Mg6GaAl 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 Ga(1), and two equivalent Al(1) atoms to form distorted MgMg8Al2Ga2 cuboctahedra that share corners with four equivalent Ga(1)Mg10Al2 cuboctahedra, corners with four equivalent Al(1)Mg10Ga2 cuboctahedra, corners with ten equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, edges with two equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, edges with two equivalent Ga(1)Mg10Al2 cuboctahedra, edges with two equivalent Al(1)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(3)Mg10Al2 cuboctahedra, edges with four equivalent Mg(4)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(2)Mg8Al2Ga2 cuboctahedra, faces with two equivalent Mg(3)Mg10Al2 cuboctahedra, faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra, faces with two equivalent Ga(1)Mg10Al2 cuboctahedra, faces with two equivalent Al(1)Mg10Ga2 cuboctahedra, faces with four equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, and faces with eight equivalent Mg(2)Mg8Al2Ga2 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 Ga(1), and two equivalent Al(1) atoms to form distorted MgMg8Al2Ga2 cuboctahedra that share corners with four equivalent Mg(3)Mg10Al2 cuboctahedra, corners with four equivalent Mg(4)Mg10Ga2 cuboctahedra, corners with ten equivalent Mg(2)Mg8Al2Ga2 cuboctahedra, edges with two equivalent Mg(3)Mg10Al2 cuboctahedra, edges with two equivalent Mg(4)Mg10Ga2 cuboctahedra, edges with two equivalent Mg(2)Mg8Al2Ga2 cuboctahedra, edges with four equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, edges with four equivalent Ga(1)Mg10Al2 cuboctahedra, edges with four equivalent Al(1)Mg10Ga2 cuboctahedra, faces with two equivalent Mg(3)Mg10Al2 cuboctahedra, faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra, faces with two equivalent Ga(1)Mg10Al2 cuboctahedra, faces with two equivalent Al(1)Mg10Ga2 cuboctahedra, faces with four equivalent Mg(2)Mg8Al2Ga2 cuboctahedra, and faces with eight equivalent Mg(1)Mg8Al2Ga2 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)Mg10Ga2 cuboctahedra, corners with six equivalent Mg(3)Mg10Al2 cuboctahedra, corners with eight equivalent Mg(2)Mg8Al2Ga2 cuboctahedra, edges with two equivalent Mg(4)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(2)Mg8Al2Ga2 cuboctahedra, edges with four equivalent Al(1)Mg10Ga2 cuboctahedra, edges with eight equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, faces with two equivalent Mg(3)Mg10Al2 cuboctahedra, faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra, faces with two equivalent Al(1)Mg10Ga2 cuboctahedra, faces with four equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, faces with four equivalent Mg(2)Mg8Al2Ga2 cuboctahedra, and faces with six equivalent Ga(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 Ga(1) atoms to form distorted MgMg10Ga2 cuboctahedra that share corners with four equivalent Mg(3)Mg10Al2 cuboctahedra, corners with six equivalent Mg(4)Mg10Ga2 cuboctahedra, corners with eight equivalent Mg(2)Mg8Al2Ga2 cuboctahedra, edges with two equivalent Mg(3)Mg10Al2 cuboctahedra, edges with four equivalent Mg(2)Mg8Al2Ga2 cuboctahedra, edges with four equivalent Ga(1)Mg10Al2 cuboctahedra, edges with eight equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, faces with two equivalent Mg(3)Mg10Al2 cuboctahedra, faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra, faces with two equivalent Ga(1)Mg10Al2 cuboctahedra, faces with four equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, faces with four equivalent Mg(2)Mg8Al2Ga2 cuboctahedra, and faces with six equivalent Al(1)Mg10Ga2 cuboctahedra. Ga(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 GaMg10Al2 cuboctahedra that share corners with four equivalent Al(1)Mg10Ga2 cuboctahedra, corners with six equivalent Ga(1)Mg10Al2 cuboctahedra, corners with eight equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, edges with two equivalent Al(1)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(4)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, edges with eight equivalent Mg(2)Mg8Al2Ga2 cuboctahedra, faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra, faces with two equivalent Ga(1)Mg10Al2 cuboctahedra, faces with two equivalent Al(1)Mg10Ga2 cuboctahedra, faces with four equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, faces with four equivalent Mg(2)Mg8Al2Ga2 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 Ga(1) atoms to form distorted AlMg10Ga2 cuboctahedra that share corners with four equivalent Ga(1)Mg10Al2 cuboctahedra, corners with six equivalent Al(1)Mg10Ga2 cuboctahedra, corners with eight equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, edges with two equivalent Ga(1)Mg10Al2 cuboctahedra, edges with four equivalent Mg(3)Mg10Al2 cuboctahedra, edges with four equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, edges with eight equivalent Mg(2)Mg8Al2Ga2 cuboctahedra, faces with two equivalent Mg(3)Mg10Al2 cuboctahedra, faces with two equivalent Ga(1)Mg10Al2 cuboctahedra, faces with two equivalent Al(1)Mg10Ga2 cuboctahedra, faces with four equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, faces with four equivalent Mg(2)Mg8Al2Ga2 cuboctahedra, and faces with six equivalent Mg(4)Mg10Ga2 cuboctahedra.
Mg6GaAl 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 Ga(1), and two equivalent Al(1) atoms to form distorted MgMg8Al2Ga2 cuboctahedra that share corners with four equivalent Ga(1)Mg10Al2 cuboctahedra, corners with four equivalent Al(1)Mg10Ga2 cuboctahedra, corners with ten equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, edges with two equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, edges with two equivalent Ga(1)Mg10Al2 cuboctahedra, edges with two equivalent Al(1)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(3)Mg10Al2 cuboctahedra, edges with four equivalent Mg(4)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(2)Mg8Al2Ga2 cuboctahedra, faces with two equivalent Mg(3)Mg10Al2 cuboctahedra, faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra, faces with two equivalent Ga(1)Mg10Al2 cuboctahedra, faces with two equivalent Al(1)Mg10Ga2 cuboctahedra, faces with four equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, and faces with eight equivalent Mg(2)Mg8Al2Ga2 cuboctahedra. Both Mg(1)-Mg(1) bond lengths are 3.16 Å. Both Mg(1)-Mg(2) bond lengths are 3.08 Å. Both Mg(1)-Mg(3) bond lengths are 3.09 Å. Both Mg(1)-Mg(4) bond lengths are 3.08 Å. There is one shorter (3.12 Å) and one longer (3.13 Å) Mg(1)-Ga(1) bond length. Both Mg(1)-Al(1) bond lengths are 3.12 Å. 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 Ga(1), and two equivalent Al(1) atoms to form distorted MgMg8Al2Ga2 cuboctahedra that share corners with four equivalent Mg(3)Mg10Al2 cuboctahedra, corners with four equivalent Mg(4)Mg10Ga2 cuboctahedra, corners with ten equivalent Mg(2)Mg8Al2Ga2 cuboctahedra, edges with two equivalent Mg(3)Mg10Al2 cuboctahedra, edges with two equivalent Mg(4)Mg10Ga2 cuboctahedra, edges with two equivalent Mg(2)Mg8Al2Ga2 cuboctahedra, edges with four equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, edges with four equivalent Ga(1)Mg10Al2 cuboctahedra, edges with four equivalent Al(1)Mg10Ga2 cuboctahedra, faces with two equivalent Mg(3)Mg10Al2 cuboctahedra, faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra, faces with two equivalent Ga(1)Mg10Al2 cuboctahedra, faces with two equivalent Al(1)Mg10Ga2 cuboctahedra, faces with four equivalent Mg(2)Mg8Al2Ga2 cuboctahedra, and faces with eight equivalent Mg(1)Mg8Al2Ga2 cuboctahedra. There is one shorter (3.16 Å) and one longer (3.17 Å) Mg(2)-Mg(2) bond length. There is one shorter (3.08 Å) and one longer (3.17 Å) Mg(2)-Mg(3) bond length. There is one shorter (3.09 Å) and one longer (3.16 Å) Mg(2)-Mg(4) bond length. Both Mg(2)-Ga(1) bond lengths are 3.07 Å. Both Mg(2)-Al(1) bond lengths are 3.07 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)Mg10Ga2 cuboctahedra, corners with six equivalent Mg(3)Mg10Al2 cuboctahedra, corners with eight equivalent Mg(2)Mg8Al2Ga2 cuboctahedra, edges with two equivalent Mg(4)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(2)Mg8Al2Ga2 cuboctahedra, edges with four equivalent Al(1)Mg10Ga2 cuboctahedra, edges with eight equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, faces with two equivalent Mg(3)Mg10Al2 cuboctahedra, faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra, faces with two equivalent Al(1)Mg10Ga2 cuboctahedra, faces with four equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, faces with four equivalent Mg(2)Mg8Al2Ga2 cuboctahedra, and faces with six equivalent Ga(1)Mg10Al2 cuboctahedra. Both Mg(3)-Mg(4) bond lengths are 3.16 Å. Both Mg(3)-Al(1) bond lengths are 3.05 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 Ga(1) atoms to form distorted MgMg10Ga2 cuboctahedra that share corners with four equivalent Mg(3)Mg10Al2 cuboctahedra, corners with six equivalent Mg(4)Mg10Ga2 cuboctahedra, corners with eight equivalent Mg(2)Mg8Al2Ga2 cuboctahedra, edges with two equivalent Mg(3)Mg10Al2 cuboctahedra, edges with four equivalent Mg(2)Mg8Al2Ga2 cuboctahedra, edges with four equivalent Ga(1)Mg10Al2 cuboctahedra, edges with eight equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, faces with two equivalent Mg(3)Mg10Al2 cuboctahedra, faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra, faces with two equivalent Ga(1)Mg10Al2 cuboctahedra, faces with four equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, faces with four equivalent Mg(2)Mg8Al2Ga2 cuboctahedra, and faces with six equivalent Al(1)Mg10Ga2 cuboctahedra. Both Mg(4)-Ga(1) bond lengths are 3.05 Å. Ga(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 GaMg10Al2 cuboctahedra that share corners with four equivalent Al(1)Mg10Ga2 cuboctahedra, corners with six equivalent Ga(1)Mg10Al2 cuboctahedra, corners with eight equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, edges with two equivalent Al(1)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(4)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, edges with eight equivalent Mg(2)Mg8Al2Ga2 cuboctahedra, faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra, faces with two equivalent Ga(1)Mg10Al2 cuboctahedra, faces with two equivalent Al(1)Mg10Ga2 cuboctahedra, faces with four equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, faces with four equivalent Mg(2)Mg8Al2Ga2 cuboctahedra, and faces with six equivalent Mg(3)Mg10Al2 cuboctahedra. Both Ga(1)-Al(1) bond lengths are 3.16 Å. Al(1) is bonded to two equivalent Mg(3), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Ga(1) atoms to form distorted AlMg10Ga2 cuboctahedra that share corners with four equivalent Ga(1)Mg10Al2 cuboctahedra, corners with six equivalent Al(1)Mg10Ga2 cuboctahedra, corners with eight equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, edges with two equivalent Ga(1)Mg10Al2 cuboctahedra, edges with four equivalent Mg(3)Mg10Al2 cuboctahedra, edges with four equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, edges with eight equivalent Mg(2)Mg8Al2Ga2 cuboctahedra, faces with two equivalent Mg(3)Mg10Al2 cuboctahedra, faces with two equivalent Ga(1)Mg10Al2 cuboctahedra, faces with two equivalent Al(1)Mg10Ga2 cuboctahedra, faces with four equivalent Mg(1)Mg8Al2Ga2 cuboctahedra, faces with four equivalent Mg(2)Mg8Al2Ga2 cuboctahedra, and faces with six equivalent Mg(4)Mg10Ga2 cuboctahedra.