Mg6CdZn is beta Cu3Ti-derived structured and 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 Cd(1), and two equivalent Zn(1) atoms to form distorted MgMg8Zn2Cd2 cuboctahedra that share corners with four equivalent Mg(2)Mg10Zn2 cuboctahedra, corners with four equivalent Zn(1)Mg10Cd2 cuboctahedra, corners with ten equivalent Mg(1)Mg8Zn2Cd2 cuboctahedra, edges with two equivalent Mg(2)Mg10Zn2 cuboctahedra, edges with two equivalent Mg(1)Mg8Zn2Cd2 cuboctahedra, edges with two equivalent Zn(1)Mg10Cd2 cuboctahedra, edges with four equivalent Mg(4)Mg10Cd2 cuboctahedra, edges with four equivalent Mg(3)Mg8Zn2Cd2 cuboctahedra, edges with four equivalent Cd(1)Mg10Zn2 cuboctahedra, faces with two equivalent Mg(4)Mg10Cd2 cuboctahedra, faces with two equivalent Mg(2)Mg10Zn2 cuboctahedra, faces with two equivalent Cd(1)Mg10Zn2 cuboctahedra, faces with two equivalent Zn(1)Mg10Cd2 cuboctahedra, faces with four equivalent Mg(1)Mg8Zn2Cd2 cuboctahedra, and faces with eight equivalent Mg(3)Mg8Zn2Cd2 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Zn(1) atoms to form distorted MgMg10Zn2 cuboctahedra that share corners with four equivalent Zn(1)Mg10Cd2 cuboctahedra, corners with six equivalent Mg(2)Mg10Zn2 cuboctahedra, corners with eight equivalent Mg(1)Mg8Zn2Cd2 cuboctahedra, edges with two equivalent Zn(1)Mg10Cd2 cuboctahedra, edges with four equivalent Mg(4)Mg10Cd2 cuboctahedra, edges with four equivalent Mg(1)Mg8Zn2Cd2 cuboctahedra, edges with eight equivalent Mg(3)Mg8Zn2Cd2 cuboctahedra, faces with two equivalent Mg(4)Mg10Cd2 cuboctahedra, faces with two equivalent Mg(2)Mg10Zn2 cuboctahedra, faces with two equivalent Zn(1)Mg10Cd2 cuboctahedra, faces with four equivalent Mg(1)Mg8Zn2Cd2 cuboctahedra, faces with four equivalent Mg(3)Mg8Zn2Cd2 cuboctahedra, and faces with six equivalent Cd(1)Mg10Zn2 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Cd(1), and two equivalent Zn(1) atoms to form distorted MgMg8Zn2Cd2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Cd2 cuboctahedra, corners with four equivalent Cd(1)Mg10Zn2 cuboctahedra, corners with ten equivalent Mg(3)Mg8Zn2Cd2 cuboctahedra, edges with two equivalent Mg(4)Mg10Cd2 cuboctahedra, edges with two equivalent Mg(3)Mg8Zn2Cd2 cuboctahedra, edges with two equivalent Cd(1)Mg10Zn2 cuboctahedra, edges with four equivalent Mg(2)Mg10Zn2 cuboctahedra, edges with four equivalent Mg(1)Mg8Zn2Cd2 cuboctahedra, edges with four equivalent Zn(1)Mg10Cd2 cuboctahedra, faces with two equivalent Mg(4)Mg10Cd2 cuboctahedra, faces with two equivalent Mg(2)Mg10Zn2 cuboctahedra, faces with two equivalent Cd(1)Mg10Zn2 cuboctahedra, faces with two equivalent Zn(1)Mg10Cd2 cuboctahedra, faces with four equivalent Mg(3)Mg8Zn2Cd2 cuboctahedra, and faces with eight equivalent Mg(1)Mg8Zn2Cd2 cuboctahedra. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(2), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Cd(1) atoms to form distorted MgMg10Cd2 cuboctahedra that share corners with four equivalent Cd(1)Mg10Zn2 cuboctahedra, corners with six equivalent Mg(4)Mg10Cd2 cuboctahedra, corners with eight equivalent Mg(3)Mg8Zn2Cd2 cuboctahedra, edges with two equivalent Cd(1)Mg10Zn2 cuboctahedra, edges with four equivalent Mg(2)Mg10Zn2 cuboctahedra, edges with four equivalent Mg(3)Mg8Zn2Cd2 cuboctahedra, edges with eight equivalent Mg(1)Mg8Zn2Cd2 cuboctahedra, faces with two equivalent Mg(4)Mg10Cd2 cuboctahedra, faces with two equivalent Mg(2)Mg10Zn2 cuboctahedra, faces with two equivalent Cd(1)Mg10Zn2 cuboctahedra, faces with four equivalent Mg(1)Mg8Zn2Cd2 cuboctahedra, faces with four equivalent Mg(3)Mg8Zn2Cd2 cuboctahedra, and faces with six equivalent Zn(1)Mg10Cd2 cuboctahedra. Cd(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Zn(1) atoms to form CdMg10Zn2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Cd2 cuboctahedra, corners with six equivalent Cd(1)Mg10Zn2 cuboctahedra, corners with eight equivalent Mg(3)Mg8Zn2Cd2 cuboctahedra, edges with two equivalent Mg(4)Mg10Cd2 cuboctahedra, edges with four equivalent Mg(3)Mg8Zn2Cd2 cuboctahedra, edges with four equivalent Zn(1)Mg10Cd2 cuboctahedra, edges with eight equivalent Mg(1)Mg8Zn2Cd2 cuboctahedra, faces with two equivalent Mg(4)Mg10Cd2 cuboctahedra, faces with two equivalent Cd(1)Mg10Zn2 cuboctahedra, faces with two equivalent Zn(1)Mg10Cd2 cuboctahedra, faces with four equivalent Mg(1)Mg8Zn2Cd2 cuboctahedra, faces with four equivalent Mg(3)Mg8Zn2Cd2 cuboctahedra, and faces with six equivalent Mg(2)Mg10Zn2 cuboctahedra. Zn(1) is bonded to two equivalent Mg(2), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Cd(1) atoms to form ZnMg10Cd2 cuboctahedra that share corners with four equivalent Mg(2)Mg10Zn2 cuboctahedra, corners with six equivalent Zn(1)Mg10Cd2 cuboctahedra, corners with eight equivalent Mg(1)Mg8Zn2Cd2 cuboctahedra, edges with two equivalent Mg(2)Mg10Zn2 cuboctahedra, edges with four equivalent Mg(1)Mg8Zn2Cd2 cuboctahedra, edges with four equivalent Cd(1)Mg10Zn2 cuboctahedra, edges with eight equivalent Mg(3)Mg8Zn2Cd2 cuboctahedra, faces with two equivalent Mg(2)Mg10Zn2 cuboctahedra, faces with two equivalent Cd(1)Mg10Zn2 cuboctahedra, faces with two equivalent Zn(1)Mg10Cd2 cuboctahedra, faces with four equivalent Mg(1)Mg8Zn2Cd2 cuboctahedra, faces with four equivalent Mg(3)Mg8Zn2Cd2 cuboctahedra, and faces with six equivalent Mg(4)Mg10Cd2 cuboctahedra.
Mg6CdZn is beta Cu3Ti-derived structured and 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 Cd(1), and two equivalent Zn(1) atoms to form distorted MgMg8Zn2Cd2 cuboctahedra that share corners with four equivalent Mg(2)Mg10Zn2 cuboctahedra, corners with four equivalent Zn(1)Mg10Cd2 cuboctahedra, corners with ten equivalent Mg(1)Mg8Zn2Cd2 cuboctahedra, edges with two equivalent Mg(2)Mg10Zn2 cuboctahedra, edges with two equivalent Mg(1)Mg8Zn2Cd2 cuboctahedra, edges with two equivalent Zn(1)Mg10Cd2 cuboctahedra, edges with four equivalent Mg(4)Mg10Cd2 cuboctahedra, edges with four equivalent Mg(3)Mg8Zn2Cd2 cuboctahedra, edges with four equivalent Cd(1)Mg10Zn2 cuboctahedra, faces with two equivalent Mg(4)Mg10Cd2 cuboctahedra, faces with two equivalent Mg(2)Mg10Zn2 cuboctahedra, faces with two equivalent Cd(1)Mg10Zn2 cuboctahedra, faces with two equivalent Zn(1)Mg10Cd2 cuboctahedra, faces with four equivalent Mg(1)Mg8Zn2Cd2 cuboctahedra, and faces with eight equivalent Mg(3)Mg8Zn2Cd2 cuboctahedra. Both Mg(1)-Mg(1) bond lengths are 3.12 Å. There is one shorter (3.11 Å) and one longer (3.15 Å) Mg(1)-Mg(2) bond length. Both Mg(1)-Mg(3) bond lengths are 3.13 Å. Both Mg(1)-Mg(4) bond lengths are 3.10 Å. Both Mg(1)-Cd(1) bond lengths are 3.09 Å. There is one shorter (3.10 Å) and one longer (3.17 Å) Mg(1)-Zn(1) bond length. In the second Mg site, Mg(2) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Zn(1) atoms to form distorted MgMg10Zn2 cuboctahedra that share corners with four equivalent Zn(1)Mg10Cd2 cuboctahedra, corners with six equivalent Mg(2)Mg10Zn2 cuboctahedra, corners with eight equivalent Mg(1)Mg8Zn2Cd2 cuboctahedra, edges with two equivalent Zn(1)Mg10Cd2 cuboctahedra, edges with four equivalent Mg(4)Mg10Cd2 cuboctahedra, edges with four equivalent Mg(1)Mg8Zn2Cd2 cuboctahedra, edges with eight equivalent Mg(3)Mg8Zn2Cd2 cuboctahedra, faces with two equivalent Mg(4)Mg10Cd2 cuboctahedra, faces with two equivalent Mg(2)Mg10Zn2 cuboctahedra, faces with two equivalent Zn(1)Mg10Cd2 cuboctahedra, faces with four equivalent Mg(1)Mg8Zn2Cd2 cuboctahedra, faces with four equivalent Mg(3)Mg8Zn2Cd2 cuboctahedra, and faces with six equivalent Cd(1)Mg10Zn2 cuboctahedra. Both Mg(2)-Mg(4) bond lengths are 3.09 Å. All Mg(2)-Mg(3) bond lengths are 3.10 Å. Both Mg(2)-Zn(1) bond lengths are 3.12 Å. In the third Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Cd(1), and two equivalent Zn(1) atoms to form distorted MgMg8Zn2Cd2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Cd2 cuboctahedra, corners with four equivalent Cd(1)Mg10Zn2 cuboctahedra, corners with ten equivalent Mg(3)Mg8Zn2Cd2 cuboctahedra, edges with two equivalent Mg(4)Mg10Cd2 cuboctahedra, edges with two equivalent Mg(3)Mg8Zn2Cd2 cuboctahedra, edges with two equivalent Cd(1)Mg10Zn2 cuboctahedra, edges with four equivalent Mg(2)Mg10Zn2 cuboctahedra, edges with four equivalent Mg(1)Mg8Zn2Cd2 cuboctahedra, edges with four equivalent Zn(1)Mg10Cd2 cuboctahedra, faces with two equivalent Mg(4)Mg10Cd2 cuboctahedra, faces with two equivalent Mg(2)Mg10Zn2 cuboctahedra, faces with two equivalent Cd(1)Mg10Zn2 cuboctahedra, faces with two equivalent Zn(1)Mg10Cd2 cuboctahedra, faces with four equivalent Mg(3)Mg8Zn2Cd2 cuboctahedra, and faces with eight equivalent Mg(1)Mg8Zn2Cd2 cuboctahedra. There is one shorter (3.06 Å) and one longer (3.18 Å) Mg(3)-Mg(3) bond length. There is one shorter (3.11 Å) and one longer (3.16 Å) Mg(3)-Mg(4) bond length. There is one shorter (3.09 Å) and one longer (3.18 Å) Mg(3)-Cd(1) bond length. Both Mg(3)-Zn(1) bond lengths are 3.06 Å. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(2), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Cd(1) atoms to form distorted MgMg10Cd2 cuboctahedra that share corners with four equivalent Cd(1)Mg10Zn2 cuboctahedra, corners with six equivalent Mg(4)Mg10Cd2 cuboctahedra, corners with eight equivalent Mg(3)Mg8Zn2Cd2 cuboctahedra, edges with two equivalent Cd(1)Mg10Zn2 cuboctahedra, edges with four equivalent Mg(2)Mg10Zn2 cuboctahedra, edges with four equivalent Mg(3)Mg8Zn2Cd2 cuboctahedra, edges with eight equivalent Mg(1)Mg8Zn2Cd2 cuboctahedra, faces with two equivalent Mg(4)Mg10Cd2 cuboctahedra, faces with two equivalent Mg(2)Mg10Zn2 cuboctahedra, faces with two equivalent Cd(1)Mg10Zn2 cuboctahedra, faces with four equivalent Mg(1)Mg8Zn2Cd2 cuboctahedra, faces with four equivalent Mg(3)Mg8Zn2Cd2 cuboctahedra, and faces with six equivalent Zn(1)Mg10Cd2 cuboctahedra. Both Mg(4)-Cd(1) bond lengths are 3.12 Å. Cd(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Zn(1) atoms to form CdMg10Zn2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Cd2 cuboctahedra, corners with six equivalent Cd(1)Mg10Zn2 cuboctahedra, corners with eight equivalent Mg(3)Mg8Zn2Cd2 cuboctahedra, edges with two equivalent Mg(4)Mg10Cd2 cuboctahedra, edges with four equivalent Mg(3)Mg8Zn2Cd2 cuboctahedra, edges with four equivalent Zn(1)Mg10Cd2 cuboctahedra, edges with eight equivalent Mg(1)Mg8Zn2Cd2 cuboctahedra, faces with two equivalent Mg(4)Mg10Cd2 cuboctahedra, faces with two equivalent Cd(1)Mg10Zn2 cuboctahedra, faces with two equivalent Zn(1)Mg10Cd2 cuboctahedra, faces with four equivalent Mg(1)Mg8Zn2Cd2 cuboctahedra, faces with four equivalent Mg(3)Mg8Zn2Cd2 cuboctahedra, and faces with six equivalent Mg(2)Mg10Zn2 cuboctahedra. Both Cd(1)-Zn(1) bond lengths are 3.13 Å. Zn(1) is bonded to two equivalent Mg(2), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Cd(1) atoms to form ZnMg10Cd2 cuboctahedra that share corners with four equivalent Mg(2)Mg10Zn2 cuboctahedra, corners with six equivalent Zn(1)Mg10Cd2 cuboctahedra, corners with eight equivalent Mg(1)Mg8Zn2Cd2 cuboctahedra, edges with two equivalent Mg(2)Mg10Zn2 cuboctahedra, edges with four equivalent Mg(1)Mg8Zn2Cd2 cuboctahedra, edges with four equivalent Cd(1)Mg10Zn2 cuboctahedra, edges with eight equivalent Mg(3)Mg8Zn2Cd2 cuboctahedra, faces with two equivalent Mg(2)Mg10Zn2 cuboctahedra, faces with two equivalent Cd(1)Mg10Zn2 cuboctahedra, faces with two equivalent Zn(1)Mg10Cd2 cuboctahedra, faces with four equivalent Mg(1)Mg8Zn2Cd2 cuboctahedra, faces with four equivalent Mg(3)Mg8Zn2Cd2 cuboctahedra, and faces with six equivalent Mg(4)Mg10Cd2 cuboctahedra.