Mg6LaZr 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 La(1), and two equivalent Zr(1) atoms to form MgLa2Mg8Zr2 cuboctahedra that share corners with four equivalent La(1)Mg10Zr2 cuboctahedra, corners with four equivalent Zr(1)La2Mg10 cuboctahedra, corners with ten equivalent Mg(1)La2Mg8Zr2 cuboctahedra, edges with two equivalent Mg(1)La2Mg8Zr2 cuboctahedra, edges with two equivalent La(1)Mg10Zr2 cuboctahedra, edges with two equivalent Zr(1)La2Mg10 cuboctahedra, edges with four equivalent Mg(4)La2Mg10 cuboctahedra, edges with four equivalent Mg(2)La2Mg8Zr2 cuboctahedra, edges with four equivalent Mg(3)Mg10Zr2 cuboctahedra, faces with two equivalent Mg(4)La2Mg10 cuboctahedra, faces with two equivalent Mg(3)Mg10Zr2 cuboctahedra, faces with two equivalent La(1)Mg10Zr2 cuboctahedra, faces with two equivalent Zr(1)La2Mg10 cuboctahedra, faces with four equivalent Mg(1)La2Mg8Zr2 cuboctahedra, and faces with eight equivalent Mg(2)La2Mg8Zr2 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 La(1), and two equivalent Zr(1) atoms to form distorted MgLa2Mg8Zr2 cuboctahedra that share corners with four equivalent Mg(4)La2Mg10 cuboctahedra, corners with four equivalent Mg(3)Mg10Zr2 cuboctahedra, corners with ten equivalent Mg(2)La2Mg8Zr2 cuboctahedra, edges with two equivalent Mg(4)La2Mg10 cuboctahedra, edges with two equivalent Mg(2)La2Mg8Zr2 cuboctahedra, edges with two equivalent Mg(3)Mg10Zr2 cuboctahedra, edges with four equivalent Mg(1)La2Mg8Zr2 cuboctahedra, edges with four equivalent La(1)Mg10Zr2 cuboctahedra, edges with four equivalent Zr(1)La2Mg10 cuboctahedra, faces with two equivalent Mg(4)La2Mg10 cuboctahedra, faces with two equivalent Mg(3)Mg10Zr2 cuboctahedra, faces with two equivalent La(1)Mg10Zr2 cuboctahedra, faces with two equivalent Zr(1)La2Mg10 cuboctahedra, faces with four equivalent Mg(2)La2Mg8Zr2 cuboctahedra, and faces with eight equivalent Mg(1)La2Mg8Zr2 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 Zr(1) atoms to form MgMg10Zr2 cuboctahedra that share corners with four equivalent Mg(4)La2Mg10 cuboctahedra, corners with six equivalent Mg(3)Mg10Zr2 cuboctahedra, corners with eight equivalent Mg(2)La2Mg8Zr2 cuboctahedra, edges with two equivalent Mg(4)La2Mg10 cuboctahedra, edges with four equivalent Mg(2)La2Mg8Zr2 cuboctahedra, edges with four equivalent Zr(1)La2Mg10 cuboctahedra, edges with eight equivalent Mg(1)La2Mg8Zr2 cuboctahedra, faces with two equivalent Mg(4)La2Mg10 cuboctahedra, faces with two equivalent Mg(3)Mg10Zr2 cuboctahedra, faces with two equivalent Zr(1)La2Mg10 cuboctahedra, faces with four equivalent Mg(1)La2Mg8Zr2 cuboctahedra, faces with four equivalent Mg(2)La2Mg8Zr2 cuboctahedra, and faces with six equivalent La(1)Mg10Zr2 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 La(1) atoms to form distorted MgLa2Mg10 cuboctahedra that share corners with four equivalent Mg(3)Mg10Zr2 cuboctahedra, corners with six equivalent Mg(4)La2Mg10 cuboctahedra, corners with eight equivalent Mg(2)La2Mg8Zr2 cuboctahedra, edges with two equivalent Mg(3)Mg10Zr2 cuboctahedra, edges with four equivalent Mg(2)La2Mg8Zr2 cuboctahedra, edges with four equivalent La(1)Mg10Zr2 cuboctahedra, edges with eight equivalent Mg(1)La2Mg8Zr2 cuboctahedra, faces with two equivalent Mg(4)La2Mg10 cuboctahedra, faces with two equivalent Mg(3)Mg10Zr2 cuboctahedra, faces with two equivalent La(1)Mg10Zr2 cuboctahedra, faces with four equivalent Mg(1)La2Mg8Zr2 cuboctahedra, faces with four equivalent Mg(2)La2Mg8Zr2 cuboctahedra, and faces with six equivalent Zr(1)La2Mg10 cuboctahedra. La(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Zr(1) atoms to form LaMg10Zr2 cuboctahedra that share corners with four equivalent Zr(1)La2Mg10 cuboctahedra, corners with six equivalent La(1)Mg10Zr2 cuboctahedra, corners with eight equivalent Mg(1)La2Mg8Zr2 cuboctahedra, edges with two equivalent Zr(1)La2Mg10 cuboctahedra, edges with four equivalent Mg(4)La2Mg10 cuboctahedra, edges with four equivalent Mg(1)La2Mg8Zr2 cuboctahedra, edges with eight equivalent Mg(2)La2Mg8Zr2 cuboctahedra, faces with two equivalent Mg(4)La2Mg10 cuboctahedra, faces with two equivalent La(1)Mg10Zr2 cuboctahedra, faces with two equivalent Zr(1)La2Mg10 cuboctahedra, faces with four equivalent Mg(1)La2Mg8Zr2 cuboctahedra, faces with four equivalent Mg(2)La2Mg8Zr2 cuboctahedra, and faces with six equivalent Mg(3)Mg10Zr2 cuboctahedra. Zr(1) is bonded to two equivalent Mg(3), four equivalent Mg(1), four equivalent Mg(2), and two equivalent La(1) atoms to form ZrLa2Mg10 cuboctahedra that share corners with four equivalent La(1)Mg10Zr2 cuboctahedra, corners with six equivalent Zr(1)La2Mg10 cuboctahedra, corners with eight equivalent Mg(1)La2Mg8Zr2 cuboctahedra, edges with two equivalent La(1)Mg10Zr2 cuboctahedra, edges with four equivalent Mg(1)La2Mg8Zr2 cuboctahedra, edges with four equivalent Mg(3)Mg10Zr2 cuboctahedra, edges with eight equivalent Mg(2)La2Mg8Zr2 cuboctahedra, faces with two equivalent Mg(3)Mg10Zr2 cuboctahedra, faces with two equivalent La(1)Mg10Zr2 cuboctahedra, faces with two equivalent Zr(1)La2Mg10 cuboctahedra, faces with four equivalent Mg(1)La2Mg8Zr2 cuboctahedra, faces with four equivalent Mg(2)La2Mg8Zr2 cuboctahedra, and faces with six equivalent Mg(4)La2Mg10 cuboctahedra.
Mg6LaZr 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 La(1), and two equivalent Zr(1) atoms to form MgLa2Mg8Zr2 cuboctahedra that share corners with four equivalent La(1)Mg10Zr2 cuboctahedra, corners with four equivalent Zr(1)La2Mg10 cuboctahedra, corners with ten equivalent Mg(1)La2Mg8Zr2 cuboctahedra, edges with two equivalent Mg(1)La2Mg8Zr2 cuboctahedra, edges with two equivalent La(1)Mg10Zr2 cuboctahedra, edges with two equivalent Zr(1)La2Mg10 cuboctahedra, edges with four equivalent Mg(4)La2Mg10 cuboctahedra, edges with four equivalent Mg(2)La2Mg8Zr2 cuboctahedra, edges with four equivalent Mg(3)Mg10Zr2 cuboctahedra, faces with two equivalent Mg(4)La2Mg10 cuboctahedra, faces with two equivalent Mg(3)Mg10Zr2 cuboctahedra, faces with two equivalent La(1)Mg10Zr2 cuboctahedra, faces with two equivalent Zr(1)La2Mg10 cuboctahedra, faces with four equivalent Mg(1)La2Mg8Zr2 cuboctahedra, and faces with eight equivalent Mg(2)La2Mg8Zr2 cuboctahedra. There is one shorter (3.25 Å) and one longer (3.26 Å) Mg(1)-Mg(1) bond length. Both Mg(1)-Mg(2) bond lengths are 3.27 Å. Both Mg(1)-Mg(3) bond lengths are 3.26 Å. Both Mg(1)-Mg(4) bond lengths are 3.22 Å. There is one shorter (3.34 Å) and one longer (3.35 Å) Mg(1)-La(1) bond length. There is one shorter (3.29 Å) and one longer (3.40 Å) Mg(1)-Zr(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 La(1), and two equivalent Zr(1) atoms to form distorted MgLa2Mg8Zr2 cuboctahedra that share corners with four equivalent Mg(4)La2Mg10 cuboctahedra, corners with four equivalent Mg(3)Mg10Zr2 cuboctahedra, corners with ten equivalent Mg(2)La2Mg8Zr2 cuboctahedra, edges with two equivalent Mg(4)La2Mg10 cuboctahedra, edges with two equivalent Mg(2)La2Mg8Zr2 cuboctahedra, edges with two equivalent Mg(3)Mg10Zr2 cuboctahedra, edges with four equivalent Mg(1)La2Mg8Zr2 cuboctahedra, edges with four equivalent La(1)Mg10Zr2 cuboctahedra, edges with four equivalent Zr(1)La2Mg10 cuboctahedra, faces with two equivalent Mg(4)La2Mg10 cuboctahedra, faces with two equivalent Mg(3)Mg10Zr2 cuboctahedra, faces with two equivalent La(1)Mg10Zr2 cuboctahedra, faces with two equivalent Zr(1)La2Mg10 cuboctahedra, faces with four equivalent Mg(2)La2Mg8Zr2 cuboctahedra, and faces with eight equivalent Mg(1)La2Mg8Zr2 cuboctahedra. There is one shorter (3.10 Å) and one longer (3.40 Å) Mg(2)-Mg(2) bond length. There is one shorter (3.29 Å) and one longer (3.41 Å) Mg(2)-Mg(3) bond length. There is one shorter (3.23 Å) and one longer (3.46 Å) Mg(2)-Mg(4) bond length. Both Mg(2)-La(1) bond lengths are 3.29 Å. Both Mg(2)-Zr(1) bond lengths are 3.19 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 Zr(1) atoms to form MgMg10Zr2 cuboctahedra that share corners with four equivalent Mg(4)La2Mg10 cuboctahedra, corners with six equivalent Mg(3)Mg10Zr2 cuboctahedra, corners with eight equivalent Mg(2)La2Mg8Zr2 cuboctahedra, edges with two equivalent Mg(4)La2Mg10 cuboctahedra, edges with four equivalent Mg(2)La2Mg8Zr2 cuboctahedra, edges with four equivalent Zr(1)La2Mg10 cuboctahedra, edges with eight equivalent Mg(1)La2Mg8Zr2 cuboctahedra, faces with two equivalent Mg(4)La2Mg10 cuboctahedra, faces with two equivalent Mg(3)Mg10Zr2 cuboctahedra, faces with two equivalent Zr(1)La2Mg10 cuboctahedra, faces with four equivalent Mg(1)La2Mg8Zr2 cuboctahedra, faces with four equivalent Mg(2)La2Mg8Zr2 cuboctahedra, and faces with six equivalent La(1)Mg10Zr2 cuboctahedra. Both Mg(3)-Mg(4) bond lengths are 3.25 Å. Both Mg(3)-Zr(1) bond lengths are 3.28 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 La(1) atoms to form distorted MgLa2Mg10 cuboctahedra that share corners with four equivalent Mg(3)Mg10Zr2 cuboctahedra, corners with six equivalent Mg(4)La2Mg10 cuboctahedra, corners with eight equivalent Mg(2)La2Mg8Zr2 cuboctahedra, edges with two equivalent Mg(3)Mg10Zr2 cuboctahedra, edges with four equivalent Mg(2)La2Mg8Zr2 cuboctahedra, edges with four equivalent La(1)Mg10Zr2 cuboctahedra, edges with eight equivalent Mg(1)La2Mg8Zr2 cuboctahedra, faces with two equivalent Mg(4)La2Mg10 cuboctahedra, faces with two equivalent Mg(3)Mg10Zr2 cuboctahedra, faces with two equivalent La(1)Mg10Zr2 cuboctahedra, faces with four equivalent Mg(1)La2Mg8Zr2 cuboctahedra, faces with four equivalent Mg(2)La2Mg8Zr2 cuboctahedra, and faces with six equivalent Zr(1)La2Mg10 cuboctahedra. Both Mg(4)-La(1) bond lengths are 3.32 Å. La(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Zr(1) atoms to form LaMg10Zr2 cuboctahedra that share corners with four equivalent Zr(1)La2Mg10 cuboctahedra, corners with six equivalent La(1)Mg10Zr2 cuboctahedra, corners with eight equivalent Mg(1)La2Mg8Zr2 cuboctahedra, edges with two equivalent Zr(1)La2Mg10 cuboctahedra, edges with four equivalent Mg(4)La2Mg10 cuboctahedra, edges with four equivalent Mg(1)La2Mg8Zr2 cuboctahedra, edges with eight equivalent Mg(2)La2Mg8Zr2 cuboctahedra, faces with two equivalent Mg(4)La2Mg10 cuboctahedra, faces with two equivalent La(1)Mg10Zr2 cuboctahedra, faces with two equivalent Zr(1)La2Mg10 cuboctahedra, faces with four equivalent Mg(1)La2Mg8Zr2 cuboctahedra, faces with four equivalent Mg(2)La2Mg8Zr2 cuboctahedra, and faces with six equivalent Mg(3)Mg10Zr2 cuboctahedra. Both La(1)-Zr(1) bond lengths are 3.25 Å. Zr(1) is bonded to two equivalent Mg(3), four equivalent Mg(1), four equivalent Mg(2), and two equivalent La(1) atoms to form ZrLa2Mg10 cuboctahedra that share corners with four equivalent La(1)Mg10Zr2 cuboctahedra, corners with six equivalent Zr(1)La2Mg10 cuboctahedra, corners with eight equivalent Mg(1)La2Mg8Zr2 cuboctahedra, edges with two equivalent La(1)Mg10Zr2 cuboctahedra, edges with four equivalent Mg(1)La2Mg8Zr2 cuboctahedra, edges with four equivalent Mg(3)Mg10Zr2 cuboctahedra, edges with eight equivalent Mg(2)La2Mg8Zr2 cuboctahedra, faces with two equivalent Mg(3)Mg10Zr2 cuboctahedra, faces with two equivalent La(1)Mg10Zr2 cuboctahedra, faces with two equivalent Zr(1)La2Mg10 cuboctahedra, faces with four equivalent Mg(1)La2Mg8Zr2 cuboctahedra, faces with four equivalent Mg(2)La2Mg8Zr2 cuboctahedra, and faces with six equivalent Mg(4)La2Mg10 cuboctahedra.