BaMg14Fe crystallizes in the orthorhombic Amm2 space group. Ba(1) is bonded to two equivalent Mg(7), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Fe(1) atoms to form BaMg10Fe2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra, corners with six equivalent Ba(1)Mg10Fe2 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with four equivalent Mg(3)Ba2Mg8Fe2 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, and faces with four equivalent Mg(3)Ba2Mg8Fe2 cuboctahedra. There are seven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(2), two equivalent Mg(6), four equivalent Mg(4), and four equivalent Mg(5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Ba(1)Mg10Fe2 cuboctahedra, corners with six equivalent Mg(1)Mg12 cuboctahedra, corners with eight equivalent Mg(3)Ba2Mg8Fe2 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, and faces with four equivalent Mg(4)Mg12 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(1), two equivalent Mg(7), four equivalent Mg(4), and four equivalent Mg(5) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(2)Mg12 cuboctahedra, corners with eight equivalent Mg(3)Ba2Mg8Fe2 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Ba(1)Mg10Fe2 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, and faces with four equivalent Mg(4)Mg12 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Ba(1), two equivalent Mg(3), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and two equivalent Fe(1) atoms to form distorted MgBa2Mg8Fe2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra, corners with four equivalent Mg(2)Mg12 cuboctahedra, corners with four equivalent Mg(4)Mg12 cuboctahedra, corners with six equivalent Mg(3)Ba2Mg8Fe2 cuboctahedra, edges with two equivalent Ba(1)Mg10Fe2 cuboctahedra, edges with two equivalent Mg(3)Ba2Mg8Fe2 cuboctahedra, faces with two equivalent Ba(1)Mg10Fe2 cuboctahedra, faces with two equivalent Mg(3)Ba2Mg8Fe2 cuboctahedra, and faces with two equivalent Mg(4)Mg12 cuboctahedra. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), two equivalent Mg(5), two equivalent Mg(6), and two equivalent Mg(7) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Ba(1)Mg10Fe2 cuboctahedra, corners with four equivalent Mg(3)Ba2Mg8Fe2 cuboctahedra, corners with six equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(3)Ba2Mg8Fe2 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, and faces with two equivalent Mg(4)Mg12 cuboctahedra. In the fifth Mg site, Mg(5) is bonded in a 12-coordinate geometry to one Ba(1), one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and one Fe(1) atom. In the sixth Mg site, Mg(6) is bonded in a distorted single-bond geometry to one Mg(1), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(7), four equivalent Mg(5), and one Fe(1) atom. In the seventh Mg site, Mg(7) is bonded in a 12-coordinate geometry to one Ba(1), one Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(6), and four equivalent Mg(5) atoms. Fe(1) is bonded in a 10-coordinate geometry to two equivalent Ba(1), two equivalent Mg(6), four equivalent Mg(3), and four equivalent Mg(5) atoms.
BaMg14Fe crystallizes in the orthorhombic Amm2 space group. Ba(1) is bonded to two equivalent Mg(7), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Fe(1) atoms to form BaMg10Fe2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra, corners with six equivalent Ba(1)Mg10Fe2 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with four equivalent Mg(3)Ba2Mg8Fe2 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, and faces with four equivalent Mg(3)Ba2Mg8Fe2 cuboctahedra. Both Ba(1)-Mg(7) bond lengths are 3.36 Å. There are two shorter (3.30 Å) and two longer (3.32 Å) Ba(1)-Mg(3) bond lengths. All Ba(1)-Mg(5) bond lengths are 3.28 Å. Both Ba(1)-Fe(1) bond lengths are 3.09 Å. There are seven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(2), two equivalent Mg(6), four equivalent Mg(4), and four equivalent Mg(5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Ba(1)Mg10Fe2 cuboctahedra, corners with six equivalent Mg(1)Mg12 cuboctahedra, corners with eight equivalent Mg(3)Ba2Mg8Fe2 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, and faces with four equivalent Mg(4)Mg12 cuboctahedra. Both Mg(1)-Mg(2) bond lengths are 3.08 Å. Both Mg(1)-Mg(6) bond lengths are 3.34 Å. There are two shorter (3.28 Å) and two longer (3.34 Å) Mg(1)-Mg(4) bond lengths. All Mg(1)-Mg(5) bond lengths are 3.16 Å. In the second Mg site, Mg(2) is bonded to two equivalent Mg(1), two equivalent Mg(7), four equivalent Mg(4), and four equivalent Mg(5) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(2)Mg12 cuboctahedra, corners with eight equivalent Mg(3)Ba2Mg8Fe2 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Ba(1)Mg10Fe2 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, and faces with four equivalent Mg(4)Mg12 cuboctahedra. Both Mg(2)-Mg(7) bond lengths are 3.15 Å. There are two shorter (3.26 Å) and two longer (3.36 Å) Mg(2)-Mg(4) bond lengths. All Mg(2)-Mg(5) bond lengths are 3.20 Å. In the third Mg site, Mg(3) is bonded to two equivalent Ba(1), two equivalent Mg(3), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and two equivalent Fe(1) atoms to form distorted MgBa2Mg8Fe2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra, corners with four equivalent Mg(2)Mg12 cuboctahedra, corners with four equivalent Mg(4)Mg12 cuboctahedra, corners with six equivalent Mg(3)Ba2Mg8Fe2 cuboctahedra, edges with two equivalent Ba(1)Mg10Fe2 cuboctahedra, edges with two equivalent Mg(3)Ba2Mg8Fe2 cuboctahedra, faces with two equivalent Ba(1)Mg10Fe2 cuboctahedra, faces with two equivalent Mg(3)Ba2Mg8Fe2 cuboctahedra, and faces with two equivalent Mg(4)Mg12 cuboctahedra. There is one shorter (2.98 Å) and one longer (3.19 Å) Mg(3)-Mg(3) bond length. Both Mg(3)-Mg(5) bond lengths are 3.20 Å. Both Mg(3)-Mg(6) bond lengths are 3.11 Å. Both Mg(3)-Mg(7) bond lengths are 3.31 Å. There is one shorter (3.13 Å) and one longer (3.49 Å) Mg(3)-Fe(1) bond length. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), two equivalent Mg(5), two equivalent Mg(6), and two equivalent Mg(7) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Ba(1)Mg10Fe2 cuboctahedra, corners with four equivalent Mg(3)Ba2Mg8Fe2 cuboctahedra, corners with six equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(3)Ba2Mg8Fe2 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, and faces with two equivalent Mg(4)Mg12 cuboctahedra. There is one shorter (3.02 Å) and one longer (3.14 Å) Mg(4)-Mg(4) bond length. Both Mg(4)-Mg(5) bond lengths are 3.20 Å. Both Mg(4)-Mg(6) bond lengths are 3.40 Å. Both Mg(4)-Mg(7) bond lengths are 3.07 Å. In the fifth Mg site, Mg(5) is bonded in a 12-coordinate geometry to one Ba(1), one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), and one Fe(1) atom. There is one shorter (2.94 Å) and one longer (3.22 Å) Mg(5)-Mg(5) bond length. There is one shorter (3.21 Å) and one longer (3.43 Å) Mg(5)-Mg(6) bond length. There is one shorter (3.22 Å) and one longer (3.40 Å) Mg(5)-Mg(7) bond length. The Mg(5)-Fe(1) bond length is 3.16 Å. In the sixth Mg site, Mg(6) is bonded in a distorted single-bond geometry to one Mg(1), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(7), four equivalent Mg(5), and one Fe(1) atom. Both Mg(6)-Mg(7) bond lengths are 3.11 Å. The Mg(6)-Fe(1) bond length is 3.06 Å. In the seventh Mg site, Mg(7) is bonded in a 12-coordinate geometry to one Ba(1), one Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(6), and four equivalent Mg(5) atoms. Fe(1) is bonded in a 10-coordinate geometry to two equivalent Ba(1), two equivalent Mg(6), four equivalent Mg(3), and four equivalent Mg(5) atoms.