Mg14ZrCr crystallizes in the hexagonal P-6m2 space group. 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 Mg(3,3); and two equivalent Zr(1) atoms to form MgMg10Zr2 cuboctahedra that share corners with four equivalent Cr(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Zr2 cuboctahedra; corners with eight equivalent Mg(2)Mg10Cr2 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 Mg(3,3)Mg10ZrCr cuboctahedra; faces with two equivalent Mg(2)Mg10Cr2 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 Mg(3,3)Mg10ZrCr 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 Cr(1) atoms to form MgMg10Cr2 cuboctahedra that share corners with four equivalent Zr(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Cr2 cuboctahedra; corners with eight Mg(1,1)Mg10Zr2 cuboctahedra; edges with two equivalent Cr(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Cr2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)Mg10ZrCr cuboctahedra; faces with two equivalent Mg(1)Mg10Zr2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Cr(1)Mg12 cuboctahedra; faces with four equivalent Mg(2)Mg10Cr2 cuboctahedra; and faces with ten Mg(3,3)Mg10ZrCr 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 Cr(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Zr2 cuboctahedra; corners with eight equivalent Mg(2)Mg10Cr2 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)Mg10ZrCr cuboctahedra; faces with two equivalent Mg(2)Mg10Cr2 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 Mg(3,3)Mg10ZrCr cuboctahedra. In the fourth Mg site, Mg(3) is bonded to two Mg(1,1); two equivalent Mg(2); two equivalent Mg(4); four Mg(3,3); one Zr(1); and one Cr(1) atom to form distorted MgMg10ZrCr cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)Mg10ZrCr cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Zr(1)Mg12 cuboctahedra; edges with two equivalent Cr(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Cr2 cuboctahedra; edges with four Mg(1,1)Mg10Zr2 cuboctahedra; edges with four Mg(3,3)Mg10ZrCr cuboctahedra;  a faceface with one Zr(1)Mg12 cuboctahedra;  a faceface with one Cr(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five equivalent Mg(2)Mg10Cr2 cuboctahedra; faces with five Mg(1,1)Mg10Zr2 cuboctahedra; and faces with six Mg(3,3)Mg10ZrCr cuboctahedra. In the fifth Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), four equivalent Mg(3), one Zr(1), and one Cr(1) atom to form distorted MgMg10ZrCr cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)Mg10ZrCr cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Zr(1)Mg12 cuboctahedra; edges with two equivalent Cr(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Cr2 cuboctahedra; edges with four equivalent Mg(1)Mg10Zr2 cuboctahedra; edges with four equivalent Mg(3)Mg10ZrCr cuboctahedra;  a faceface with one Zr(1)Mg12 cuboctahedra;  a faceface with one Cr(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five equivalent Mg(2)Mg10Cr2 cuboctahedra; faces with five Mg(1,1)Mg10Zr2 cuboctahedra; and faces with six Mg(3,3)Mg10ZrCr cuboctahedra. In the sixth Mg site, Mg(4) is bonded to three Mg(1,1); 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)Mg10ZrCr cuboctahedra; edges with six equivalent Mg(2)Mg10Cr2 cuboctahedra; edges with six Mg(1,1)Mg10Zr2 cuboctahedra; edges with six Mg(3,3)Mg10ZrCr cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Mg(2)Mg10Cr2 cuboctahedra; faces with three Mg(1,1)Mg10Zr2 cuboctahedra; faces with three equivalent Zr(1)Mg12 cuboctahedra; faces with three equivalent Cr(1)Mg12 cuboctahedra; and faces with six Mg(3,3)Mg10ZrCr cuboctahedra. Zr(1) is bonded to six Mg(1,1) and six Mg(3,3) atoms to form ZrMg12 cuboctahedra that share corners with six equivalent Zr(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(2)Mg10Cr2 cuboctahedra; edges with six Mg(1,1)Mg10Zr2 cuboctahedra; edges with twelve Mg(3,3)Mg10ZrCr cuboctahedra; faces with two equivalent Cr(1)Mg12 cuboctahedra; faces with six Mg(1,1)Mg10Zr2 cuboctahedra; faces with six Mg(3,3)Mg10ZrCr cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. Cr(1) is bonded to six equivalent Mg(2) and six Mg(3,3) atoms to form CrMg12 cuboctahedra that share corners with six equivalent Cr(1)Mg12 cuboctahedra; corners with twelve Mg(1,1)Mg10Zr2 cuboctahedra; edges with six equivalent Mg(2)Mg10Cr2 cuboctahedra; edges with twelve Mg(3,3)Mg10ZrCr cuboctahedra; faces with two equivalent Zr(1)Mg12 cuboctahedra; faces with six equivalent Mg(2)Mg10Cr2 cuboctahedra; faces with six Mg(3,3)Mg10ZrCr cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra.
Mg14ZrCr crystallizes in the hexagonal P-6m2 space group. 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 Mg(3,3); and two equivalent Zr(1) atoms to form MgMg10Zr2 cuboctahedra that share corners with four equivalent Cr(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Zr2 cuboctahedra; corners with eight equivalent Mg(2)Mg10Cr2 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 Mg(3,3)Mg10ZrCr cuboctahedra; faces with two equivalent Mg(2)Mg10Cr2 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 Mg(3,3)Mg10ZrCr cuboctahedra. Both Mg(1)-Mg(4) bond lengths are 3.13 Å. There are two shorter (3.13 Å) and two longer (3.26 Å) Mg(1)-Mg(1,1) bond lengths. All Mg(1)-Mg(3,3) bond lengths are 3.15 Å. Both Mg(1)-Zr(1) bond lengths are 3.19 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 Cr(1) atoms to form MgMg10Cr2 cuboctahedra that share corners with four equivalent Zr(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Cr2 cuboctahedra; corners with eight Mg(1,1)Mg10Zr2 cuboctahedra; edges with two equivalent Cr(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Cr2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)Mg10ZrCr cuboctahedra; faces with two equivalent Mg(1)Mg10Zr2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Cr(1)Mg12 cuboctahedra; faces with four equivalent Mg(2)Mg10Cr2 cuboctahedra; and faces with ten Mg(3,3)Mg10ZrCr cuboctahedra. Both Mg(2)-Mg(4) bond lengths are 3.16 Å. All Mg(2)-Mg(2) bond lengths are 3.19 Å. All Mg(2)-Mg(3,3) bond lengths are 3.13 Å. Both Mg(2)-Cr(1) 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 Cr(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Zr2 cuboctahedra; corners with eight equivalent Mg(2)Mg10Cr2 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)Mg10ZrCr cuboctahedra; faces with two equivalent Mg(2)Mg10Cr2 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 Mg(3,3)Mg10ZrCr cuboctahedra. Both Mg(1)-Mg(4) bond lengths are 3.13 Å. All Mg(1)-Mg(3) bond lengths are 3.15 Å. Both Mg(1)-Zr(1) bond lengths are 3.19 Å. In the fourth Mg site, Mg(3) is bonded to two Mg(1,1); two equivalent Mg(2); two equivalent Mg(4); four Mg(3,3); one Zr(1); and one Cr(1) atom to form distorted MgMg10ZrCr cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)Mg10ZrCr cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Zr(1)Mg12 cuboctahedra; edges with two equivalent Cr(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Cr2 cuboctahedra; edges with four Mg(1,1)Mg10Zr2 cuboctahedra; edges with four Mg(3,3)Mg10ZrCr cuboctahedra;  a faceface with one Zr(1)Mg12 cuboctahedra;  a faceface with one Cr(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five equivalent Mg(2)Mg10Cr2 cuboctahedra; faces with five Mg(1,1)Mg10Zr2 cuboctahedra; and faces with six Mg(3,3)Mg10ZrCr cuboctahedra. Both Mg(3)-Mg(4) bond lengths are 3.19 Å. There are two shorter (3.11 Å) and two longer (3.27 Å) Mg(3)-Mg(3,3) bond lengths. The Mg(3)-Zr(1) bond length is 3.12 Å. The Mg(3)-Cr(1) bond length is 3.08 Å. In the fifth Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), four equivalent Mg(3), one Zr(1), and one Cr(1) atom to form distorted MgMg10ZrCr cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)Mg10ZrCr cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Zr(1)Mg12 cuboctahedra; edges with two equivalent Cr(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Cr2 cuboctahedra; edges with four equivalent Mg(1)Mg10Zr2 cuboctahedra; edges with four equivalent Mg(3)Mg10ZrCr cuboctahedra;  a faceface with one Zr(1)Mg12 cuboctahedra;  a faceface with one Cr(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five equivalent Mg(2)Mg10Cr2 cuboctahedra; faces with five Mg(1,1)Mg10Zr2 cuboctahedra; and faces with six Mg(3,3)Mg10ZrCr cuboctahedra. Both Mg(3)-Mg(4) bond lengths are 3.19 Å. The Mg(3)-Zr(1) bond length is 3.12 Å. The Mg(3)-Cr(1) bond length is 3.08 Å. In the sixth Mg site, Mg(4) is bonded to three Mg(1,1); 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)Mg10ZrCr cuboctahedra; edges with six equivalent Mg(2)Mg10Cr2 cuboctahedra; edges with six Mg(1,1)Mg10Zr2 cuboctahedra; edges with six Mg(3,3)Mg10ZrCr cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Mg(2)Mg10Cr2 cuboctahedra; faces with three Mg(1,1)Mg10Zr2 cuboctahedra; faces with three equivalent Zr(1)Mg12 cuboctahedra; faces with three equivalent Cr(1)Mg12 cuboctahedra; and faces with six Mg(3,3)Mg10ZrCr cuboctahedra. Zr(1) is bonded to six Mg(1,1) and six Mg(3,3) atoms to form ZrMg12 cuboctahedra that share corners with six equivalent Zr(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(2)Mg10Cr2 cuboctahedra; edges with six Mg(1,1)Mg10Zr2 cuboctahedra; edges with twelve Mg(3,3)Mg10ZrCr cuboctahedra; faces with two equivalent Cr(1)Mg12 cuboctahedra; faces with six Mg(1,1)Mg10Zr2 cuboctahedra; faces with six Mg(3,3)Mg10ZrCr cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. Cr(1) is bonded to six equivalent Mg(2) and six Mg(3,3) atoms to form CrMg12 cuboctahedra that share corners with six equivalent Cr(1)Mg12 cuboctahedra; corners with twelve Mg(1,1)Mg10Zr2 cuboctahedra; edges with six equivalent Mg(2)Mg10Cr2 cuboctahedra; edges with twelve Mg(3,3)Mg10ZrCr cuboctahedra; faces with two equivalent Zr(1)Mg12 cuboctahedra; faces with six equivalent Mg(2)Mg10Cr2 cuboctahedra; faces with six Mg(3,3)Mg10ZrCr cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra.