Mg6HfGa 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 Ga(1) atoms to form distorted MgHf2Mg8Ga2 cuboctahedra that share corners with four equivalent Hf(1)Mg10Ga2 cuboctahedra, corners with four equivalent Ga(1)Hf2Mg10 cuboctahedra, corners with ten equivalent Mg(1)Hf2Mg8Ga2 cuboctahedra, edges with two equivalent Mg(1)Hf2Mg8Ga2 cuboctahedra, edges with two equivalent Hf(1)Mg10Ga2 cuboctahedra, edges with two equivalent Ga(1)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(2)Hf2Mg8Ga2 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Hf(1)Mg10Ga2 cuboctahedra, faces with two equivalent Ga(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Ga2 cuboctahedra, and faces with eight equivalent Mg(2)Hf2Mg8Ga2 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 Ga(1) atoms to form distorted MgHf2Mg8Ga2 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra, corners with ten equivalent Mg(2)Hf2Mg8Ga2 cuboctahedra, edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with two equivalent Mg(2)Hf2Mg8Ga2 cuboctahedra, edges with four equivalent Mg(1)Hf2Mg8Ga2 cuboctahedra, edges with four equivalent Hf(1)Mg10Ga2 cuboctahedra, edges with four equivalent Ga(1)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Hf(1)Mg10Ga2 cuboctahedra, faces with two equivalent Ga(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(2)Hf2Mg8Ga2 cuboctahedra, and faces with eight equivalent Mg(1)Hf2Mg8Ga2 cuboctahedra. In the third Mg site, Mg(3) is bonded in a 2-coordinate geometry to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Ga(1) atoms. 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 six equivalent Mg(4)Hf2Mg10 cuboctahedra, corners with eight equivalent Mg(2)Hf2Mg8Ga2 cuboctahedra, edges with four equivalent Mg(2)Hf2Mg8Ga2 cuboctahedra, edges with four equivalent Hf(1)Mg10Ga2 cuboctahedra, edges with eight equivalent Mg(1)Hf2Mg8Ga2 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Hf(1)Mg10Ga2 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Ga2 cuboctahedra, faces with four equivalent Mg(2)Hf2Mg8Ga2 cuboctahedra, and faces with six equivalent Ga(1)Hf2Mg10 cuboctahedra. Hf(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Ga(1) atoms to form distorted HfMg10Ga2 cuboctahedra that share corners with four equivalent Ga(1)Hf2Mg10 cuboctahedra, corners with six equivalent Hf(1)Mg10Ga2 cuboctahedra, corners with eight equivalent Mg(1)Hf2Mg8Ga2 cuboctahedra, edges with two equivalent Ga(1)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(1)Hf2Mg8Ga2 cuboctahedra, edges with eight equivalent Mg(2)Hf2Mg8Ga2 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Hf(1)Mg10Ga2 cuboctahedra, faces with two equivalent Ga(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Ga2 cuboctahedra, and faces with four equivalent Mg(2)Hf2Mg8Ga2 cuboctahedra. Ga(1) is bonded to two equivalent Mg(3), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Hf(1) atoms to form distorted GaHf2Mg10 cuboctahedra that share corners with four equivalent Hf(1)Mg10Ga2 cuboctahedra, corners with six equivalent Ga(1)Hf2Mg10 cuboctahedra, corners with eight equivalent Mg(1)Hf2Mg8Ga2 cuboctahedra, edges with two equivalent Hf(1)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(1)Hf2Mg8Ga2 cuboctahedra, edges with eight equivalent Mg(2)Hf2Mg8Ga2 cuboctahedra, faces with two equivalent Hf(1)Mg10Ga2 cuboctahedra, faces with two equivalent Ga(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Ga2 cuboctahedra, faces with four equivalent Mg(2)Hf2Mg8Ga2 cuboctahedra, and faces with six equivalent Mg(4)Hf2Mg10 cuboctahedra.
Mg6HfGa 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 Ga(1) atoms to form distorted MgHf2Mg8Ga2 cuboctahedra that share corners with four equivalent Hf(1)Mg10Ga2 cuboctahedra, corners with four equivalent Ga(1)Hf2Mg10 cuboctahedra, corners with ten equivalent Mg(1)Hf2Mg8Ga2 cuboctahedra, edges with two equivalent Mg(1)Hf2Mg8Ga2 cuboctahedra, edges with two equivalent Hf(1)Mg10Ga2 cuboctahedra, edges with two equivalent Ga(1)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(2)Hf2Mg8Ga2 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Hf(1)Mg10Ga2 cuboctahedra, faces with two equivalent Ga(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Ga2 cuboctahedra, and faces with eight equivalent Mg(2)Hf2Mg8Ga2 cuboctahedra. Both Mg(1)-Mg(1) bond lengths are 3.00 Å. Both Mg(1)-Mg(2) bond lengths are 3.05 Å. Both Mg(1)-Mg(3) bond lengths are 3.14 Å. Both Mg(1)-Mg(4) bond lengths are 3.11 Å. There is one shorter (3.18 Å) and one longer (3.22 Å) Mg(1)-Hf(1) bond length. There is one shorter (3.13 Å) and one longer (3.27 Å) Mg(1)-Ga(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 Ga(1) atoms to form distorted MgHf2Mg8Ga2 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra, corners with ten equivalent Mg(2)Hf2Mg8Ga2 cuboctahedra, edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with two equivalent Mg(2)Hf2Mg8Ga2 cuboctahedra, edges with four equivalent Mg(1)Hf2Mg8Ga2 cuboctahedra, edges with four equivalent Hf(1)Mg10Ga2 cuboctahedra, edges with four equivalent Ga(1)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Hf(1)Mg10Ga2 cuboctahedra, faces with two equivalent Ga(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(2)Hf2Mg8Ga2 cuboctahedra, and faces with eight equivalent Mg(1)Hf2Mg8Ga2 cuboctahedra. There is one shorter (2.94 Å) and one longer (3.06 Å) Mg(2)-Mg(2) bond length. There is one shorter (3.13 Å) and one longer (3.28 Å) Mg(2)-Mg(3) bond length. There is one shorter (3.19 Å) and one longer (3.22 Å) Mg(2)-Mg(4) bond length. Both Mg(2)-Hf(1) bond lengths are 3.10 Å. Both Mg(2)-Ga(1) bond lengths are 3.10 Å. In the third Mg site, Mg(3) is bonded in a 2-coordinate geometry to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Ga(1) atoms. Both Mg(3)-Mg(4) bond lengths are 3.00 Å. Both Mg(3)-Ga(1) bond lengths are 3.04 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 six equivalent Mg(4)Hf2Mg10 cuboctahedra, corners with eight equivalent Mg(2)Hf2Mg8Ga2 cuboctahedra, edges with four equivalent Mg(2)Hf2Mg8Ga2 cuboctahedra, edges with four equivalent Hf(1)Mg10Ga2 cuboctahedra, edges with eight equivalent Mg(1)Hf2Mg8Ga2 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Hf(1)Mg10Ga2 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Ga2 cuboctahedra, faces with four equivalent Mg(2)Hf2Mg8Ga2 cuboctahedra, and faces with six equivalent Ga(1)Hf2Mg10 cuboctahedra. Both Mg(4)-Hf(1) bond lengths are 3.04 Å. Hf(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Ga(1) atoms to form distorted HfMg10Ga2 cuboctahedra that share corners with four equivalent Ga(1)Hf2Mg10 cuboctahedra, corners with six equivalent Hf(1)Mg10Ga2 cuboctahedra, corners with eight equivalent Mg(1)Hf2Mg8Ga2 cuboctahedra, edges with two equivalent Ga(1)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(1)Hf2Mg8Ga2 cuboctahedra, edges with eight equivalent Mg(2)Hf2Mg8Ga2 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Hf(1)Mg10Ga2 cuboctahedra, faces with two equivalent Ga(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Ga2 cuboctahedra, and faces with four equivalent Mg(2)Hf2Mg8Ga2 cuboctahedra. Both Hf(1)-Ga(1) bond lengths are 3.00 Å. Ga(1) is bonded to two equivalent Mg(3), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Hf(1) atoms to form distorted GaHf2Mg10 cuboctahedra that share corners with four equivalent Hf(1)Mg10Ga2 cuboctahedra, corners with six equivalent Ga(1)Hf2Mg10 cuboctahedra, corners with eight equivalent Mg(1)Hf2Mg8Ga2 cuboctahedra, edges with two equivalent Hf(1)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(1)Hf2Mg8Ga2 cuboctahedra, edges with eight equivalent Mg(2)Hf2Mg8Ga2 cuboctahedra, faces with two equivalent Hf(1)Mg10Ga2 cuboctahedra, faces with two equivalent Ga(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Ga2 cuboctahedra, faces with four equivalent Mg(2)Hf2Mg8Ga2 cuboctahedra, and faces with six equivalent Mg(4)Hf2Mg10 cuboctahedra.