Mg14LaZn crystallizes in the hexagonal P-6m2 space group. There are six inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(4); four equivalent Mg(1); four Mg(3,3); and two equivalent Zn(1) atoms to form distorted MgMg10Zn2 cuboctahedra that share corners with four equivalent La(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Zn2 cuboctahedra; corners with eight Mg(2,2)La2Mg10 cuboctahedra; edges with two equivalent Zn(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Mg10Zn2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)LaMg10Zn cuboctahedra; faces with two equivalent Mg(2)La2Mg10 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Zn(1)Mg12 cuboctahedra; faces with four equivalent Mg(1)Mg10Zn2 cuboctahedra; and faces with ten Mg(3,3)LaMg10Zn cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(4); four Mg(2,2); four Mg(3,3); and two equivalent La(1) atoms to form distorted MgLa2Mg10 cuboctahedra that share corners with four equivalent Zn(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)La2Mg10 cuboctahedra; corners with eight equivalent Mg(1)Mg10Zn2 cuboctahedra; edges with two equivalent La(1)Mg12 cuboctahedra; edges with four Mg(2,2)La2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)LaMg10Zn cuboctahedra; faces with two equivalent Mg(1)Mg10Zn2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent La(1)Mg12 cuboctahedra; faces with four Mg(2,2)La2Mg10 cuboctahedra; and faces with ten Mg(3,3)LaMg10Zn cuboctahedra. In the third Mg site, Mg(2) is bonded to two equivalent Mg(4), four equivalent Mg(2), four equivalent Mg(3), and two equivalent La(1) atoms to form distorted MgLa2Mg10 cuboctahedra that share corners with four equivalent Zn(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)La2Mg10 cuboctahedra; corners with eight equivalent Mg(1)Mg10Zn2 cuboctahedra; edges with two equivalent La(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)La2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)LaMg10Zn cuboctahedra; faces with two equivalent Mg(1)Mg10Zn2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent La(1)Mg12 cuboctahedra; faces with four equivalent Mg(2)La2Mg10 cuboctahedra; and faces with ten Mg(3,3)LaMg10Zn cuboctahedra. In the fourth Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), four equivalent Mg(3), one La(1), and one Zn(1) atom to form distorted MgLaMg10Zn cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)LaMg10Zn cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent La(1)Mg12 cuboctahedra; edges with two equivalent Zn(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)La2Mg10 cuboctahedra; edges with four equivalent Mg(3)LaMg10Zn cuboctahedra; edges with four equivalent Mg(1)Mg10Zn2 cuboctahedra;  a faceface with one La(1)Mg12 cuboctahedra;  a faceface with one Zn(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(2,2)La2Mg10 cuboctahedra; faces with five equivalent Mg(1)Mg10Zn2 cuboctahedra; and faces with six Mg(3,3)LaMg10Zn cuboctahedra. In the fifth Mg site, Mg(3) is bonded to two equivalent Mg(1); two Mg(2,2); two equivalent Mg(4); four Mg(3,3); one La(1); and one Zn(1) atom to form distorted MgLaMg10Zn cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)LaMg10Zn cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent La(1)Mg12 cuboctahedra; edges with two equivalent Zn(1)Mg12 cuboctahedra; edges with four Mg(2,2)La2Mg10 cuboctahedra; edges with four Mg(3,3)LaMg10Zn cuboctahedra; edges with four equivalent Mg(1)Mg10Zn2 cuboctahedra;  a faceface with one La(1)Mg12 cuboctahedra;  a faceface with one Zn(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(2,2)La2Mg10 cuboctahedra; faces with five equivalent Mg(1)Mg10Zn2 cuboctahedra; and faces with six Mg(3,3)LaMg10Zn cuboctahedra. In the sixth Mg site, Mg(4) is bonded to three equivalent Mg(1); three Mg(2,2); and six Mg(3,3) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(4)Mg12 cuboctahedra; corners with twelve Mg(3,3)LaMg10Zn cuboctahedra; edges with six Mg(2,2)La2Mg10 cuboctahedra; edges with six Mg(3,3)LaMg10Zn cuboctahedra; edges with six equivalent Mg(1)Mg10Zn2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three Mg(2,2)La2Mg10 cuboctahedra; faces with three equivalent Mg(1)Mg10Zn2 cuboctahedra; faces with three equivalent La(1)Mg12 cuboctahedra; faces with three equivalent Zn(1)Mg12 cuboctahedra; and faces with six Mg(3,3)LaMg10Zn cuboctahedra. La(1) is bonded to six Mg(2,2) and six Mg(3,3) atoms to form LaMg12 cuboctahedra that share corners with six equivalent La(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(1)Mg10Zn2 cuboctahedra; edges with six Mg(2,2)La2Mg10 cuboctahedra; edges with twelve Mg(3,3)LaMg10Zn cuboctahedra; faces with two equivalent Zn(1)Mg12 cuboctahedra; faces with six Mg(2,2)La2Mg10 cuboctahedra; faces with six Mg(3,3)LaMg10Zn cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. Zn(1) is bonded to six equivalent Mg(1) and six Mg(3,3) atoms to form ZnMg12 cuboctahedra that share corners with six equivalent Zn(1)Mg12 cuboctahedra; corners with twelve Mg(2,2)La2Mg10 cuboctahedra; edges with six equivalent Mg(1)Mg10Zn2 cuboctahedra; edges with twelve Mg(3,3)LaMg10Zn cuboctahedra; faces with two equivalent La(1)Mg12 cuboctahedra; faces with six Mg(3,3)LaMg10Zn cuboctahedra; faces with six equivalent Mg(1)Mg10Zn2 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra.
Mg14LaZn crystallizes in the hexagonal P-6m2 space group. There are six inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(4); four equivalent Mg(1); four Mg(3,3); and two equivalent Zn(1) atoms to form distorted MgMg10Zn2 cuboctahedra that share corners with four equivalent La(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Zn2 cuboctahedra; corners with eight Mg(2,2)La2Mg10 cuboctahedra; edges with two equivalent Zn(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Mg10Zn2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)LaMg10Zn cuboctahedra; faces with two equivalent Mg(2)La2Mg10 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Zn(1)Mg12 cuboctahedra; faces with four equivalent Mg(1)Mg10Zn2 cuboctahedra; and faces with ten Mg(3,3)LaMg10Zn cuboctahedra. Both Mg(1)-Mg(4) bond lengths are 3.23 Å. There are two shorter (3.25 Å) and two longer (3.31 Å) Mg(1)-Mg(1) bond lengths. All Mg(1)-Mg(3,3) bond lengths are 3.11 Å. Both Mg(1)-Zn(1) bond lengths are 3.28 Å. In the second Mg site, Mg(2) is bonded to two equivalent Mg(4); four Mg(2,2); four Mg(3,3); and two equivalent La(1) atoms to form distorted MgLa2Mg10 cuboctahedra that share corners with four equivalent Zn(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)La2Mg10 cuboctahedra; corners with eight equivalent Mg(1)Mg10Zn2 cuboctahedra; edges with two equivalent La(1)Mg12 cuboctahedra; edges with four Mg(2,2)La2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)LaMg10Zn cuboctahedra; faces with two equivalent Mg(1)Mg10Zn2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent La(1)Mg12 cuboctahedra; faces with four Mg(2,2)La2Mg10 cuboctahedra; and faces with ten Mg(3,3)LaMg10Zn cuboctahedra. Both Mg(2)-Mg(4) bond lengths are 3.20 Å. There are two shorter (3.15 Å) and two longer (3.40 Å) Mg(2)-Mg(2,2) bond lengths. All Mg(2)-Mg(3,3) bond lengths are 3.27 Å. Both Mg(2)-La(1) bond lengths are 3.28 Å. In the third Mg site, Mg(2) is bonded to two equivalent Mg(4), four equivalent Mg(2), four equivalent Mg(3), and two equivalent La(1) atoms to form distorted MgLa2Mg10 cuboctahedra that share corners with four equivalent Zn(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)La2Mg10 cuboctahedra; corners with eight equivalent Mg(1)Mg10Zn2 cuboctahedra; edges with two equivalent La(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)La2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)LaMg10Zn cuboctahedra; faces with two equivalent Mg(1)Mg10Zn2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent La(1)Mg12 cuboctahedra; faces with four equivalent Mg(2)La2Mg10 cuboctahedra; and faces with ten Mg(3,3)LaMg10Zn cuboctahedra. Both Mg(2)-Mg(4) bond lengths are 3.20 Å. All Mg(2)-Mg(3) bond lengths are 3.27 Å. Both Mg(2)-La(1) bond lengths are 3.28 Å. In the fourth Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), four equivalent Mg(3), one La(1), and one Zn(1) atom to form distorted MgLaMg10Zn cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)LaMg10Zn cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent La(1)Mg12 cuboctahedra; edges with two equivalent Zn(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)La2Mg10 cuboctahedra; edges with four equivalent Mg(3)LaMg10Zn cuboctahedra; edges with four equivalent Mg(1)Mg10Zn2 cuboctahedra;  a faceface with one La(1)Mg12 cuboctahedra;  a faceface with one Zn(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(2,2)La2Mg10 cuboctahedra; faces with five equivalent Mg(1)Mg10Zn2 cuboctahedra; and faces with six Mg(3,3)LaMg10Zn cuboctahedra. Both Mg(3)-Mg(4) bond lengths are 3.28 Å. There are two shorter (3.27 Å) and two longer (3.28 Å) Mg(3)-Mg(3) bond lengths. The Mg(3)-La(1) bond length is 3.29 Å. The Mg(3)-Zn(1) bond length is 3.11 Å. In the fifth Mg site, Mg(3) is bonded to two equivalent Mg(1); two Mg(2,2); two equivalent Mg(4); four Mg(3,3); one La(1); and one Zn(1) atom to form distorted MgLaMg10Zn cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)LaMg10Zn cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent La(1)Mg12 cuboctahedra; edges with two equivalent Zn(1)Mg12 cuboctahedra; edges with four Mg(2,2)La2Mg10 cuboctahedra; edges with four Mg(3,3)LaMg10Zn cuboctahedra; edges with four equivalent Mg(1)Mg10Zn2 cuboctahedra;  a faceface with one La(1)Mg12 cuboctahedra;  a faceface with one Zn(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(2,2)La2Mg10 cuboctahedra; faces with five equivalent Mg(1)Mg10Zn2 cuboctahedra; and faces with six Mg(3,3)LaMg10Zn cuboctahedra. Both Mg(3)-Mg(4) bond lengths are 3.28 Å. There is one shorter (3.27 Å) and one longer (3.28 Å) Mg(3)-Mg(3) bond length. The Mg(3)-La(1) bond length is 3.29 Å. The Mg(3)-Zn(1) bond length is 3.11 Å. In the sixth Mg site, Mg(4) is bonded to three equivalent Mg(1); three Mg(2,2); and six Mg(3,3) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(4)Mg12 cuboctahedra; corners with twelve Mg(3,3)LaMg10Zn cuboctahedra; edges with six Mg(2,2)La2Mg10 cuboctahedra; edges with six Mg(3,3)LaMg10Zn cuboctahedra; edges with six equivalent Mg(1)Mg10Zn2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three Mg(2,2)La2Mg10 cuboctahedra; faces with three equivalent Mg(1)Mg10Zn2 cuboctahedra; faces with three equivalent La(1)Mg12 cuboctahedra; faces with three equivalent Zn(1)Mg12 cuboctahedra; and faces with six Mg(3,3)LaMg10Zn cuboctahedra. La(1) is bonded to six Mg(2,2) and six Mg(3,3) atoms to form LaMg12 cuboctahedra that share corners with six equivalent La(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(1)Mg10Zn2 cuboctahedra; edges with six Mg(2,2)La2Mg10 cuboctahedra; edges with twelve Mg(3,3)LaMg10Zn cuboctahedra; faces with two equivalent Zn(1)Mg12 cuboctahedra; faces with six Mg(2,2)La2Mg10 cuboctahedra; faces with six Mg(3,3)LaMg10Zn cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. Zn(1) is bonded to six equivalent Mg(1) and six Mg(3,3) atoms to form ZnMg12 cuboctahedra that share corners with six equivalent Zn(1)Mg12 cuboctahedra; corners with twelve Mg(2,2)La2Mg10 cuboctahedra; edges with six equivalent Mg(1)Mg10Zn2 cuboctahedra; edges with twelve Mg(3,3)LaMg10Zn cuboctahedra; faces with two equivalent La(1)Mg12 cuboctahedra; faces with six Mg(3,3)LaMg10Zn cuboctahedra; faces with six equivalent Mg(1)Mg10Zn2 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra.