Mg6CdGa is beta Cu3Ti-derived structured and crystallizes in the orthorhombic Amm2 space group. There are six 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 Cd(1), and two equivalent Ga(1) atoms to form distorted MgMg8Cd2Ga2 cuboctahedra that share corners with four equivalent Mg(2)Mg10Cd2 cuboctahedra; corners with four equivalent Cd(1)Mg10Ga2 cuboctahedra; corners with ten Mg(1,1)Mg8Cd2Ga2 cuboctahedra; edges with two equivalent Mg(2)Mg10Cd2 cuboctahedra; edges with two equivalent Mg(1)Mg8Cd2Ga2 cuboctahedra; edges with two equivalent Cd(1)Mg10Ga2 cuboctahedra; edges with four equivalent Mg(4)Mg10Ga2 cuboctahedra; edges with four equivalent Mg(3)Mg8Cd2Ga2 cuboctahedra; edges with four equivalent Ga(1)Mg10Cd2 cuboctahedra; faces with two equivalent Mg(2)Mg10Cd2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra; faces with two equivalent Cd(1)Mg10Ga2 cuboctahedra; faces with two equivalent Ga(1)Mg10Cd2 cuboctahedra; faces with four Mg(1,1)Mg8Cd2Ga2 cuboctahedra; and faces with eight Mg(3,3)Mg8Cd2Ga2 cuboctahedra. In the second 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 Cd(1), and two equivalent Ga(1) atoms to form distorted MgMg8Cd2Ga2 cuboctahedra that share corners with four equivalent Mg(2)Mg10Cd2 cuboctahedra; corners with four equivalent Cd(1)Mg10Ga2 cuboctahedra; corners with ten Mg(1,1)Mg8Cd2Ga2 cuboctahedra; edges with two equivalent Mg(2)Mg10Cd2 cuboctahedra; edges with two equivalent Mg(1)Mg8Cd2Ga2 cuboctahedra; edges with two equivalent Cd(1)Mg10Ga2 cuboctahedra; edges with four equivalent Mg(4)Mg10Ga2 cuboctahedra; edges with four equivalent Mg(3)Mg8Cd2Ga2 cuboctahedra; edges with four equivalent Ga(1)Mg10Cd2 cuboctahedra; faces with two equivalent Mg(2)Mg10Cd2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra; faces with two equivalent Cd(1)Mg10Ga2 cuboctahedra; faces with two equivalent Ga(1)Mg10Cd2 cuboctahedra; faces with four Mg(1,1)Mg8Cd2Ga2 cuboctahedra; and faces with eight equivalent Mg(3)Mg8Cd2Ga2 cuboctahedra. In the third Mg site, Mg(2) is bonded to two equivalent Mg(4); four Mg(1,1); four Mg(3,3); and two equivalent Cd(1) atoms to form distorted MgMg10Cd2 cuboctahedra that share corners with four equivalent Cd(1)Mg10Ga2 cuboctahedra; corners with six equivalent Mg(2)Mg10Cd2 cuboctahedra; corners with eight Mg(1,1)Mg8Cd2Ga2 cuboctahedra; edges with two equivalent Cd(1)Mg10Ga2 cuboctahedra; edges with four equivalent Mg(4)Mg10Ga2 cuboctahedra; edges with four Mg(1,1)Mg8Cd2Ga2 cuboctahedra; edges with eight Mg(3,3)Mg8Cd2Ga2 cuboctahedra; faces with two equivalent Mg(2)Mg10Cd2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra; faces with two equivalent Cd(1)Mg10Ga2 cuboctahedra; faces with four Mg(1,1)Mg8Cd2Ga2 cuboctahedra; faces with four Mg(3,3)Mg8Cd2Ga2 cuboctahedra; and faces with six equivalent Ga(1)Mg10Cd2 cuboctahedra. In the fourth 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 Cd(1), and two equivalent Ga(1) atoms to form distorted MgMg8Cd2Ga2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Ga2 cuboctahedra; corners with four equivalent Ga(1)Mg10Cd2 cuboctahedra; corners with ten Mg(3,3)Mg8Cd2Ga2 cuboctahedra; edges with two equivalent Mg(4)Mg10Ga2 cuboctahedra; edges with two equivalent Mg(3)Mg8Cd2Ga2 cuboctahedra; edges with two equivalent Ga(1)Mg10Cd2 cuboctahedra; edges with four equivalent Mg(2)Mg10Cd2 cuboctahedra; edges with four equivalent Mg(1)Mg8Cd2Ga2 cuboctahedra; edges with four equivalent Cd(1)Mg10Ga2 cuboctahedra; faces with two equivalent Mg(2)Mg10Cd2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra; faces with two equivalent Cd(1)Mg10Ga2 cuboctahedra; faces with two equivalent Ga(1)Mg10Cd2 cuboctahedra; faces with four Mg(3,3)Mg8Cd2Ga2 cuboctahedra; and faces with eight Mg(1,1)Mg8Cd2Ga2 cuboctahedra. In the fifth 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 Cd(1), and two equivalent Ga(1) atoms to form distorted MgMg8Cd2Ga2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Ga2 cuboctahedra; corners with four equivalent Ga(1)Mg10Cd2 cuboctahedra; corners with ten Mg(3,3)Mg8Cd2Ga2 cuboctahedra; edges with two equivalent Mg(4)Mg10Ga2 cuboctahedra; edges with two equivalent Mg(3)Mg8Cd2Ga2 cuboctahedra; edges with two equivalent Ga(1)Mg10Cd2 cuboctahedra; edges with four equivalent Mg(2)Mg10Cd2 cuboctahedra; edges with four equivalent Mg(1)Mg8Cd2Ga2 cuboctahedra; edges with four equivalent Cd(1)Mg10Ga2 cuboctahedra; faces with two equivalent Mg(2)Mg10Cd2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra; faces with two equivalent Cd(1)Mg10Ga2 cuboctahedra; faces with two equivalent Ga(1)Mg10Cd2 cuboctahedra; faces with four Mg(3,3)Mg8Cd2Ga2 cuboctahedra; and faces with eight Mg(1,1)Mg8Cd2Ga2 cuboctahedra. In the sixth Mg site, Mg(4) is bonded to two equivalent Mg(2); four Mg(1,1); four Mg(3,3); and two equivalent Ga(1) atoms to form distorted MgMg10Ga2 cuboctahedra that share corners with four equivalent Ga(1)Mg10Cd2 cuboctahedra; corners with six equivalent Mg(4)Mg10Ga2 cuboctahedra; corners with eight Mg(3,3)Mg8Cd2Ga2 cuboctahedra; edges with two equivalent Ga(1)Mg10Cd2 cuboctahedra; edges with four equivalent Mg(2)Mg10Cd2 cuboctahedra; edges with four Mg(3,3)Mg8Cd2Ga2 cuboctahedra; edges with eight Mg(1,1)Mg8Cd2Ga2 cuboctahedra; faces with two equivalent Mg(2)Mg10Cd2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra; faces with two equivalent Ga(1)Mg10Cd2 cuboctahedra; faces with four Mg(1,1)Mg8Cd2Ga2 cuboctahedra; faces with four Mg(3,3)Mg8Cd2Ga2 cuboctahedra; and faces with six equivalent Cd(1)Mg10Ga2 cuboctahedra. Cd(1) is bonded to two equivalent Mg(2); four Mg(1,1); four Mg(3,3); and two equivalent Ga(1) atoms to form CdMg10Ga2 cuboctahedra that share corners with four equivalent Mg(2)Mg10Cd2 cuboctahedra; corners with six equivalent Cd(1)Mg10Ga2 cuboctahedra; corners with eight Mg(1,1)Mg8Cd2Ga2 cuboctahedra; edges with two equivalent Mg(2)Mg10Cd2 cuboctahedra; edges with four Mg(1,1)Mg8Cd2Ga2 cuboctahedra; edges with four equivalent Ga(1)Mg10Cd2 cuboctahedra; edges with eight Mg(3,3)Mg8Cd2Ga2 cuboctahedra; faces with two equivalent Mg(2)Mg10Cd2 cuboctahedra; faces with two equivalent Cd(1)Mg10Ga2 cuboctahedra; faces with two equivalent Ga(1)Mg10Cd2 cuboctahedra; faces with four Mg(1,1)Mg8Cd2Ga2 cuboctahedra; faces with four Mg(3,3)Mg8Cd2Ga2 cuboctahedra; and faces with six equivalent Mg(4)Mg10Ga2 cuboctahedra. Ga(1) is bonded to two equivalent Mg(4); four Mg(1,1); four Mg(3,3); and two equivalent Cd(1) atoms to form GaMg10Cd2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Ga2 cuboctahedra; corners with six equivalent Ga(1)Mg10Cd2 cuboctahedra; corners with eight Mg(3,3)Mg8Cd2Ga2 cuboctahedra; edges with two equivalent Mg(4)Mg10Ga2 cuboctahedra; edges with four Mg(3,3)Mg8Cd2Ga2 cuboctahedra; edges with four equivalent Cd(1)Mg10Ga2 cuboctahedra; edges with eight Mg(1,1)Mg8Cd2Ga2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra; faces with two equivalent Cd(1)Mg10Ga2 cuboctahedra; faces with two equivalent Ga(1)Mg10Cd2 cuboctahedra; faces with four Mg(1,1)Mg8Cd2Ga2 cuboctahedra; faces with four Mg(3,3)Mg8Cd2Ga2 cuboctahedra; and faces with six equivalent Mg(2)Mg10Cd2 cuboctahedra.
Mg6CdGa is beta Cu3Ti-derived structured and crystallizes in the orthorhombic Amm2 space group. There are six 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 Cd(1), and two equivalent Ga(1) atoms to form distorted MgMg8Cd2Ga2 cuboctahedra that share corners with four equivalent Mg(2)Mg10Cd2 cuboctahedra; corners with four equivalent Cd(1)Mg10Ga2 cuboctahedra; corners with ten Mg(1,1)Mg8Cd2Ga2 cuboctahedra; edges with two equivalent Mg(2)Mg10Cd2 cuboctahedra; edges with two equivalent Mg(1)Mg8Cd2Ga2 cuboctahedra; edges with two equivalent Cd(1)Mg10Ga2 cuboctahedra; edges with four equivalent Mg(4)Mg10Ga2 cuboctahedra; edges with four equivalent Mg(3)Mg8Cd2Ga2 cuboctahedra; edges with four equivalent Ga(1)Mg10Cd2 cuboctahedra; faces with two equivalent Mg(2)Mg10Cd2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra; faces with two equivalent Cd(1)Mg10Ga2 cuboctahedra; faces with two equivalent Ga(1)Mg10Cd2 cuboctahedra; faces with four Mg(1,1)Mg8Cd2Ga2 cuboctahedra; and faces with eight Mg(3,3)Mg8Cd2Ga2 cuboctahedra. There is one shorter (3.08 Å) and one longer (3.17 Å) Mg(1)-Mg(1) bond length. There is one shorter (3.13 Å) and one longer (3.17 Å) Mg(1)-Mg(2) bond length. Both Mg(1)-Mg(3) bond lengths are 3.16 Å. Both Mg(1)-Mg(4) bond lengths are 3.12 Å. There is one shorter (3.14 Å) and one longer (3.15 Å) Mg(1)-Cd(1) bond length. Both Mg(1)-Ga(1) bond lengths are 3.08 Å. In the second 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 Cd(1), and two equivalent Ga(1) atoms to form distorted MgMg8Cd2Ga2 cuboctahedra that share corners with four equivalent Mg(2)Mg10Cd2 cuboctahedra; corners with four equivalent Cd(1)Mg10Ga2 cuboctahedra; corners with ten Mg(1,1)Mg8Cd2Ga2 cuboctahedra; edges with two equivalent Mg(2)Mg10Cd2 cuboctahedra; edges with two equivalent Mg(1)Mg8Cd2Ga2 cuboctahedra; edges with two equivalent Cd(1)Mg10Ga2 cuboctahedra; edges with four equivalent Mg(4)Mg10Ga2 cuboctahedra; edges with four equivalent Mg(3)Mg8Cd2Ga2 cuboctahedra; edges with four equivalent Ga(1)Mg10Cd2 cuboctahedra; faces with two equivalent Mg(2)Mg10Cd2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra; faces with two equivalent Cd(1)Mg10Ga2 cuboctahedra; faces with two equivalent Ga(1)Mg10Cd2 cuboctahedra; faces with four Mg(1,1)Mg8Cd2Ga2 cuboctahedra; and faces with eight equivalent Mg(3)Mg8Cd2Ga2 cuboctahedra. There is one shorter (3.13 Å) and one longer (3.17 Å) Mg(1)-Mg(2) bond length. Both Mg(1)-Mg(3) bond lengths are 3.16 Å. Both Mg(1)-Mg(4) bond lengths are 3.12 Å. There is one shorter (3.14 Å) and one longer (3.15 Å) Mg(1)-Cd(1) bond length. Both Mg(1)-Ga(1) bond lengths are 3.08 Å. In the third Mg site, Mg(2) is bonded to two equivalent Mg(4); four Mg(1,1); four Mg(3,3); and two equivalent Cd(1) atoms to form distorted MgMg10Cd2 cuboctahedra that share corners with four equivalent Cd(1)Mg10Ga2 cuboctahedra; corners with six equivalent Mg(2)Mg10Cd2 cuboctahedra; corners with eight Mg(1,1)Mg8Cd2Ga2 cuboctahedra; edges with two equivalent Cd(1)Mg10Ga2 cuboctahedra; edges with four equivalent Mg(4)Mg10Ga2 cuboctahedra; edges with four Mg(1,1)Mg8Cd2Ga2 cuboctahedra; edges with eight Mg(3,3)Mg8Cd2Ga2 cuboctahedra; faces with two equivalent Mg(2)Mg10Cd2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra; faces with two equivalent Cd(1)Mg10Ga2 cuboctahedra; faces with four Mg(1,1)Mg8Cd2Ga2 cuboctahedra; faces with four Mg(3,3)Mg8Cd2Ga2 cuboctahedra; and faces with six equivalent Ga(1)Mg10Cd2 cuboctahedra. Both Mg(2)-Mg(4) bond lengths are 3.12 Å. All Mg(2)-Mg(3,3) bond lengths are 3.12 Å. Both Mg(2)-Cd(1) bond lengths are 3.12 Å. In the fourth 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 Cd(1), and two equivalent Ga(1) atoms to form distorted MgMg8Cd2Ga2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Ga2 cuboctahedra; corners with four equivalent Ga(1)Mg10Cd2 cuboctahedra; corners with ten Mg(3,3)Mg8Cd2Ga2 cuboctahedra; edges with two equivalent Mg(4)Mg10Ga2 cuboctahedra; edges with two equivalent Mg(3)Mg8Cd2Ga2 cuboctahedra; edges with two equivalent Ga(1)Mg10Cd2 cuboctahedra; edges with four equivalent Mg(2)Mg10Cd2 cuboctahedra; edges with four equivalent Mg(1)Mg8Cd2Ga2 cuboctahedra; edges with four equivalent Cd(1)Mg10Ga2 cuboctahedra; faces with two equivalent Mg(2)Mg10Cd2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra; faces with two equivalent Cd(1)Mg10Ga2 cuboctahedra; faces with two equivalent Ga(1)Mg10Cd2 cuboctahedra; faces with four Mg(3,3)Mg8Cd2Ga2 cuboctahedra; and faces with eight Mg(1,1)Mg8Cd2Ga2 cuboctahedra. There is one shorter (3.11 Å) and one longer (3.13 Å) Mg(3)-Mg(3) bond length. There is one shorter (3.13 Å) and one longer (3.16 Å) Mg(3)-Mg(4) bond length. Both Mg(3)-Cd(1) bond lengths are 3.10 Å. There is one shorter (3.10 Å) and one longer (3.19 Å) Mg(3)-Ga(1) bond length. In the fifth 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 Cd(1), and two equivalent Ga(1) atoms to form distorted MgMg8Cd2Ga2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Ga2 cuboctahedra; corners with four equivalent Ga(1)Mg10Cd2 cuboctahedra; corners with ten Mg(3,3)Mg8Cd2Ga2 cuboctahedra; edges with two equivalent Mg(4)Mg10Ga2 cuboctahedra; edges with two equivalent Mg(3)Mg8Cd2Ga2 cuboctahedra; edges with two equivalent Ga(1)Mg10Cd2 cuboctahedra; edges with four equivalent Mg(2)Mg10Cd2 cuboctahedra; edges with four equivalent Mg(1)Mg8Cd2Ga2 cuboctahedra; edges with four equivalent Cd(1)Mg10Ga2 cuboctahedra; faces with two equivalent Mg(2)Mg10Cd2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra; faces with two equivalent Cd(1)Mg10Ga2 cuboctahedra; faces with two equivalent Ga(1)Mg10Cd2 cuboctahedra; faces with four Mg(3,3)Mg8Cd2Ga2 cuboctahedra; and faces with eight Mg(1,1)Mg8Cd2Ga2 cuboctahedra. Both Mg(3)-Mg(1) bond lengths are 3.16 Å. There is one shorter (3.13 Å) and one longer (3.16 Å) Mg(3)-Mg(4) bond length. Both Mg(3)-Cd(1) bond lengths are 3.10 Å. There is one shorter (3.10 Å) and one longer (3.19 Å) Mg(3)-Ga(1) bond length. In the sixth Mg site, Mg(4) is bonded to two equivalent Mg(2); four Mg(1,1); four Mg(3,3); and two equivalent Ga(1) atoms to form distorted MgMg10Ga2 cuboctahedra that share corners with four equivalent Ga(1)Mg10Cd2 cuboctahedra; corners with six equivalent Mg(4)Mg10Ga2 cuboctahedra; corners with eight Mg(3,3)Mg8Cd2Ga2 cuboctahedra; edges with two equivalent Ga(1)Mg10Cd2 cuboctahedra; edges with four equivalent Mg(2)Mg10Cd2 cuboctahedra; edges with four Mg(3,3)Mg8Cd2Ga2 cuboctahedra; edges with eight Mg(1,1)Mg8Cd2Ga2 cuboctahedra; faces with two equivalent Mg(2)Mg10Cd2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra; faces with two equivalent Ga(1)Mg10Cd2 cuboctahedra; faces with four Mg(1,1)Mg8Cd2Ga2 cuboctahedra; faces with four Mg(3,3)Mg8Cd2Ga2 cuboctahedra; and faces with six equivalent Cd(1)Mg10Ga2 cuboctahedra. Both Mg(4)-Ga(1) bond lengths are 3.12 Å. Cd(1) is bonded to two equivalent Mg(2); four Mg(1,1); four Mg(3,3); and two equivalent Ga(1) atoms to form CdMg10Ga2 cuboctahedra that share corners with four equivalent Mg(2)Mg10Cd2 cuboctahedra; corners with six equivalent Cd(1)Mg10Ga2 cuboctahedra; corners with eight Mg(1,1)Mg8Cd2Ga2 cuboctahedra; edges with two equivalent Mg(2)Mg10Cd2 cuboctahedra; edges with four Mg(1,1)Mg8Cd2Ga2 cuboctahedra; edges with four equivalent Ga(1)Mg10Cd2 cuboctahedra; edges with eight Mg(3,3)Mg8Cd2Ga2 cuboctahedra; faces with two equivalent Mg(2)Mg10Cd2 cuboctahedra; faces with two equivalent Cd(1)Mg10Ga2 cuboctahedra; faces with two equivalent Ga(1)Mg10Cd2 cuboctahedra; faces with four Mg(1,1)Mg8Cd2Ga2 cuboctahedra; faces with four Mg(3,3)Mg8Cd2Ga2 cuboctahedra; and faces with six equivalent Mg(4)Mg10Ga2 cuboctahedra. Both Cd(1)-Ga(1) bond lengths are 3.19 Å. Ga(1) is bonded to two equivalent Mg(4); four Mg(1,1); four Mg(3,3); and two equivalent Cd(1) atoms to form GaMg10Cd2 cuboctahedra that share corners with four equivalent Mg(4)Mg10Ga2 cuboctahedra; corners with six equivalent Ga(1)Mg10Cd2 cuboctahedra; corners with eight Mg(3,3)Mg8Cd2Ga2 cuboctahedra; edges with two equivalent Mg(4)Mg10Ga2 cuboctahedra; edges with four Mg(3,3)Mg8Cd2Ga2 cuboctahedra; edges with four equivalent Cd(1)Mg10Ga2 cuboctahedra; edges with eight Mg(1,1)Mg8Cd2Ga2 cuboctahedra; faces with two equivalent Mg(4)Mg10Ga2 cuboctahedra; faces with two equivalent Cd(1)Mg10Ga2 cuboctahedra; faces with two equivalent Ga(1)Mg10Cd2 cuboctahedra; faces with four Mg(1,1)Mg8Cd2Ga2 cuboctahedra; faces with four Mg(3,3)Mg8Cd2Ga2 cuboctahedra; and faces with six equivalent Mg(2)Mg10Cd2 cuboctahedra.