Mg14HfSi 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 Si(1) atoms to form distorted MgMg10Si2 cuboctahedra that share corners with four equivalent Hf(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Si2 cuboctahedra; corners with eight equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with two equivalent Si(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Mg10Si2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)HfMg10Si cuboctahedra; faces with two equivalent Mg(2)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Si(1)Mg12 cuboctahedra; faces with four equivalent Mg(1)Mg10Si2 cuboctahedra; and faces with ten Mg(3,3)HfMg10Si 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 Hf(1) atoms to form MgHf2Mg10 cuboctahedra that share corners with four equivalent Si(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Hf2Mg10 cuboctahedra; corners with eight equivalent Mg(1)Mg10Si2 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)HfMg10Si cuboctahedra; faces with two equivalent Mg(1)Mg10Si2 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)HfMg10Si cuboctahedra. In the third 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 Si(1) atom to form distorted MgHfMg10Si cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)HfMg10Si cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Hf(1)Mg12 cuboctahedra; edges with two equivalent Si(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with four Mg(3,3)HfMg10Si cuboctahedra; edges with four equivalent Mg(1)Mg10Si2 cuboctahedra;  a faceface with one Hf(1)Mg12 cuboctahedra;  a faceface with one Si(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)Mg10Si2 cuboctahedra; and faces with six Mg(3,3)HfMg10Si cuboctahedra. In the fourth 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 Si(1) atom to form distorted MgHfMg10Si cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)HfMg10Si cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Hf(1)Mg12 cuboctahedra; edges with two equivalent Si(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(3)HfMg10Si cuboctahedra; edges with four equivalent Mg(1)Mg10Si2 cuboctahedra;  a faceface with one Hf(1)Mg12 cuboctahedra;  a faceface with one Si(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)Mg10Si2 cuboctahedra; and faces with six Mg(3,3)HfMg10Si 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)HfMg10Si cuboctahedra; edges with six equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with six Mg(3,3)HfMg10Si cuboctahedra; edges with six equivalent Mg(1)Mg10Si2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Mg(2)Hf2Mg10 cuboctahedra; faces with three equivalent Mg(1)Mg10Si2 cuboctahedra; faces with three equivalent Hf(1)Mg12 cuboctahedra; faces with three equivalent Si(1)Mg12 cuboctahedra; and faces with six Mg(3,3)HfMg10Si cuboctahedra. Hf(1) is bonded to six equivalent Mg(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)Mg10Si2 cuboctahedra; edges with six equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with twelve Mg(3,3)HfMg10Si cuboctahedra; faces with two equivalent Si(1)Mg12 cuboctahedra; faces with six equivalent Mg(2)Hf2Mg10 cuboctahedra; faces with six Mg(3,3)HfMg10Si cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. Si(1) is bonded to six equivalent Mg(1) and six Mg(3,3) atoms to form SiMg12 cuboctahedra that share corners with six equivalent Si(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with six equivalent Mg(1)Mg10Si2 cuboctahedra; edges with twelve Mg(3,3)HfMg10Si cuboctahedra; faces with two equivalent Hf(1)Mg12 cuboctahedra; faces with six Mg(3,3)HfMg10Si cuboctahedra; faces with six equivalent Mg(1)Mg10Si2 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra.
Mg14HfSi 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 Si(1) atoms to form distorted MgMg10Si2 cuboctahedra that share corners with four equivalent Hf(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Si2 cuboctahedra; corners with eight equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with two equivalent Si(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Mg10Si2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)HfMg10Si cuboctahedra; faces with two equivalent Mg(2)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Si(1)Mg12 cuboctahedra; faces with four equivalent Mg(1)Mg10Si2 cuboctahedra; and faces with ten Mg(3,3)HfMg10Si cuboctahedra. Both Mg(1)-Mg(4) bond lengths are 3.17 Å. There are two shorter (3.12 Å) and two longer (3.16 Å) Mg(1)-Mg(1) bond lengths. All Mg(1)-Mg(3,3) bond lengths are 3.14 Å. Both Mg(1)-Si(1) bond lengths are 3.14 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 Hf(1) atoms to form MgHf2Mg10 cuboctahedra that share corners with four equivalent Si(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Hf2Mg10 cuboctahedra; corners with eight equivalent Mg(1)Mg10Si2 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)HfMg10Si cuboctahedra; faces with two equivalent Mg(1)Mg10Si2 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)HfMg10Si cuboctahedra. Both Mg(2)-Mg(4) bond lengths are 3.10 Å. There are two shorter (3.09 Å) and two longer (3.18 Å) Mg(2)-Mg(2) bond lengths. All Mg(2)-Mg(3,3) bond lengths are 3.15 Å. Both Mg(2)-Hf(1) bond lengths are 3.14 Å. In the third 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 Si(1) atom to form distorted MgHfMg10Si cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)HfMg10Si cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Hf(1)Mg12 cuboctahedra; edges with two equivalent Si(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with four Mg(3,3)HfMg10Si cuboctahedra; edges with four equivalent Mg(1)Mg10Si2 cuboctahedra;  a faceface with one Hf(1)Mg12 cuboctahedra;  a faceface with one Si(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)Mg10Si2 cuboctahedra; and faces with six Mg(3,3)HfMg10Si cuboctahedra. Both Mg(3)-Mg(4) bond lengths are 3.14 Å. There are two shorter (3.04 Å) and two longer (3.24 Å) Mg(3)-Mg(3,3) bond lengths. The Mg(3)-Hf(1) bond length is 3.11 Å. The Mg(3)-Si(1) bond length is 3.08 Å. In the fourth 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 Si(1) atom to form distorted MgHfMg10Si cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)HfMg10Si cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Hf(1)Mg12 cuboctahedra; edges with two equivalent Si(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(3)HfMg10Si cuboctahedra; edges with four equivalent Mg(1)Mg10Si2 cuboctahedra;  a faceface with one Hf(1)Mg12 cuboctahedra;  a faceface with one Si(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)Mg10Si2 cuboctahedra; and faces with six Mg(3,3)HfMg10Si cuboctahedra. Both Mg(3)-Mg(4) bond lengths are 3.14 Å. The Mg(3)-Hf(1) bond length is 3.11 Å. The Mg(3)-Si(1) bond length is 3.08 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)HfMg10Si cuboctahedra; edges with six equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with six Mg(3,3)HfMg10Si cuboctahedra; edges with six equivalent Mg(1)Mg10Si2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Mg(2)Hf2Mg10 cuboctahedra; faces with three equivalent Mg(1)Mg10Si2 cuboctahedra; faces with three equivalent Hf(1)Mg12 cuboctahedra; faces with three equivalent Si(1)Mg12 cuboctahedra; and faces with six Mg(3,3)HfMg10Si cuboctahedra. Hf(1) is bonded to six equivalent Mg(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)Mg10Si2 cuboctahedra; edges with six equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with twelve Mg(3,3)HfMg10Si cuboctahedra; faces with two equivalent Si(1)Mg12 cuboctahedra; faces with six equivalent Mg(2)Hf2Mg10 cuboctahedra; faces with six Mg(3,3)HfMg10Si cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. Si(1) is bonded to six equivalent Mg(1) and six Mg(3,3) atoms to form SiMg12 cuboctahedra that share corners with six equivalent Si(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with six equivalent Mg(1)Mg10Si2 cuboctahedra; edges with twelve Mg(3,3)HfMg10Si cuboctahedra; faces with two equivalent Hf(1)Mg12 cuboctahedra; faces with six Mg(3,3)HfMg10Si cuboctahedra; faces with six equivalent Mg(1)Mg10Si2 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra.