Mg6CrBi crystallizes in the orthorhombic Amm2 space group. There are six 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 Cr(1), and two equivalent Bi(1) atoms to form distorted MgMg8Cr2Bi2 cuboctahedra that share corners with four equivalent Cr(1)Mg10Bi2 cuboctahedra; corners with four equivalent Bi(1)Mg10Cr2 cuboctahedra; corners with ten Mg(1,1)Mg8Cr2Bi2 cuboctahedra; edges with two equivalent Mg(1)Mg8Cr2Bi2 cuboctahedra; edges with two equivalent Cr(1)Mg10Bi2 cuboctahedra; edges with two equivalent Bi(1)Mg10Cr2 cuboctahedra; edges with four equivalent Mg(4)Mg10Bi2 cuboctahedra; edges with four equivalent Mg(3)Mg10Cr2 cuboctahedra; edges with four equivalent Mg(2)Mg8Cr2Bi2 cuboctahedra; faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(3)Mg10Cr2 cuboctahedra; faces with two equivalent Cr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Cr2 cuboctahedra; faces with four Mg(1,1)Mg8Cr2Bi2 cuboctahedra; and faces with eight Mg(2,2)Mg8Cr2Bi2 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 Cr(1), and two equivalent Bi(1) atoms to form distorted MgMg8Cr2Bi2 cuboctahedra that share corners with four equivalent Cr(1)Mg10Bi2 cuboctahedra; corners with four equivalent Bi(1)Mg10Cr2 cuboctahedra; corners with ten Mg(1,1)Mg8Cr2Bi2 cuboctahedra; edges with two equivalent Mg(1)Mg8Cr2Bi2 cuboctahedra; edges with two equivalent Cr(1)Mg10Bi2 cuboctahedra; edges with two equivalent Bi(1)Mg10Cr2 cuboctahedra; edges with four equivalent Mg(4)Mg10Bi2 cuboctahedra; edges with four equivalent Mg(3)Mg10Cr2 cuboctahedra; edges with four equivalent Mg(2)Mg8Cr2Bi2 cuboctahedra; faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(3)Mg10Cr2 cuboctahedra; faces with two equivalent Cr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Cr2 cuboctahedra; faces with four Mg(1,1)Mg8Cr2Bi2 cuboctahedra; and faces with eight Mg(2,2)Mg8Cr2Bi2 cuboctahedra. In the third 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 Cr(1), and two equivalent Bi(1) atoms to form distorted MgMg8Cr2Bi2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Bi2 cuboctahedra; corners with four equivalent Mg(3)Mg10Cr2 cuboctahedra; corners with ten Mg(2,2)Mg8Cr2Bi2 cuboctahedra; edges with two equivalent Mg(4)Mg10Bi2 cuboctahedra; edges with two equivalent Mg(3)Mg10Cr2 cuboctahedra; edges with two equivalent Mg(2)Mg8Cr2Bi2 cuboctahedra; edges with four equivalent Mg(1)Mg8Cr2Bi2 cuboctahedra; edges with four equivalent Cr(1)Mg10Bi2 cuboctahedra; edges with four equivalent Bi(1)Mg10Cr2 cuboctahedra; faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(3)Mg10Cr2 cuboctahedra; faces with two equivalent Cr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Cr2 cuboctahedra; faces with four Mg(2,2)Mg8Cr2Bi2 cuboctahedra; and faces with eight Mg(1,1)Mg8Cr2Bi2 cuboctahedra. In the fourth 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 Cr(1), and two equivalent Bi(1) atoms to form distorted MgMg8Cr2Bi2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Bi2 cuboctahedra; corners with four equivalent Mg(3)Mg10Cr2 cuboctahedra; corners with ten Mg(2,2)Mg8Cr2Bi2 cuboctahedra; edges with two equivalent Mg(4)Mg10Bi2 cuboctahedra; edges with two equivalent Mg(3)Mg10Cr2 cuboctahedra; edges with two equivalent Mg(2)Mg8Cr2Bi2 cuboctahedra; edges with four equivalent Mg(1)Mg8Cr2Bi2 cuboctahedra; edges with four equivalent Cr(1)Mg10Bi2 cuboctahedra; edges with four equivalent Bi(1)Mg10Cr2 cuboctahedra; faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(3)Mg10Cr2 cuboctahedra; faces with two equivalent Cr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Cr2 cuboctahedra; faces with four Mg(2,2)Mg8Cr2Bi2 cuboctahedra; and faces with eight equivalent Mg(1)Mg8Cr2Bi2 cuboctahedra. In the fifth Mg site, Mg(3) is bonded to two equivalent Mg(4); four Mg(1,1); four Mg(2,2); and two equivalent Cr(1) atoms to form distorted MgMg10Cr2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Bi2 cuboctahedra; corners with six equivalent Mg(3)Mg10Cr2 cuboctahedra; corners with eight Mg(2,2)Mg8Cr2Bi2 cuboctahedra; edges with two equivalent Mg(4)Mg10Bi2 cuboctahedra; edges with four Mg(2,2)Mg8Cr2Bi2 cuboctahedra; edges with four equivalent Cr(1)Mg10Bi2 cuboctahedra; edges with eight Mg(1,1)Mg8Cr2Bi2 cuboctahedra; faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(3)Mg10Cr2 cuboctahedra; faces with two equivalent Cr(1)Mg10Bi2 cuboctahedra; faces with four Mg(1,1)Mg8Cr2Bi2 cuboctahedra; faces with four Mg(2,2)Mg8Cr2Bi2 cuboctahedra; and faces with six equivalent Bi(1)Mg10Cr2 cuboctahedra. In the sixth Mg site, Mg(4) is bonded to two equivalent Mg(3); four Mg(1,1); four Mg(2,2); and two equivalent Bi(1) atoms to form distorted MgMg10Bi2 cuboctahedra that share corners with four equivalent Mg(3)Mg10Cr2 cuboctahedra; corners with six equivalent Mg(4)Mg10Bi2 cuboctahedra; corners with eight Mg(2,2)Mg8Cr2Bi2 cuboctahedra; edges with two equivalent Mg(3)Mg10Cr2 cuboctahedra; edges with four Mg(2,2)Mg8Cr2Bi2 cuboctahedra; edges with four equivalent Bi(1)Mg10Cr2 cuboctahedra; edges with eight Mg(1,1)Mg8Cr2Bi2 cuboctahedra; faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(3)Mg10Cr2 cuboctahedra; faces with two equivalent Bi(1)Mg10Cr2 cuboctahedra; faces with four Mg(1,1)Mg8Cr2Bi2 cuboctahedra; faces with four Mg(2,2)Mg8Cr2Bi2 cuboctahedra; and faces with six equivalent Cr(1)Mg10Bi2 cuboctahedra. Cr(1) is bonded to two equivalent Mg(3); four Mg(1,1); four Mg(2,2); and two equivalent Bi(1) atoms to form CrMg10Bi2 cuboctahedra that share corners with four equivalent Bi(1)Mg10Cr2 cuboctahedra; corners with six equivalent Cr(1)Mg10Bi2 cuboctahedra; corners with eight Mg(1,1)Mg8Cr2Bi2 cuboctahedra; edges with two equivalent Bi(1)Mg10Cr2 cuboctahedra; edges with four equivalent Mg(3)Mg10Cr2 cuboctahedra; edges with four Mg(1,1)Mg8Cr2Bi2 cuboctahedra; edges with eight Mg(2,2)Mg8Cr2Bi2 cuboctahedra; faces with two equivalent Mg(3)Mg10Cr2 cuboctahedra; faces with two equivalent Cr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Cr2 cuboctahedra; faces with four Mg(1,1)Mg8Cr2Bi2 cuboctahedra; faces with four Mg(2,2)Mg8Cr2Bi2 cuboctahedra; and faces with six equivalent Mg(4)Mg10Bi2 cuboctahedra. Bi(1) is bonded to two equivalent Mg(4); four Mg(1,1); four Mg(2,2); and two equivalent Cr(1) atoms to form BiMg10Cr2 cuboctahedra that share corners with four equivalent Cr(1)Mg10Bi2 cuboctahedra; corners with six equivalent Bi(1)Mg10Cr2 cuboctahedra; corners with eight Mg(1,1)Mg8Cr2Bi2 cuboctahedra; edges with two equivalent Cr(1)Mg10Bi2 cuboctahedra; edges with four equivalent Mg(4)Mg10Bi2 cuboctahedra; edges with four Mg(1,1)Mg8Cr2Bi2 cuboctahedra; edges with eight Mg(2,2)Mg8Cr2Bi2 cuboctahedra; faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Cr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Cr2 cuboctahedra; faces with four Mg(1,1)Mg8Cr2Bi2 cuboctahedra; faces with four Mg(2,2)Mg8Cr2Bi2 cuboctahedra; and faces with six equivalent Mg(3)Mg10Cr2 cuboctahedra.
Mg6CrBi crystallizes in the orthorhombic Amm2 space group. There are six 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 Cr(1), and two equivalent Bi(1) atoms to form distorted MgMg8Cr2Bi2 cuboctahedra that share corners with four equivalent Cr(1)Mg10Bi2 cuboctahedra; corners with four equivalent Bi(1)Mg10Cr2 cuboctahedra; corners with ten Mg(1,1)Mg8Cr2Bi2 cuboctahedra; edges with two equivalent Mg(1)Mg8Cr2Bi2 cuboctahedra; edges with two equivalent Cr(1)Mg10Bi2 cuboctahedra; edges with two equivalent Bi(1)Mg10Cr2 cuboctahedra; edges with four equivalent Mg(4)Mg10Bi2 cuboctahedra; edges with four equivalent Mg(3)Mg10Cr2 cuboctahedra; edges with four equivalent Mg(2)Mg8Cr2Bi2 cuboctahedra; faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(3)Mg10Cr2 cuboctahedra; faces with two equivalent Cr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Cr2 cuboctahedra; faces with four Mg(1,1)Mg8Cr2Bi2 cuboctahedra; and faces with eight Mg(2,2)Mg8Cr2Bi2 cuboctahedra. There is one shorter (3.16 Å) and one longer (3.18 Å) Mg(1)-Mg(1) bond length. Both Mg(1)-Mg(2) bond lengths are 3.18 Å. Both Mg(1)-Mg(3) bond lengths are 3.19 Å. Both Mg(1)-Mg(4) bond lengths are 3.17 Å. There is one shorter (3.17 Å) and one longer (3.19 Å) Mg(1)-Cr(1) bond length. There is one shorter (3.17 Å) and one longer (3.19 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 Cr(1), and two equivalent Bi(1) atoms to form distorted MgMg8Cr2Bi2 cuboctahedra that share corners with four equivalent Cr(1)Mg10Bi2 cuboctahedra; corners with four equivalent Bi(1)Mg10Cr2 cuboctahedra; corners with ten Mg(1,1)Mg8Cr2Bi2 cuboctahedra; edges with two equivalent Mg(1)Mg8Cr2Bi2 cuboctahedra; edges with two equivalent Cr(1)Mg10Bi2 cuboctahedra; edges with two equivalent Bi(1)Mg10Cr2 cuboctahedra; edges with four equivalent Mg(4)Mg10Bi2 cuboctahedra; edges with four equivalent Mg(3)Mg10Cr2 cuboctahedra; edges with four equivalent Mg(2)Mg8Cr2Bi2 cuboctahedra; faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(3)Mg10Cr2 cuboctahedra; faces with two equivalent Cr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Cr2 cuboctahedra; faces with four Mg(1,1)Mg8Cr2Bi2 cuboctahedra; and faces with eight Mg(2,2)Mg8Cr2Bi2 cuboctahedra. Both Mg(1)-Mg(2) bond lengths are 3.18 Å. Both Mg(1)-Mg(3) bond lengths are 3.19 Å. Both Mg(1)-Mg(4) bond lengths are 3.17 Å. There is one shorter (3.17 Å) and one longer (3.19 Å) Mg(1)-Cr(1) bond length. There is one shorter (3.17 Å) and one longer (3.19 Å) Mg(1)-Bi(1) bond length. In the third 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 Cr(1), and two equivalent Bi(1) atoms to form distorted MgMg8Cr2Bi2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Bi2 cuboctahedra; corners with four equivalent Mg(3)Mg10Cr2 cuboctahedra; corners with ten Mg(2,2)Mg8Cr2Bi2 cuboctahedra; edges with two equivalent Mg(4)Mg10Bi2 cuboctahedra; edges with two equivalent Mg(3)Mg10Cr2 cuboctahedra; edges with two equivalent Mg(2)Mg8Cr2Bi2 cuboctahedra; edges with four equivalent Mg(1)Mg8Cr2Bi2 cuboctahedra; edges with four equivalent Cr(1)Mg10Bi2 cuboctahedra; edges with four equivalent Bi(1)Mg10Cr2 cuboctahedra; faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(3)Mg10Cr2 cuboctahedra; faces with two equivalent Cr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Cr2 cuboctahedra; faces with four Mg(2,2)Mg8Cr2Bi2 cuboctahedra; and faces with eight Mg(1,1)Mg8Cr2Bi2 cuboctahedra. Both Mg(2)-Mg(1) bond lengths are 3.18 Å. There is one shorter (3.03 Å) and one longer (3.31 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)-Cr(1) bond lengths are 3.15 Å. Both Mg(2)-Bi(1) bond lengths are 3.22 Å. In the fourth 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 Cr(1), and two equivalent Bi(1) atoms to form distorted MgMg8Cr2Bi2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Bi2 cuboctahedra; corners with four equivalent Mg(3)Mg10Cr2 cuboctahedra; corners with ten Mg(2,2)Mg8Cr2Bi2 cuboctahedra; edges with two equivalent Mg(4)Mg10Bi2 cuboctahedra; edges with two equivalent Mg(3)Mg10Cr2 cuboctahedra; edges with two equivalent Mg(2)Mg8Cr2Bi2 cuboctahedra; edges with four equivalent Mg(1)Mg8Cr2Bi2 cuboctahedra; edges with four equivalent Cr(1)Mg10Bi2 cuboctahedra; edges with four equivalent Bi(1)Mg10Cr2 cuboctahedra; faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(3)Mg10Cr2 cuboctahedra; faces with two equivalent Cr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Cr2 cuboctahedra; faces with four Mg(2,2)Mg8Cr2Bi2 cuboctahedra; and faces with eight equivalent Mg(1)Mg8Cr2Bi2 cuboctahedra. 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)-Cr(1) bond lengths are 3.15 Å. Both Mg(2)-Bi(1) bond lengths are 3.22 Å. In the fifth Mg site, Mg(3) is bonded to two equivalent Mg(4); four Mg(1,1); four Mg(2,2); and two equivalent Cr(1) atoms to form distorted MgMg10Cr2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Bi2 cuboctahedra; corners with six equivalent Mg(3)Mg10Cr2 cuboctahedra; corners with eight Mg(2,2)Mg8Cr2Bi2 cuboctahedra; edges with two equivalent Mg(4)Mg10Bi2 cuboctahedra; edges with four Mg(2,2)Mg8Cr2Bi2 cuboctahedra; edges with four equivalent Cr(1)Mg10Bi2 cuboctahedra; edges with eight Mg(1,1)Mg8Cr2Bi2 cuboctahedra; faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(3)Mg10Cr2 cuboctahedra; faces with two equivalent Cr(1)Mg10Bi2 cuboctahedra; faces with four Mg(1,1)Mg8Cr2Bi2 cuboctahedra; faces with four Mg(2,2)Mg8Cr2Bi2 cuboctahedra; and faces with six equivalent Bi(1)Mg10Cr2 cuboctahedra. Both Mg(3)-Mg(4) bond lengths are 3.17 Å. Both Mg(3)-Cr(1) bond lengths are 3.17 Å. In the sixth Mg site, Mg(4) is bonded to two equivalent Mg(3); four Mg(1,1); four Mg(2,2); and two equivalent Bi(1) atoms to form distorted MgMg10Bi2 cuboctahedra that share corners with four equivalent Mg(3)Mg10Cr2 cuboctahedra; corners with six equivalent Mg(4)Mg10Bi2 cuboctahedra; corners with eight Mg(2,2)Mg8Cr2Bi2 cuboctahedra; edges with two equivalent Mg(3)Mg10Cr2 cuboctahedra; edges with four Mg(2,2)Mg8Cr2Bi2 cuboctahedra; edges with four equivalent Bi(1)Mg10Cr2 cuboctahedra; edges with eight Mg(1,1)Mg8Cr2Bi2 cuboctahedra; faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Mg(3)Mg10Cr2 cuboctahedra; faces with two equivalent Bi(1)Mg10Cr2 cuboctahedra; faces with four Mg(1,1)Mg8Cr2Bi2 cuboctahedra; faces with four Mg(2,2)Mg8Cr2Bi2 cuboctahedra; and faces with six equivalent Cr(1)Mg10Bi2 cuboctahedra. Both Mg(4)-Bi(1) bond lengths are 3.21 Å. Cr(1) is bonded to two equivalent Mg(3); four Mg(1,1); four Mg(2,2); and two equivalent Bi(1) atoms to form CrMg10Bi2 cuboctahedra that share corners with four equivalent Bi(1)Mg10Cr2 cuboctahedra; corners with six equivalent Cr(1)Mg10Bi2 cuboctahedra; corners with eight Mg(1,1)Mg8Cr2Bi2 cuboctahedra; edges with two equivalent Bi(1)Mg10Cr2 cuboctahedra; edges with four equivalent Mg(3)Mg10Cr2 cuboctahedra; edges with four Mg(1,1)Mg8Cr2Bi2 cuboctahedra; edges with eight Mg(2,2)Mg8Cr2Bi2 cuboctahedra; faces with two equivalent Mg(3)Mg10Cr2 cuboctahedra; faces with two equivalent Cr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Cr2 cuboctahedra; faces with four Mg(1,1)Mg8Cr2Bi2 cuboctahedra; faces with four Mg(2,2)Mg8Cr2Bi2 cuboctahedra; and faces with six equivalent Mg(4)Mg10Bi2 cuboctahedra. Both Cr(1)-Bi(1) bond lengths are 3.17 Å. Bi(1) is bonded to two equivalent Mg(4); four Mg(1,1); four Mg(2,2); and two equivalent Cr(1) atoms to form BiMg10Cr2 cuboctahedra that share corners with four equivalent Cr(1)Mg10Bi2 cuboctahedra; corners with six equivalent Bi(1)Mg10Cr2 cuboctahedra; corners with eight Mg(1,1)Mg8Cr2Bi2 cuboctahedra; edges with two equivalent Cr(1)Mg10Bi2 cuboctahedra; edges with four equivalent Mg(4)Mg10Bi2 cuboctahedra; edges with four Mg(1,1)Mg8Cr2Bi2 cuboctahedra; edges with eight Mg(2,2)Mg8Cr2Bi2 cuboctahedra; faces with two equivalent Mg(4)Mg10Bi2 cuboctahedra; faces with two equivalent Cr(1)Mg10Bi2 cuboctahedra; faces with two equivalent Bi(1)Mg10Cr2 cuboctahedra; faces with four Mg(1,1)Mg8Cr2Bi2 cuboctahedra; faces with four Mg(2,2)Mg8Cr2Bi2 cuboctahedra; and faces with six equivalent Mg(3)Mg10Cr2 cuboctahedra.