Mg14HfCd crystallizes in the hexagonal P-6m2 space group. There are four 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 Cd(1) atoms to form distorted MgMg10Cd2 cuboctahedra that share corners with four equivalent Hf(1)Mg12 cuboctahedra, corners with six equivalent Mg(1)Mg10Cd2 cuboctahedra, corners with eight equivalent Mg(2)Hf2Mg10 cuboctahedra, edges with two equivalent Cd(1)Mg12 cuboctahedra, edges with four equivalent Mg(1)Mg10Cd2 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with eight equivalent Mg(3)HfMg10Cd cuboctahedra, faces with two equivalent Mg(2)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Cd(1)Mg12 cuboctahedra, faces with four equivalent Mg(1)Mg10Cd2 cuboctahedra, and faces with ten equivalent Mg(3)HfMg10Cd 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 Hf(1) atoms to form MgHf2Mg10 cuboctahedra that share corners with four equivalent Cd(1)Mg12 cuboctahedra, corners with six equivalent Mg(2)Hf2Mg10 cuboctahedra, corners with eight equivalent Mg(1)Mg10Cd2 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)HfMg10Cd cuboctahedra, faces with two equivalent Mg(1)Mg10Cd2 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 equivalent Mg(3)HfMg10Cd 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 Hf(1), and one Cd(1) atom to form distorted MgHfMg10Cd cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra, corners with fourteen equivalent Mg(3)HfMg10Cd cuboctahedra, edges with two equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Hf(1)Mg12 cuboctahedra, edges with two equivalent Cd(1)Mg12 cuboctahedra, edges with four equivalent Mg(2)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(3)HfMg10Cd cuboctahedra, edges with four equivalent Mg(1)Mg10Cd2 cuboctahedra,  a faceface with one Hf(1)Mg12 cuboctahedra,  a faceface with one Cd(1)Mg12 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with five equivalent Mg(2)Hf2Mg10 cuboctahedra, faces with five equivalent Mg(1)Mg10Cd2 cuboctahedra, and faces with six equivalent Mg(3)HfMg10Cd cuboctahedra. In the fourth Mg site, Mg(4) is bonded to three equivalent Mg(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)HfMg10Cd cuboctahedra, edges with six equivalent Mg(2)Hf2Mg10 cuboctahedra, edges with six equivalent Mg(3)HfMg10Cd cuboctahedra, edges with six equivalent Mg(1)Mg10Cd2 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with three equivalent Mg(2)Hf2Mg10 cuboctahedra, faces with three equivalent Mg(1)Mg10Cd2 cuboctahedra, faces with three equivalent Hf(1)Mg12 cuboctahedra, faces with three equivalent Cd(1)Mg12 cuboctahedra, and faces with six equivalent Mg(3)HfMg10Cd cuboctahedra. Hf(1) is bonded to six equivalent Mg(2) and six equivalent Mg(3) atoms to form HfMg12 cuboctahedra that share corners with six equivalent Hf(1)Mg12 cuboctahedra, corners with twelve equivalent Mg(1)Mg10Cd2 cuboctahedra, edges with six equivalent Mg(2)Hf2Mg10 cuboctahedra, edges with twelve equivalent Mg(3)HfMg10Cd cuboctahedra, faces with two equivalent Cd(1)Mg12 cuboctahedra, faces with six equivalent Mg(2)Hf2Mg10 cuboctahedra, faces with six equivalent Mg(3)HfMg10Cd cuboctahedra, and faces with six equivalent Mg(4)Mg12 cuboctahedra. Cd(1) is bonded to six equivalent Mg(1) and six equivalent Mg(3) atoms to form CdMg12 cuboctahedra that share corners with six equivalent Cd(1)Mg12 cuboctahedra, corners with twelve equivalent Mg(2)Hf2Mg10 cuboctahedra, edges with six equivalent Mg(1)Mg10Cd2 cuboctahedra, edges with twelve equivalent Mg(3)HfMg10Cd cuboctahedra, faces with two equivalent Hf(1)Mg12 cuboctahedra, faces with six equivalent Mg(3)HfMg10Cd cuboctahedra, faces with six equivalent Mg(1)Mg10Cd2 cuboctahedra, and faces with six equivalent Mg(4)Mg12 cuboctahedra.
Mg14HfCd crystallizes in the hexagonal P-6m2 space group. There are four 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 Cd(1) atoms to form distorted MgMg10Cd2 cuboctahedra that share corners with four equivalent Hf(1)Mg12 cuboctahedra, corners with six equivalent Mg(1)Mg10Cd2 cuboctahedra, corners with eight equivalent Mg(2)Hf2Mg10 cuboctahedra, edges with two equivalent Cd(1)Mg12 cuboctahedra, edges with four equivalent Mg(1)Mg10Cd2 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with eight equivalent Mg(3)HfMg10Cd cuboctahedra, faces with two equivalent Mg(2)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Cd(1)Mg12 cuboctahedra, faces with four equivalent Mg(1)Mg10Cd2 cuboctahedra, and faces with ten equivalent Mg(3)HfMg10Cd cuboctahedra. Both Mg(1)-Mg(4) bond lengths are 3.15 Å. There are two shorter (3.18 Å) and two longer (3.21 Å) Mg(1)-Mg(1) bond lengths. All Mg(1)-Mg(3) bond lengths are 3.16 Å. Both Mg(1)-Cd(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 equivalent Mg(3), and two equivalent Hf(1) atoms to form MgHf2Mg10 cuboctahedra that share corners with four equivalent Cd(1)Mg12 cuboctahedra, corners with six equivalent Mg(2)Hf2Mg10 cuboctahedra, corners with eight equivalent Mg(1)Mg10Cd2 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)HfMg10Cd cuboctahedra, faces with two equivalent Mg(1)Mg10Cd2 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 equivalent Mg(3)HfMg10Cd cuboctahedra. Both Mg(2)-Mg(4) bond lengths are 3.14 Å. There are two shorter (3.15 Å) and two longer (3.24 Å) Mg(2)-Mg(2) bond lengths. All Mg(2)-Mg(3) bond lengths are 3.14 Å. Both Mg(2)-Hf(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 Hf(1), and one Cd(1) atom to form distorted MgHfMg10Cd cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra, corners with fourteen equivalent Mg(3)HfMg10Cd cuboctahedra, edges with two equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Hf(1)Mg12 cuboctahedra, edges with two equivalent Cd(1)Mg12 cuboctahedra, edges with four equivalent Mg(2)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(3)HfMg10Cd cuboctahedra, edges with four equivalent Mg(1)Mg10Cd2 cuboctahedra,  a faceface with one Hf(1)Mg12 cuboctahedra,  a faceface with one Cd(1)Mg12 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with five equivalent Mg(2)Hf2Mg10 cuboctahedra, faces with five equivalent Mg(1)Mg10Cd2 cuboctahedra, and faces with six equivalent Mg(3)HfMg10Cd cuboctahedra. Both Mg(3)-Mg(4) bond lengths are 3.20 Å. There are two shorter (3.15 Å) and two longer (3.25 Å) Mg(3)-Mg(3) bond lengths. The Mg(3)-Hf(1) bond length is 3.12 Å. The Mg(3)-Cd(1) bond length is 3.13 Å. In the fourth Mg site, Mg(4) is bonded to three equivalent Mg(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)HfMg10Cd cuboctahedra, edges with six equivalent Mg(2)Hf2Mg10 cuboctahedra, edges with six equivalent Mg(3)HfMg10Cd cuboctahedra, edges with six equivalent Mg(1)Mg10Cd2 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with three equivalent Mg(2)Hf2Mg10 cuboctahedra, faces with three equivalent Mg(1)Mg10Cd2 cuboctahedra, faces with three equivalent Hf(1)Mg12 cuboctahedra, faces with three equivalent Cd(1)Mg12 cuboctahedra, and faces with six equivalent Mg(3)HfMg10Cd cuboctahedra. Hf(1) is bonded to six equivalent Mg(2) and six equivalent Mg(3) atoms to form HfMg12 cuboctahedra that share corners with six equivalent Hf(1)Mg12 cuboctahedra, corners with twelve equivalent Mg(1)Mg10Cd2 cuboctahedra, edges with six equivalent Mg(2)Hf2Mg10 cuboctahedra, edges with twelve equivalent Mg(3)HfMg10Cd cuboctahedra, faces with two equivalent Cd(1)Mg12 cuboctahedra, faces with six equivalent Mg(2)Hf2Mg10 cuboctahedra, faces with six equivalent Mg(3)HfMg10Cd cuboctahedra, and faces with six equivalent Mg(4)Mg12 cuboctahedra. Cd(1) is bonded to six equivalent Mg(1) and six equivalent Mg(3) atoms to form CdMg12 cuboctahedra that share corners with six equivalent Cd(1)Mg12 cuboctahedra, corners with twelve equivalent Mg(2)Hf2Mg10 cuboctahedra, edges with six equivalent Mg(1)Mg10Cd2 cuboctahedra, edges with twelve equivalent Mg(3)HfMg10Cd cuboctahedra, faces with two equivalent Hf(1)Mg12 cuboctahedra, faces with six equivalent Mg(3)HfMg10Cd cuboctahedra, faces with six equivalent Mg(1)Mg10Cd2 cuboctahedra, and faces with six equivalent Mg(4)Mg12 cuboctahedra.