Ba4Fe9O20 crystallizes in the monoclinic C2/m space group. There are two inequivalent Ba sites. In the first Ba site, Ba(1) is bonded to one O(5), two equivalent O(2), three equivalent O(6), and six equivalent O(3) atoms to form BaO12 cuboctahedra that share corners with three equivalent Ba(2)O12 cuboctahedra, corners with six equivalent Ba(1)O12 cuboctahedra, corners with three equivalent Fe(3)O4 tetrahedra, faces with three equivalent Ba(1)O12 cuboctahedra, faces with three equivalent Ba(2)O12 cuboctahedra,  a faceface with one Fe(2)O6 octahedra, and faces with three equivalent Fe(5)O6 octahedra. In the second Ba site, Ba(2) is bonded to one O(4), one O(6), two equivalent O(1), two equivalent O(3), two equivalent O(5), and four equivalent O(2) atoms to form distorted BaO12 cuboctahedra that share corners with three equivalent Ba(1)O12 cuboctahedra, corners with six equivalent Ba(2)O12 cuboctahedra, corners with two equivalent Fe(6)O6 octahedra, corners with four equivalent Fe(4)O6 octahedra, edges with three equivalent Fe(3)O4 tetrahedra, faces with three equivalent Ba(1)O12 cuboctahedra,  a faceface with one Fe(1)O6 octahedra,  a faceface with one Fe(5)O6 octahedra, and faces with three equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 47-48°. There are six inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to two equivalent O(4) and four equivalent O(1) atoms to form FeO6 octahedra that share corners with six equivalent Fe(2)O6 octahedra, edges with two equivalent Fe(6)O6 octahedra, edges with four equivalent Fe(4)O6 octahedra, and faces with two equivalent Ba(2)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 9°. In the second Fe site, Fe(2) is bonded to one O(4), one O(5), two equivalent O(1), and two equivalent O(2) atoms to form FeO6 octahedra that share corners with three equivalent Fe(1)O6 octahedra, corners with three equivalent Fe(3)O4 tetrahedra,  an edgeedge with one Fe(6)O6 octahedra, edges with two equivalent Fe(4)O6 octahedra,  a faceface with one Ba(1)O12 cuboctahedra, and faces with three equivalent Ba(2)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 9°. In the third Fe site, Fe(3) is bonded to one O(5), one O(7), and two equivalent O(2) atoms to form FeO4 tetrahedra that share corners with three equivalent Ba(1)O12 cuboctahedra,  a cornercorner with one Fe(6)O6 octahedra, corners with two equivalent Fe(4)O6 octahedra, corners with three equivalent Fe(2)O6 octahedra, and edges with three equivalent Ba(2)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 47-58°. In the fourth Fe site, Fe(4) is bonded to two equivalent O(1), two equivalent O(4), and two equivalent O(7) atoms to form FeO6 octahedra that share corners with four equivalent Ba(2)O12 cuboctahedra, corners with two equivalent Fe(3)O4 tetrahedra, edges with two equivalent Fe(1)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, edges with two equivalent Fe(4)O6 octahedra, and edges with two equivalent Fe(6)O6 octahedra. In the fifth Fe site, Fe(5) is bonded to two equivalent O(6) and four equivalent O(3) atoms to form FeO6 octahedra that share faces with two equivalent Ba(2)O12 cuboctahedra and faces with six equivalent Ba(1)O12 cuboctahedra. In the sixth Fe site, Fe(6) is bonded to two equivalent O(7) and four equivalent O(1) atoms to form FeO6 octahedra that share corners with four equivalent Ba(2)O12 cuboctahedra, corners with two equivalent Fe(3)O4 tetrahedra, edges with two equivalent Fe(1)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, and edges with four equivalent Fe(4)O6 octahedra. There are seven inequivalent O sites. In the first O site, O(3) is bonded in a distorted single-bond geometry to one Ba(2), three equivalent Ba(1), and one Fe(5) atom. In the second O site, O(4) is bonded in a distorted rectangular see-saw-like geometry to one Ba(2), one Fe(1), one Fe(2), and two equivalent Fe(4) atoms. In the third O site, O(5) is bonded in a 2-coordinate geometry to one Ba(1), two equivalent Ba(2), one Fe(2), and one Fe(3) atom. In the fourth O site, O(6) is bonded in a distorted single-bond geometry to one Ba(2), three equivalent Ba(1), and one Fe(5) atom. In the fifth O site, O(7) is bonded to one Fe(3), one Fe(6), and two equivalent Fe(4) atoms to form distorted corner-sharing OFe4 trigonal pyramids. In the sixth O site, O(1) is bonded in a distorted rectangular see-saw-like geometry to one Ba(2), one Fe(1), one Fe(2), one Fe(4), and one Fe(6) atom. In the seventh O site, O(2) is bonded in a 2-coordinate geometry to one Ba(1), two equivalent Ba(2), one Fe(2), and one Fe(3) atom.
Ba4Fe9O20 crystallizes in the monoclinic C2/m space group. There are two inequivalent Ba sites. In the first Ba site, Ba(1) is bonded to one O(5), two equivalent O(2), three equivalent O(6), and six equivalent O(3) atoms to form BaO12 cuboctahedra that share corners with three equivalent Ba(2)O12 cuboctahedra, corners with six equivalent Ba(1)O12 cuboctahedra, corners with three equivalent Fe(3)O4 tetrahedra, faces with three equivalent Ba(1)O12 cuboctahedra, faces with three equivalent Ba(2)O12 cuboctahedra,  a faceface with one Fe(2)O6 octahedra, and faces with three equivalent Fe(5)O6 octahedra. The Ba(1)-O(5) bond length is 2.97 Å. Both Ba(1)-O(2) bond lengths are 3.06 Å. There is one shorter (2.99 Å) and two longer (3.00 Å) Ba(1)-O(6) bond lengths. There are a spread of Ba(1)-O(3) bond distances ranging from 2.91-3.04 Å. In the second Ba site, Ba(2) is bonded to one O(4), one O(6), two equivalent O(1), two equivalent O(3), two equivalent O(5), and four equivalent O(2) atoms to form distorted BaO12 cuboctahedra that share corners with three equivalent Ba(1)O12 cuboctahedra, corners with six equivalent Ba(2)O12 cuboctahedra, corners with two equivalent Fe(6)O6 octahedra, corners with four equivalent Fe(4)O6 octahedra, edges with three equivalent Fe(3)O4 tetrahedra, faces with three equivalent Ba(1)O12 cuboctahedra,  a faceface with one Fe(1)O6 octahedra,  a faceface with one Fe(5)O6 octahedra, and faces with three equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 47-48°. The Ba(2)-O(4) bond length is 3.23 Å. The Ba(2)-O(6) bond length is 2.75 Å. Both Ba(2)-O(1) bond lengths are 3.26 Å. Both Ba(2)-O(3) bond lengths are 2.89 Å. Both Ba(2)-O(5) bond lengths are 3.00 Å. There are two shorter (2.96 Å) and two longer (3.04 Å) Ba(2)-O(2) bond lengths. There are six inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to two equivalent O(4) and four equivalent O(1) atoms to form FeO6 octahedra that share corners with six equivalent Fe(2)O6 octahedra, edges with two equivalent Fe(6)O6 octahedra, edges with four equivalent Fe(4)O6 octahedra, and faces with two equivalent Ba(2)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 9°. Both Fe(1)-O(4) bond lengths are 2.07 Å. All Fe(1)-O(1) bond lengths are 2.08 Å. In the second Fe site, Fe(2) is bonded to one O(4), one O(5), two equivalent O(1), and two equivalent O(2) atoms to form FeO6 octahedra that share corners with three equivalent Fe(1)O6 octahedra, corners with three equivalent Fe(3)O4 tetrahedra,  an edgeedge with one Fe(6)O6 octahedra, edges with two equivalent Fe(4)O6 octahedra,  a faceface with one Ba(1)O12 cuboctahedra, and faces with three equivalent Ba(2)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 9°. The Fe(2)-O(4) bond length is 2.23 Å. The Fe(2)-O(5) bond length is 1.94 Å. Both Fe(2)-O(1) bond lengths are 2.23 Å. Both Fe(2)-O(2) bond lengths are 1.94 Å. In the third Fe site, Fe(3) is bonded to one O(5), one O(7), and two equivalent O(2) atoms to form FeO4 tetrahedra that share corners with three equivalent Ba(1)O12 cuboctahedra,  a cornercorner with one Fe(6)O6 octahedra, corners with two equivalent Fe(4)O6 octahedra, corners with three equivalent Fe(2)O6 octahedra, and edges with three equivalent Ba(2)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 47-58°. The Fe(3)-O(5) bond length is 1.88 Å. The Fe(3)-O(7) bond length is 1.99 Å. Both Fe(3)-O(2) bond lengths are 1.87 Å. In the fourth Fe site, Fe(4) is bonded to two equivalent O(1), two equivalent O(4), and two equivalent O(7) atoms to form FeO6 octahedra that share corners with four equivalent Ba(2)O12 cuboctahedra, corners with two equivalent Fe(3)O4 tetrahedra, edges with two equivalent Fe(1)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, edges with two equivalent Fe(4)O6 octahedra, and edges with two equivalent Fe(6)O6 octahedra. Both Fe(4)-O(1) bond lengths are 2.02 Å. Both Fe(4)-O(4) bond lengths are 2.03 Å. Both Fe(4)-O(7) bond lengths are 2.04 Å. In the fifth Fe site, Fe(5) is bonded to two equivalent O(6) and four equivalent O(3) atoms to form FeO6 octahedra that share faces with two equivalent Ba(2)O12 cuboctahedra and faces with six equivalent Ba(1)O12 cuboctahedra. Both Fe(5)-O(6) bond lengths are 1.85 Å. All Fe(5)-O(3) bond lengths are 1.85 Å. In the sixth Fe site, Fe(6) is bonded to two equivalent O(7) and four equivalent O(1) atoms to form FeO6 octahedra that share corners with four equivalent Ba(2)O12 cuboctahedra, corners with two equivalent Fe(3)O4 tetrahedra, edges with two equivalent Fe(1)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, and edges with four equivalent Fe(4)O6 octahedra. Both Fe(6)-O(7) bond lengths are 2.03 Å. All Fe(6)-O(1) bond lengths are 2.03 Å. There are seven inequivalent O sites. In the first O site, O(3) is bonded in a distorted single-bond geometry to one Ba(2), three equivalent Ba(1), and one Fe(5) atom. In the second O site, O(4) is bonded in a distorted rectangular see-saw-like geometry to one Ba(2), one Fe(1), one Fe(2), and two equivalent Fe(4) atoms. In the third O site, O(5) is bonded in a 2-coordinate geometry to one Ba(1), two equivalent Ba(2), one Fe(2), and one Fe(3) atom. In the fourth O site, O(6) is bonded in a distorted single-bond geometry to one Ba(2), three equivalent Ba(1), and one Fe(5) atom. In the fifth O site, O(7) is bonded to one Fe(3), one Fe(6), and two equivalent Fe(4) atoms to form distorted corner-sharing OFe4 trigonal pyramids. In the sixth O site, O(1) is bonded in a distorted rectangular see-saw-like geometry to one Ba(2), one Fe(1), one Fe(2), one Fe(4), and one Fe(6) atom. In the seventh O site, O(2) is bonded in a 2-coordinate geometry to one Ba(1), two equivalent Ba(2), one Fe(2), and one Fe(3) atom.