Mg14LaSn crystallizes in the hexagonal P-6m2 space group. There are five inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Sn(1) atoms to form distorted MgMg10Sn2 cuboctahedra that share corners with four equivalent La(1)Mg12 cuboctahedra, corners with six equivalent Mg(1)Mg10Sn2 cuboctahedra, corners with eight equivalent Mg(2)La2Mg10 cuboctahedra, edges with two equivalent Sn(1)Mg12 cuboctahedra, edges with four equivalent Mg(1)Mg10Sn2 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with eight equivalent Mg(3)LaMg10Sn cuboctahedra, faces with two equivalent Mg(2)La2Mg10 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Sn(1)Mg12 cuboctahedra, faces with four equivalent Mg(1)Mg10Sn2 cuboctahedra, and faces with ten equivalent Mg(3)LaMg10Sn cuboctahedra. In the second 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 Sn(1)Mg12 cuboctahedra, corners with six equivalent Mg(2)La2Mg10 cuboctahedra, corners with eight equivalent Mg(1)Mg10Sn2 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)LaMg10Sn cuboctahedra, faces with two equivalent Mg(1)Mg10Sn2 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 equivalent Mg(3)LaMg10Sn cuboctahedra. In the third Mg site, Mg(2) is bonded to two equivalent Mg(4); four Mg(2,2); four equivalent Mg(3); and two equivalent La(1) atoms to form distorted MgLa2Mg10 cuboctahedra that share corners with four equivalent Sn(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)La2Mg10 cuboctahedra; corners with eight equivalent Mg(1)Mg10Sn2 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 equivalent Mg(3)LaMg10Sn cuboctahedra; faces with two equivalent Mg(1)Mg10Sn2 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 equivalent Mg(3)LaMg10Sn cuboctahedra. In the fourth Mg site, Mg(3) is bonded to two equivalent Mg(1); two Mg(2,2); two equivalent Mg(4); four equivalent Mg(3); one La(1); and one Sn(1) atom to form distorted MgLaMg10Sn cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen equivalent Mg(3)LaMg10Sn cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent La(1)Mg12 cuboctahedra; edges with two equivalent Sn(1)Mg12 cuboctahedra; edges with four Mg(2,2)La2Mg10 cuboctahedra; edges with four equivalent Mg(3)LaMg10Sn cuboctahedra; edges with four equivalent Mg(1)Mg10Sn2 cuboctahedra;  a faceface with one La(1)Mg12 cuboctahedra;  a faceface with one Sn(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)Mg10Sn2 cuboctahedra; and faces with six equivalent Mg(3)LaMg10Sn cuboctahedra. In the fifth Mg site, Mg(4) is bonded to three equivalent Mg(1); three Mg(2,2); and six equivalent Mg(3) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(4)Mg12 cuboctahedra; corners with twelve equivalent Mg(3)LaMg10Sn cuboctahedra; edges with six Mg(2,2)La2Mg10 cuboctahedra; edges with six equivalent Mg(3)LaMg10Sn cuboctahedra; edges with six equivalent Mg(1)Mg10Sn2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three Mg(2,2)La2Mg10 cuboctahedra; faces with three equivalent Mg(1)Mg10Sn2 cuboctahedra; faces with three equivalent La(1)Mg12 cuboctahedra; faces with three equivalent Sn(1)Mg12 cuboctahedra; and faces with six equivalent Mg(3)LaMg10Sn cuboctahedra. La(1) is bonded to six Mg(2,2) and six equivalent Mg(3) atoms to form LaMg12 cuboctahedra that share corners with six equivalent La(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(1)Mg10Sn2 cuboctahedra; edges with six Mg(2,2)La2Mg10 cuboctahedra; edges with twelve equivalent Mg(3)LaMg10Sn cuboctahedra; faces with two equivalent Sn(1)Mg12 cuboctahedra; faces with six Mg(2,2)La2Mg10 cuboctahedra; faces with six equivalent Mg(3)LaMg10Sn cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. Sn(1) is bonded to six equivalent Mg(1) and six equivalent Mg(3) atoms to form SnMg12 cuboctahedra that share corners with six equivalent Sn(1)Mg12 cuboctahedra; corners with twelve Mg(2,2)La2Mg10 cuboctahedra; edges with six equivalent Mg(1)Mg10Sn2 cuboctahedra; edges with twelve equivalent Mg(3)LaMg10Sn cuboctahedra; faces with two equivalent La(1)Mg12 cuboctahedra; faces with six equivalent Mg(3)LaMg10Sn cuboctahedra; faces with six equivalent Mg(1)Mg10Sn2 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra.
Mg14LaSn crystallizes in the hexagonal P-6m2 space group. There are five inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Sn(1) atoms to form distorted MgMg10Sn2 cuboctahedra that share corners with four equivalent La(1)Mg12 cuboctahedra, corners with six equivalent Mg(1)Mg10Sn2 cuboctahedra, corners with eight equivalent Mg(2)La2Mg10 cuboctahedra, edges with two equivalent Sn(1)Mg12 cuboctahedra, edges with four equivalent Mg(1)Mg10Sn2 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with eight equivalent Mg(3)LaMg10Sn cuboctahedra, faces with two equivalent Mg(2)La2Mg10 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Sn(1)Mg12 cuboctahedra, faces with four equivalent Mg(1)Mg10Sn2 cuboctahedra, and faces with ten equivalent Mg(3)LaMg10Sn cuboctahedra. Both Mg(1)-Mg(4) bond lengths are 3.32 Å. There are two shorter (3.20 Å) and two longer (3.31 Å) Mg(1)-Mg(1) bond lengths. All Mg(1)-Mg(3) bond lengths are 3.20 Å. Both Mg(1)-Sn(1) bond lengths are 3.25 Å. In the second 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 Sn(1)Mg12 cuboctahedra, corners with six equivalent Mg(2)La2Mg10 cuboctahedra, corners with eight equivalent Mg(1)Mg10Sn2 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)LaMg10Sn cuboctahedra, faces with two equivalent Mg(1)Mg10Sn2 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 equivalent Mg(3)LaMg10Sn cuboctahedra. Both Mg(2)-Mg(4) bond lengths are 3.20 Å. There are two shorter (3.13 Å) and two longer (3.38 Å) Mg(2)-Mg(2) bond lengths. All Mg(2)-Mg(3) bond lengths are 3.28 Å. Both Mg(2)-La(1) bond lengths are 3.26 Å. In the third Mg site, Mg(2) is bonded to two equivalent Mg(4); four Mg(2,2); four equivalent Mg(3); and two equivalent La(1) atoms to form distorted MgLa2Mg10 cuboctahedra that share corners with four equivalent Sn(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)La2Mg10 cuboctahedra; corners with eight equivalent Mg(1)Mg10Sn2 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 equivalent Mg(3)LaMg10Sn cuboctahedra; faces with two equivalent Mg(1)Mg10Sn2 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 equivalent Mg(3)LaMg10Sn cuboctahedra. Both Mg(2)-Mg(4) bond lengths are 3.20 Å. There is one shorter (3.13 Å) and one longer (3.38 Å) Mg(2)-Mg(2) bond length. All Mg(2)-Mg(3) bond lengths are 3.28 Å. Both Mg(2)-La(1) bond lengths are 3.26 Å. In the fourth Mg site, Mg(3) is bonded to two equivalent Mg(1); two Mg(2,2); two equivalent Mg(4); four equivalent Mg(3); one La(1); and one Sn(1) atom to form distorted MgLaMg10Sn cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen equivalent Mg(3)LaMg10Sn cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent La(1)Mg12 cuboctahedra; edges with two equivalent Sn(1)Mg12 cuboctahedra; edges with four Mg(2,2)La2Mg10 cuboctahedra; edges with four equivalent Mg(3)LaMg10Sn cuboctahedra; edges with four equivalent Mg(1)Mg10Sn2 cuboctahedra;  a faceface with one La(1)Mg12 cuboctahedra;  a faceface with one Sn(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)Mg10Sn2 cuboctahedra; and faces with six equivalent Mg(3)LaMg10Sn cuboctahedra. Both Mg(3)-Mg(4) bond lengths are 3.26 Å. There are two shorter (3.23 Å) and two longer (3.28 Å) Mg(3)-Mg(3) bond lengths. The Mg(3)-La(1) bond length is 3.31 Å. The Mg(3)-Sn(1) bond length is 3.20 Å. In the fifth Mg site, Mg(4) is bonded to three equivalent Mg(1); three Mg(2,2); and six equivalent Mg(3) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(4)Mg12 cuboctahedra; corners with twelve equivalent Mg(3)LaMg10Sn cuboctahedra; edges with six Mg(2,2)La2Mg10 cuboctahedra; edges with six equivalent Mg(3)LaMg10Sn cuboctahedra; edges with six equivalent Mg(1)Mg10Sn2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three Mg(2,2)La2Mg10 cuboctahedra; faces with three equivalent Mg(1)Mg10Sn2 cuboctahedra; faces with three equivalent La(1)Mg12 cuboctahedra; faces with three equivalent Sn(1)Mg12 cuboctahedra; and faces with six equivalent Mg(3)LaMg10Sn cuboctahedra. La(1) is bonded to six Mg(2,2) and six equivalent Mg(3) atoms to form LaMg12 cuboctahedra that share corners with six equivalent La(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(1)Mg10Sn2 cuboctahedra; edges with six Mg(2,2)La2Mg10 cuboctahedra; edges with twelve equivalent Mg(3)LaMg10Sn cuboctahedra; faces with two equivalent Sn(1)Mg12 cuboctahedra; faces with six Mg(2,2)La2Mg10 cuboctahedra; faces with six equivalent Mg(3)LaMg10Sn cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. Sn(1) is bonded to six equivalent Mg(1) and six equivalent Mg(3) atoms to form SnMg12 cuboctahedra that share corners with six equivalent Sn(1)Mg12 cuboctahedra; corners with twelve Mg(2,2)La2Mg10 cuboctahedra; edges with six equivalent Mg(1)Mg10Sn2 cuboctahedra; edges with twelve equivalent Mg(3)LaMg10Sn cuboctahedra; faces with two equivalent La(1)Mg12 cuboctahedra; faces with six equivalent Mg(3)LaMg10Sn cuboctahedra; faces with six equivalent Mg(1)Mg10Sn2 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra.