BaMg14Zr crystallizes in the hexagonal P-6m2 space group. Ba(1) is bonded to six equivalent Mg(2) and six Mg(3,3) atoms to form BaMg12 cuboctahedra that share corners with six equivalent Ba(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(1)Mg10Zr2 cuboctahedra; edges with twelve Mg(3,3)BaMg10Zr cuboctahedra; faces with two equivalent Zr(1)Mg12 cuboctahedra; faces with six Mg(3,3)BaMg10Zr cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. 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 Zr(1) atoms to form MgMg10Zr2 cuboctahedra that share corners with four equivalent Ba(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Zr2 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 Mg(3,3)BaMg10Zr 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)BaMg10Zr cuboctahedra. In the second Mg site, Mg(2) is bonded in a 12-coordinate geometry to two equivalent Ba(1); two equivalent Mg(4); four equivalent Mg(2); and four Mg(3,3) atoms. In the third Mg site, Mg(3) is bonded to one Ba(1); two equivalent Mg(1); two equivalent Mg(2); two equivalent Mg(4); four Mg(3,3); and one Zr(1) atom to form distorted MgBaMg10Zr cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)BaMg10Zr cuboctahedra; edges with two equivalent Ba(1)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Zr(1)Mg12 cuboctahedra; edges with four Mg(3,3)BaMg10Zr cuboctahedra; edges with four equivalent Mg(1)Mg10Zr2 cuboctahedra;  a faceface with one Ba(1)Mg12 cuboctahedra;  a faceface with one Zr(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five equivalent Mg(1)Mg10Zr2 cuboctahedra; and faces with six Mg(3,3)BaMg10Zr cuboctahedra. In the fourth Mg site, Mg(3) is bonded to one Ba(1), two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), four equivalent Mg(3), and one Zr(1) atom to form distorted MgBaMg10Zr cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)BaMg10Zr cuboctahedra; edges with two equivalent Ba(1)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Zr(1)Mg12 cuboctahedra; edges with four equivalent Mg(3)BaMg10Zr cuboctahedra; edges with four equivalent Mg(1)Mg10Zr2 cuboctahedra;  a faceface with one Ba(1)Mg12 cuboctahedra;  a faceface with one Zr(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five equivalent Mg(1)Mg10Zr2 cuboctahedra; and faces with six Mg(3,3)BaMg10Zr 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)BaMg10Zr cuboctahedra; edges with six Mg(3,3)BaMg10Zr cuboctahedra; edges with six equivalent Mg(1)Mg10Zr2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Ba(1)Mg12 cuboctahedra; faces with three equivalent Mg(1)Mg10Zr2 cuboctahedra; faces with three equivalent Zr(1)Mg12 cuboctahedra; and faces with six Mg(3,3)BaMg10Zr cuboctahedra. Zr(1) is bonded to six equivalent Mg(1) and six Mg(3,3) atoms to form ZrMg12 cuboctahedra that share corners with six equivalent Zr(1)Mg12 cuboctahedra; edges with six equivalent Mg(1)Mg10Zr2 cuboctahedra; edges with twelve Mg(3,3)BaMg10Zr cuboctahedra; faces with two equivalent Ba(1)Mg12 cuboctahedra; faces with six Mg(3,3)BaMg10Zr cuboctahedra; faces with six equivalent Mg(1)Mg10Zr2 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra.
BaMg14Zr crystallizes in the hexagonal P-6m2 space group. Ba(1) is bonded to six equivalent Mg(2) and six Mg(3,3) atoms to form BaMg12 cuboctahedra that share corners with six equivalent Ba(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(1)Mg10Zr2 cuboctahedra; edges with twelve Mg(3,3)BaMg10Zr cuboctahedra; faces with two equivalent Zr(1)Mg12 cuboctahedra; faces with six Mg(3,3)BaMg10Zr cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. All Ba(1)-Mg(2) bond lengths are 3.33 Å. All Ba(1)-Mg(3,3) bond lengths are 3.37 Å. 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 Zr(1) atoms to form MgMg10Zr2 cuboctahedra that share corners with four equivalent Ba(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Zr2 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 Mg(3,3)BaMg10Zr 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)BaMg10Zr cuboctahedra. Both Mg(1)-Mg(4) bond lengths are 3.26 Å. All Mg(1)-Mg(1) bond lengths are 3.33 Å. All Mg(1)-Mg(3,3) bond lengths are 3.09 Å. Both Mg(1)-Zr(1) bond lengths are 3.33 Å. In the second Mg site, Mg(2) is bonded in a 12-coordinate geometry to two equivalent Ba(1); two equivalent Mg(4); four equivalent Mg(2); and four Mg(3,3) atoms. Both Mg(2)-Mg(4) bond lengths are 3.24 Å. There are two shorter (3.20 Å) and two longer (3.47 Å) Mg(2)-Mg(2) bond lengths. All Mg(2)-Mg(3,3) bond lengths are 3.31 Å. In the third Mg site, Mg(3) is bonded to one Ba(1); two equivalent Mg(1); two equivalent Mg(2); two equivalent Mg(4); four Mg(3,3); and one Zr(1) atom to form distorted MgBaMg10Zr cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)BaMg10Zr cuboctahedra; edges with two equivalent Ba(1)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Zr(1)Mg12 cuboctahedra; edges with four Mg(3,3)BaMg10Zr cuboctahedra; edges with four equivalent Mg(1)Mg10Zr2 cuboctahedra;  a faceface with one Ba(1)Mg12 cuboctahedra;  a faceface with one Zr(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five equivalent Mg(1)Mg10Zr2 cuboctahedra; and faces with six Mg(3,3)BaMg10Zr cuboctahedra. Both Mg(3)-Mg(4) bond lengths are 3.34 Å. There are two shorter (3.25 Å) and two longer (3.42 Å) Mg(3)-Mg(3,3) bond lengths. The Mg(3)-Zr(1) bond length is 3.14 Å. In the fourth Mg site, Mg(3) is bonded to one Ba(1), two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), four equivalent Mg(3), and one Zr(1) atom to form distorted MgBaMg10Zr cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)BaMg10Zr cuboctahedra; edges with two equivalent Ba(1)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Zr(1)Mg12 cuboctahedra; edges with four equivalent Mg(3)BaMg10Zr cuboctahedra; edges with four equivalent Mg(1)Mg10Zr2 cuboctahedra;  a faceface with one Ba(1)Mg12 cuboctahedra;  a faceface with one Zr(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five equivalent Mg(1)Mg10Zr2 cuboctahedra; and faces with six Mg(3,3)BaMg10Zr cuboctahedra. Both Mg(3)-Mg(4) bond lengths are 3.34 Å. The Mg(3)-Zr(1) bond length is 3.14 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)BaMg10Zr cuboctahedra; edges with six Mg(3,3)BaMg10Zr cuboctahedra; edges with six equivalent Mg(1)Mg10Zr2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Ba(1)Mg12 cuboctahedra; faces with three equivalent Mg(1)Mg10Zr2 cuboctahedra; faces with three equivalent Zr(1)Mg12 cuboctahedra; and faces with six Mg(3,3)BaMg10Zr cuboctahedra. Zr(1) is bonded to six equivalent Mg(1) and six Mg(3,3) atoms to form ZrMg12 cuboctahedra that share corners with six equivalent Zr(1)Mg12 cuboctahedra; edges with six equivalent Mg(1)Mg10Zr2 cuboctahedra; edges with twelve Mg(3,3)BaMg10Zr cuboctahedra; faces with two equivalent Ba(1)Mg12 cuboctahedra; faces with six Mg(3,3)BaMg10Zr cuboctahedra; faces with six equivalent Mg(1)Mg10Zr2 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra.