Mg14HfTi 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 Ti(1) atoms to form MgMg10Ti2 cuboctahedra that share corners with four equivalent Hf(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Ti2 cuboctahedra; corners with eight Mg(2,2)Hf2Mg10 cuboctahedra; edges with two equivalent Ti(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Mg10Ti2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)HfMg10Ti cuboctahedra; faces with two equivalent Mg(2)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Ti(1)Mg12 cuboctahedra; faces with four equivalent Mg(1)Mg10Ti2 cuboctahedra; and faces with ten Mg(3,3)HfMg10Ti 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 Ti(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Hf2Mg10 cuboctahedra; corners with eight equivalent Mg(1)Mg10Ti2 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)HfMg10Ti cuboctahedra; faces with two equivalent Mg(1)Mg10Ti2 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)HfMg10Ti 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 Hf(1) atoms to form MgHf2Mg10 cuboctahedra that share corners with four equivalent Ti(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Hf2Mg10 cuboctahedra; corners with eight equivalent Mg(1)Mg10Ti2 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 Mg(3,3)HfMg10Ti cuboctahedra; faces with two equivalent Mg(1)Mg10Ti2 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)HfMg10Ti cuboctahedra. In the fourth Mg site, Mg(3) is bonded to two equivalent Mg(1); two equivalent Mg(2); two equivalent Mg(4); four Mg(3,3); one Hf(1); and one Ti(1) atom to form distorted MgHfMg10Ti cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)HfMg10Ti cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Hf(1)Mg12 cuboctahedra; edges with two equivalent Ti(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with four Mg(3,3)HfMg10Ti cuboctahedra; edges with four equivalent Mg(1)Mg10Ti2 cuboctahedra;  a faceface with one Hf(1)Mg12 cuboctahedra;  a faceface with one Ti(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)Mg10Ti2 cuboctahedra; and faces with six Mg(3,3)HfMg10Ti 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 Hf(1); and one Ti(1) atom to form distorted MgHfMg10Ti cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)HfMg10Ti cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Hf(1)Mg12 cuboctahedra; edges with two equivalent Ti(1)Mg12 cuboctahedra; edges with four Mg(2,2)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(3)HfMg10Ti cuboctahedra; edges with four equivalent Mg(1)Mg10Ti2 cuboctahedra;  a faceface with one Hf(1)Mg12 cuboctahedra;  a faceface with one Ti(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)Mg10Ti2 cuboctahedra; and faces with six Mg(3,3)HfMg10Ti 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)HfMg10Ti cuboctahedra; edges with six Mg(2,2)Hf2Mg10 cuboctahedra; edges with six Mg(3,3)HfMg10Ti cuboctahedra; edges with six equivalent Mg(1)Mg10Ti2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three Mg(2,2)Hf2Mg10 cuboctahedra; faces with three equivalent Mg(1)Mg10Ti2 cuboctahedra; faces with three equivalent Hf(1)Mg12 cuboctahedra; faces with three equivalent Ti(1)Mg12 cuboctahedra; and faces with six Mg(3,3)HfMg10Ti 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)Mg10Ti2 cuboctahedra; edges with six Mg(2,2)Hf2Mg10 cuboctahedra; edges with twelve Mg(3,3)HfMg10Ti cuboctahedra; faces with two equivalent Ti(1)Mg12 cuboctahedra; faces with six Mg(2,2)Hf2Mg10 cuboctahedra; faces with six Mg(3,3)HfMg10Ti cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. Ti(1) is bonded to six equivalent Mg(1) and six Mg(3,3) atoms to form TiMg12 cuboctahedra that share corners with six equivalent Ti(1)Mg12 cuboctahedra; corners with twelve Mg(2,2)Hf2Mg10 cuboctahedra; edges with six equivalent Mg(1)Mg10Ti2 cuboctahedra; edges with twelve Mg(3,3)HfMg10Ti cuboctahedra; faces with two equivalent Hf(1)Mg12 cuboctahedra; faces with six Mg(3,3)HfMg10Ti cuboctahedra; faces with six equivalent Mg(1)Mg10Ti2 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra.
Mg14HfTi 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 Ti(1) atoms to form MgMg10Ti2 cuboctahedra that share corners with four equivalent Hf(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Ti2 cuboctahedra; corners with eight Mg(2,2)Hf2Mg10 cuboctahedra; edges with two equivalent Ti(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Mg10Ti2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)HfMg10Ti cuboctahedra; faces with two equivalent Mg(2)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Ti(1)Mg12 cuboctahedra; faces with four equivalent Mg(1)Mg10Ti2 cuboctahedra; and faces with ten Mg(3,3)HfMg10Ti cuboctahedra. Both Mg(1)-Mg(4) bond lengths are 3.14 Å. There are two shorter (3.17 Å) and two longer (3.20 Å) Mg(1)-Mg(1) bond lengths. All Mg(1)-Mg(3,3) bond lengths are 3.12 Å. Both Mg(1)-Ti(1) bond lengths are 3.18 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 Ti(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Hf2Mg10 cuboctahedra; corners with eight equivalent Mg(1)Mg10Ti2 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)HfMg10Ti cuboctahedra; faces with two equivalent Mg(1)Mg10Ti2 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)HfMg10Ti cuboctahedra. Both Mg(2)-Mg(4) bond lengths are 3.13 Å. There are two shorter (3.15 Å) and two longer (3.22 Å) Mg(2)-Mg(2,2) bond lengths. All Mg(2)-Mg(3,3) bond lengths are 3.14 Å. Both Mg(2)-Hf(1) bond lengths are 3.18 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 Hf(1) atoms to form MgHf2Mg10 cuboctahedra that share corners with four equivalent Ti(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Hf2Mg10 cuboctahedra; corners with eight equivalent Mg(1)Mg10Ti2 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 Mg(3,3)HfMg10Ti cuboctahedra; faces with two equivalent Mg(1)Mg10Ti2 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)HfMg10Ti cuboctahedra. Both Mg(2)-Mg(4) bond lengths are 3.13 Å. All Mg(2)-Mg(3,3) bond lengths are 3.14 Å. Both Mg(2)-Hf(1) bond lengths are 3.18 Å. In the fourth Mg site, Mg(3) is bonded to two equivalent Mg(1); two equivalent Mg(2); two equivalent Mg(4); four Mg(3,3); one Hf(1); and one Ti(1) atom to form distorted MgHfMg10Ti cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)HfMg10Ti cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Hf(1)Mg12 cuboctahedra; edges with two equivalent Ti(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with four Mg(3,3)HfMg10Ti cuboctahedra; edges with four equivalent Mg(1)Mg10Ti2 cuboctahedra;  a faceface with one Hf(1)Mg12 cuboctahedra;  a faceface with one Ti(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)Mg10Ti2 cuboctahedra; and faces with six Mg(3,3)HfMg10Ti cuboctahedra. Both Mg(3)-Mg(4) bond lengths are 3.18 Å. There are two shorter (3.13 Å) and two longer (3.24 Å) Mg(3)-Mg(3,3) bond lengths. The Mg(3)-Hf(1) bond length is 3.12 Å. The Mg(3)-Ti(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 Hf(1); and one Ti(1) atom to form distorted MgHfMg10Ti cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)HfMg10Ti cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Hf(1)Mg12 cuboctahedra; edges with two equivalent Ti(1)Mg12 cuboctahedra; edges with four Mg(2,2)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(3)HfMg10Ti cuboctahedra; edges with four equivalent Mg(1)Mg10Ti2 cuboctahedra;  a faceface with one Hf(1)Mg12 cuboctahedra;  a faceface with one Ti(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)Mg10Ti2 cuboctahedra; and faces with six Mg(3,3)HfMg10Ti cuboctahedra. Both Mg(3)-Mg(4) bond lengths are 3.18 Å. The Mg(3)-Hf(1) bond length is 3.12 Å. The Mg(3)-Ti(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)HfMg10Ti cuboctahedra; edges with six Mg(2,2)Hf2Mg10 cuboctahedra; edges with six Mg(3,3)HfMg10Ti cuboctahedra; edges with six equivalent Mg(1)Mg10Ti2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three Mg(2,2)Hf2Mg10 cuboctahedra; faces with three equivalent Mg(1)Mg10Ti2 cuboctahedra; faces with three equivalent Hf(1)Mg12 cuboctahedra; faces with three equivalent Ti(1)Mg12 cuboctahedra; and faces with six Mg(3,3)HfMg10Ti 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)Mg10Ti2 cuboctahedra; edges with six Mg(2,2)Hf2Mg10 cuboctahedra; edges with twelve Mg(3,3)HfMg10Ti cuboctahedra; faces with two equivalent Ti(1)Mg12 cuboctahedra; faces with six Mg(2,2)Hf2Mg10 cuboctahedra; faces with six Mg(3,3)HfMg10Ti cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. Ti(1) is bonded to six equivalent Mg(1) and six Mg(3,3) atoms to form TiMg12 cuboctahedra that share corners with six equivalent Ti(1)Mg12 cuboctahedra; corners with twelve Mg(2,2)Hf2Mg10 cuboctahedra; edges with six equivalent Mg(1)Mg10Ti2 cuboctahedra; edges with twelve Mg(3,3)HfMg10Ti cuboctahedra; faces with two equivalent Hf(1)Mg12 cuboctahedra; faces with six Mg(3,3)HfMg10Ti cuboctahedra; faces with six equivalent Mg(1)Mg10Ti2 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra.