NaMg14Hf crystallizes in the hexagonal P-6m2 space group. Na(1) is bonded to six equivalent Mg(1) and six Mg(3,3) atoms to form NaMg12 cuboctahedra that share corners with six equivalent Na(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with six equivalent Mg(1)Na2Mg10 cuboctahedra; edges with twelve Mg(3,3)NaHfMg10 cuboctahedra; faces with two equivalent Hf(1)Mg12 cuboctahedra; faces with six equivalent Mg(4)Mg12 cuboctahedra; faces with six equivalent Mg(1)Na2Mg10 cuboctahedra; and faces with six Mg(3,3)NaHfMg10 cuboctahedra. There are five inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Na(1), two equivalent Mg(4), four equivalent Mg(1), and four equivalent Mg(3) atoms to form distorted MgNa2Mg10 cuboctahedra that share corners with four equivalent Hf(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Na2Mg10 cuboctahedra; corners with eight equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with two equivalent Na(1)Mg12 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with four equivalent Mg(1)Na2Mg10 cuboctahedra; edges with eight equivalent Mg(3)NaHfMg10 cuboctahedra; faces with two equivalent Na(1)Mg12 cuboctahedra; faces with two equivalent Mg(2)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with four equivalent Mg(1)Na2Mg10 cuboctahedra; and faces with ten Mg(3,3)NaHfMg10 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 Na(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Hf2Mg10 cuboctahedra; corners with eight equivalent Mg(1)Na2Mg10 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)NaHfMg10 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(1)Na2Mg10 cuboctahedra; faces with two equivalent Hf(1)Mg12 cuboctahedra; faces with four equivalent Mg(2)Hf2Mg10 cuboctahedra; and faces with ten Mg(3,3)NaHfMg10 cuboctahedra. In the third Mg site, Mg(3) is bonded to one Na(1); two equivalent Mg(1); two equivalent Mg(2); two equivalent Mg(4); four Mg(3,3); and one Hf(1) atom to form distorted MgNaHfMg10 cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)NaHfMg10 cuboctahedra; edges with two equivalent Na(1)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Hf(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(1)Na2Mg10 cuboctahedra; edges with four Mg(3,3)NaHfMg10 cuboctahedra;  a faceface with one Na(1)Mg12 cuboctahedra;  a faceface with one Hf(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)Na2Mg10 cuboctahedra; and faces with six Mg(3,3)NaHfMg10 cuboctahedra. In the fourth Mg site, Mg(3) is bonded to one Na(1), two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), four equivalent Mg(3), and one Hf(1) atom to form distorted MgNaHfMg10 cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)NaHfMg10 cuboctahedra; edges with two equivalent Na(1)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Hf(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(1)Na2Mg10 cuboctahedra; edges with four equivalent Mg(3)NaHfMg10 cuboctahedra;  a faceface with one Na(1)Mg12 cuboctahedra;  a faceface with one Hf(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)Na2Mg10 cuboctahedra; and faces with six Mg(3,3)NaHfMg10 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)NaHfMg10 cuboctahedra; edges with six equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with six equivalent Mg(1)Na2Mg10 cuboctahedra; edges with six Mg(3,3)NaHfMg10 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Na(1)Mg12 cuboctahedra; faces with three equivalent Mg(2)Hf2Mg10 cuboctahedra; faces with three equivalent Mg(1)Na2Mg10 cuboctahedra; faces with three equivalent Hf(1)Mg12 cuboctahedra; and faces with six Mg(3,3)NaHfMg10 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)Na2Mg10 cuboctahedra; edges with six equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with twelve Mg(3,3)NaHfMg10 cuboctahedra; faces with two equivalent Na(1)Mg12 cuboctahedra; faces with six equivalent Mg(2)Hf2Mg10 cuboctahedra; faces with six equivalent Mg(4)Mg12 cuboctahedra; and faces with six Mg(3,3)NaHfMg10 cuboctahedra.
NaMg14Hf crystallizes in the hexagonal P-6m2 space group. Na(1) is bonded to six equivalent Mg(1) and six Mg(3,3) atoms to form NaMg12 cuboctahedra that share corners with six equivalent Na(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with six equivalent Mg(1)Na2Mg10 cuboctahedra; edges with twelve Mg(3,3)NaHfMg10 cuboctahedra; faces with two equivalent Hf(1)Mg12 cuboctahedra; faces with six equivalent Mg(4)Mg12 cuboctahedra; faces with six equivalent Mg(1)Na2Mg10 cuboctahedra; and faces with six Mg(3,3)NaHfMg10 cuboctahedra. All Na(1)-Mg(1) bond lengths are 3.24 Å. All Na(1)-Mg(3,3) bond lengths are 3.19 Å. There are five inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Na(1), two equivalent Mg(4), four equivalent Mg(1), and four equivalent Mg(3) atoms to form distorted MgNa2Mg10 cuboctahedra that share corners with four equivalent Hf(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Na2Mg10 cuboctahedra; corners with eight equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with two equivalent Na(1)Mg12 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with four equivalent Mg(1)Na2Mg10 cuboctahedra; edges with eight equivalent Mg(3)NaHfMg10 cuboctahedra; faces with two equivalent Na(1)Mg12 cuboctahedra; faces with two equivalent Mg(2)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with four equivalent Mg(1)Na2Mg10 cuboctahedra; and faces with ten Mg(3,3)NaHfMg10 cuboctahedra. Both Mg(1)-Mg(4) bond lengths are 3.18 Å. There are two shorter (3.21 Å) and two longer (3.26 Å) Mg(1)-Mg(1) bond lengths. All Mg(1)-Mg(3) 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 Na(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Hf2Mg10 cuboctahedra; corners with eight equivalent Mg(1)Na2Mg10 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)NaHfMg10 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(1)Na2Mg10 cuboctahedra; faces with two equivalent Hf(1)Mg12 cuboctahedra; faces with four equivalent Mg(2)Hf2Mg10 cuboctahedra; and faces with ten Mg(3,3)NaHfMg10 cuboctahedra. Both Mg(2)-Mg(4) bond lengths are 3.18 Å. There are two shorter (3.18 Å) and two longer (3.29 Å) Mg(2)-Mg(2) bond lengths. All Mg(2)-Mg(3) bond lengths are 3.13 Å. Both Mg(2)-Hf(1) bond lengths are 3.24 Å. In the third Mg site, Mg(3) is bonded to one Na(1); two equivalent Mg(1); two equivalent Mg(2); two equivalent Mg(4); four Mg(3,3); and one Hf(1) atom to form distorted MgNaHfMg10 cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)NaHfMg10 cuboctahedra; edges with two equivalent Na(1)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Hf(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(1)Na2Mg10 cuboctahedra; edges with four Mg(3,3)NaHfMg10 cuboctahedra;  a faceface with one Na(1)Mg12 cuboctahedra;  a faceface with one Hf(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)Na2Mg10 cuboctahedra; and faces with six Mg(3,3)NaHfMg10 cuboctahedra. Both Mg(3)-Mg(4) bond lengths are 3.24 Å. There are two shorter (3.21 Å) and two longer (3.26 Å) Mg(3)-Mg(3,3) bond lengths. The Mg(3)-Hf(1) bond length is 3.12 Å. In the fourth Mg site, Mg(3) is bonded to one Na(1), two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), four equivalent Mg(3), and one Hf(1) atom to form distorted MgNaHfMg10 cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)NaHfMg10 cuboctahedra; edges with two equivalent Na(1)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Hf(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(1)Na2Mg10 cuboctahedra; edges with four equivalent Mg(3)NaHfMg10 cuboctahedra;  a faceface with one Na(1)Mg12 cuboctahedra;  a faceface with one Hf(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)Na2Mg10 cuboctahedra; and faces with six Mg(3,3)NaHfMg10 cuboctahedra. Both Mg(3)-Mg(1) bond lengths are 3.20 Å. Both Mg(3)-Mg(2) bond lengths are 3.13 Å. Both Mg(3)-Mg(4) bond lengths are 3.24 Å. The Mg(3)-Hf(1) bond length is 3.12 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)NaHfMg10 cuboctahedra; edges with six equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with six equivalent Mg(1)Na2Mg10 cuboctahedra; edges with six Mg(3,3)NaHfMg10 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Na(1)Mg12 cuboctahedra; faces with three equivalent Mg(2)Hf2Mg10 cuboctahedra; faces with three equivalent Mg(1)Na2Mg10 cuboctahedra; faces with three equivalent Hf(1)Mg12 cuboctahedra; and faces with six Mg(3,3)NaHfMg10 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)Na2Mg10 cuboctahedra; edges with six equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with twelve Mg(3,3)NaHfMg10 cuboctahedra; faces with two equivalent Na(1)Mg12 cuboctahedra; faces with six equivalent Mg(2)Hf2Mg10 cuboctahedra; faces with six equivalent Mg(4)Mg12 cuboctahedra; and faces with six Mg(3,3)NaHfMg10 cuboctahedra.