Mg14ZrBi 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 equivalent Mg(3), and two equivalent Zr(1) atoms to form MgMg10Zr2 cuboctahedra that share corners with four equivalent Bi(1)Mg12 cuboctahedra, corners with six equivalent Mg(1)Mg10Zr2 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 equivalent Mg(3)Mg10ZrBi 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 equivalent Mg(3)Mg10ZrBi cuboctahedra. In the second Mg site, Mg(2) is bonded in a distorted linear geometry to two equivalent Mg(4), four equivalent Mg(3), and two equivalent Bi(1) atoms. In the third Mg site, Mg(1) is bonded to two equivalent Mg(4); four Mg(1,1); four equivalent Mg(3); and two equivalent Zr(1) atoms to form MgMg10Zr2 cuboctahedra that share corners with four equivalent Bi(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Zr2 cuboctahedra; edges with two equivalent Zr(1)Mg12 cuboctahedra; edges with four Mg(1,1)Mg10Zr2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)Mg10ZrBi cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Zr(1)Mg12 cuboctahedra; faces with four Mg(1,1)Mg10Zr2 cuboctahedra; and faces with ten equivalent Mg(3)Mg10ZrBi cuboctahedra. In the fourth Mg site, Mg(3) is bonded to two Mg(1,1); two equivalent Mg(2); two equivalent Mg(4); four equivalent Mg(3); one Zr(1); and one Bi(1) atom to form distorted MgMg10ZrBi cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen equivalent Mg(3)Mg10ZrBi cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Zr(1)Mg12 cuboctahedra; edges with two equivalent Bi(1)Mg12 cuboctahedra; edges with four Mg(1,1)Mg10Zr2 cuboctahedra; edges with four equivalent Mg(3)Mg10ZrBi cuboctahedra;  a faceface with one Zr(1)Mg12 cuboctahedra;  a faceface with one Bi(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(1,1)Mg10Zr2 cuboctahedra; and faces with six equivalent Mg(3)Mg10ZrBi cuboctahedra. In the fifth Mg site, Mg(4) is bonded to three Mg(1,1); three equivalent Mg(2); and six equivalent Mg(3) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(4)Mg12 cuboctahedra; corners with twelve equivalent Mg(3)Mg10ZrBi cuboctahedra; edges with six Mg(1,1)Mg10Zr2 cuboctahedra; edges with six equivalent Mg(3)Mg10ZrBi cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three Mg(1,1)Mg10Zr2 cuboctahedra; faces with three equivalent Zr(1)Mg12 cuboctahedra; faces with three equivalent Bi(1)Mg12 cuboctahedra; and faces with six equivalent Mg(3)Mg10ZrBi cuboctahedra. Zr(1) is bonded to six Mg(1,1) and six equivalent Mg(3) atoms to form ZrMg12 cuboctahedra that share corners with six equivalent Zr(1)Mg12 cuboctahedra; edges with six Mg(1,1)Mg10Zr2 cuboctahedra; edges with twelve equivalent Mg(3)Mg10ZrBi cuboctahedra; faces with two equivalent Bi(1)Mg12 cuboctahedra; faces with six Mg(1,1)Mg10Zr2 cuboctahedra; faces with six equivalent Mg(3)Mg10ZrBi cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. Bi(1) is bonded to six equivalent Mg(2) and six equivalent Mg(3) atoms to form BiMg12 cuboctahedra that share corners with six equivalent Bi(1)Mg12 cuboctahedra; corners with twelve Mg(1,1)Mg10Zr2 cuboctahedra; edges with twelve equivalent Mg(3)Mg10ZrBi cuboctahedra; faces with two equivalent Zr(1)Mg12 cuboctahedra; faces with six equivalent Mg(3)Mg10ZrBi cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra.
Mg14ZrBi 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 equivalent Mg(3), and two equivalent Zr(1) atoms to form MgMg10Zr2 cuboctahedra that share corners with four equivalent Bi(1)Mg12 cuboctahedra, corners with six equivalent Mg(1)Mg10Zr2 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 equivalent Mg(3)Mg10ZrBi 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 equivalent Mg(3)Mg10ZrBi cuboctahedra. Both Mg(1)-Mg(4) bond lengths are 3.17 Å. There are two shorter (3.15 Å) and two longer (3.25 Å) Mg(1)-Mg(1) bond lengths. All Mg(1)-Mg(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 in a distorted linear geometry to two equivalent Mg(4), four equivalent Mg(3), and two equivalent Bi(1) atoms. Both Mg(2)-Mg(4) bond lengths are 3.26 Å. All Mg(2)-Mg(3) bond lengths are 3.29 Å. Both Mg(2)-Bi(1) bond lengths are 3.20 Å. In the third Mg site, Mg(1) is bonded to two equivalent Mg(4); four Mg(1,1); four equivalent Mg(3); and two equivalent Zr(1) atoms to form MgMg10Zr2 cuboctahedra that share corners with four equivalent Bi(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Zr2 cuboctahedra; edges with two equivalent Zr(1)Mg12 cuboctahedra; edges with four Mg(1,1)Mg10Zr2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)Mg10ZrBi cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Zr(1)Mg12 cuboctahedra; faces with four Mg(1,1)Mg10Zr2 cuboctahedra; and faces with ten equivalent Mg(3)Mg10ZrBi cuboctahedra. Both Mg(1)-Mg(4) bond lengths are 3.17 Å. There is one shorter (3.15 Å) and one longer (3.25 Å) Mg(1)-Mg(1) bond length. All Mg(1)-Mg(3) bond lengths are 3.15 Å. Both Mg(1)-Zr(1) bond lengths are 3.20 Å. In the fourth Mg site, Mg(3) is bonded to two Mg(1,1); two equivalent Mg(2); two equivalent Mg(4); four equivalent Mg(3); one Zr(1); and one Bi(1) atom to form distorted MgMg10ZrBi cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen equivalent Mg(3)Mg10ZrBi cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Zr(1)Mg12 cuboctahedra; edges with two equivalent Bi(1)Mg12 cuboctahedra; edges with four Mg(1,1)Mg10Zr2 cuboctahedra; edges with four equivalent Mg(3)Mg10ZrBi cuboctahedra;  a faceface with one Zr(1)Mg12 cuboctahedra;  a faceface with one Bi(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(1,1)Mg10Zr2 cuboctahedra; and faces with six equivalent Mg(3)Mg10ZrBi cuboctahedra. Both Mg(3)-Mg(4) bond lengths are 3.20 Å. There are two shorter (3.14 Å) and two longer (3.25 Å) Mg(3)-Mg(3) bond lengths. The Mg(3)-Zr(1) bond length is 3.13 Å. The Mg(3)-Bi(1) bond length is 3.26 Å. In the fifth Mg site, Mg(4) is bonded to three Mg(1,1); three equivalent Mg(2); and six equivalent Mg(3) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(4)Mg12 cuboctahedra; corners with twelve equivalent Mg(3)Mg10ZrBi cuboctahedra; edges with six Mg(1,1)Mg10Zr2 cuboctahedra; edges with six equivalent Mg(3)Mg10ZrBi cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three Mg(1,1)Mg10Zr2 cuboctahedra; faces with three equivalent Zr(1)Mg12 cuboctahedra; faces with three equivalent Bi(1)Mg12 cuboctahedra; and faces with six equivalent Mg(3)Mg10ZrBi cuboctahedra. Zr(1) is bonded to six Mg(1,1) and six equivalent Mg(3) atoms to form ZrMg12 cuboctahedra that share corners with six equivalent Zr(1)Mg12 cuboctahedra; edges with six Mg(1,1)Mg10Zr2 cuboctahedra; edges with twelve equivalent Mg(3)Mg10ZrBi cuboctahedra; faces with two equivalent Bi(1)Mg12 cuboctahedra; faces with six Mg(1,1)Mg10Zr2 cuboctahedra; faces with six equivalent Mg(3)Mg10ZrBi cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. Bi(1) is bonded to six equivalent Mg(2) and six equivalent Mg(3) atoms to form BiMg12 cuboctahedra that share corners with six equivalent Bi(1)Mg12 cuboctahedra; corners with twelve Mg(1,1)Mg10Zr2 cuboctahedra; edges with twelve equivalent Mg(3)Mg10ZrBi cuboctahedra; faces with two equivalent Zr(1)Mg12 cuboctahedra; faces with six equivalent Mg(3)Mg10ZrBi cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra.