BaMg14Al crystallizes in the hexagonal P-6m2 space group. Ba(1) is bonded to six Mg(2,2) 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)Mg10Al2 cuboctahedra; edges with six Mg(2,2)Ba2Mg10 cuboctahedra; edges with twelve Mg(3,3)BaMg10Al cuboctahedra; faces with two equivalent Al(1)Mg12 cuboctahedra; faces with six Mg(2,2)Ba2Mg10 cuboctahedra; faces with six Mg(3,3)BaMg10Al cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. There are six inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Al(1) atoms to form distorted MgMg10Al2 cuboctahedra that share corners with four equivalent Ba(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Al2 cuboctahedra; corners with eight equivalent Mg(2)Ba2Mg10 cuboctahedra; edges with two equivalent Al(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Mg10Al2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)BaMg10Al cuboctahedra; faces with two equivalent Mg(2)Ba2Mg10 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Al(1)Mg12 cuboctahedra; faces with four equivalent Mg(1)Mg10Al2 cuboctahedra; and faces with ten Mg(3,3)BaMg10Al cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Ba(1), two equivalent Mg(4), four equivalent Mg(2), and four equivalent Mg(3) atoms to form distorted MgBa2Mg10 cuboctahedra that share corners with four equivalent Al(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Ba2Mg10 cuboctahedra; corners with eight equivalent Mg(1)Mg10Al2 cuboctahedra; edges with two equivalent Ba(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Ba2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)BaMg10Al cuboctahedra; faces with two equivalent Ba(1)Mg12 cuboctahedra; faces with two equivalent Mg(1)Mg10Al2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with four equivalent Mg(2)Ba2Mg10 cuboctahedra; and faces with ten Mg(3,3)BaMg10Al cuboctahedra. In the third Mg site, Mg(2) is bonded to two equivalent Ba(1); two equivalent Mg(4); four Mg(2,2); and four Mg(3,3) atoms to form distorted MgBa2Mg10 cuboctahedra that share corners with four equivalent Al(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Ba2Mg10 cuboctahedra; corners with eight equivalent Mg(1)Mg10Al2 cuboctahedra; edges with two equivalent Ba(1)Mg12 cuboctahedra; edges with four Mg(2,2)Ba2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)BaMg10Al cuboctahedra; faces with two equivalent Ba(1)Mg12 cuboctahedra; faces with two equivalent Mg(1)Mg10Al2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with four Mg(2,2)Ba2Mg10 cuboctahedra; and faces with ten Mg(3,3)BaMg10Al cuboctahedra. In the fourth Mg site, Mg(3) is bonded to one Ba(1); two equivalent Mg(1); two Mg(2,2); two equivalent Mg(4); four Mg(3,3); and one Al(1) atom to form distorted MgBaMg10Al cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)BaMg10Al cuboctahedra; edges with two equivalent Ba(1)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Al(1)Mg12 cuboctahedra; edges with four Mg(2,2)Ba2Mg10 cuboctahedra; edges with four Mg(3,3)BaMg10Al cuboctahedra; edges with four equivalent Mg(1)Mg10Al2 cuboctahedra;  a faceface with one Ba(1)Mg12 cuboctahedra;  a faceface with one Al(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(2,2)Ba2Mg10 cuboctahedra; faces with five equivalent Mg(1)Mg10Al2 cuboctahedra; and faces with six Mg(3,3)BaMg10Al cuboctahedra. In the fifth 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 Al(1) atom to form distorted MgBaMg10Al cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)BaMg10Al cuboctahedra; edges with two equivalent Ba(1)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Al(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Ba2Mg10 cuboctahedra; edges with four equivalent Mg(3)BaMg10Al cuboctahedra; edges with four equivalent Mg(1)Mg10Al2 cuboctahedra;  a faceface with one Ba(1)Mg12 cuboctahedra;  a faceface with one Al(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(2,2)Ba2Mg10 cuboctahedra; faces with five equivalent Mg(1)Mg10Al2 cuboctahedra; and faces with six Mg(3,3)BaMg10Al cuboctahedra. In the sixth Mg site, Mg(4) is bonded to three equivalent Mg(1); three Mg(2,2); 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)BaMg10Al cuboctahedra; edges with six Mg(2,2)Ba2Mg10 cuboctahedra; edges with six Mg(3,3)BaMg10Al cuboctahedra; edges with six equivalent Mg(1)Mg10Al2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Ba(1)Mg12 cuboctahedra; faces with three Mg(2,2)Ba2Mg10 cuboctahedra; faces with three equivalent Mg(1)Mg10Al2 cuboctahedra; faces with three equivalent Al(1)Mg12 cuboctahedra; and faces with six Mg(3,3)BaMg10Al cuboctahedra. Al(1) is bonded to six equivalent Mg(1) and six Mg(3,3) atoms to form AlMg12 cuboctahedra that share corners with six equivalent Al(1)Mg12 cuboctahedra; corners with twelve Mg(2,2)Ba2Mg10 cuboctahedra; edges with six equivalent Mg(1)Mg10Al2 cuboctahedra; edges with twelve Mg(3,3)BaMg10Al cuboctahedra; faces with two equivalent Ba(1)Mg12 cuboctahedra; faces with six Mg(3,3)BaMg10Al cuboctahedra; faces with six equivalent Mg(1)Mg10Al2 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra.
BaMg14Al crystallizes in the hexagonal P-6m2 space group. Ba(1) is bonded to six Mg(2,2) 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)Mg10Al2 cuboctahedra; edges with six Mg(2,2)Ba2Mg10 cuboctahedra; edges with twelve Mg(3,3)BaMg10Al cuboctahedra; faces with two equivalent Al(1)Mg12 cuboctahedra; faces with six Mg(2,2)Ba2Mg10 cuboctahedra; faces with six Mg(3,3)BaMg10Al cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. All Ba(1)-Mg(2,2) bond lengths are 3.28 Å. All Ba(1)-Mg(3,3) bond lengths are 3.43 Å. There are six inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Al(1) atoms to form distorted MgMg10Al2 cuboctahedra that share corners with four equivalent Ba(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Al2 cuboctahedra; corners with eight equivalent Mg(2)Ba2Mg10 cuboctahedra; edges with two equivalent Al(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Mg10Al2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)BaMg10Al cuboctahedra; faces with two equivalent Mg(2)Ba2Mg10 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Al(1)Mg12 cuboctahedra; faces with four equivalent Mg(1)Mg10Al2 cuboctahedra; and faces with ten Mg(3,3)BaMg10Al cuboctahedra. Both Mg(1)-Mg(4) bond lengths are 3.30 Å. There are two shorter (3.23 Å) and two longer (3.34 Å) Mg(1)-Mg(1) bond lengths. All Mg(1)-Mg(3) bond lengths are 3.12 Å. Both Mg(1)-Al(1) bond lengths are 3.28 Å. In the second Mg site, Mg(2) is bonded to two equivalent Ba(1), two equivalent Mg(4), four equivalent Mg(2), and four equivalent Mg(3) atoms to form distorted MgBa2Mg10 cuboctahedra that share corners with four equivalent Al(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Ba2Mg10 cuboctahedra; corners with eight equivalent Mg(1)Mg10Al2 cuboctahedra; edges with two equivalent Ba(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Ba2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)BaMg10Al cuboctahedra; faces with two equivalent Ba(1)Mg12 cuboctahedra; faces with two equivalent Mg(1)Mg10Al2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with four equivalent Mg(2)Ba2Mg10 cuboctahedra; and faces with ten Mg(3,3)BaMg10Al cuboctahedra. Both Mg(2)-Mg(4) bond lengths are 3.25 Å. There are two shorter (3.15 Å) and two longer (3.41 Å) Mg(2)-Mg(2) bond lengths. All Mg(2)-Mg(3) bond lengths are 3.38 Å. In the third Mg site, Mg(2) is bonded to two equivalent Ba(1); two equivalent Mg(4); four Mg(2,2); and four Mg(3,3) atoms to form distorted MgBa2Mg10 cuboctahedra that share corners with four equivalent Al(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Ba2Mg10 cuboctahedra; corners with eight equivalent Mg(1)Mg10Al2 cuboctahedra; edges with two equivalent Ba(1)Mg12 cuboctahedra; edges with four Mg(2,2)Ba2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)BaMg10Al cuboctahedra; faces with two equivalent Ba(1)Mg12 cuboctahedra; faces with two equivalent Mg(1)Mg10Al2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with four Mg(2,2)Ba2Mg10 cuboctahedra; and faces with ten Mg(3,3)BaMg10Al cuboctahedra. Both Mg(2)-Mg(4) bond lengths are 3.25 Å. There is one shorter (3.15 Å) and one longer (3.41 Å) Mg(2)-Mg(2) bond length. All Mg(2)-Mg(3,3) bond lengths are 3.38 Å. In the fourth Mg site, Mg(3) is bonded to one Ba(1); two equivalent Mg(1); two Mg(2,2); two equivalent Mg(4); four Mg(3,3); and one Al(1) atom to form distorted MgBaMg10Al cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)BaMg10Al cuboctahedra; edges with two equivalent Ba(1)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Al(1)Mg12 cuboctahedra; edges with four Mg(2,2)Ba2Mg10 cuboctahedra; edges with four Mg(3,3)BaMg10Al cuboctahedra; edges with four equivalent Mg(1)Mg10Al2 cuboctahedra;  a faceface with one Ba(1)Mg12 cuboctahedra;  a faceface with one Al(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(2,2)Ba2Mg10 cuboctahedra; faces with five equivalent Mg(1)Mg10Al2 cuboctahedra; and faces with six Mg(3,3)BaMg10Al cuboctahedra. Both Mg(3)-Mg(4) bond lengths are 3.29 Å. There are two shorter (3.22 Å) and two longer (3.34 Å) Mg(3)-Mg(3,3) bond lengths. The Mg(3)-Al(1) bond length is 3.14 Å. In the fifth 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 Al(1) atom to form distorted MgBaMg10Al cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3)BaMg10Al cuboctahedra; edges with two equivalent Ba(1)Mg12 cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Al(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Ba2Mg10 cuboctahedra; edges with four equivalent Mg(3)BaMg10Al cuboctahedra; edges with four equivalent Mg(1)Mg10Al2 cuboctahedra;  a faceface with one Ba(1)Mg12 cuboctahedra;  a faceface with one Al(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(2,2)Ba2Mg10 cuboctahedra; faces with five equivalent Mg(1)Mg10Al2 cuboctahedra; and faces with six Mg(3,3)BaMg10Al cuboctahedra. Both Mg(3)-Mg(1) bond lengths are 3.12 Å. Both Mg(3)-Mg(4) bond lengths are 3.29 Å. The Mg(3)-Al(1) bond length is 3.14 Å. In the sixth Mg site, Mg(4) is bonded to three equivalent Mg(1); three Mg(2,2); 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)BaMg10Al cuboctahedra; edges with six Mg(2,2)Ba2Mg10 cuboctahedra; edges with six Mg(3,3)BaMg10Al cuboctahedra; edges with six equivalent Mg(1)Mg10Al2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Ba(1)Mg12 cuboctahedra; faces with three Mg(2,2)Ba2Mg10 cuboctahedra; faces with three equivalent Mg(1)Mg10Al2 cuboctahedra; faces with three equivalent Al(1)Mg12 cuboctahedra; and faces with six Mg(3,3)BaMg10Al cuboctahedra. Al(1) is bonded to six equivalent Mg(1) and six Mg(3,3) atoms to form AlMg12 cuboctahedra that share corners with six equivalent Al(1)Mg12 cuboctahedra; corners with twelve Mg(2,2)Ba2Mg10 cuboctahedra; edges with six equivalent Mg(1)Mg10Al2 cuboctahedra; edges with twelve Mg(3,3)BaMg10Al cuboctahedra; faces with two equivalent Ba(1)Mg12 cuboctahedra; faces with six Mg(3,3)BaMg10Al cuboctahedra; faces with six equivalent Mg(1)Mg10Al2 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra.