482) crystallize in the La₃Al₁₁ structure type, which is also observed for K₃Hg₁₁ and is closely related to the BaAl₄ type: The square pyramidal nets are corrugated leading to a triplication of the BaAl₄ unit cell along one of the tetragonal axes. In each third subcell the tips of adjacent pyramids are directly fused, this position being occupied exclusively by In and Cd. With the smaller triel gallium, the 3:11 compound Ba₃Ga_0.2Hg_10.8 crystallizes in the Ba₃ZnHg₁₀ structure type (orthorhombic, oP28, space group Pmmn, a = 709.36(4), b = 1707.96(9), c = 630.78(4) pm, Z = 2, R1 = 0.0342). The structure contains folded layers of flat rectangular Ga/Hg pyramids, leaving large channels at the folds, in which Ba(1) and Hg(2) atoms alternate. The formation and stability ranges of 1:4, 3:11 and related 5:19 trieles/mercurides are discussed taking geometric, electronic and M¹³/Hg ‘coloring’ aspects into account.