BaMg14Cd crystallizes in the hexagonal P-6m2 space group. Ba(1) is bonded to six Mg(1,1) and six equivalent Mg(3) atoms to form BaMg12 cuboctahedra that share corners with six equivalent Ba(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(2)Mg10Cd2 cuboctahedra; edges with six Mg(1,1)Ba2Mg10 cuboctahedra; faces with two equivalent Cd(1)Mg12 cuboctahedra; faces with six Mg(1,1)Ba2Mg10 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 Ba(1); two equivalent Mg(4); four Mg(1,1); and four equivalent Mg(3) atoms to form distorted MgBa2Mg10 cuboctahedra that share corners with four equivalent Cd(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Ba2Mg10 cuboctahedra; corners with eight equivalent Mg(2)Mg10Cd2 cuboctahedra; edges with two equivalent Ba(1)Mg12 cuboctahedra; edges with four Mg(1,1)Ba2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Ba(1)Mg12 cuboctahedra; faces with two equivalent Mg(2)Mg10Cd2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; and faces with four Mg(1,1)Ba2Mg10 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 Cd(1) atoms to form distorted MgMg10Cd2 cuboctahedra that share corners with four equivalent Ba(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Cd2 cuboctahedra; corners with eight Mg(1,1)Ba2Mg10 cuboctahedra; edges with two equivalent Cd(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Cd2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(1)Ba2Mg10 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Cd(1)Mg12 cuboctahedra; and faces with four equivalent Mg(2)Mg10Cd2 cuboctahedra. In the third Mg site, Mg(1) is bonded to two equivalent Ba(1), two equivalent Mg(4), four equivalent Mg(1), and four equivalent Mg(3) atoms to form distorted MgBa2Mg10 cuboctahedra that share corners with four equivalent Cd(1)Mg12 cuboctahedra, corners with six equivalent Mg(1)Ba2Mg10 cuboctahedra, corners with eight equivalent Mg(2)Mg10Cd2 cuboctahedra, edges with two equivalent Ba(1)Mg12 cuboctahedra, edges with four equivalent Mg(1)Ba2Mg10 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Ba(1)Mg12 cuboctahedra, faces with two equivalent Mg(2)Mg10Cd2 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, and faces with four equivalent Mg(1)Ba2Mg10 cuboctahedra. In the fourth Mg site, Mg(3) is bonded in a 12-coordinate geometry to one Ba(1); two Mg(1,1); two equivalent Mg(2); two equivalent Mg(4); four equivalent Mg(3); and one Cd(1) atom. In the fifth Mg site, Mg(4) is bonded to three Mg(1,1); three equivalent Mg(2); and six equivalent Mg(3) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(4)Mg12 cuboctahedra; edges with six Mg(1,1)Ba2Mg10 cuboctahedra; edges with six equivalent Mg(2)Mg10Cd2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Ba(1)Mg12 cuboctahedra; faces with three Mg(1,1)Ba2Mg10 cuboctahedra; faces with three equivalent Mg(2)Mg10Cd2 cuboctahedra; and faces with three equivalent Cd(1)Mg12 cuboctahedra. Cd(1) is bonded to six equivalent Mg(2) and six equivalent Mg(3) atoms to form CdMg12 cuboctahedra that share corners with six equivalent Cd(1)Mg12 cuboctahedra; corners with twelve Mg(1,1)Ba2Mg10 cuboctahedra; edges with six equivalent Mg(2)Mg10Cd2 cuboctahedra; faces with two equivalent Ba(1)Mg12 cuboctahedra; faces with six equivalent Mg(2)Mg10Cd2 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra.
BaMg14Cd crystallizes in the hexagonal P-6m2 space group. Ba(1) is bonded to six Mg(1,1) and six equivalent Mg(3) atoms to form BaMg12 cuboctahedra that share corners with six equivalent Ba(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(2)Mg10Cd2 cuboctahedra; edges with six Mg(1,1)Ba2Mg10 cuboctahedra; faces with two equivalent Cd(1)Mg12 cuboctahedra; faces with six Mg(1,1)Ba2Mg10 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. All Ba(1)-Mg(1,1) bond lengths are 3.32 Å. All Ba(1)-Mg(3) bond lengths are 3.43 Å. There are five inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Ba(1); two equivalent Mg(4); four Mg(1,1); and four equivalent Mg(3) atoms to form distorted MgBa2Mg10 cuboctahedra that share corners with four equivalent Cd(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Ba2Mg10 cuboctahedra; corners with eight equivalent Mg(2)Mg10Cd2 cuboctahedra; edges with two equivalent Ba(1)Mg12 cuboctahedra; edges with four Mg(1,1)Ba2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Ba(1)Mg12 cuboctahedra; faces with two equivalent Mg(2)Mg10Cd2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; and faces with four Mg(1,1)Ba2Mg10 cuboctahedra. Both Mg(1)-Mg(4) bond lengths are 3.27 Å. There are two shorter (3.20 Å) and two longer (3.45 Å) Mg(1)-Mg(1,1) bond lengths. All Mg(1)-Mg(3) bond lengths are 3.35 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 Cd(1) atoms to form distorted MgMg10Cd2 cuboctahedra that share corners with four equivalent Ba(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Mg10Cd2 cuboctahedra; corners with eight Mg(1,1)Ba2Mg10 cuboctahedra; edges with two equivalent Cd(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Mg10Cd2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Mg(1)Ba2Mg10 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Cd(1)Mg12 cuboctahedra; and faces with four equivalent Mg(2)Mg10Cd2 cuboctahedra. Both Mg(2)-Mg(4) bond lengths are 3.28 Å. There are two shorter (3.29 Å) and two longer (3.36 Å) Mg(2)-Mg(2) bond lengths. All Mg(2)-Mg(3) bond lengths are 3.12 Å. Both Mg(2)-Cd(1) bond lengths are 3.32 Å. In the third Mg site, Mg(1) is bonded to two equivalent Ba(1), two equivalent Mg(4), four equivalent Mg(1), and four equivalent Mg(3) atoms to form distorted MgBa2Mg10 cuboctahedra that share corners with four equivalent Cd(1)Mg12 cuboctahedra, corners with six equivalent Mg(1)Ba2Mg10 cuboctahedra, corners with eight equivalent Mg(2)Mg10Cd2 cuboctahedra, edges with two equivalent Ba(1)Mg12 cuboctahedra, edges with four equivalent Mg(1)Ba2Mg10 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Ba(1)Mg12 cuboctahedra, faces with two equivalent Mg(2)Mg10Cd2 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, and faces with four equivalent Mg(1)Ba2Mg10 cuboctahedra. Both Mg(1)-Mg(4) bond lengths are 3.27 Å. All Mg(1)-Mg(3) bond lengths are 3.35 Å. In the fourth Mg site, Mg(3) is bonded in a 12-coordinate geometry to one Ba(1); two Mg(1,1); two equivalent Mg(2); two equivalent Mg(4); four equivalent Mg(3); and one Cd(1) atom. Both Mg(3)-Mg(4) bond lengths are 3.33 Å. There are two shorter (3.21 Å) and two longer (3.43 Å) Mg(3)-Mg(3) bond lengths. The Mg(3)-Cd(1) bond length is 3.17 Å. In the fifth Mg site, Mg(4) is bonded to three Mg(1,1); three equivalent Mg(2); and six equivalent Mg(3) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(4)Mg12 cuboctahedra; edges with six Mg(1,1)Ba2Mg10 cuboctahedra; edges with six equivalent Mg(2)Mg10Cd2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Ba(1)Mg12 cuboctahedra; faces with three Mg(1,1)Ba2Mg10 cuboctahedra; faces with three equivalent Mg(2)Mg10Cd2 cuboctahedra; and faces with three equivalent Cd(1)Mg12 cuboctahedra. Cd(1) is bonded to six equivalent Mg(2) and six equivalent Mg(3) atoms to form CdMg12 cuboctahedra that share corners with six equivalent Cd(1)Mg12 cuboctahedra; corners with twelve Mg(1,1)Ba2Mg10 cuboctahedra; edges with six equivalent Mg(2)Mg10Cd2 cuboctahedra; faces with two equivalent Ba(1)Mg12 cuboctahedra; faces with six equivalent Mg(2)Mg10Cd2 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra.