Mg15Zr is Magnesium-derived structured and crystallizes in the hexagonal P-6m2 space group. There are seven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to six equivalent Mg(3) and six Mg(4,4) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(1)Mg12 cuboctahedra; corners with twelve Mg(2,2)Mg10Zr2 cuboctahedra; edges with six equivalent Mg(3)Mg12 cuboctahedra; edges with twelve Mg(4,4)Mg11Zr cuboctahedra; faces with two equivalent Zr(1)Mg12 cuboctahedra; faces with six Mg(4,4)Mg11Zr cuboctahedra; faces with six equivalent Mg(3)Mg12 cuboctahedra; and faces with six equivalent Mg(5)Mg12 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(5), four equivalent Mg(2), four equivalent Mg(4), and two equivalent Zr(1) atoms to form MgMg10Zr2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Zr2 cuboctahedra; corners with eight equivalent Mg(3)Mg12 cuboctahedra; edges with two equivalent Zr(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Zr2 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight equivalent Mg(4)Mg11Zr cuboctahedra; faces with two equivalent Mg(3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with two equivalent Zr(1)Mg12 cuboctahedra; faces with four equivalent Mg(2)Mg10Zr2 cuboctahedra; and faces with ten Mg(4,4)Mg11Zr cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(5), four equivalent Mg(3), and four equivalent Mg(4) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Zr(1)Mg12 cuboctahedra; corners with six equivalent Mg(3)Mg12 cuboctahedra; corners with eight equivalent Mg(2)Mg10Zr2 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Mg(3)Mg12 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight equivalent Mg(4)Mg11Zr cuboctahedra; faces with two equivalent Mg(2)Mg10Zr2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with four equivalent Mg(3)Mg12 cuboctahedra; and faces with ten Mg(4,4)Mg11Zr cuboctahedra. In the fourth Mg site, Mg(2) is bonded to two equivalent Mg(5); four Mg(2,2); four Mg(4,4); and two equivalent Zr(1) atoms to form MgMg10Zr2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Zr2 cuboctahedra; corners with eight equivalent Mg(3)Mg12 cuboctahedra; edges with two equivalent Zr(1)Mg12 cuboctahedra; edges with four Mg(2,2)Mg10Zr2 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight Mg(4,4)Mg11Zr cuboctahedra; faces with two equivalent Mg(3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with two equivalent Zr(1)Mg12 cuboctahedra; faces with four Mg(2,2)Mg10Zr2 cuboctahedra; and faces with ten Mg(4,4)Mg11Zr cuboctahedra. In the fifth Mg site, Mg(4) is bonded to one Mg(1); two Mg(2,2); two equivalent Mg(3); two equivalent Mg(5); four Mg(4,4); and one Zr(1) atom to form MgMg11Zr cuboctahedra that share corners with four equivalent Mg(5)Mg12 cuboctahedra; corners with fourteen Mg(4,4)Mg11Zr cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(5)Mg12 cuboctahedra; edges with two equivalent Zr(1)Mg12 cuboctahedra; edges with four Mg(2,2)Mg10Zr2 cuboctahedra; edges with four Mg(4,4)Mg11Zr cuboctahedra; edges with four equivalent Mg(3)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Zr(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with five Mg(2,2)Mg10Zr2 cuboctahedra; faces with five equivalent Mg(3)Mg12 cuboctahedra; and faces with six Mg(4,4)Mg11Zr cuboctahedra. In the sixth Mg site, Mg(4) is bonded to one Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(5), four equivalent Mg(4), and one Zr(1) atom to form MgMg11Zr cuboctahedra that share corners with four equivalent Mg(5)Mg12 cuboctahedra; corners with fourteen Mg(4,4)Mg11Zr cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(5)Mg12 cuboctahedra; edges with two equivalent Zr(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Zr2 cuboctahedra; edges with four equivalent Mg(4)Mg11Zr cuboctahedra; edges with four equivalent Mg(3)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Zr(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with five Mg(2,2)Mg10Zr2 cuboctahedra; faces with five equivalent Mg(3)Mg12 cuboctahedra; and faces with six Mg(4,4)Mg11Zr cuboctahedra. In the seventh Mg site, Mg(5) is bonded to three Mg(2,2); three equivalent Mg(3); and six Mg(4,4) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(5)Mg12 cuboctahedra; corners with twelve Mg(4,4)Mg11Zr cuboctahedra; edges with six Mg(2,2)Mg10Zr2 cuboctahedra; edges with six Mg(4,4)Mg11Zr cuboctahedra; edges with six equivalent Mg(3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with three Mg(2,2)Mg10Zr2 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; faces with three equivalent Mg(3)Mg12 cuboctahedra; faces with three equivalent Zr(1)Mg12 cuboctahedra; and faces with six Mg(4,4)Mg11Zr cuboctahedra. Zr(1) is bonded to six Mg(2,2) and six Mg(4,4) atoms to form ZrMg12 cuboctahedra that share corners with six equivalent Zr(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(3)Mg12 cuboctahedra; edges with six Mg(2,2)Mg10Zr2 cuboctahedra; edges with twelve Mg(4,4)Mg11Zr cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with six Mg(2,2)Mg10Zr2 cuboctahedra; faces with six Mg(4,4)Mg11Zr cuboctahedra; and faces with six equivalent Mg(5)Mg12 cuboctahedra.
Mg15Zr is Magnesium-derived structured and crystallizes in the hexagonal P-6m2 space group. There are seven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to six equivalent Mg(3) and six Mg(4,4) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(1)Mg12 cuboctahedra; corners with twelve Mg(2,2)Mg10Zr2 cuboctahedra; edges with six equivalent Mg(3)Mg12 cuboctahedra; edges with twelve Mg(4,4)Mg11Zr cuboctahedra; faces with two equivalent Zr(1)Mg12 cuboctahedra; faces with six Mg(4,4)Mg11Zr cuboctahedra; faces with six equivalent Mg(3)Mg12 cuboctahedra; and faces with six equivalent Mg(5)Mg12 cuboctahedra. All Mg(1)-Mg(3) bond lengths are 3.19 Å. All Mg(1)-Mg(4,4) bond lengths are 3.14 Å. In the second Mg site, Mg(2) is bonded to two equivalent Mg(5), four equivalent Mg(2), four equivalent Mg(4), and two equivalent Zr(1) atoms to form MgMg10Zr2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Zr2 cuboctahedra; corners with eight equivalent Mg(3)Mg12 cuboctahedra; edges with two equivalent Zr(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Zr2 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight equivalent Mg(4)Mg11Zr cuboctahedra; faces with two equivalent Mg(3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with two equivalent Zr(1)Mg12 cuboctahedra; faces with four equivalent Mg(2)Mg10Zr2 cuboctahedra; and faces with ten Mg(4,4)Mg11Zr cuboctahedra. Both Mg(2)-Mg(5) bond lengths are 3.12 Å. There are two shorter (3.12 Å) and two longer (3.26 Å) Mg(2)-Mg(2) bond lengths. All Mg(2)-Mg(4) bond lengths are 3.12 Å. Both Mg(2)-Zr(1) bond lengths are 3.19 Å. In the third Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(5), four equivalent Mg(3), and four equivalent Mg(4) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Zr(1)Mg12 cuboctahedra; corners with six equivalent Mg(3)Mg12 cuboctahedra; corners with eight equivalent Mg(2)Mg10Zr2 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Mg(3)Mg12 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight equivalent Mg(4)Mg11Zr cuboctahedra; faces with two equivalent Mg(2)Mg10Zr2 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with four equivalent Mg(3)Mg12 cuboctahedra; and faces with ten Mg(4,4)Mg11Zr cuboctahedra. Both Mg(3)-Mg(5) bond lengths are 3.18 Å. There are two shorter (3.19 Å) and two longer (3.20 Å) Mg(3)-Mg(3) bond lengths. All Mg(3)-Mg(4) bond lengths are 3.17 Å. In the fourth Mg site, Mg(2) is bonded to two equivalent Mg(5); four Mg(2,2); four Mg(4,4); and two equivalent Zr(1) atoms to form MgMg10Zr2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Zr2 cuboctahedra; corners with eight equivalent Mg(3)Mg12 cuboctahedra; edges with two equivalent Zr(1)Mg12 cuboctahedra; edges with four Mg(2,2)Mg10Zr2 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight Mg(4,4)Mg11Zr cuboctahedra; faces with two equivalent Mg(3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with two equivalent Zr(1)Mg12 cuboctahedra; faces with four Mg(2,2)Mg10Zr2 cuboctahedra; and faces with ten Mg(4,4)Mg11Zr cuboctahedra. Both Mg(2)-Mg(5) bond lengths are 3.12 Å. There is one shorter (3.12 Å) and one longer (3.26 Å) Mg(2)-Mg(2) bond length. All Mg(2)-Mg(4,4) bond lengths are 3.12 Å. Both Mg(2)-Zr(1) bond lengths are 3.19 Å. In the fifth Mg site, Mg(4) is bonded to one Mg(1); two Mg(2,2); two equivalent Mg(3); two equivalent Mg(5); four Mg(4,4); and one Zr(1) atom to form MgMg11Zr cuboctahedra that share corners with four equivalent Mg(5)Mg12 cuboctahedra; corners with fourteen Mg(4,4)Mg11Zr cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(5)Mg12 cuboctahedra; edges with two equivalent Zr(1)Mg12 cuboctahedra; edges with four Mg(2,2)Mg10Zr2 cuboctahedra; edges with four Mg(4,4)Mg11Zr cuboctahedra; edges with four equivalent Mg(3)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Zr(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with five Mg(2,2)Mg10Zr2 cuboctahedra; faces with five equivalent Mg(3)Mg12 cuboctahedra; and faces with six Mg(4,4)Mg11Zr cuboctahedra. Both Mg(4)-Mg(5) bond lengths are 3.19 Å. There are two shorter (3.14 Å) and two longer (3.25 Å) Mg(4)-Mg(4,4) bond lengths. The Mg(4)-Zr(1) bond length is 3.10 Å. In the sixth Mg site, Mg(4) is bonded to one Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(5), four equivalent Mg(4), and one Zr(1) atom to form MgMg11Zr cuboctahedra that share corners with four equivalent Mg(5)Mg12 cuboctahedra; corners with fourteen Mg(4,4)Mg11Zr cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(5)Mg12 cuboctahedra; edges with two equivalent Zr(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Zr2 cuboctahedra; edges with four equivalent Mg(4)Mg11Zr cuboctahedra; edges with four equivalent Mg(3)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Zr(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with five Mg(2,2)Mg10Zr2 cuboctahedra; faces with five equivalent Mg(3)Mg12 cuboctahedra; and faces with six Mg(4,4)Mg11Zr cuboctahedra. Both Mg(4)-Mg(3) bond lengths are 3.17 Å. Both Mg(4)-Mg(5) bond lengths are 3.19 Å. The Mg(4)-Zr(1) bond length is 3.10 Å. In the seventh Mg site, Mg(5) is bonded to three Mg(2,2); three equivalent Mg(3); and six Mg(4,4) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(5)Mg12 cuboctahedra; corners with twelve Mg(4,4)Mg11Zr cuboctahedra; edges with six Mg(2,2)Mg10Zr2 cuboctahedra; edges with six Mg(4,4)Mg11Zr cuboctahedra; edges with six equivalent Mg(3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with three Mg(2,2)Mg10Zr2 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; faces with three equivalent Mg(3)Mg12 cuboctahedra; faces with three equivalent Zr(1)Mg12 cuboctahedra; and faces with six Mg(4,4)Mg11Zr cuboctahedra. Zr(1) is bonded to six Mg(2,2) and six Mg(4,4) atoms to form ZrMg12 cuboctahedra that share corners with six equivalent Zr(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(3)Mg12 cuboctahedra; edges with six Mg(2,2)Mg10Zr2 cuboctahedra; edges with twelve Mg(4,4)Mg11Zr cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with six Mg(2,2)Mg10Zr2 cuboctahedra; faces with six Mg(4,4)Mg11Zr cuboctahedra; and faces with six equivalent Mg(5)Mg12 cuboctahedra.