Mg14ZrTi 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 Mg(3,3); and two equivalent Zr(1) atoms to form MgMg10Zr2 cuboctahedra that share corners with four equivalent Ti(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Zr2 cuboctahedra; corners with eight equivalent Mg(2)Mg10Ti2 cuboctahedra; edges with two equivalent Zr(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Mg10Zr2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)Mg10ZrTi cuboctahedra; faces with two equivalent Mg(2)Mg10Ti2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Zr(1)Mg12 cuboctahedra; faces with four equivalent Mg(1)Mg10Zr2 cuboctahedra; and faces with ten Mg(3,3)Mg10ZrTi cuboctahedra. In the second 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 Zr(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Ti2 cuboctahedra; corners with eight equivalent Mg(1)Mg10Zr2 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)Mg10ZrTi cuboctahedra; faces with two equivalent Mg(1)Mg10Zr2 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)Mg10ZrTi cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), four equivalent Mg(3), one Zr(1), and one Ti(1) atom to form distorted MgMg10ZrTi cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)Mg10ZrTi cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Zr(1)Mg12 cuboctahedra; edges with two equivalent Ti(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Ti2 cuboctahedra; edges with four equivalent Mg(1)Mg10Zr2 cuboctahedra; edges with four equivalent Mg(3)Mg10ZrTi cuboctahedra;  a faceface with one Zr(1)Mg12 cuboctahedra;  a faceface with one Ti(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five equivalent Mg(2)Mg10Ti2 cuboctahedra; faces with five equivalent Mg(1)Mg10Zr2 cuboctahedra; and faces with six Mg(3,3)Mg10ZrTi 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 Zr(1); and one Ti(1) atom to form distorted MgMg10ZrTi cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)Mg10ZrTi cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Zr(1)Mg12 cuboctahedra; edges with two equivalent Ti(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Ti2 cuboctahedra; edges with four equivalent Mg(1)Mg10Zr2 cuboctahedra; edges with four Mg(3,3)Mg10ZrTi cuboctahedra;  a faceface with one Zr(1)Mg12 cuboctahedra;  a faceface with one Ti(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five equivalent Mg(2)Mg10Ti2 cuboctahedra; faces with five equivalent Mg(1)Mg10Zr2 cuboctahedra; and faces with six Mg(3,3)Mg10ZrTi cuboctahedra. In the fifth Mg site, Mg(4) is bonded to three equivalent Mg(1); three equivalent Mg(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)Mg10ZrTi cuboctahedra; edges with six equivalent Mg(2)Mg10Ti2 cuboctahedra; edges with six equivalent Mg(1)Mg10Zr2 cuboctahedra; edges with six Mg(3,3)Mg10ZrTi cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Mg(2)Mg10Ti2 cuboctahedra; faces with three equivalent Mg(1)Mg10Zr2 cuboctahedra; faces with three equivalent Zr(1)Mg12 cuboctahedra; faces with three equivalent Ti(1)Mg12 cuboctahedra; and faces with six Mg(3,3)Mg10ZrTi cuboctahedra. Zr(1) is bonded to six equivalent Mg(1) and six Mg(3,3) atoms to form ZrMg12 cuboctahedra that share corners with six equivalent Zr(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(2)Mg10Ti2 cuboctahedra; edges with six equivalent Mg(1)Mg10Zr2 cuboctahedra; edges with twelve Mg(3,3)Mg10ZrTi cuboctahedra; faces with two equivalent Ti(1)Mg12 cuboctahedra; faces with six equivalent Mg(1)Mg10Zr2 cuboctahedra; faces with six Mg(3,3)Mg10ZrTi cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. Ti(1) is bonded to six equivalent Mg(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)Mg10Zr2 cuboctahedra; edges with six equivalent Mg(2)Mg10Ti2 cuboctahedra; edges with twelve Mg(3,3)Mg10ZrTi cuboctahedra; faces with two equivalent Zr(1)Mg12 cuboctahedra; faces with six equivalent Mg(2)Mg10Ti2 cuboctahedra; faces with six Mg(3,3)Mg10ZrTi cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra.
Mg14ZrTi 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 Mg(3,3); and two equivalent Zr(1) atoms to form MgMg10Zr2 cuboctahedra that share corners with four equivalent Ti(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Zr2 cuboctahedra; corners with eight equivalent Mg(2)Mg10Ti2 cuboctahedra; edges with two equivalent Zr(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Mg10Zr2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)Mg10ZrTi cuboctahedra; faces with two equivalent Mg(2)Mg10Ti2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Zr(1)Mg12 cuboctahedra; faces with four equivalent Mg(1)Mg10Zr2 cuboctahedra; and faces with ten Mg(3,3)Mg10ZrTi cuboctahedra. Both Mg(1)-Mg(4) bond lengths are 3.14 Å. There are two shorter (3.16 Å) and two longer (3.25 Å) Mg(1)-Mg(1) bond lengths. All Mg(1)-Mg(3,3) bond lengths are 3.15 Å. Both Mg(1)-Zr(1) bond lengths are 3.20 Å. In the second 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 Zr(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Ti2 cuboctahedra; corners with eight equivalent Mg(1)Mg10Zr2 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)Mg10ZrTi cuboctahedra; faces with two equivalent Mg(1)Mg10Zr2 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)Mg10ZrTi cuboctahedra. Both Mg(2)-Mg(4) bond lengths are 3.15 Å. There are two shorter (3.19 Å) and two longer (3.22 Å) Mg(2)-Mg(2) bond lengths. All Mg(2)-Mg(3,3) bond lengths are 3.13 Å. Both Mg(2)-Ti(1) bond lengths are 3.20 Å. In the third Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), four equivalent Mg(3), one Zr(1), and one Ti(1) atom to form distorted MgMg10ZrTi cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)Mg10ZrTi cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Zr(1)Mg12 cuboctahedra; edges with two equivalent Ti(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Ti2 cuboctahedra; edges with four equivalent Mg(1)Mg10Zr2 cuboctahedra; edges with four equivalent Mg(3)Mg10ZrTi cuboctahedra;  a faceface with one Zr(1)Mg12 cuboctahedra;  a faceface with one Ti(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five equivalent Mg(2)Mg10Ti2 cuboctahedra; faces with five equivalent Mg(1)Mg10Zr2 cuboctahedra; and faces with six Mg(3,3)Mg10ZrTi cuboctahedra. Both Mg(3)-Mg(4) bond lengths are 3.20 Å. There are two shorter (3.15 Å) and two longer (3.26 Å) Mg(3)-Mg(3) bond lengths. The Mg(3)-Zr(1) bond length is 3.13 Å. The Mg(3)-Ti(1) bond length is 3.10 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 Zr(1); and one Ti(1) atom to form distorted MgMg10ZrTi cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)Mg10ZrTi cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Zr(1)Mg12 cuboctahedra; edges with two equivalent Ti(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Ti2 cuboctahedra; edges with four equivalent Mg(1)Mg10Zr2 cuboctahedra; edges with four Mg(3,3)Mg10ZrTi cuboctahedra;  a faceface with one Zr(1)Mg12 cuboctahedra;  a faceface with one Ti(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five equivalent Mg(2)Mg10Ti2 cuboctahedra; faces with five equivalent Mg(1)Mg10Zr2 cuboctahedra; and faces with six Mg(3,3)Mg10ZrTi cuboctahedra. Both Mg(3)-Mg(4) bond lengths are 3.20 Å. There is one shorter (3.15 Å) and one longer (3.26 Å) Mg(3)-Mg(3) bond length. The Mg(3)-Zr(1) bond length is 3.13 Å. The Mg(3)-Ti(1) bond length is 3.10 Å. In the fifth Mg site, Mg(4) is bonded to three equivalent Mg(1); three equivalent Mg(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)Mg10ZrTi cuboctahedra; edges with six equivalent Mg(2)Mg10Ti2 cuboctahedra; edges with six equivalent Mg(1)Mg10Zr2 cuboctahedra; edges with six Mg(3,3)Mg10ZrTi cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Mg(2)Mg10Ti2 cuboctahedra; faces with three equivalent Mg(1)Mg10Zr2 cuboctahedra; faces with three equivalent Zr(1)Mg12 cuboctahedra; faces with three equivalent Ti(1)Mg12 cuboctahedra; and faces with six Mg(3,3)Mg10ZrTi cuboctahedra. Zr(1) is bonded to six equivalent Mg(1) and six Mg(3,3) atoms to form ZrMg12 cuboctahedra that share corners with six equivalent Zr(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(2)Mg10Ti2 cuboctahedra; edges with six equivalent Mg(1)Mg10Zr2 cuboctahedra; edges with twelve Mg(3,3)Mg10ZrTi cuboctahedra; faces with two equivalent Ti(1)Mg12 cuboctahedra; faces with six equivalent Mg(1)Mg10Zr2 cuboctahedra; faces with six Mg(3,3)Mg10ZrTi cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. Ti(1) is bonded to six equivalent Mg(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)Mg10Zr2 cuboctahedra; edges with six equivalent Mg(2)Mg10Ti2 cuboctahedra; edges with twelve Mg(3,3)Mg10ZrTi cuboctahedra; faces with two equivalent Zr(1)Mg12 cuboctahedra; faces with six equivalent Mg(2)Mg10Ti2 cuboctahedra; faces with six Mg(3,3)Mg10ZrTi cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra.