Mg6LaHf 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 La(1), and two equivalent Hf(1) atoms to form distorted MgLa2Hf2Mg8 cuboctahedra that share corners with four equivalent Mg(2)La2Mg10 cuboctahedra, corners with four equivalent La(1)Hf2Mg10 cuboctahedra, corners with ten equivalent Mg(1)La2Hf2Mg8 cuboctahedra, edges with two equivalent Mg(1)La2Hf2Mg8 cuboctahedra, edges with two equivalent Mg(2)La2Mg10 cuboctahedra, edges with two equivalent La(1)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(3)La2Hf2Mg8 cuboctahedra, edges with four equivalent Hf(1)La2Mg10 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(2)La2Mg10 cuboctahedra, faces with two equivalent La(1)Hf2Mg10 cuboctahedra, faces with two equivalent Hf(1)La2Mg10 cuboctahedra, faces with four equivalent Mg(1)La2Hf2Mg8 cuboctahedra, and faces with eight equivalent Mg(3)La2Hf2Mg8 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 La(1) atoms to form MgLa2Mg10 cuboctahedra that share corners with four equivalent La(1)Hf2Mg10 cuboctahedra, corners with six equivalent Mg(2)La2Mg10 cuboctahedra, corners with eight equivalent Mg(1)La2Hf2Mg8 cuboctahedra, edges with two equivalent La(1)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(1)La2Hf2Mg8 cuboctahedra, edges with eight equivalent Mg(3)La2Hf2Mg8 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(2)La2Mg10 cuboctahedra, faces with two equivalent La(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(1)La2Hf2Mg8 cuboctahedra, faces with four equivalent Mg(3)La2Hf2Mg8 cuboctahedra, and faces with six equivalent Hf(1)La2Mg10 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 La(1), and two equivalent Hf(1) atoms to form distorted MgLa2Hf2Mg8 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra, corners with four equivalent Hf(1)La2Mg10 cuboctahedra, corners with ten equivalent Mg(3)La2Hf2Mg8 cuboctahedra, edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with two equivalent Mg(3)La2Hf2Mg8 cuboctahedra, edges with two equivalent Hf(1)La2Mg10 cuboctahedra, edges with four equivalent Mg(1)La2Hf2Mg8 cuboctahedra, edges with four equivalent Mg(2)La2Mg10 cuboctahedra, edges with four equivalent La(1)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(2)La2Mg10 cuboctahedra, faces with two equivalent La(1)Hf2Mg10 cuboctahedra, faces with two equivalent Hf(1)La2Mg10 cuboctahedra, faces with four equivalent Mg(3)La2Hf2Mg8 cuboctahedra, and faces with eight equivalent Mg(1)La2Hf2Mg8 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 four equivalent Hf(1)La2Mg10 cuboctahedra, corners with six equivalent Mg(4)Hf2Mg10 cuboctahedra, corners with eight equivalent Mg(3)La2Hf2Mg8 cuboctahedra, edges with two equivalent Hf(1)La2Mg10 cuboctahedra, edges with four equivalent Mg(3)La2Hf2Mg8 cuboctahedra, edges with four equivalent Mg(2)La2Mg10 cuboctahedra, edges with eight equivalent Mg(1)La2Hf2Mg8 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(2)La2Mg10 cuboctahedra, faces with two equivalent Hf(1)La2Mg10 cuboctahedra, faces with four equivalent Mg(1)La2Hf2Mg8 cuboctahedra, faces with four equivalent Mg(3)La2Hf2Mg8 cuboctahedra, and faces with six equivalent La(1)Hf2Mg10 cuboctahedra. La(1) is bonded to two equivalent Mg(2), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Hf(1) atoms to form LaHf2Mg10 cuboctahedra that share corners with four equivalent Mg(2)La2Mg10 cuboctahedra, corners with six equivalent La(1)Hf2Mg10 cuboctahedra, corners with eight equivalent Mg(1)La2Hf2Mg8 cuboctahedra, edges with two equivalent Mg(2)La2Mg10 cuboctahedra, edges with four equivalent Mg(1)La2Hf2Mg8 cuboctahedra, edges with four equivalent Hf(1)La2Mg10 cuboctahedra, edges with eight equivalent Mg(3)La2Hf2Mg8 cuboctahedra, faces with two equivalent Mg(2)La2Mg10 cuboctahedra, faces with two equivalent La(1)Hf2Mg10 cuboctahedra, faces with two equivalent Hf(1)La2Mg10 cuboctahedra, faces with four equivalent Mg(1)La2Hf2Mg8 cuboctahedra, faces with four equivalent Mg(3)La2Hf2Mg8 cuboctahedra, and faces with six equivalent Mg(4)Hf2Mg10 cuboctahedra. Hf(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(3), and two equivalent La(1) atoms to form HfLa2Mg10 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra, corners with six equivalent Hf(1)La2Mg10 cuboctahedra, corners with eight equivalent Mg(3)La2Hf2Mg8 cuboctahedra, edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(3)La2Hf2Mg8 cuboctahedra, edges with four equivalent La(1)Hf2Mg10 cuboctahedra, edges with eight equivalent Mg(1)La2Hf2Mg8 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent La(1)Hf2Mg10 cuboctahedra, faces with two equivalent Hf(1)La2Mg10 cuboctahedra, faces with four equivalent Mg(1)La2Hf2Mg8 cuboctahedra, faces with four equivalent Mg(3)La2Hf2Mg8 cuboctahedra, and faces with six equivalent Mg(2)La2Mg10 cuboctahedra.
Mg6LaHf 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 La(1), and two equivalent Hf(1) atoms to form distorted MgLa2Hf2Mg8 cuboctahedra that share corners with four equivalent Mg(2)La2Mg10 cuboctahedra, corners with four equivalent La(1)Hf2Mg10 cuboctahedra, corners with ten equivalent Mg(1)La2Hf2Mg8 cuboctahedra, edges with two equivalent Mg(1)La2Hf2Mg8 cuboctahedra, edges with two equivalent Mg(2)La2Mg10 cuboctahedra, edges with two equivalent La(1)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(3)La2Hf2Mg8 cuboctahedra, edges with four equivalent Hf(1)La2Mg10 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(2)La2Mg10 cuboctahedra, faces with two equivalent La(1)Hf2Mg10 cuboctahedra, faces with two equivalent Hf(1)La2Mg10 cuboctahedra, faces with four equivalent Mg(1)La2Hf2Mg8 cuboctahedra, and faces with eight equivalent Mg(3)La2Hf2Mg8 cuboctahedra. There is one shorter (3.21 Å) and one longer (3.42 Å) Mg(1)-Mg(1) bond length. There is one shorter (3.28 Å) and one longer (3.35 Å) Mg(1)-Mg(2) bond length. Both Mg(1)-Mg(3) bond lengths are 3.22 Å. Both Mg(1)-Mg(4) bond lengths are 3.26 Å. There is one shorter (3.23 Å) and one longer (3.40 Å) Mg(1)-La(1) bond length. Both Mg(1)-Hf(1) bond lengths are 3.20 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 La(1) atoms to form MgLa2Mg10 cuboctahedra that share corners with four equivalent La(1)Hf2Mg10 cuboctahedra, corners with six equivalent Mg(2)La2Mg10 cuboctahedra, corners with eight equivalent Mg(1)La2Hf2Mg8 cuboctahedra, edges with two equivalent La(1)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(1)La2Hf2Mg8 cuboctahedra, edges with eight equivalent Mg(3)La2Hf2Mg8 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(2)La2Mg10 cuboctahedra, faces with two equivalent La(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(1)La2Hf2Mg8 cuboctahedra, faces with four equivalent Mg(3)La2Hf2Mg8 cuboctahedra, and faces with six equivalent Hf(1)La2Mg10 cuboctahedra. Both Mg(2)-Mg(4) bond lengths are 3.25 Å. All Mg(2)-Mg(3) bond lengths are 3.21 Å. Both Mg(2)-La(1) bond lengths are 3.32 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 La(1), and two equivalent Hf(1) atoms to form distorted MgLa2Hf2Mg8 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra, corners with four equivalent Hf(1)La2Mg10 cuboctahedra, corners with ten equivalent Mg(3)La2Hf2Mg8 cuboctahedra, edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with two equivalent Mg(3)La2Hf2Mg8 cuboctahedra, edges with two equivalent Hf(1)La2Mg10 cuboctahedra, edges with four equivalent Mg(1)La2Hf2Mg8 cuboctahedra, edges with four equivalent Mg(2)La2Mg10 cuboctahedra, edges with four equivalent La(1)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(2)La2Mg10 cuboctahedra, faces with two equivalent La(1)Hf2Mg10 cuboctahedra, faces with two equivalent Hf(1)La2Mg10 cuboctahedra, faces with four equivalent Mg(3)La2Hf2Mg8 cuboctahedra, and faces with eight equivalent Mg(1)La2Hf2Mg8 cuboctahedra. There is one shorter (3.23 Å) and one longer (3.40 Å) Mg(3)-Mg(3) bond length. There is one shorter (3.30 Å) and one longer (3.32 Å) Mg(3)-Mg(4) bond length. Both Mg(3)-La(1) bond lengths are 3.28 Å. There is one shorter (3.25 Å) and one longer (3.37 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 four equivalent Hf(1)La2Mg10 cuboctahedra, corners with six equivalent Mg(4)Hf2Mg10 cuboctahedra, corners with eight equivalent Mg(3)La2Hf2Mg8 cuboctahedra, edges with two equivalent Hf(1)La2Mg10 cuboctahedra, edges with four equivalent Mg(3)La2Hf2Mg8 cuboctahedra, edges with four equivalent Mg(2)La2Mg10 cuboctahedra, edges with eight equivalent Mg(1)La2Hf2Mg8 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(2)La2Mg10 cuboctahedra, faces with two equivalent Hf(1)La2Mg10 cuboctahedra, faces with four equivalent Mg(1)La2Hf2Mg8 cuboctahedra, faces with four equivalent Mg(3)La2Hf2Mg8 cuboctahedra, and faces with six equivalent La(1)Hf2Mg10 cuboctahedra. Both Mg(4)-Hf(1) bond lengths are 3.32 Å. La(1) is bonded to two equivalent Mg(2), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Hf(1) atoms to form LaHf2Mg10 cuboctahedra that share corners with four equivalent Mg(2)La2Mg10 cuboctahedra, corners with six equivalent La(1)Hf2Mg10 cuboctahedra, corners with eight equivalent Mg(1)La2Hf2Mg8 cuboctahedra, edges with two equivalent Mg(2)La2Mg10 cuboctahedra, edges with four equivalent Mg(1)La2Hf2Mg8 cuboctahedra, edges with four equivalent Hf(1)La2Mg10 cuboctahedra, edges with eight equivalent Mg(3)La2Hf2Mg8 cuboctahedra, faces with two equivalent Mg(2)La2Mg10 cuboctahedra, faces with two equivalent La(1)Hf2Mg10 cuboctahedra, faces with two equivalent Hf(1)La2Mg10 cuboctahedra, faces with four equivalent Mg(1)La2Hf2Mg8 cuboctahedra, faces with four equivalent Mg(3)La2Hf2Mg8 cuboctahedra, and faces with six equivalent Mg(4)Hf2Mg10 cuboctahedra. Both La(1)-Hf(1) bond lengths are 3.21 Å. Hf(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(3), and two equivalent La(1) atoms to form HfLa2Mg10 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra, corners with six equivalent Hf(1)La2Mg10 cuboctahedra, corners with eight equivalent Mg(3)La2Hf2Mg8 cuboctahedra, edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(3)La2Hf2Mg8 cuboctahedra, edges with four equivalent La(1)Hf2Mg10 cuboctahedra, edges with eight equivalent Mg(1)La2Hf2Mg8 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent La(1)Hf2Mg10 cuboctahedra, faces with two equivalent Hf(1)La2Mg10 cuboctahedra, faces with four equivalent Mg(1)La2Hf2Mg8 cuboctahedra, faces with four equivalent Mg(3)La2Hf2Mg8 cuboctahedra, and faces with six equivalent Mg(2)La2Mg10 cuboctahedra.