Mg6AlBi crystallizes in the orthorhombic Amm2 space group. There are five 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 Al(1), and two equivalent Bi(1) atoms to form distorted MgMg8Al2Bi2 cuboctahedra that share corners with four equivalent Al(1)Mg10Bi2 cuboctahedra; corners with four equivalent Bi(1)Mg10Al2 cuboctahedra; corners with ten Mg(1,1)Mg8Al2Bi2 cuboctahedra; edges with two equivalent Mg(1)Mg8Al2Bi2 cuboctahedra; edges with two equivalent Al(1)Mg10Bi2 cuboctahedra; edges with two equivalent Bi(1)Mg10Al2 cuboctahedra; edges with four equivalent Mg(3)Mg10Al2 cuboctahedra; edges with four equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(3)Mg10Al2 cuboctahedra; faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Al(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Al2 cuboctahedra; and faces with four Mg(1,1)Mg8Al2Bi2 cuboctahedra. In the second 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 Al(1), and two equivalent Bi(1) atoms to form distorted MgMg8Al2Bi2 cuboctahedra that share corners with four equivalent Al(1)Mg10Bi2 cuboctahedra; corners with four equivalent Bi(1)Mg10Al2 cuboctahedra; corners with ten Mg(1,1)Mg8Al2Bi2 cuboctahedra; edges with two equivalent Mg(1)Mg8Al2Bi2 cuboctahedra; edges with two equivalent Al(1)Mg10Bi2 cuboctahedra; edges with two equivalent Bi(1)Mg10Al2 cuboctahedra; edges with four equivalent Mg(3)Mg10Al2 cuboctahedra; edges with four equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(3)Mg10Al2 cuboctahedra; faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Al(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Al2 cuboctahedra; and faces with four Mg(1,1)Mg8Al2Bi2 cuboctahedra. In the third Mg site, Mg(2) is bonded in a 12-coordinate geometry to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Al(1), and two equivalent Bi(1) atoms. In the fourth Mg site, Mg(3) is bonded to two equivalent Mg(4); four Mg(1,1); four equivalent Mg(2); and two equivalent Al(1) atoms to form distorted MgMg10Al2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Bi2 cuboctahedra; corners with six equivalent Mg(3)Mg10Al2 cuboctahedra; edges with two equivalent Mg(4)Mg10Bi2 cuboctahedra; edges with four equivalent Al(1)Mg10Bi2 cuboctahedra; edges with eight Mg(1,1)Mg8Al2Bi2 cuboctahedra; faces with two equivalent Mg(3)Mg10Al2 cuboctahedra; faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Al(1)Mg10Bi2 cuboctahedra; faces with four Mg(1,1)Mg8Al2Bi2 cuboctahedra; and faces with six equivalent Bi(1)Mg10Al2 cuboctahedra. In the fifth 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)Mg10Al2 cuboctahedra; corners with six equivalent Mg(4)Mg10Bi2 cuboctahedra; edges with two equivalent Mg(3)Mg10Al2 cuboctahedra; edges with four equivalent Bi(1)Mg10Al2 cuboctahedra; edges with eight Mg(1,1)Mg8Al2Bi2 cuboctahedra; faces with two equivalent Mg(3)Mg10Al2 cuboctahedra; faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Al2 cuboctahedra; faces with four equivalent Mg(1)Mg8Al2Bi2 cuboctahedra; and faces with six equivalent Al(1)Mg10Bi2 cuboctahedra. Al(1) is bonded to two equivalent Mg(3); four Mg(1,1); four equivalent Mg(2); and two equivalent Bi(1) atoms to form AlMg10Bi2 cuboctahedra that share corners with four equivalent Bi(1)Mg10Al2 cuboctahedra; corners with six equivalent Al(1)Mg10Bi2 cuboctahedra; corners with eight Mg(1,1)Mg8Al2Bi2 cuboctahedra; edges with two equivalent Bi(1)Mg10Al2 cuboctahedra; edges with four equivalent Mg(3)Mg10Al2 cuboctahedra; edges with four Mg(1,1)Mg8Al2Bi2 cuboctahedra; faces with two equivalent Mg(3)Mg10Al2 cuboctahedra; faces with two equivalent Al(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Al2 cuboctahedra; faces with four Mg(1,1)Mg8Al2Bi2 cuboctahedra; and faces with six equivalent Mg(4)Mg10Bi2 cuboctahedra. Bi(1) is bonded to two equivalent Mg(4); four Mg(1,1); four equivalent Mg(2); and two equivalent Al(1) atoms to form BiMg10Al2 cuboctahedra that share corners with four equivalent Al(1)Mg10Bi2 cuboctahedra; corners with six equivalent Bi(1)Mg10Al2 cuboctahedra; corners with eight Mg(1,1)Mg8Al2Bi2 cuboctahedra; edges with two equivalent Al(1)Mg10Bi2 cuboctahedra; edges with four equivalent Mg(4)Mg10Bi2 cuboctahedra; edges with four Mg(1,1)Mg8Al2Bi2 cuboctahedra; faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Al(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Al2 cuboctahedra; faces with four Mg(1,1)Mg8Al2Bi2 cuboctahedra; and faces with six equivalent Mg(3)Mg10Al2 cuboctahedra.
Mg6AlBi crystallizes in the orthorhombic Amm2 space group. There are five 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 Al(1), and two equivalent Bi(1) atoms to form distorted MgMg8Al2Bi2 cuboctahedra that share corners with four equivalent Al(1)Mg10Bi2 cuboctahedra; corners with four equivalent Bi(1)Mg10Al2 cuboctahedra; corners with ten Mg(1,1)Mg8Al2Bi2 cuboctahedra; edges with two equivalent Mg(1)Mg8Al2Bi2 cuboctahedra; edges with two equivalent Al(1)Mg10Bi2 cuboctahedra; edges with two equivalent Bi(1)Mg10Al2 cuboctahedra; edges with four equivalent Mg(3)Mg10Al2 cuboctahedra; edges with four equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(3)Mg10Al2 cuboctahedra; faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Al(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Al2 cuboctahedra; and faces with four Mg(1,1)Mg8Al2Bi2 cuboctahedra. There is one shorter (3.26 Å) and one longer (3.28 Å) Mg(1)-Mg(1) bond length. Both Mg(1)-Mg(2) bond lengths are 3.20 Å. Both Mg(1)-Mg(3) bond lengths are 3.23 Å. Both Mg(1)-Mg(4) bond lengths are 3.22 Å. There is one shorter (3.15 Å) and one longer (3.18 Å) Mg(1)-Al(1) bond length. There is one shorter (3.16 Å) and one longer (3.17 Å) Mg(1)-Bi(1) bond length. In the second 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 Al(1), and two equivalent Bi(1) atoms to form distorted MgMg8Al2Bi2 cuboctahedra that share corners with four equivalent Al(1)Mg10Bi2 cuboctahedra; corners with four equivalent Bi(1)Mg10Al2 cuboctahedra; corners with ten Mg(1,1)Mg8Al2Bi2 cuboctahedra; edges with two equivalent Mg(1)Mg8Al2Bi2 cuboctahedra; edges with two equivalent Al(1)Mg10Bi2 cuboctahedra; edges with two equivalent Bi(1)Mg10Al2 cuboctahedra; edges with four equivalent Mg(3)Mg10Al2 cuboctahedra; edges with four equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(3)Mg10Al2 cuboctahedra; faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Al(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Al2 cuboctahedra; and faces with four Mg(1,1)Mg8Al2Bi2 cuboctahedra. Both Mg(1)-Mg(2) bond lengths are 3.20 Å. Both Mg(1)-Mg(3) bond lengths are 3.23 Å. Both Mg(1)-Mg(4) bond lengths are 3.22 Å. There is one shorter (3.15 Å) and one longer (3.18 Å) Mg(1)-Al(1) bond length. There is one shorter (3.16 Å) and one longer (3.17 Å) Mg(1)-Bi(1) bond length. In the third Mg site, Mg(2) is bonded in a 12-coordinate geometry to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Al(1), and two equivalent Bi(1) atoms. There is one shorter (3.14 Å) and one longer (3.40 Å) Mg(2)-Mg(2) bond length. There is one shorter (3.11 Å) and one longer (3.22 Å) Mg(2)-Mg(3) bond length. There is one shorter (3.11 Å) and one longer (3.22 Å) Mg(2)-Mg(4) bond length. Both Mg(2)-Al(1) bond lengths are 3.20 Å. Both Mg(2)-Bi(1) bond lengths are 3.26 Å. In the fourth Mg site, Mg(3) is bonded to two equivalent Mg(4); four Mg(1,1); four equivalent Mg(2); and two equivalent Al(1) atoms to form distorted MgMg10Al2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Bi2 cuboctahedra; corners with six equivalent Mg(3)Mg10Al2 cuboctahedra; edges with two equivalent Mg(4)Mg10Bi2 cuboctahedra; edges with four equivalent Al(1)Mg10Bi2 cuboctahedra; edges with eight Mg(1,1)Mg8Al2Bi2 cuboctahedra; faces with two equivalent Mg(3)Mg10Al2 cuboctahedra; faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Al(1)Mg10Bi2 cuboctahedra; faces with four Mg(1,1)Mg8Al2Bi2 cuboctahedra; and faces with six equivalent Bi(1)Mg10Al2 cuboctahedra. Both Mg(3)-Mg(4) bond lengths are 3.27 Å. Both Mg(3)-Al(1) bond lengths are 3.17 Å. In the fifth 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)Mg10Al2 cuboctahedra; corners with six equivalent Mg(4)Mg10Bi2 cuboctahedra; edges with two equivalent Mg(3)Mg10Al2 cuboctahedra; edges with four equivalent Bi(1)Mg10Al2 cuboctahedra; edges with eight Mg(1,1)Mg8Al2Bi2 cuboctahedra; faces with two equivalent Mg(3)Mg10Al2 cuboctahedra; faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Al2 cuboctahedra; faces with four equivalent Mg(1)Mg8Al2Bi2 cuboctahedra; and faces with six equivalent Al(1)Mg10Bi2 cuboctahedra. Both Mg(4)-Bi(1) bond lengths are 3.21 Å. Al(1) is bonded to two equivalent Mg(3); four Mg(1,1); four equivalent Mg(2); and two equivalent Bi(1) atoms to form AlMg10Bi2 cuboctahedra that share corners with four equivalent Bi(1)Mg10Al2 cuboctahedra; corners with six equivalent Al(1)Mg10Bi2 cuboctahedra; corners with eight Mg(1,1)Mg8Al2Bi2 cuboctahedra; edges with two equivalent Bi(1)Mg10Al2 cuboctahedra; edges with four equivalent Mg(3)Mg10Al2 cuboctahedra; edges with four Mg(1,1)Mg8Al2Bi2 cuboctahedra; faces with two equivalent Mg(3)Mg10Al2 cuboctahedra; faces with two equivalent Al(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Al2 cuboctahedra; faces with four Mg(1,1)Mg8Al2Bi2 cuboctahedra; and faces with six equivalent Mg(4)Mg10Bi2 cuboctahedra. Both Al(1)-Bi(1) bond lengths are 3.27 Å. Bi(1) is bonded to two equivalent Mg(4); four Mg(1,1); four equivalent Mg(2); and two equivalent Al(1) atoms to form BiMg10Al2 cuboctahedra that share corners with four equivalent Al(1)Mg10Bi2 cuboctahedra; corners with six equivalent Bi(1)Mg10Al2 cuboctahedra; corners with eight Mg(1,1)Mg8Al2Bi2 cuboctahedra; edges with two equivalent Al(1)Mg10Bi2 cuboctahedra; edges with four equivalent Mg(4)Mg10Bi2 cuboctahedra; edges with four Mg(1,1)Mg8Al2Bi2 cuboctahedra; faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Al(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Al2 cuboctahedra; faces with four Mg(1,1)Mg8Al2Bi2 cuboctahedra; and faces with six equivalent Mg(3)Mg10Al2 cuboctahedra.