Mg14HfV 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 V(1) atoms to form MgMg10V2 cuboctahedra that share corners with four equivalent Hf(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10V2 cuboctahedra; corners with eight Mg(2,2)Hf2Mg10 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 Mg(3,3)HfMg10V cuboctahedra; faces with two equivalent Mg(2)Hf2Mg10 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)HfMg10V 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 Hf(1) atoms to form MgHf2Mg10 cuboctahedra that share corners with four equivalent V(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Hf2Mg10 cuboctahedra; corners with eight equivalent Mg(1)Mg10V2 cuboctahedra; edges with two equivalent Hf(1)Mg12 cuboctahedra; edges with four Mg(2,2)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)HfMg10V cuboctahedra; faces with two equivalent Mg(1)Mg10V2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Hf(1)Mg12 cuboctahedra; faces with four Mg(2,2)Hf2Mg10 cuboctahedra; and faces with ten Mg(3,3)HfMg10V 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 Hf(1) atoms to form MgHf2Mg10 cuboctahedra that share corners with four equivalent V(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Hf2Mg10 cuboctahedra; corners with eight equivalent Mg(1)Mg10V2 cuboctahedra; edges with two equivalent Hf(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)HfMg10V cuboctahedra; faces with two equivalent Mg(1)Mg10V2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Hf(1)Mg12 cuboctahedra; faces with four equivalent Mg(2)Hf2Mg10 cuboctahedra; and faces with ten Mg(3,3)HfMg10V 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 Hf(1); and one V(1) atom to form distorted MgHfMg10V cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)HfMg10V cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Hf(1)Mg12 cuboctahedra; edges with two equivalent V(1)Mg12 cuboctahedra; edges with four Mg(2,2)Hf2Mg10 cuboctahedra; edges with four Mg(3,3)HfMg10V cuboctahedra; edges with four equivalent Mg(1)Mg10V2 cuboctahedra;  a faceface with one Hf(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)Hf2Mg10 cuboctahedra; faces with five equivalent Mg(1)Mg10V2 cuboctahedra; and faces with six Mg(3,3)HfMg10V cuboctahedra. In the fifth Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), four equivalent Mg(3), one Hf(1), and one V(1) atom to form distorted MgHfMg10V cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)HfMg10V cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Hf(1)Mg12 cuboctahedra; edges with two equivalent V(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(3)HfMg10V cuboctahedra; edges with four equivalent Mg(1)Mg10V2 cuboctahedra;  a faceface with one Hf(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)Hf2Mg10 cuboctahedra; faces with five equivalent Mg(1)Mg10V2 cuboctahedra; and faces with six Mg(3,3)HfMg10V 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)HfMg10V cuboctahedra; edges with six Mg(2,2)Hf2Mg10 cuboctahedra; edges with six Mg(3,3)HfMg10V cuboctahedra; edges with six equivalent Mg(1)Mg10V2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three Mg(2,2)Hf2Mg10 cuboctahedra; faces with three equivalent Mg(1)Mg10V2 cuboctahedra; faces with three equivalent Hf(1)Mg12 cuboctahedra; faces with three equivalent V(1)Mg12 cuboctahedra; and faces with six Mg(3,3)HfMg10V cuboctahedra. Hf(1) is bonded to six Mg(2,2) and six Mg(3,3) atoms to form HfMg12 cuboctahedra that share corners with six equivalent Hf(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(1)Mg10V2 cuboctahedra; edges with six Mg(2,2)Hf2Mg10 cuboctahedra; edges with twelve Mg(3,3)HfMg10V cuboctahedra; faces with two equivalent V(1)Mg12 cuboctahedra; faces with six Mg(2,2)Hf2Mg10 cuboctahedra; faces with six Mg(3,3)HfMg10V 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)Hf2Mg10 cuboctahedra; edges with six equivalent Mg(1)Mg10V2 cuboctahedra; edges with twelve Mg(3,3)HfMg10V cuboctahedra; faces with two equivalent Hf(1)Mg12 cuboctahedra; faces with six Mg(3,3)HfMg10V cuboctahedra; faces with six equivalent Mg(1)Mg10V2 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra.
Mg14HfV 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 V(1) atoms to form MgMg10V2 cuboctahedra that share corners with four equivalent Hf(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10V2 cuboctahedra; corners with eight Mg(2,2)Hf2Mg10 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 Mg(3,3)HfMg10V cuboctahedra; faces with two equivalent Mg(2)Hf2Mg10 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)HfMg10V cuboctahedra. Both Mg(1)-Mg(4) bond lengths are 3.18 Å. There are two shorter (3.16 Å) and two longer (3.18 Å) Mg(1)-Mg(1) bond lengths. All Mg(1)-Mg(3,3) bond lengths are 3.13 Å. Both Mg(1)-V(1) bond lengths are 3.17 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 Hf(1) atoms to form MgHf2Mg10 cuboctahedra that share corners with four equivalent V(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Hf2Mg10 cuboctahedra; corners with eight equivalent Mg(1)Mg10V2 cuboctahedra; edges with two equivalent Hf(1)Mg12 cuboctahedra; edges with four Mg(2,2)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)HfMg10V cuboctahedra; faces with two equivalent Mg(1)Mg10V2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Hf(1)Mg12 cuboctahedra; faces with four Mg(2,2)Hf2Mg10 cuboctahedra; and faces with ten Mg(3,3)HfMg10V cuboctahedra. Both Mg(2)-Mg(4) bond lengths are 3.13 Å. There are two shorter (3.11 Å) and two longer (3.24 Å) Mg(2)-Mg(2,2) bond lengths. All Mg(2)-Mg(3,3) bond lengths are 3.17 Å. Both Mg(2)-Hf(1) bond lengths are 3.17 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 Hf(1) atoms to form MgHf2Mg10 cuboctahedra that share corners with four equivalent V(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Hf2Mg10 cuboctahedra; corners with eight equivalent Mg(1)Mg10V2 cuboctahedra; edges with two equivalent Hf(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)HfMg10V cuboctahedra; faces with two equivalent Mg(1)Mg10V2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Hf(1)Mg12 cuboctahedra; faces with four equivalent Mg(2)Hf2Mg10 cuboctahedra; and faces with ten Mg(3,3)HfMg10V cuboctahedra. Both Mg(2)-Mg(4) bond lengths are 3.13 Å. All Mg(2)-Mg(3) bond lengths are 3.17 Å. Both Mg(2)-Hf(1) bond lengths are 3.17 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 Hf(1); and one V(1) atom to form distorted MgHfMg10V cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)HfMg10V cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Hf(1)Mg12 cuboctahedra; edges with two equivalent V(1)Mg12 cuboctahedra; edges with four Mg(2,2)Hf2Mg10 cuboctahedra; edges with four Mg(3,3)HfMg10V cuboctahedra; edges with four equivalent Mg(1)Mg10V2 cuboctahedra;  a faceface with one Hf(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)Hf2Mg10 cuboctahedra; faces with five equivalent Mg(1)Mg10V2 cuboctahedra; and faces with six Mg(3,3)HfMg10V cuboctahedra. Both Mg(3)-Mg(4) bond lengths are 3.17 Å. There are two shorter (3.09 Å) and two longer (3.26 Å) Mg(3)-Mg(3,3) bond lengths. The Mg(3)-Hf(1) bond length is 3.14 Å. The Mg(3)-V(1) bond length is 3.08 Å. In the fifth Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), four equivalent Mg(3), one Hf(1), and one V(1) atom to form distorted MgHfMg10V cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)HfMg10V cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Hf(1)Mg12 cuboctahedra; edges with two equivalent V(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(3)HfMg10V cuboctahedra; edges with four equivalent Mg(1)Mg10V2 cuboctahedra;  a faceface with one Hf(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)Hf2Mg10 cuboctahedra; faces with five equivalent Mg(1)Mg10V2 cuboctahedra; and faces with six Mg(3,3)HfMg10V cuboctahedra. Both Mg(3)-Mg(4) bond lengths are 3.17 Å. The Mg(3)-Hf(1) bond length is 3.14 Å. The Mg(3)-V(1) bond length is 3.08 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)HfMg10V cuboctahedra; edges with six Mg(2,2)Hf2Mg10 cuboctahedra; edges with six Mg(3,3)HfMg10V cuboctahedra; edges with six equivalent Mg(1)Mg10V2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three Mg(2,2)Hf2Mg10 cuboctahedra; faces with three equivalent Mg(1)Mg10V2 cuboctahedra; faces with three equivalent Hf(1)Mg12 cuboctahedra; faces with three equivalent V(1)Mg12 cuboctahedra; and faces with six Mg(3,3)HfMg10V cuboctahedra. Hf(1) is bonded to six Mg(2,2) and six Mg(3,3) atoms to form HfMg12 cuboctahedra that share corners with six equivalent Hf(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(1)Mg10V2 cuboctahedra; edges with six Mg(2,2)Hf2Mg10 cuboctahedra; edges with twelve Mg(3,3)HfMg10V cuboctahedra; faces with two equivalent V(1)Mg12 cuboctahedra; faces with six Mg(2,2)Hf2Mg10 cuboctahedra; faces with six Mg(3,3)HfMg10V 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)Hf2Mg10 cuboctahedra; edges with six equivalent Mg(1)Mg10V2 cuboctahedra; edges with twelve Mg(3,3)HfMg10V cuboctahedra; faces with two equivalent Hf(1)Mg12 cuboctahedra; faces with six Mg(3,3)HfMg10V cuboctahedra; faces with six equivalent Mg(1)Mg10V2 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra.