Mg14TiFe 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 Fe(1) atoms to form distorted MgMg10Fe2 cuboctahedra that share corners with four equivalent Ti(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Fe2 cuboctahedra; corners with eight equivalent Mg(2)Mg10Ti2 cuboctahedra; edges with two equivalent Fe(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Mg10Fe2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)Mg10TiFe cuboctahedra; faces with two equivalent Mg(2)Mg10Ti2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Fe(1)Mg12 cuboctahedra; faces with four equivalent Mg(1)Mg10Fe2 cuboctahedra; and faces with ten Mg(3,3)Mg10TiFe 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 Ti(1) atoms to form MgMg10Ti2 cuboctahedra that share corners with four equivalent Fe(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Ti2 cuboctahedra; corners with eight equivalent Mg(1)Mg10Fe2 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 equivalent Mg(3)Mg10TiFe cuboctahedra; faces with two equivalent Mg(1)Mg10Fe2 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)Mg10TiFe cuboctahedra. In the third Mg site, Mg(2) is bonded to two equivalent Mg(4); four Mg(2,2); four Mg(3,3); and two equivalent Ti(1) atoms to form MgMg10Ti2 cuboctahedra that share corners with four equivalent Fe(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Ti2 cuboctahedra; corners with eight equivalent Mg(1)Mg10Fe2 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 Mg(3,3)Mg10TiFe cuboctahedra; faces with two equivalent Mg(1)Mg10Fe2 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)Mg10TiFe 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 Fe(1) atom to form distorted MgMg10TiFe cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)Mg10TiFe cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Ti(1)Mg12 cuboctahedra; edges with two equivalent Fe(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Mg10Fe2 cuboctahedra; edges with four Mg(2,2)Mg10Ti2 cuboctahedra; edges with four Mg(3,3)Mg10TiFe cuboctahedra;  a faceface with one Ti(1)Mg12 cuboctahedra;  a faceface with one Fe(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five equivalent Mg(1)Mg10Fe2 cuboctahedra; faces with five Mg(2,2)Mg10Ti2 cuboctahedra; and faces with six Mg(3,3)Mg10TiFe 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 Ti(1), and one Fe(1) atom to form distorted MgMg10TiFe cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)Mg10TiFe cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Ti(1)Mg12 cuboctahedra; edges with two equivalent Fe(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Mg10Fe2 cuboctahedra; edges with four equivalent Mg(2)Mg10Ti2 cuboctahedra; edges with four equivalent Mg(3)Mg10TiFe cuboctahedra;  a faceface with one Ti(1)Mg12 cuboctahedra;  a faceface with one Fe(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five equivalent Mg(1)Mg10Fe2 cuboctahedra; faces with five Mg(2,2)Mg10Ti2 cuboctahedra; and faces with six Mg(3,3)Mg10TiFe 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)Mg10TiFe cuboctahedra; edges with six equivalent Mg(1)Mg10Fe2 cuboctahedra; edges with six Mg(2,2)Mg10Ti2 cuboctahedra; edges with six Mg(3,3)Mg10TiFe cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Mg(1)Mg10Fe2 cuboctahedra; faces with three Mg(2,2)Mg10Ti2 cuboctahedra; faces with three equivalent Ti(1)Mg12 cuboctahedra; faces with three equivalent Fe(1)Mg12 cuboctahedra; and faces with six Mg(3,3)Mg10TiFe 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)Mg10Fe2 cuboctahedra; edges with six Mg(2,2)Mg10Ti2 cuboctahedra; edges with twelve Mg(3,3)Mg10TiFe cuboctahedra; faces with two equivalent Fe(1)Mg12 cuboctahedra; faces with six Mg(2,2)Mg10Ti2 cuboctahedra; faces with six Mg(3,3)Mg10TiFe cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. Fe(1) is bonded to six equivalent Mg(1) and six Mg(3,3) atoms to form FeMg12 cuboctahedra that share corners with six equivalent Fe(1)Mg12 cuboctahedra; corners with twelve Mg(2,2)Mg10Ti2 cuboctahedra; edges with six equivalent Mg(1)Mg10Fe2 cuboctahedra; edges with twelve Mg(3,3)Mg10TiFe cuboctahedra; faces with two equivalent Ti(1)Mg12 cuboctahedra; faces with six equivalent Mg(1)Mg10Fe2 cuboctahedra; faces with six Mg(3,3)Mg10TiFe cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra.
Mg14TiFe 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 Fe(1) atoms to form distorted MgMg10Fe2 cuboctahedra that share corners with four equivalent Ti(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Fe2 cuboctahedra; corners with eight equivalent Mg(2)Mg10Ti2 cuboctahedra; edges with two equivalent Fe(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Mg10Fe2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)Mg10TiFe cuboctahedra; faces with two equivalent Mg(2)Mg10Ti2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Fe(1)Mg12 cuboctahedra; faces with four equivalent Mg(1)Mg10Fe2 cuboctahedra; and faces with ten Mg(3,3)Mg10TiFe cuboctahedra. Both Mg(1)-Mg(4) bond lengths are 3.11 Å. There are two shorter (3.14 Å) and two longer (3.16 Å) Mg(1)-Mg(1) bond lengths. All Mg(1)-Mg(3) bond lengths are 3.07 Å. Both Mg(1)-Fe(1) bond lengths are 3.15 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 Ti(1) atoms to form MgMg10Ti2 cuboctahedra that share corners with four equivalent Fe(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Ti2 cuboctahedra; corners with eight equivalent Mg(1)Mg10Fe2 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 equivalent Mg(3)Mg10TiFe cuboctahedra; faces with two equivalent Mg(1)Mg10Fe2 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)Mg10TiFe cuboctahedra. Both Mg(2)-Mg(4) bond lengths are 3.07 Å. There are two shorter (3.10 Å) and two longer (3.20 Å) Mg(2)-Mg(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 Mg(2,2); four Mg(3,3); and two equivalent Ti(1) atoms to form MgMg10Ti2 cuboctahedra that share corners with four equivalent Fe(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Ti2 cuboctahedra; corners with eight equivalent Mg(1)Mg10Fe2 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 Mg(3,3)Mg10TiFe cuboctahedra; faces with two equivalent Mg(1)Mg10Fe2 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)Mg10TiFe cuboctahedra. Both Mg(2)-Mg(4) bond lengths are 3.07 Å. There is one shorter (3.10 Å) and one longer (3.20 Å) Mg(2)-Mg(2) bond length. 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 Fe(1) atom to form distorted MgMg10TiFe cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)Mg10TiFe cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Ti(1)Mg12 cuboctahedra; edges with two equivalent Fe(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Mg10Fe2 cuboctahedra; edges with four Mg(2,2)Mg10Ti2 cuboctahedra; edges with four Mg(3,3)Mg10TiFe cuboctahedra;  a faceface with one Ti(1)Mg12 cuboctahedra;  a faceface with one Fe(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five equivalent Mg(1)Mg10Fe2 cuboctahedra; faces with five Mg(2,2)Mg10Ti2 cuboctahedra; and faces with six Mg(3,3)Mg10TiFe cuboctahedra. Both Mg(3)-Mg(4) bond lengths are 3.15 Å. There are two shorter (3.02 Å) and two longer (3.28 Å) Mg(3)-Mg(3,3) bond lengths. The Mg(3)-Ti(1) bond length is 3.08 Å. The Mg(3)-Fe(1) bond length is 3.00 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 Ti(1), and one Fe(1) atom to form distorted MgMg10TiFe cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)Mg10TiFe cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Ti(1)Mg12 cuboctahedra; edges with two equivalent Fe(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Mg10Fe2 cuboctahedra; edges with four equivalent Mg(2)Mg10Ti2 cuboctahedra; edges with four equivalent Mg(3)Mg10TiFe cuboctahedra;  a faceface with one Ti(1)Mg12 cuboctahedra;  a faceface with one Fe(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five equivalent Mg(1)Mg10Fe2 cuboctahedra; faces with five Mg(2,2)Mg10Ti2 cuboctahedra; and faces with six Mg(3,3)Mg10TiFe cuboctahedra. Both Mg(3)-Mg(1) bond lengths are 3.07 Å. Both Mg(3)-Mg(4) bond lengths are 3.15 Å. The Mg(3)-Ti(1) bond length is 3.08 Å. The Mg(3)-Fe(1) bond length is 3.00 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)Mg10TiFe cuboctahedra; edges with six equivalent Mg(1)Mg10Fe2 cuboctahedra; edges with six Mg(2,2)Mg10Ti2 cuboctahedra; edges with six Mg(3,3)Mg10TiFe cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Mg(1)Mg10Fe2 cuboctahedra; faces with three Mg(2,2)Mg10Ti2 cuboctahedra; faces with three equivalent Ti(1)Mg12 cuboctahedra; faces with three equivalent Fe(1)Mg12 cuboctahedra; and faces with six Mg(3,3)Mg10TiFe 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)Mg10Fe2 cuboctahedra; edges with six Mg(2,2)Mg10Ti2 cuboctahedra; edges with twelve Mg(3,3)Mg10TiFe cuboctahedra; faces with two equivalent Fe(1)Mg12 cuboctahedra; faces with six Mg(2,2)Mg10Ti2 cuboctahedra; faces with six Mg(3,3)Mg10TiFe cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. Fe(1) is bonded to six equivalent Mg(1) and six Mg(3,3) atoms to form FeMg12 cuboctahedra that share corners with six equivalent Fe(1)Mg12 cuboctahedra; corners with twelve Mg(2,2)Mg10Ti2 cuboctahedra; edges with six equivalent Mg(1)Mg10Fe2 cuboctahedra; edges with twelve Mg(3,3)Mg10TiFe cuboctahedra; faces with two equivalent Ti(1)Mg12 cuboctahedra; faces with six equivalent Mg(1)Mg10Fe2 cuboctahedra; faces with six Mg(3,3)Mg10TiFe cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra.