Mg6CuGa crystallizes in the orthorhombic Amm2 space group. There are five 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 Cu(1), and two equivalent Ga(1) atoms to form distorted MgMg8Ga2Cu2 cuboctahedra that share corners with four equivalent Cu(1)Mg10Ga2 cuboctahedra; corners with four equivalent Ga(1)Mg10Cu2 cuboctahedra; corners with ten equivalent Mg(1)Mg8Ga2Cu2 cuboctahedra; edges with two equivalent Mg(1)Mg8Ga2Cu2 cuboctahedra; edges with two equivalent Cu(1)Mg10Ga2 cuboctahedra; edges with two equivalent Ga(1)Mg10Cu2 cuboctahedra; edges with four equivalent Mg(3)Mg10Cu2 cuboctahedra; edges with four equivalent Mg(4)Mg10Ga2 cuboctahedra; edges with four equivalent Mg(2)Mg8Ga2Cu2 cuboctahedra; faces with two equivalent Mg(3)Mg10Cu2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra; faces with two equivalent Cu(1)Mg10Ga2 cuboctahedra; faces with two equivalent Ga(1)Mg10Cu2 cuboctahedra; faces with four equivalent Mg(1)Mg8Ga2Cu2 cuboctahedra; and faces with eight Mg(2,2)Mg8Ga2Cu2 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 Cu(1), and two equivalent Ga(1) atoms to form distorted MgMg8Ga2Cu2 cuboctahedra that share corners with four equivalent Mg(3)Mg10Cu2 cuboctahedra; corners with four equivalent Mg(4)Mg10Ga2 cuboctahedra; corners with ten Mg(2,2)Mg8Ga2Cu2 cuboctahedra; edges with two equivalent Mg(3)Mg10Cu2 cuboctahedra; edges with two equivalent Mg(4)Mg10Ga2 cuboctahedra; edges with two equivalent Mg(2)Mg8Ga2Cu2 cuboctahedra; edges with four equivalent Mg(1)Mg8Ga2Cu2 cuboctahedra; edges with four equivalent Cu(1)Mg10Ga2 cuboctahedra; edges with four equivalent Ga(1)Mg10Cu2 cuboctahedra; faces with two equivalent Mg(3)Mg10Cu2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra; faces with two equivalent Cu(1)Mg10Ga2 cuboctahedra; faces with two equivalent Ga(1)Mg10Cu2 cuboctahedra; faces with four equivalent Mg(2)Mg8Ga2Cu2 cuboctahedra; and faces with eight equivalent Mg(1)Mg8Ga2Cu2 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(4); four equivalent Mg(1); four Mg(2,2); and two equivalent Cu(1) atoms to form distorted MgMg10Cu2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Ga2 cuboctahedra; corners with six equivalent Mg(3)Mg10Cu2 cuboctahedra; corners with eight Mg(2,2)Mg8Ga2Cu2 cuboctahedra; edges with two equivalent Mg(4)Mg10Ga2 cuboctahedra; edges with four Mg(2,2)Mg8Ga2Cu2 cuboctahedra; edges with four equivalent Cu(1)Mg10Ga2 cuboctahedra; edges with eight equivalent Mg(1)Mg8Ga2Cu2 cuboctahedra; faces with two equivalent Mg(3)Mg10Cu2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra; faces with two equivalent Cu(1)Mg10Ga2 cuboctahedra; faces with four equivalent Mg(1)Mg8Ga2Cu2 cuboctahedra; faces with four Mg(2,2)Mg8Ga2Cu2 cuboctahedra; and faces with six equivalent Ga(1)Mg10Cu2 cuboctahedra. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(3); four equivalent Mg(1); four Mg(2,2); and two equivalent Ga(1) atoms to form distorted MgMg10Ga2 cuboctahedra that share corners with four equivalent Mg(3)Mg10Cu2 cuboctahedra; corners with six equivalent Mg(4)Mg10Ga2 cuboctahedra; corners with eight Mg(2,2)Mg8Ga2Cu2 cuboctahedra; edges with two equivalent Mg(3)Mg10Cu2 cuboctahedra; edges with four Mg(2,2)Mg8Ga2Cu2 cuboctahedra; edges with four equivalent Ga(1)Mg10Cu2 cuboctahedra; edges with eight equivalent Mg(1)Mg8Ga2Cu2 cuboctahedra; faces with two equivalent Mg(3)Mg10Cu2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra; faces with two equivalent Ga(1)Mg10Cu2 cuboctahedra; faces with four equivalent Mg(1)Mg8Ga2Cu2 cuboctahedra; faces with four Mg(2,2)Mg8Ga2Cu2 cuboctahedra; and faces with six equivalent Cu(1)Mg10Ga2 cuboctahedra. In the fifth 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 Cu(1), and two equivalent Ga(1) atoms to form distorted MgMg8Ga2Cu2 cuboctahedra that share corners with four equivalent Mg(3)Mg10Cu2 cuboctahedra; corners with four equivalent Mg(4)Mg10Ga2 cuboctahedra; corners with ten Mg(2,2)Mg8Ga2Cu2 cuboctahedra; edges with two equivalent Mg(3)Mg10Cu2 cuboctahedra; edges with two equivalent Mg(4)Mg10Ga2 cuboctahedra; edges with two equivalent Mg(2)Mg8Ga2Cu2 cuboctahedra; edges with four equivalent Mg(1)Mg8Ga2Cu2 cuboctahedra; edges with four equivalent Cu(1)Mg10Ga2 cuboctahedra; edges with four equivalent Ga(1)Mg10Cu2 cuboctahedra; faces with two equivalent Mg(3)Mg10Cu2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra; faces with two equivalent Cu(1)Mg10Ga2 cuboctahedra; faces with two equivalent Ga(1)Mg10Cu2 cuboctahedra; faces with four equivalent Mg(2)Mg8Ga2Cu2 cuboctahedra; and faces with eight equivalent Mg(1)Mg8Ga2Cu2 cuboctahedra. Cu(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 CuMg10Ga2 cuboctahedra that share corners with four equivalent Ga(1)Mg10Cu2 cuboctahedra; corners with six equivalent Cu(1)Mg10Ga2 cuboctahedra; corners with eight equivalent Mg(1)Mg8Ga2Cu2 cuboctahedra; edges with two equivalent Ga(1)Mg10Cu2 cuboctahedra; edges with four equivalent Mg(3)Mg10Cu2 cuboctahedra; edges with four equivalent Mg(1)Mg8Ga2Cu2 cuboctahedra; edges with eight Mg(2,2)Mg8Ga2Cu2 cuboctahedra; faces with two equivalent Mg(3)Mg10Cu2 cuboctahedra; faces with two equivalent Cu(1)Mg10Ga2 cuboctahedra; faces with two equivalent Ga(1)Mg10Cu2 cuboctahedra; faces with four equivalent Mg(1)Mg8Ga2Cu2 cuboctahedra; faces with four equivalent Mg(2)Mg8Ga2Cu2 cuboctahedra; and faces with six equivalent Mg(4)Mg10Ga2 cuboctahedra. Ga(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Cu(1) atoms to form GaMg10Cu2 cuboctahedra that share corners with four equivalent Cu(1)Mg10Ga2 cuboctahedra; corners with six equivalent Ga(1)Mg10Cu2 cuboctahedra; corners with eight equivalent Mg(1)Mg8Ga2Cu2 cuboctahedra; edges with two equivalent Cu(1)Mg10Ga2 cuboctahedra; edges with four equivalent Mg(4)Mg10Ga2 cuboctahedra; edges with four equivalent Mg(1)Mg8Ga2Cu2 cuboctahedra; edges with eight Mg(2,2)Mg8Ga2Cu2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra; faces with two equivalent Cu(1)Mg10Ga2 cuboctahedra; faces with two equivalent Ga(1)Mg10Cu2 cuboctahedra; faces with four equivalent Mg(1)Mg8Ga2Cu2 cuboctahedra; faces with four equivalent Mg(2)Mg8Ga2Cu2 cuboctahedra; and faces with six equivalent Mg(3)Mg10Cu2 cuboctahedra.
Mg6CuGa crystallizes in the orthorhombic Amm2 space group. There are five 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 Cu(1), and two equivalent Ga(1) atoms to form distorted MgMg8Ga2Cu2 cuboctahedra that share corners with four equivalent Cu(1)Mg10Ga2 cuboctahedra; corners with four equivalent Ga(1)Mg10Cu2 cuboctahedra; corners with ten equivalent Mg(1)Mg8Ga2Cu2 cuboctahedra; edges with two equivalent Mg(1)Mg8Ga2Cu2 cuboctahedra; edges with two equivalent Cu(1)Mg10Ga2 cuboctahedra; edges with two equivalent Ga(1)Mg10Cu2 cuboctahedra; edges with four equivalent Mg(3)Mg10Cu2 cuboctahedra; edges with four equivalent Mg(4)Mg10Ga2 cuboctahedra; edges with four equivalent Mg(2)Mg8Ga2Cu2 cuboctahedra; faces with two equivalent Mg(3)Mg10Cu2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra; faces with two equivalent Cu(1)Mg10Ga2 cuboctahedra; faces with two equivalent Ga(1)Mg10Cu2 cuboctahedra; faces with four equivalent Mg(1)Mg8Ga2Cu2 cuboctahedra; and faces with eight Mg(2,2)Mg8Ga2Cu2 cuboctahedra. There is one shorter (3.11 Å) and one longer (3.12 Å) Mg(1)-Mg(1) bond length. Both Mg(1)-Mg(2) bond lengths are 3.01 Å. Both Mg(1)-Mg(3) bond lengths are 3.02 Å. Both Mg(1)-Mg(4) bond lengths are 3.01 Å. There is one shorter (3.02 Å) and one longer (3.05 Å) Mg(1)-Cu(1) bond length. There is one shorter (3.02 Å) and one longer (3.05 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 Cu(1), and two equivalent Ga(1) atoms to form distorted MgMg8Ga2Cu2 cuboctahedra that share corners with four equivalent Mg(3)Mg10Cu2 cuboctahedra; corners with four equivalent Mg(4)Mg10Ga2 cuboctahedra; corners with ten Mg(2,2)Mg8Ga2Cu2 cuboctahedra; edges with two equivalent Mg(3)Mg10Cu2 cuboctahedra; edges with two equivalent Mg(4)Mg10Ga2 cuboctahedra; edges with two equivalent Mg(2)Mg8Ga2Cu2 cuboctahedra; edges with four equivalent Mg(1)Mg8Ga2Cu2 cuboctahedra; edges with four equivalent Cu(1)Mg10Ga2 cuboctahedra; edges with four equivalent Ga(1)Mg10Cu2 cuboctahedra; faces with two equivalent Mg(3)Mg10Cu2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra; faces with two equivalent Cu(1)Mg10Ga2 cuboctahedra; faces with two equivalent Ga(1)Mg10Cu2 cuboctahedra; faces with four equivalent Mg(2)Mg8Ga2Cu2 cuboctahedra; and faces with eight equivalent Mg(1)Mg8Ga2Cu2 cuboctahedra. There is one shorter (3.06 Å) and one longer (3.18 Å) Mg(2)-Mg(2) bond length. There is one shorter (2.93 Å) and one longer (3.14 Å) Mg(2)-Mg(3) bond length. There is one shorter (2.99 Å) and one longer (3.08 Å) Mg(2)-Mg(4) bond length. Both Mg(2)-Cu(1) bond lengths are 2.98 Å. Both Mg(2)-Ga(1) bond lengths are 3.01 Å. In the third Mg site, Mg(3) is bonded to two equivalent Mg(4); four equivalent Mg(1); four Mg(2,2); and two equivalent Cu(1) atoms to form distorted MgMg10Cu2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Ga2 cuboctahedra; corners with six equivalent Mg(3)Mg10Cu2 cuboctahedra; corners with eight Mg(2,2)Mg8Ga2Cu2 cuboctahedra; edges with two equivalent Mg(4)Mg10Ga2 cuboctahedra; edges with four Mg(2,2)Mg8Ga2Cu2 cuboctahedra; edges with four equivalent Cu(1)Mg10Ga2 cuboctahedra; edges with eight equivalent Mg(1)Mg8Ga2Cu2 cuboctahedra; faces with two equivalent Mg(3)Mg10Cu2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra; faces with two equivalent Cu(1)Mg10Ga2 cuboctahedra; faces with four equivalent Mg(1)Mg8Ga2Cu2 cuboctahedra; faces with four Mg(2,2)Mg8Ga2Cu2 cuboctahedra; and faces with six equivalent Ga(1)Mg10Cu2 cuboctahedra. Both Mg(3)-Mg(4) bond lengths are 3.12 Å. Both Mg(3)-Mg(2) bond lengths are 2.93 Å. Both Mg(3)-Cu(1) bond lengths are 2.94 Å. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(3); four equivalent Mg(1); four Mg(2,2); and two equivalent Ga(1) atoms to form distorted MgMg10Ga2 cuboctahedra that share corners with four equivalent Mg(3)Mg10Cu2 cuboctahedra; corners with six equivalent Mg(4)Mg10Ga2 cuboctahedra; corners with eight Mg(2,2)Mg8Ga2Cu2 cuboctahedra; edges with two equivalent Mg(3)Mg10Cu2 cuboctahedra; edges with four Mg(2,2)Mg8Ga2Cu2 cuboctahedra; edges with four equivalent Ga(1)Mg10Cu2 cuboctahedra; edges with eight equivalent Mg(1)Mg8Ga2Cu2 cuboctahedra; faces with two equivalent Mg(3)Mg10Cu2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra; faces with two equivalent Ga(1)Mg10Cu2 cuboctahedra; faces with four equivalent Mg(1)Mg8Ga2Cu2 cuboctahedra; faces with four Mg(2,2)Mg8Ga2Cu2 cuboctahedra; and faces with six equivalent Cu(1)Mg10Ga2 cuboctahedra. Both Mg(4)-Mg(2) bond lengths are 3.08 Å. Both Mg(4)-Ga(1) bond lengths are 2.96 Å. In the fifth 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 Cu(1), and two equivalent Ga(1) atoms to form distorted MgMg8Ga2Cu2 cuboctahedra that share corners with four equivalent Mg(3)Mg10Cu2 cuboctahedra; corners with four equivalent Mg(4)Mg10Ga2 cuboctahedra; corners with ten Mg(2,2)Mg8Ga2Cu2 cuboctahedra; edges with two equivalent Mg(3)Mg10Cu2 cuboctahedra; edges with two equivalent Mg(4)Mg10Ga2 cuboctahedra; edges with two equivalent Mg(2)Mg8Ga2Cu2 cuboctahedra; edges with four equivalent Mg(1)Mg8Ga2Cu2 cuboctahedra; edges with four equivalent Cu(1)Mg10Ga2 cuboctahedra; edges with four equivalent Ga(1)Mg10Cu2 cuboctahedra; faces with two equivalent Mg(3)Mg10Cu2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra; faces with two equivalent Cu(1)Mg10Ga2 cuboctahedra; faces with two equivalent Ga(1)Mg10Cu2 cuboctahedra; faces with four equivalent Mg(2)Mg8Ga2Cu2 cuboctahedra; and faces with eight equivalent Mg(1)Mg8Ga2Cu2 cuboctahedra. Both Mg(2)-Mg(1) bond lengths are 3.01 Å. There is one shorter (3.06 Å) and one longer (3.18 Å) Mg(2)-Mg(2) bond length. Both Mg(2)-Cu(1) bond lengths are 2.98 Å. Both Mg(2)-Ga(1) bond lengths are 3.01 Å. Cu(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 CuMg10Ga2 cuboctahedra that share corners with four equivalent Ga(1)Mg10Cu2 cuboctahedra; corners with six equivalent Cu(1)Mg10Ga2 cuboctahedra; corners with eight equivalent Mg(1)Mg8Ga2Cu2 cuboctahedra; edges with two equivalent Ga(1)Mg10Cu2 cuboctahedra; edges with four equivalent Mg(3)Mg10Cu2 cuboctahedra; edges with four equivalent Mg(1)Mg8Ga2Cu2 cuboctahedra; edges with eight Mg(2,2)Mg8Ga2Cu2 cuboctahedra; faces with two equivalent Mg(3)Mg10Cu2 cuboctahedra; faces with two equivalent Cu(1)Mg10Ga2 cuboctahedra; faces with two equivalent Ga(1)Mg10Cu2 cuboctahedra; faces with four equivalent Mg(1)Mg8Ga2Cu2 cuboctahedra; faces with four equivalent Mg(2)Mg8Ga2Cu2 cuboctahedra; and faces with six equivalent Mg(4)Mg10Ga2 cuboctahedra. Both Cu(1)-Ga(1) bond lengths are 3.12 Å. Ga(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Cu(1) atoms to form GaMg10Cu2 cuboctahedra that share corners with four equivalent Cu(1)Mg10Ga2 cuboctahedra; corners with six equivalent Ga(1)Mg10Cu2 cuboctahedra; corners with eight equivalent Mg(1)Mg8Ga2Cu2 cuboctahedra; edges with two equivalent Cu(1)Mg10Ga2 cuboctahedra; edges with four equivalent Mg(4)Mg10Ga2 cuboctahedra; edges with four equivalent Mg(1)Mg8Ga2Cu2 cuboctahedra; edges with eight Mg(2,2)Mg8Ga2Cu2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra; faces with two equivalent Cu(1)Mg10Ga2 cuboctahedra; faces with two equivalent Ga(1)Mg10Cu2 cuboctahedra; faces with four equivalent Mg(1)Mg8Ga2Cu2 cuboctahedra; faces with four equivalent Mg(2)Mg8Ga2Cu2 cuboctahedra; and faces with six equivalent Mg(3)Mg10Cu2 cuboctahedra.