Mg6CeHf 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 Ce(1), and two equivalent Hf(1) atoms to form distorted MgCe2Hf2Mg8 cuboctahedra that share corners with four equivalent Mg(2)Ce2Mg10 cuboctahedra, corners with four equivalent Ce(1)Hf2Mg10 cuboctahedra, corners with ten equivalent Mg(1)Ce2Hf2Mg8 cuboctahedra, edges with two equivalent Mg(1)Ce2Hf2Mg8 cuboctahedra, edges with two equivalent Mg(2)Ce2Mg10 cuboctahedra, edges with two equivalent Ce(1)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(3)Ce2Hf2Mg8 cuboctahedra, edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(2)Ce2Mg10 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Ce(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(1)Ce2Hf2Mg8 cuboctahedra, and faces with eight equivalent Mg(3)Ce2Hf2Mg8 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 Ce(1) atoms to form distorted MgCe2Mg10 cuboctahedra that share corners with four equivalent Ce(1)Hf2Mg10 cuboctahedra, corners with six equivalent Mg(2)Ce2Mg10 cuboctahedra, corners with eight equivalent Mg(1)Ce2Hf2Mg8 cuboctahedra, edges with two equivalent Ce(1)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(1)Ce2Hf2Mg8 cuboctahedra, edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with eight equivalent Mg(3)Ce2Hf2Mg8 cuboctahedra, faces with two equivalent Mg(2)Ce2Mg10 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Ce(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(1)Ce2Hf2Mg8 cuboctahedra, and faces with four equivalent Mg(3)Ce2Hf2Mg8 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 Ce(1), and two equivalent Hf(1) atoms to form MgCe2Hf2Mg8 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra, corners with ten equivalent Mg(3)Ce2Hf2Mg8 cuboctahedra, edges with two equivalent Mg(3)Ce2Hf2Mg8 cuboctahedra, edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(1)Ce2Hf2Mg8 cuboctahedra, edges with four equivalent Mg(2)Ce2Mg10 cuboctahedra, edges with four equivalent Ce(1)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(2)Ce2Mg10 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Ce(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(3)Ce2Hf2Mg8 cuboctahedra, and faces with eight equivalent Mg(1)Ce2Hf2Mg8 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 Hf(1) atoms to form MgHf2Mg10 cuboctahedra that share corners with six equivalent Mg(4)Hf2Mg10 cuboctahedra, corners with eight equivalent Mg(3)Ce2Hf2Mg8 cuboctahedra, edges with four equivalent Mg(3)Ce2Hf2Mg8 cuboctahedra, edges with four equivalent Mg(2)Ce2Mg10 cuboctahedra, edges with eight equivalent Mg(1)Ce2Hf2Mg8 cuboctahedra, faces with two equivalent Mg(2)Ce2Mg10 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(1)Ce2Hf2Mg8 cuboctahedra, faces with four equivalent Mg(3)Ce2Hf2Mg8 cuboctahedra, and faces with six equivalent Ce(1)Hf2Mg10 cuboctahedra. Ce(1) is bonded to two equivalent Mg(2), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Hf(1) atoms to form distorted CeHf2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Ce2Mg10 cuboctahedra, corners with six equivalent Ce(1)Hf2Mg10 cuboctahedra, corners with eight equivalent Mg(1)Ce2Hf2Mg8 cuboctahedra, edges with two equivalent Mg(2)Ce2Mg10 cuboctahedra, edges with four equivalent Mg(1)Ce2Hf2Mg8 cuboctahedra, edges with eight equivalent Mg(3)Ce2Hf2Mg8 cuboctahedra, faces with two equivalent Mg(2)Ce2Mg10 cuboctahedra, faces with two equivalent Ce(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(1)Ce2Hf2Mg8 cuboctahedra, faces with four equivalent Mg(3)Ce2Hf2Mg8 cuboctahedra, and faces with six equivalent Mg(4)Hf2Mg10 cuboctahedra. Hf(1) is bonded in a distorted bent 120 degrees geometry to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Ce(1) atoms.
Mg6CeHf 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 Ce(1), and two equivalent Hf(1) atoms to form distorted MgCe2Hf2Mg8 cuboctahedra that share corners with four equivalent Mg(2)Ce2Mg10 cuboctahedra, corners with four equivalent Ce(1)Hf2Mg10 cuboctahedra, corners with ten equivalent Mg(1)Ce2Hf2Mg8 cuboctahedra, edges with two equivalent Mg(1)Ce2Hf2Mg8 cuboctahedra, edges with two equivalent Mg(2)Ce2Mg10 cuboctahedra, edges with two equivalent Ce(1)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(3)Ce2Hf2Mg8 cuboctahedra, edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(2)Ce2Mg10 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Ce(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(1)Ce2Hf2Mg8 cuboctahedra, and faces with eight equivalent Mg(3)Ce2Hf2Mg8 cuboctahedra. There is one shorter (3.11 Å) and one longer (3.40 Å) Mg(1)-Mg(1) bond length. There is one shorter (3.23 Å) and one longer (3.39 Å) Mg(1)-Mg(2) bond length. Both Mg(1)-Mg(3) bond lengths are 3.06 Å. Both Mg(1)-Mg(4) bond lengths are 3.24 Å. There is one shorter (3.15 Å) and one longer (3.47 Å) Mg(1)-Ce(1) bond length. Both Mg(1)-Hf(1) bond lengths are 3.23 Å. 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 Ce(1) atoms to form distorted MgCe2Mg10 cuboctahedra that share corners with four equivalent Ce(1)Hf2Mg10 cuboctahedra, corners with six equivalent Mg(2)Ce2Mg10 cuboctahedra, corners with eight equivalent Mg(1)Ce2Hf2Mg8 cuboctahedra, edges with two equivalent Ce(1)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(1)Ce2Hf2Mg8 cuboctahedra, edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with eight equivalent Mg(3)Ce2Hf2Mg8 cuboctahedra, faces with two equivalent Mg(2)Ce2Mg10 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Ce(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(1)Ce2Hf2Mg8 cuboctahedra, and faces with four equivalent Mg(3)Ce2Hf2Mg8 cuboctahedra. Both Mg(2)-Mg(4) bond lengths are 3.12 Å. All Mg(2)-Mg(3) bond lengths are 3.19 Å. Both Mg(2)-Ce(1) bond lengths are 3.26 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 Ce(1), and two equivalent Hf(1) atoms to form MgCe2Hf2Mg8 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra, corners with ten equivalent Mg(3)Ce2Hf2Mg8 cuboctahedra, edges with two equivalent Mg(3)Ce2Hf2Mg8 cuboctahedra, edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(1)Ce2Hf2Mg8 cuboctahedra, edges with four equivalent Mg(2)Ce2Mg10 cuboctahedra, edges with four equivalent Ce(1)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(2)Ce2Mg10 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Ce(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(3)Ce2Hf2Mg8 cuboctahedra, and faces with eight equivalent Mg(1)Ce2Hf2Mg8 cuboctahedra. There is one shorter (3.18 Å) and one longer (3.32 Å) Mg(3)-Mg(3) bond length. There is one shorter (3.27 Å) and one longer (3.35 Å) Mg(3)-Mg(4) bond length. Both Mg(3)-Ce(1) bond lengths are 3.30 Å. There is one shorter (3.23 Å) and one longer (3.39 Å) Mg(3)-Hf(1) bond length. 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 Hf(1) atoms to form MgHf2Mg10 cuboctahedra that share corners with six equivalent Mg(4)Hf2Mg10 cuboctahedra, corners with eight equivalent Mg(3)Ce2Hf2Mg8 cuboctahedra, edges with four equivalent Mg(3)Ce2Hf2Mg8 cuboctahedra, edges with four equivalent Mg(2)Ce2Mg10 cuboctahedra, edges with eight equivalent Mg(1)Ce2Hf2Mg8 cuboctahedra, faces with two equivalent Mg(2)Ce2Mg10 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(1)Ce2Hf2Mg8 cuboctahedra, faces with four equivalent Mg(3)Ce2Hf2Mg8 cuboctahedra, and faces with six equivalent Ce(1)Hf2Mg10 cuboctahedra. Both Mg(4)-Hf(1) bond lengths are 3.26 Å. Ce(1) is bonded to two equivalent Mg(2), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Hf(1) atoms to form distorted CeHf2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Ce2Mg10 cuboctahedra, corners with six equivalent Ce(1)Hf2Mg10 cuboctahedra, corners with eight equivalent Mg(1)Ce2Hf2Mg8 cuboctahedra, edges with two equivalent Mg(2)Ce2Mg10 cuboctahedra, edges with four equivalent Mg(1)Ce2Hf2Mg8 cuboctahedra, edges with eight equivalent Mg(3)Ce2Hf2Mg8 cuboctahedra, faces with two equivalent Mg(2)Ce2Mg10 cuboctahedra, faces with two equivalent Ce(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(1)Ce2Hf2Mg8 cuboctahedra, faces with four equivalent Mg(3)Ce2Hf2Mg8 cuboctahedra, and faces with six equivalent Mg(4)Hf2Mg10 cuboctahedra. Both Ce(1)-Hf(1) bond lengths are 2.92 Å. Hf(1) is bonded in a distorted bent 120 degrees geometry to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Ce(1) atoms.