NaMg14Zr crystallizes in the hexagonal P-6m2 space group. Na(1) is bonded to six Mg(2,2) and six equivalent Mg(3) atoms to form NaMg12 cuboctahedra that share corners with six equivalent Na(1)Mg12 cuboctahedra; corners with twelve Mg(1,1)Mg10Zr2 cuboctahedra; edges with six Mg(2,2)Na2Mg10 cuboctahedra; edges with twelve equivalent Mg(3)NaMg10Zr cuboctahedra; faces with two equivalent Zr(1)Mg12 cuboctahedra; faces with six equivalent Mg(4)Mg12 cuboctahedra; faces with six Mg(2,2)Na2Mg10 cuboctahedra; and faces with six equivalent Mg(3)NaMg10Zr cuboctahedra. There are six inequivalent Mg sites. In the first 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 Na(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Zr2 cuboctahedra; corners with eight Mg(2,2)Na2Mg10 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)NaMg10Zr cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(2)Na2Mg10 cuboctahedra; faces with two equivalent Zr(1)Mg12 cuboctahedra; faces with four Mg(1,1)Mg10Zr2 cuboctahedra; and faces with ten equivalent Mg(3)NaMg10Zr cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Na(1); two equivalent Mg(4); four Mg(2,2); and four equivalent Mg(3) atoms to form distorted MgNa2Mg10 cuboctahedra that share corners with four equivalent Zr(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Na2Mg10 cuboctahedra; corners with eight Mg(1,1)Mg10Zr2 cuboctahedra; edges with two equivalent Na(1)Mg12 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with four Mg(2,2)Na2Mg10 cuboctahedra; edges with eight equivalent Mg(3)NaMg10Zr cuboctahedra; faces with two equivalent Na(1)Mg12 cuboctahedra; faces with two equivalent Mg(1)Mg10Zr2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with four Mg(2,2)Na2Mg10 cuboctahedra; and faces with ten equivalent Mg(3)NaMg10Zr cuboctahedra. In the third 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 Na(1)Mg12 cuboctahedra, corners with six equivalent Mg(1)Mg10Zr2 cuboctahedra, corners with eight equivalent Mg(2)Na2Mg10 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)NaMg10Zr cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(2)Na2Mg10 cuboctahedra, faces with two equivalent Zr(1)Mg12 cuboctahedra, faces with four equivalent Mg(1)Mg10Zr2 cuboctahedra, and faces with ten equivalent Mg(3)NaMg10Zr cuboctahedra. In the fourth Mg site, Mg(2) is bonded to two equivalent Na(1), two equivalent Mg(4), four equivalent Mg(2), and four equivalent Mg(3) atoms to form distorted MgNa2Mg10 cuboctahedra that share corners with four equivalent Zr(1)Mg12 cuboctahedra, corners with six equivalent Mg(2)Na2Mg10 cuboctahedra, corners with eight equivalent Mg(1)Mg10Zr2 cuboctahedra, edges with two equivalent Na(1)Mg12 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with four equivalent Mg(2)Na2Mg10 cuboctahedra, edges with eight equivalent Mg(3)NaMg10Zr cuboctahedra, faces with two equivalent Na(1)Mg12 cuboctahedra, faces with two equivalent Mg(1)Mg10Zr2 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with four equivalent Mg(2)Na2Mg10 cuboctahedra, and faces with ten equivalent Mg(3)NaMg10Zr cuboctahedra. In the fifth Mg site, Mg(3) is bonded to one Na(1); two Mg(1,1); two Mg(2,2); two equivalent Mg(4); four equivalent Mg(3); and one Zr(1) atom to form distorted MgNaMg10Zr cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen equivalent Mg(3)NaMg10Zr cuboctahedra; edges with two equivalent Na(1)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Zr(1)Mg12 cuboctahedra; edges with four Mg(1,1)Mg10Zr2 cuboctahedra; edges with four Mg(2,2)Na2Mg10 cuboctahedra; edges with four equivalent Mg(3)NaMg10Zr cuboctahedra;  a faceface with one Na(1)Mg12 cuboctahedra;  a faceface with one Zr(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(1,1)Mg10Zr2 cuboctahedra; faces with five Mg(2,2)Na2Mg10 cuboctahedra; and faces with six equivalent Mg(3)NaMg10Zr cuboctahedra. In the sixth Mg site, Mg(4) is bonded to three Mg(1,1); three Mg(2,2); 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)NaMg10Zr cuboctahedra; edges with six Mg(1,1)Mg10Zr2 cuboctahedra; edges with six Mg(2,2)Na2Mg10 cuboctahedra; edges with six equivalent Mg(3)NaMg10Zr cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Na(1)Mg12 cuboctahedra; faces with three Mg(1,1)Mg10Zr2 cuboctahedra; faces with three Mg(2,2)Na2Mg10 cuboctahedra; faces with three equivalent Zr(1)Mg12 cuboctahedra; and faces with six equivalent Mg(3)NaMg10Zr 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; corners with twelve Mg(2,2)Na2Mg10 cuboctahedra; edges with six Mg(1,1)Mg10Zr2 cuboctahedra; edges with twelve equivalent Mg(3)NaMg10Zr cuboctahedra; faces with two equivalent Na(1)Mg12 cuboctahedra; faces with six Mg(1,1)Mg10Zr2 cuboctahedra; faces with six equivalent Mg(4)Mg12 cuboctahedra; and faces with six equivalent Mg(3)NaMg10Zr cuboctahedra.
NaMg14Zr crystallizes in the hexagonal P-6m2 space group. Na(1) is bonded to six Mg(2,2) and six equivalent Mg(3) atoms to form NaMg12 cuboctahedra that share corners with six equivalent Na(1)Mg12 cuboctahedra; corners with twelve Mg(1,1)Mg10Zr2 cuboctahedra; edges with six Mg(2,2)Na2Mg10 cuboctahedra; edges with twelve equivalent Mg(3)NaMg10Zr cuboctahedra; faces with two equivalent Zr(1)Mg12 cuboctahedra; faces with six equivalent Mg(4)Mg12 cuboctahedra; faces with six Mg(2,2)Na2Mg10 cuboctahedra; and faces with six equivalent Mg(3)NaMg10Zr cuboctahedra. All Na(1)-Mg(2,2) bond lengths are 3.25 Å. All Na(1)-Mg(3) bond lengths are 3.19 Å. There are six inequivalent Mg sites. In the first 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 Na(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Zr2 cuboctahedra; corners with eight Mg(2,2)Na2Mg10 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)NaMg10Zr cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(2)Na2Mg10 cuboctahedra; faces with two equivalent Zr(1)Mg12 cuboctahedra; faces with four Mg(1,1)Mg10Zr2 cuboctahedra; and faces with ten equivalent Mg(3)NaMg10Zr cuboctahedra. Both Mg(1)-Mg(4) bond lengths are 3.17 Å. There are two shorter (3.20 Å) and two longer (3.30 Å) Mg(1)-Mg(1,1) bond lengths. All Mg(1)-Mg(3) bond lengths are 3.13 Å. Both Mg(1)-Zr(1) bond lengths are 3.25 Å. In the second Mg site, Mg(2) is bonded to two equivalent Na(1); two equivalent Mg(4); four Mg(2,2); and four equivalent Mg(3) atoms to form distorted MgNa2Mg10 cuboctahedra that share corners with four equivalent Zr(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Na2Mg10 cuboctahedra; corners with eight Mg(1,1)Mg10Zr2 cuboctahedra; edges with two equivalent Na(1)Mg12 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with four Mg(2,2)Na2Mg10 cuboctahedra; edges with eight equivalent Mg(3)NaMg10Zr cuboctahedra; faces with two equivalent Na(1)Mg12 cuboctahedra; faces with two equivalent Mg(1)Mg10Zr2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with four Mg(2,2)Na2Mg10 cuboctahedra; and faces with ten equivalent Mg(3)NaMg10Zr cuboctahedra. Both Mg(2)-Mg(4) bond lengths are 3.18 Å. There are two shorter (3.22 Å) and two longer (3.28 Å) Mg(2)-Mg(2,2) bond lengths. All Mg(2)-Mg(3) bond lengths are 3.19 Å. In the third 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 Na(1)Mg12 cuboctahedra, corners with six equivalent Mg(1)Mg10Zr2 cuboctahedra, corners with eight equivalent Mg(2)Na2Mg10 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)NaMg10Zr cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(2)Na2Mg10 cuboctahedra, faces with two equivalent Zr(1)Mg12 cuboctahedra, faces with four equivalent Mg(1)Mg10Zr2 cuboctahedra, and faces with ten equivalent Mg(3)NaMg10Zr cuboctahedra. Both Mg(1)-Mg(4) bond lengths are 3.17 Å. All Mg(1)-Mg(3) bond lengths are 3.13 Å. Both Mg(1)-Zr(1) bond lengths are 3.25 Å. In the fourth Mg site, Mg(2) is bonded to two equivalent Na(1), two equivalent Mg(4), four equivalent Mg(2), and four equivalent Mg(3) atoms to form distorted MgNa2Mg10 cuboctahedra that share corners with four equivalent Zr(1)Mg12 cuboctahedra, corners with six equivalent Mg(2)Na2Mg10 cuboctahedra, corners with eight equivalent Mg(1)Mg10Zr2 cuboctahedra, edges with two equivalent Na(1)Mg12 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with four equivalent Mg(2)Na2Mg10 cuboctahedra, edges with eight equivalent Mg(3)NaMg10Zr cuboctahedra, faces with two equivalent Na(1)Mg12 cuboctahedra, faces with two equivalent Mg(1)Mg10Zr2 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with four equivalent Mg(2)Na2Mg10 cuboctahedra, and faces with ten equivalent Mg(3)NaMg10Zr cuboctahedra. Both Mg(2)-Mg(4) bond lengths are 3.18 Å. All Mg(2)-Mg(3) bond lengths are 3.19 Å. In the fifth Mg site, Mg(3) is bonded to one Na(1); two Mg(1,1); two Mg(2,2); two equivalent Mg(4); four equivalent Mg(3); and one Zr(1) atom to form distorted MgNaMg10Zr cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen equivalent Mg(3)NaMg10Zr cuboctahedra; edges with two equivalent Na(1)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Zr(1)Mg12 cuboctahedra; edges with four Mg(1,1)Mg10Zr2 cuboctahedra; edges with four Mg(2,2)Na2Mg10 cuboctahedra; edges with four equivalent Mg(3)NaMg10Zr cuboctahedra;  a faceface with one Na(1)Mg12 cuboctahedra;  a faceface with one Zr(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(1,1)Mg10Zr2 cuboctahedra; faces with five Mg(2,2)Na2Mg10 cuboctahedra; and faces with six equivalent Mg(3)NaMg10Zr cuboctahedra. Both Mg(3)-Mg(4) bond lengths are 3.25 Å. There are two shorter (3.24 Å) and two longer (3.27 Å) Mg(3)-Mg(3) bond lengths. The Mg(3)-Zr(1) bond length is 3.13 Å. In the sixth Mg site, Mg(4) is bonded to three Mg(1,1); three Mg(2,2); 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)NaMg10Zr cuboctahedra; edges with six Mg(1,1)Mg10Zr2 cuboctahedra; edges with six Mg(2,2)Na2Mg10 cuboctahedra; edges with six equivalent Mg(3)NaMg10Zr cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Na(1)Mg12 cuboctahedra; faces with three Mg(1,1)Mg10Zr2 cuboctahedra; faces with three Mg(2,2)Na2Mg10 cuboctahedra; faces with three equivalent Zr(1)Mg12 cuboctahedra; and faces with six equivalent Mg(3)NaMg10Zr 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; corners with twelve Mg(2,2)Na2Mg10 cuboctahedra; edges with six Mg(1,1)Mg10Zr2 cuboctahedra; edges with twelve equivalent Mg(3)NaMg10Zr cuboctahedra; faces with two equivalent Na(1)Mg12 cuboctahedra; faces with six Mg(1,1)Mg10Zr2 cuboctahedra; faces with six equivalent Mg(4)Mg12 cuboctahedra; and faces with six equivalent Mg(3)NaMg10Zr cuboctahedra.