Mg6HfAl 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 Hf(1), and two equivalent Al(1) atoms to form MgHf2Mg8Al2 cuboctahedra that share corners with four equivalent Hf(1)Mg10Al2 cuboctahedra, corners with four equivalent Al(1)Hf2Mg10 cuboctahedra, corners with ten equivalent Mg(1)Hf2Mg8Al2 cuboctahedra, edges with two equivalent Mg(1)Hf2Mg8Al2 cuboctahedra, edges with two equivalent Hf(1)Mg10Al2 cuboctahedra, edges with two equivalent Al(1)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(2)Hf2Mg8Al2 cuboctahedra, edges with four equivalent Mg(3)Mg10Al2 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(3)Mg10Al2 cuboctahedra, faces with two equivalent Hf(1)Mg10Al2 cuboctahedra, faces with two equivalent Al(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Al2 cuboctahedra, and faces with eight equivalent Mg(2)Hf2Mg8Al2 cuboctahedra. In the second 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 Hf(1), and two equivalent Al(1) atoms to form distorted MgHf2Mg8Al2 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra, corners with four equivalent Mg(3)Mg10Al2 cuboctahedra, corners with ten equivalent Mg(2)Hf2Mg8Al2 cuboctahedra, edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with two equivalent Mg(2)Hf2Mg8Al2 cuboctahedra, edges with two equivalent Mg(3)Mg10Al2 cuboctahedra, edges with four equivalent Mg(1)Hf2Mg8Al2 cuboctahedra, edges with four equivalent Hf(1)Mg10Al2 cuboctahedra, edges with four equivalent Al(1)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(3)Mg10Al2 cuboctahedra, faces with two equivalent Hf(1)Mg10Al2 cuboctahedra, faces with two equivalent Al(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(2)Hf2Mg8Al2 cuboctahedra, and faces with eight equivalent Mg(1)Hf2Mg8Al2 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Al(1) atoms to form distorted MgMg10Al2 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra, corners with six equivalent Mg(3)Mg10Al2 cuboctahedra, corners with eight equivalent Mg(2)Hf2Mg8Al2 cuboctahedra, edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(2)Hf2Mg8Al2 cuboctahedra, edges with four equivalent Al(1)Hf2Mg10 cuboctahedra, edges with eight equivalent Mg(1)Hf2Mg8Al2 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(3)Mg10Al2 cuboctahedra, faces with two equivalent Al(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Al2 cuboctahedra, faces with four equivalent Mg(2)Hf2Mg8Al2 cuboctahedra, and faces with six equivalent Hf(1)Mg10Al2 cuboctahedra. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(3), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Hf(1) atoms to form MgHf2Mg10 cuboctahedra that share corners with four equivalent Mg(3)Mg10Al2 cuboctahedra, corners with six equivalent Mg(4)Hf2Mg10 cuboctahedra, corners with eight equivalent Mg(2)Hf2Mg8Al2 cuboctahedra, edges with two equivalent Mg(3)Mg10Al2 cuboctahedra, edges with four equivalent Mg(2)Hf2Mg8Al2 cuboctahedra, edges with four equivalent Hf(1)Mg10Al2 cuboctahedra, edges with eight equivalent Mg(1)Hf2Mg8Al2 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(3)Mg10Al2 cuboctahedra, faces with two equivalent Hf(1)Mg10Al2 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Al2 cuboctahedra, faces with four equivalent Mg(2)Hf2Mg8Al2 cuboctahedra, and faces with six equivalent Al(1)Hf2Mg10 cuboctahedra. Hf(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Al(1) atoms to form distorted HfMg10Al2 cuboctahedra that share corners with four equivalent Al(1)Hf2Mg10 cuboctahedra, corners with six equivalent Hf(1)Mg10Al2 cuboctahedra, corners with eight equivalent Mg(1)Hf2Mg8Al2 cuboctahedra, edges with two equivalent Al(1)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(1)Hf2Mg8Al2 cuboctahedra, edges with eight equivalent Mg(2)Hf2Mg8Al2 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Hf(1)Mg10Al2 cuboctahedra, faces with two equivalent Al(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Al2 cuboctahedra, faces with four equivalent Mg(2)Hf2Mg8Al2 cuboctahedra, and faces with six equivalent Mg(3)Mg10Al2 cuboctahedra. Al(1) is bonded to two equivalent Mg(3), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Hf(1) atoms to form AlHf2Mg10 cuboctahedra that share corners with four equivalent Hf(1)Mg10Al2 cuboctahedra, corners with six equivalent Al(1)Hf2Mg10 cuboctahedra, corners with eight equivalent Mg(1)Hf2Mg8Al2 cuboctahedra, edges with two equivalent Hf(1)Mg10Al2 cuboctahedra, edges with four equivalent Mg(1)Hf2Mg8Al2 cuboctahedra, edges with four equivalent Mg(3)Mg10Al2 cuboctahedra, edges with eight equivalent Mg(2)Hf2Mg8Al2 cuboctahedra, faces with two equivalent Mg(3)Mg10Al2 cuboctahedra, faces with two equivalent Hf(1)Mg10Al2 cuboctahedra, faces with two equivalent Al(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Al2 cuboctahedra, faces with four equivalent Mg(2)Hf2Mg8Al2 cuboctahedra, and faces with six equivalent Mg(4)Hf2Mg10 cuboctahedra.
Mg6HfAl 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 Hf(1), and two equivalent Al(1) atoms to form MgHf2Mg8Al2 cuboctahedra that share corners with four equivalent Hf(1)Mg10Al2 cuboctahedra, corners with four equivalent Al(1)Hf2Mg10 cuboctahedra, corners with ten equivalent Mg(1)Hf2Mg8Al2 cuboctahedra, edges with two equivalent Mg(1)Hf2Mg8Al2 cuboctahedra, edges with two equivalent Hf(1)Mg10Al2 cuboctahedra, edges with two equivalent Al(1)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(2)Hf2Mg8Al2 cuboctahedra, edges with four equivalent Mg(3)Mg10Al2 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(3)Mg10Al2 cuboctahedra, faces with two equivalent Hf(1)Mg10Al2 cuboctahedra, faces with two equivalent Al(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Al2 cuboctahedra, and faces with eight equivalent Mg(2)Hf2Mg8Al2 cuboctahedra. There is one shorter (3.03 Å) and one longer (3.05 Å) Mg(1)-Mg(1) bond length. Both Mg(1)-Mg(2) bond lengths are 3.11 Å. Both Mg(1)-Mg(3) bond lengths are 3.11 Å. Both Mg(1)-Mg(4) bond lengths are 3.10 Å. There is one shorter (3.16 Å) and one longer (3.21 Å) Mg(1)-Hf(1) bond length. There is one shorter (3.16 Å) and one longer (3.21 Å) Mg(1)-Al(1) bond length. In the second 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 Hf(1), and two equivalent Al(1) atoms to form distorted MgHf2Mg8Al2 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra, corners with four equivalent Mg(3)Mg10Al2 cuboctahedra, corners with ten equivalent Mg(2)Hf2Mg8Al2 cuboctahedra, edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with two equivalent Mg(2)Hf2Mg8Al2 cuboctahedra, edges with two equivalent Mg(3)Mg10Al2 cuboctahedra, edges with four equivalent Mg(1)Hf2Mg8Al2 cuboctahedra, edges with four equivalent Hf(1)Mg10Al2 cuboctahedra, edges with four equivalent Al(1)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(3)Mg10Al2 cuboctahedra, faces with two equivalent Hf(1)Mg10Al2 cuboctahedra, faces with two equivalent Al(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(2)Hf2Mg8Al2 cuboctahedra, and faces with eight equivalent Mg(1)Hf2Mg8Al2 cuboctahedra. There is one shorter (3.02 Å) and one longer (3.07 Å) Mg(2)-Mg(2) bond length. There is one shorter (3.15 Å) and one longer (3.22 Å) Mg(2)-Mg(3) bond length. There is one shorter (3.15 Å) and one longer (3.22 Å) Mg(2)-Mg(4) bond length. Both Mg(2)-Hf(1) bond lengths are 3.09 Å. Both Mg(2)-Al(1) bond lengths are 3.09 Å. In the third Mg site, Mg(3) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Al(1) atoms to form distorted MgMg10Al2 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra, corners with six equivalent Mg(3)Mg10Al2 cuboctahedra, corners with eight equivalent Mg(2)Hf2Mg8Al2 cuboctahedra, edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(2)Hf2Mg8Al2 cuboctahedra, edges with four equivalent Al(1)Hf2Mg10 cuboctahedra, edges with eight equivalent Mg(1)Hf2Mg8Al2 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(3)Mg10Al2 cuboctahedra, faces with two equivalent Al(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Al2 cuboctahedra, faces with four equivalent Mg(2)Hf2Mg8Al2 cuboctahedra, and faces with six equivalent Hf(1)Mg10Al2 cuboctahedra. Both Mg(3)-Mg(4) bond lengths are 3.04 Å. Both Mg(3)-Al(1) bond lengths are 3.10 Å. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(3), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Hf(1) atoms to form MgHf2Mg10 cuboctahedra that share corners with four equivalent Mg(3)Mg10Al2 cuboctahedra, corners with six equivalent Mg(4)Hf2Mg10 cuboctahedra, corners with eight equivalent Mg(2)Hf2Mg8Al2 cuboctahedra, edges with two equivalent Mg(3)Mg10Al2 cuboctahedra, edges with four equivalent Mg(2)Hf2Mg8Al2 cuboctahedra, edges with four equivalent Hf(1)Mg10Al2 cuboctahedra, edges with eight equivalent Mg(1)Hf2Mg8Al2 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(3)Mg10Al2 cuboctahedra, faces with two equivalent Hf(1)Mg10Al2 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Al2 cuboctahedra, faces with four equivalent Mg(2)Hf2Mg8Al2 cuboctahedra, and faces with six equivalent Al(1)Hf2Mg10 cuboctahedra. Both Mg(4)-Hf(1) bond lengths are 3.08 Å. Hf(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Al(1) atoms to form distorted HfMg10Al2 cuboctahedra that share corners with four equivalent Al(1)Hf2Mg10 cuboctahedra, corners with six equivalent Hf(1)Mg10Al2 cuboctahedra, corners with eight equivalent Mg(1)Hf2Mg8Al2 cuboctahedra, edges with two equivalent Al(1)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(1)Hf2Mg8Al2 cuboctahedra, edges with eight equivalent Mg(2)Hf2Mg8Al2 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Hf(1)Mg10Al2 cuboctahedra, faces with two equivalent Al(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Al2 cuboctahedra, faces with four equivalent Mg(2)Hf2Mg8Al2 cuboctahedra, and faces with six equivalent Mg(3)Mg10Al2 cuboctahedra. Both Hf(1)-Al(1) bond lengths are 3.04 Å. Al(1) is bonded to two equivalent Mg(3), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Hf(1) atoms to form AlHf2Mg10 cuboctahedra that share corners with four equivalent Hf(1)Mg10Al2 cuboctahedra, corners with six equivalent Al(1)Hf2Mg10 cuboctahedra, corners with eight equivalent Mg(1)Hf2Mg8Al2 cuboctahedra, edges with two equivalent Hf(1)Mg10Al2 cuboctahedra, edges with four equivalent Mg(1)Hf2Mg8Al2 cuboctahedra, edges with four equivalent Mg(3)Mg10Al2 cuboctahedra, edges with eight equivalent Mg(2)Hf2Mg8Al2 cuboctahedra, faces with two equivalent Mg(3)Mg10Al2 cuboctahedra, faces with two equivalent Hf(1)Mg10Al2 cuboctahedra, faces with two equivalent Al(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Al2 cuboctahedra, faces with four equivalent Mg(2)Hf2Mg8Al2 cuboctahedra, and faces with six equivalent Mg(4)Hf2Mg10 cuboctahedra.