Mg14TiV 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 equivalent Mg(3), and two equivalent V(1) atoms to form MgMg10V2 cuboctahedra that share corners with four equivalent Ti(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10V2 cuboctahedra; corners with eight Mg(2,2)Mg10Ti2 cuboctahedra; edges with two equivalent V(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Mg10V2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)Mg10TiV cuboctahedra; faces with two equivalent Mg(2)Mg10Ti2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent V(1)Mg12 cuboctahedra; faces with four equivalent Mg(1)Mg10V2 cuboctahedra; and faces with ten Mg(3,3)Mg10TiV cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(4); four Mg(2,2); four equivalent Mg(3); and two equivalent Ti(1) atoms to form MgMg10Ti2 cuboctahedra that share corners with four equivalent V(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Ti2 cuboctahedra; corners with eight equivalent Mg(1)Mg10V2 cuboctahedra; edges with two equivalent Ti(1)Mg12 cuboctahedra; edges with four Mg(2,2)Mg10Ti2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)Mg10TiV cuboctahedra; faces with two equivalent Mg(1)Mg10V2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Ti(1)Mg12 cuboctahedra; faces with four Mg(2,2)Mg10Ti2 cuboctahedra; and faces with ten Mg(3,3)Mg10TiV cuboctahedra. In the third Mg site, Mg(2) is bonded to two equivalent Mg(4); four equivalent Mg(2); four Mg(3,3); and two equivalent Ti(1) atoms to form MgMg10Ti2 cuboctahedra that share corners with four equivalent V(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Ti2 cuboctahedra; corners with eight equivalent Mg(1)Mg10V2 cuboctahedra; edges with two equivalent Ti(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Ti2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)Mg10TiV cuboctahedra; faces with two equivalent Mg(1)Mg10V2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Ti(1)Mg12 cuboctahedra; faces with four equivalent Mg(2)Mg10Ti2 cuboctahedra; and faces with ten Mg(3,3)Mg10TiV cuboctahedra. In the fourth Mg site, Mg(3) is bonded to two equivalent Mg(1); two Mg(2,2); two equivalent Mg(4); four Mg(3,3); one Ti(1); and one V(1) atom to form distorted MgMg10TiV cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)Mg10TiV cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Ti(1)Mg12 cuboctahedra; edges with two equivalent V(1)Mg12 cuboctahedra; edges with four Mg(2,2)Mg10Ti2 cuboctahedra; edges with four Mg(3,3)Mg10TiV cuboctahedra; edges with four equivalent Mg(1)Mg10V2 cuboctahedra;  a faceface with one Ti(1)Mg12 cuboctahedra;  a faceface with one V(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(2,2)Mg10Ti2 cuboctahedra; faces with five equivalent Mg(1)Mg10V2 cuboctahedra; and faces with six Mg(3,3)Mg10TiV cuboctahedra. In the fifth Mg site, Mg(3) is bonded to two equivalent Mg(1); two Mg(2,2); two equivalent Mg(4); four equivalent Mg(3); one Ti(1); and one V(1) atom to form distorted MgMg10TiV cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)Mg10TiV cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Ti(1)Mg12 cuboctahedra; edges with two equivalent V(1)Mg12 cuboctahedra; edges with four Mg(2,2)Mg10Ti2 cuboctahedra; edges with four equivalent Mg(3)Mg10TiV cuboctahedra; edges with four equivalent Mg(1)Mg10V2 cuboctahedra;  a faceface with one Ti(1)Mg12 cuboctahedra;  a faceface with one V(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(2,2)Mg10Ti2 cuboctahedra; faces with five equivalent Mg(1)Mg10V2 cuboctahedra; and faces with six Mg(3,3)Mg10TiV 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)Mg10TiV cuboctahedra; edges with six Mg(2,2)Mg10Ti2 cuboctahedra; edges with six Mg(3,3)Mg10TiV cuboctahedra; edges with six equivalent Mg(1)Mg10V2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three Mg(2,2)Mg10Ti2 cuboctahedra; faces with three equivalent Mg(1)Mg10V2 cuboctahedra; faces with three equivalent Ti(1)Mg12 cuboctahedra; faces with three equivalent V(1)Mg12 cuboctahedra; and faces with six Mg(3,3)Mg10TiV cuboctahedra. Ti(1) is bonded to six Mg(2,2) and six Mg(3,3) atoms to form TiMg12 cuboctahedra that share corners with six equivalent Ti(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(1)Mg10V2 cuboctahedra; edges with six Mg(2,2)Mg10Ti2 cuboctahedra; edges with twelve Mg(3,3)Mg10TiV cuboctahedra; faces with two equivalent V(1)Mg12 cuboctahedra; faces with six Mg(2,2)Mg10Ti2 cuboctahedra; faces with six Mg(3,3)Mg10TiV cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. V(1) is bonded to six equivalent Mg(1) and six Mg(3,3) atoms to form VMg12 cuboctahedra that share corners with six equivalent V(1)Mg12 cuboctahedra; corners with twelve Mg(2,2)Mg10Ti2 cuboctahedra; edges with six equivalent Mg(1)Mg10V2 cuboctahedra; edges with twelve Mg(3,3)Mg10TiV cuboctahedra; faces with two equivalent Ti(1)Mg12 cuboctahedra; faces with six Mg(3,3)Mg10TiV cuboctahedra; faces with six equivalent Mg(1)Mg10V2 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra.
Mg14TiV 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 equivalent Mg(3), and two equivalent V(1) atoms to form MgMg10V2 cuboctahedra that share corners with four equivalent Ti(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10V2 cuboctahedra; corners with eight Mg(2,2)Mg10Ti2 cuboctahedra; edges with two equivalent V(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Mg10V2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)Mg10TiV cuboctahedra; faces with two equivalent Mg(2)Mg10Ti2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent V(1)Mg12 cuboctahedra; faces with four equivalent Mg(1)Mg10V2 cuboctahedra; and faces with ten Mg(3,3)Mg10TiV cuboctahedra. Both Mg(1)-Mg(4) bond lengths are 3.14 Å. There are two shorter (3.13 Å) and two longer (3.18 Å) Mg(1)-Mg(1) bond lengths. All Mg(1)-Mg(3) bond lengths are 3.13 Å. Both Mg(1)-V(1) bond lengths are 3.15 Å. In the second Mg site, Mg(2) is bonded to two equivalent Mg(4); four Mg(2,2); four equivalent Mg(3); and two equivalent Ti(1) atoms to form MgMg10Ti2 cuboctahedra that share corners with four equivalent V(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Ti2 cuboctahedra; corners with eight equivalent Mg(1)Mg10V2 cuboctahedra; edges with two equivalent Ti(1)Mg12 cuboctahedra; edges with four Mg(2,2)Mg10Ti2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)Mg10TiV cuboctahedra; faces with two equivalent Mg(1)Mg10V2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Ti(1)Mg12 cuboctahedra; faces with four Mg(2,2)Mg10Ti2 cuboctahedra; and faces with ten Mg(3,3)Mg10TiV cuboctahedra. Both Mg(2)-Mg(4) bond lengths are 3.12 Å. There are two shorter (3.12 Å) and two longer (3.19 Å) Mg(2)-Mg(2,2) bond lengths. All Mg(2)-Mg(3) bond lengths are 3.14 Å. Both Mg(2)-Ti(1) bond lengths are 3.15 Å. In the third Mg site, Mg(2) is bonded to two equivalent Mg(4); four equivalent Mg(2); four Mg(3,3); and two equivalent Ti(1) atoms to form MgMg10Ti2 cuboctahedra that share corners with four equivalent V(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Ti2 cuboctahedra; corners with eight equivalent Mg(1)Mg10V2 cuboctahedra; edges with two equivalent Ti(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Ti2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)Mg10TiV cuboctahedra; faces with two equivalent Mg(1)Mg10V2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Ti(1)Mg12 cuboctahedra; faces with four equivalent Mg(2)Mg10Ti2 cuboctahedra; and faces with ten Mg(3,3)Mg10TiV cuboctahedra. Both Mg(2)-Mg(4) bond lengths are 3.12 Å. All Mg(2)-Mg(3,3) bond lengths are 3.14 Å. Both Mg(2)-Ti(1) bond lengths are 3.15 Å. In the fourth Mg site, Mg(3) is bonded to two equivalent Mg(1); two Mg(2,2); two equivalent Mg(4); four Mg(3,3); one Ti(1); and one V(1) atom to form distorted MgMg10TiV cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)Mg10TiV cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Ti(1)Mg12 cuboctahedra; edges with two equivalent V(1)Mg12 cuboctahedra; edges with four Mg(2,2)Mg10Ti2 cuboctahedra; edges with four Mg(3,3)Mg10TiV cuboctahedra; edges with four equivalent Mg(1)Mg10V2 cuboctahedra;  a faceface with one Ti(1)Mg12 cuboctahedra;  a faceface with one V(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(2,2)Mg10Ti2 cuboctahedra; faces with five equivalent Mg(1)Mg10V2 cuboctahedra; and faces with six Mg(3,3)Mg10TiV cuboctahedra. Both Mg(3)-Mg(4) bond lengths are 3.16 Å. There are two shorter (3.06 Å) and two longer (3.25 Å) Mg(3)-Mg(3,3) bond lengths. The Mg(3)-Ti(1) bond length is 3.10 Å. The Mg(3)-V(1) bond length is 3.09 Å. In the fifth Mg site, Mg(3) is bonded to two equivalent Mg(1); two Mg(2,2); two equivalent Mg(4); four equivalent Mg(3); one Ti(1); and one V(1) atom to form distorted MgMg10TiV cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)Mg10TiV cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Ti(1)Mg12 cuboctahedra; edges with two equivalent V(1)Mg12 cuboctahedra; edges with four Mg(2,2)Mg10Ti2 cuboctahedra; edges with four equivalent Mg(3)Mg10TiV cuboctahedra; edges with four equivalent Mg(1)Mg10V2 cuboctahedra;  a faceface with one Ti(1)Mg12 cuboctahedra;  a faceface with one V(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(2,2)Mg10Ti2 cuboctahedra; faces with five equivalent Mg(1)Mg10V2 cuboctahedra; and faces with six Mg(3,3)Mg10TiV cuboctahedra. Both Mg(3)-Mg(1) bond lengths are 3.13 Å. The Mg(3)-Mg(2) bond length is 3.14 Å. Both Mg(3)-Mg(4) bond lengths are 3.16 Å. The Mg(3)-Ti(1) bond length is 3.10 Å. The Mg(3)-V(1) bond length is 3.09 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)Mg10TiV cuboctahedra; edges with six Mg(2,2)Mg10Ti2 cuboctahedra; edges with six Mg(3,3)Mg10TiV cuboctahedra; edges with six equivalent Mg(1)Mg10V2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three Mg(2,2)Mg10Ti2 cuboctahedra; faces with three equivalent Mg(1)Mg10V2 cuboctahedra; faces with three equivalent Ti(1)Mg12 cuboctahedra; faces with three equivalent V(1)Mg12 cuboctahedra; and faces with six Mg(3,3)Mg10TiV cuboctahedra. Ti(1) is bonded to six Mg(2,2) and six Mg(3,3) atoms to form TiMg12 cuboctahedra that share corners with six equivalent Ti(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(1)Mg10V2 cuboctahedra; edges with six Mg(2,2)Mg10Ti2 cuboctahedra; edges with twelve Mg(3,3)Mg10TiV cuboctahedra; faces with two equivalent V(1)Mg12 cuboctahedra; faces with six Mg(2,2)Mg10Ti2 cuboctahedra; faces with six Mg(3,3)Mg10TiV cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. V(1) is bonded to six equivalent Mg(1) and six Mg(3,3) atoms to form VMg12 cuboctahedra that share corners with six equivalent V(1)Mg12 cuboctahedra; corners with twelve Mg(2,2)Mg10Ti2 cuboctahedra; edges with six equivalent Mg(1)Mg10V2 cuboctahedra; edges with twelve Mg(3,3)Mg10TiV cuboctahedra; faces with two equivalent Ti(1)Mg12 cuboctahedra; faces with six Mg(3,3)Mg10TiV cuboctahedra; faces with six equivalent Mg(1)Mg10V2 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra.