Mg6TiBi crystallizes in the orthorhombic Amm2 space group. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Ti(1), and two equivalent Bi(1) atoms to form distorted MgMg8Ti2Bi2 cuboctahedra that share corners with four equivalent Ti(1)Mg10Bi2 cuboctahedra, corners with four equivalent Bi(1)Mg10Ti2 cuboctahedra, corners with ten equivalent Mg(1)Mg8Ti2Bi2 cuboctahedra, edges with two equivalent Mg(1)Mg8Ti2Bi2 cuboctahedra, edges with two equivalent Ti(1)Mg10Bi2 cuboctahedra, edges with two equivalent Bi(1)Mg10Ti2 cuboctahedra, edges with four equivalent Mg(4)Mg10Bi2 cuboctahedra, edges with four equivalent Mg(3)Mg10Ti2 cuboctahedra, edges with four equivalent Mg(2)Mg8Ti2Bi2 cuboctahedra, faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra, faces with two equivalent Mg(3)Mg10Ti2 cuboctahedra, faces with two equivalent Ti(1)Mg10Bi2 cuboctahedra, faces with two equivalent Bi(1)Mg10Ti2 cuboctahedra, faces with four equivalent Mg(1)Mg8Ti2Bi2 cuboctahedra, and faces with eight equivalent Mg(2)Mg8Ti2Bi2 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Ti(1), and two equivalent Bi(1) atoms to form distorted MgMg8Ti2Bi2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Bi2 cuboctahedra, corners with four equivalent Mg(3)Mg10Ti2 cuboctahedra, corners with ten equivalent Mg(2)Mg8Ti2Bi2 cuboctahedra, edges with two equivalent Mg(4)Mg10Bi2 cuboctahedra, edges with two equivalent Mg(3)Mg10Ti2 cuboctahedra, edges with two equivalent Mg(2)Mg8Ti2Bi2 cuboctahedra, edges with four equivalent Mg(1)Mg8Ti2Bi2 cuboctahedra, edges with four equivalent Ti(1)Mg10Bi2 cuboctahedra, edges with four equivalent Bi(1)Mg10Ti2 cuboctahedra, faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra, faces with two equivalent Mg(3)Mg10Ti2 cuboctahedra, faces with two equivalent Ti(1)Mg10Bi2 cuboctahedra, faces with two equivalent Bi(1)Mg10Ti2 cuboctahedra, faces with four equivalent Mg(2)Mg8Ti2Bi2 cuboctahedra, and faces with eight equivalent Mg(1)Mg8Ti2Bi2 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Ti(1) atoms to form MgMg10Ti2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Bi2 cuboctahedra, corners with six equivalent Mg(3)Mg10Ti2 cuboctahedra, corners with eight equivalent Mg(2)Mg8Ti2Bi2 cuboctahedra, edges with two equivalent Mg(4)Mg10Bi2 cuboctahedra, edges with four equivalent Mg(2)Mg8Ti2Bi2 cuboctahedra, edges with four equivalent Ti(1)Mg10Bi2 cuboctahedra, edges with eight equivalent Mg(1)Mg8Ti2Bi2 cuboctahedra, faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra, faces with two equivalent Mg(3)Mg10Ti2 cuboctahedra, faces with two equivalent Ti(1)Mg10Bi2 cuboctahedra, faces with four equivalent Mg(1)Mg8Ti2Bi2 cuboctahedra, faces with four equivalent Mg(2)Mg8Ti2Bi2 cuboctahedra, and faces with six equivalent Bi(1)Mg10Ti2 cuboctahedra. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(3), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Bi(1) atoms to form distorted MgMg10Bi2 cuboctahedra that share corners with four equivalent Mg(3)Mg10Ti2 cuboctahedra, corners with six equivalent Mg(4)Mg10Bi2 cuboctahedra, corners with eight equivalent Mg(2)Mg8Ti2Bi2 cuboctahedra, edges with two equivalent Mg(3)Mg10Ti2 cuboctahedra, edges with four equivalent Mg(2)Mg8Ti2Bi2 cuboctahedra, edges with four equivalent Bi(1)Mg10Ti2 cuboctahedra, edges with eight equivalent Mg(1)Mg8Ti2Bi2 cuboctahedra, faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra, faces with two equivalent Mg(3)Mg10Ti2 cuboctahedra, faces with two equivalent Bi(1)Mg10Ti2 cuboctahedra, faces with four equivalent Mg(1)Mg8Ti2Bi2 cuboctahedra, faces with four equivalent Mg(2)Mg8Ti2Bi2 cuboctahedra, and faces with six equivalent Ti(1)Mg10Bi2 cuboctahedra. Ti(1) is bonded to two equivalent Mg(3), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Bi(1) atoms to form TiMg10Bi2 cuboctahedra that share corners with four equivalent Bi(1)Mg10Ti2 cuboctahedra, corners with six equivalent Ti(1)Mg10Bi2 cuboctahedra, corners with eight equivalent Mg(1)Mg8Ti2Bi2 cuboctahedra, edges with two equivalent Bi(1)Mg10Ti2 cuboctahedra, edges with four equivalent Mg(3)Mg10Ti2 cuboctahedra, edges with four equivalent Mg(1)Mg8Ti2Bi2 cuboctahedra, edges with eight equivalent Mg(2)Mg8Ti2Bi2 cuboctahedra, faces with two equivalent Mg(3)Mg10Ti2 cuboctahedra, faces with two equivalent Ti(1)Mg10Bi2 cuboctahedra, faces with two equivalent Bi(1)Mg10Ti2 cuboctahedra, faces with four equivalent Mg(1)Mg8Ti2Bi2 cuboctahedra, faces with four equivalent Mg(2)Mg8Ti2Bi2 cuboctahedra, and faces with six equivalent Mg(4)Mg10Bi2 cuboctahedra. Bi(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Ti(1) atoms to form BiMg10Ti2 cuboctahedra that share corners with four equivalent Ti(1)Mg10Bi2 cuboctahedra, corners with six equivalent Bi(1)Mg10Ti2 cuboctahedra, corners with eight equivalent Mg(1)Mg8Ti2Bi2 cuboctahedra, edges with two equivalent Ti(1)Mg10Bi2 cuboctahedra, edges with four equivalent Mg(4)Mg10Bi2 cuboctahedra, edges with four equivalent Mg(1)Mg8Ti2Bi2 cuboctahedra, edges with eight equivalent Mg(2)Mg8Ti2Bi2 cuboctahedra, faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra, faces with two equivalent Ti(1)Mg10Bi2 cuboctahedra, faces with two equivalent Bi(1)Mg10Ti2 cuboctahedra, faces with four equivalent Mg(1)Mg8Ti2Bi2 cuboctahedra, faces with four equivalent Mg(2)Mg8Ti2Bi2 cuboctahedra, and faces with six equivalent Mg(3)Mg10Ti2 cuboctahedra.
Mg6TiBi crystallizes in the orthorhombic Amm2 space group. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Ti(1), and two equivalent Bi(1) atoms to form distorted MgMg8Ti2Bi2 cuboctahedra that share corners with four equivalent Ti(1)Mg10Bi2 cuboctahedra, corners with four equivalent Bi(1)Mg10Ti2 cuboctahedra, corners with ten equivalent Mg(1)Mg8Ti2Bi2 cuboctahedra, edges with two equivalent Mg(1)Mg8Ti2Bi2 cuboctahedra, edges with two equivalent Ti(1)Mg10Bi2 cuboctahedra, edges with two equivalent Bi(1)Mg10Ti2 cuboctahedra, edges with four equivalent Mg(4)Mg10Bi2 cuboctahedra, edges with four equivalent Mg(3)Mg10Ti2 cuboctahedra, edges with four equivalent Mg(2)Mg8Ti2Bi2 cuboctahedra, faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra, faces with two equivalent Mg(3)Mg10Ti2 cuboctahedra, faces with two equivalent Ti(1)Mg10Bi2 cuboctahedra, faces with two equivalent Bi(1)Mg10Ti2 cuboctahedra, faces with four equivalent Mg(1)Mg8Ti2Bi2 cuboctahedra, and faces with eight equivalent Mg(2)Mg8Ti2Bi2 cuboctahedra. There is one shorter (3.04 Å) and one longer (3.08 Å) Mg(1)-Mg(1) bond length. Both Mg(1)-Mg(2) bond lengths are 3.25 Å. Both Mg(1)-Mg(3) bond lengths are 3.22 Å. Both Mg(1)-Mg(4) bond lengths are 3.21 Å. There is one shorter (3.18 Å) and one longer (3.19 Å) Mg(1)-Ti(1) bond length. There is one shorter (3.18 Å) and one longer (3.19 Å) Mg(1)-Bi(1) bond length. In the second Mg site, Mg(2) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Ti(1), and two equivalent Bi(1) atoms to form distorted MgMg8Ti2Bi2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Bi2 cuboctahedra, corners with four equivalent Mg(3)Mg10Ti2 cuboctahedra, corners with ten equivalent Mg(2)Mg8Ti2Bi2 cuboctahedra, edges with two equivalent Mg(4)Mg10Bi2 cuboctahedra, edges with two equivalent Mg(3)Mg10Ti2 cuboctahedra, edges with two equivalent Mg(2)Mg8Ti2Bi2 cuboctahedra, edges with four equivalent Mg(1)Mg8Ti2Bi2 cuboctahedra, edges with four equivalent Ti(1)Mg10Bi2 cuboctahedra, edges with four equivalent Bi(1)Mg10Ti2 cuboctahedra, faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra, faces with two equivalent Mg(3)Mg10Ti2 cuboctahedra, faces with two equivalent Ti(1)Mg10Bi2 cuboctahedra, faces with two equivalent Bi(1)Mg10Ti2 cuboctahedra, faces with four equivalent Mg(2)Mg8Ti2Bi2 cuboctahedra, and faces with eight equivalent Mg(1)Mg8Ti2Bi2 cuboctahedra. There is one shorter (2.93 Å) and one longer (3.19 Å) Mg(2)-Mg(2) bond length. There is one shorter (3.13 Å) and one longer (3.24 Å) Mg(2)-Mg(3) bond length. There is one shorter (3.10 Å) and one longer (3.27 Å) Mg(2)-Mg(4) bond length. Both Mg(2)-Ti(1) bond lengths are 3.19 Å. Both Mg(2)-Bi(1) bond lengths are 3.25 Å. In the third Mg site, Mg(3) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Ti(1) atoms to form MgMg10Ti2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Bi2 cuboctahedra, corners with six equivalent Mg(3)Mg10Ti2 cuboctahedra, corners with eight equivalent Mg(2)Mg8Ti2Bi2 cuboctahedra, edges with two equivalent Mg(4)Mg10Bi2 cuboctahedra, edges with four equivalent Mg(2)Mg8Ti2Bi2 cuboctahedra, edges with four equivalent Ti(1)Mg10Bi2 cuboctahedra, edges with eight equivalent Mg(1)Mg8Ti2Bi2 cuboctahedra, faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra, faces with two equivalent Mg(3)Mg10Ti2 cuboctahedra, faces with two equivalent Ti(1)Mg10Bi2 cuboctahedra, faces with four equivalent Mg(1)Mg8Ti2Bi2 cuboctahedra, faces with four equivalent Mg(2)Mg8Ti2Bi2 cuboctahedra, and faces with six equivalent Bi(1)Mg10Ti2 cuboctahedra. Both Mg(3)-Mg(4) bond lengths are 3.06 Å. Both Mg(3)-Ti(1) bond lengths are 3.23 Å. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(3), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Bi(1) atoms to form distorted MgMg10Bi2 cuboctahedra that share corners with four equivalent Mg(3)Mg10Ti2 cuboctahedra, corners with six equivalent Mg(4)Mg10Bi2 cuboctahedra, corners with eight equivalent Mg(2)Mg8Ti2Bi2 cuboctahedra, edges with two equivalent Mg(3)Mg10Ti2 cuboctahedra, edges with four equivalent Mg(2)Mg8Ti2Bi2 cuboctahedra, edges with four equivalent Bi(1)Mg10Ti2 cuboctahedra, edges with eight equivalent Mg(1)Mg8Ti2Bi2 cuboctahedra, faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra, faces with two equivalent Mg(3)Mg10Ti2 cuboctahedra, faces with two equivalent Bi(1)Mg10Ti2 cuboctahedra, faces with four equivalent Mg(1)Mg8Ti2Bi2 cuboctahedra, faces with four equivalent Mg(2)Mg8Ti2Bi2 cuboctahedra, and faces with six equivalent Ti(1)Mg10Bi2 cuboctahedra. Both Mg(4)-Bi(1) bond lengths are 3.28 Å. Ti(1) is bonded to two equivalent Mg(3), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Bi(1) atoms to form TiMg10Bi2 cuboctahedra that share corners with four equivalent Bi(1)Mg10Ti2 cuboctahedra, corners with six equivalent Ti(1)Mg10Bi2 cuboctahedra, corners with eight equivalent Mg(1)Mg8Ti2Bi2 cuboctahedra, edges with two equivalent Bi(1)Mg10Ti2 cuboctahedra, edges with four equivalent Mg(3)Mg10Ti2 cuboctahedra, edges with four equivalent Mg(1)Mg8Ti2Bi2 cuboctahedra, edges with eight equivalent Mg(2)Mg8Ti2Bi2 cuboctahedra, faces with two equivalent Mg(3)Mg10Ti2 cuboctahedra, faces with two equivalent Ti(1)Mg10Bi2 cuboctahedra, faces with two equivalent Bi(1)Mg10Ti2 cuboctahedra, faces with four equivalent Mg(1)Mg8Ti2Bi2 cuboctahedra, faces with four equivalent Mg(2)Mg8Ti2Bi2 cuboctahedra, and faces with six equivalent Mg(4)Mg10Bi2 cuboctahedra. Both Ti(1)-Bi(1) bond lengths are 3.06 Å. Bi(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Ti(1) atoms to form BiMg10Ti2 cuboctahedra that share corners with four equivalent Ti(1)Mg10Bi2 cuboctahedra, corners with six equivalent Bi(1)Mg10Ti2 cuboctahedra, corners with eight equivalent Mg(1)Mg8Ti2Bi2 cuboctahedra, edges with two equivalent Ti(1)Mg10Bi2 cuboctahedra, edges with four equivalent Mg(4)Mg10Bi2 cuboctahedra, edges with four equivalent Mg(1)Mg8Ti2Bi2 cuboctahedra, edges with eight equivalent Mg(2)Mg8Ti2Bi2 cuboctahedra, faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra, faces with two equivalent Ti(1)Mg10Bi2 cuboctahedra, faces with two equivalent Bi(1)Mg10Ti2 cuboctahedra, faces with four equivalent Mg(1)Mg8Ti2Bi2 cuboctahedra, faces with four equivalent Mg(2)Mg8Ti2Bi2 cuboctahedra, and faces with six equivalent Mg(3)Mg10Ti2 cuboctahedra.