The crystal structure described by 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. is represented by the CIF file [CIF]
data_Ba4Fe9O20
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.975
_cell_length_b   5.975
_cell_length_c   14.548
_cell_angle_alpha   89.464
_cell_angle_beta   89.464
_cell_angle_gamma   60.129
_symmetry_Int_Tables_number   1
_cell_volume   450.403
_cell_formula_units_Z   1
loop_
 _symmetry_equiv_pos_site_id
 _symmetry_equiv_pos_as_xyz
  1  'x, y, z'
loop_
 _atom_site_type_symbol
 _atom_site_label
 _atom_site_symmetry_multiplicity
 _atom_site_fract_x
 _atom_site_fract_y
 _atom_site_fract_z
 _atom_site_occupancy
  Ba  Ba0  1  0.167  0.167  0.580  1.0
  Ba  Ba1  1  0.833  0.833  0.420  1.0
  Ba  Ba2  1  0.501  0.501  0.737  1.0
  Ba  Ba3  1  0.499  0.499  0.263  1.0
  Fe  Fe4  1  0.500  0.500  0.000  1.0
  Fe  Fe5  1  0.170  0.170  0.825  1.0
  Fe  Fe6  1  0.830  0.830  0.175  1.0
  Fe  Fe7  1  0.837  0.837  0.789  1.0
  Fe  Fe8  1  0.163  0.163  0.211  1.0
  Fe  Fe9  1  0.000  0.500  0.000  1.0
  Fe  Fe10  1  0.500  0.000  0.000  1.0
  Fe  Fe11  1  0.500  0.500  0.500  1.0
  Fe  Fe12  1  0.000  0.000  0.000  1.0
  O  O13  1  0.843  0.331  0.925  1.0
  O  O14  1  0.331  0.843  0.925  1.0
  O  O15  1  0.157  0.669  0.075  1.0
  O  O16  1  0.669  0.157  0.075  1.0
  O  O17  1  0.014  0.490  0.755  1.0
  O  O18  1  0.490  0.014  0.755  1.0
  O  O19  1  0.986  0.510  0.245  1.0
  O  O20  1  0.510  0.986  0.245  1.0
  O  O21  1  0.201  0.641  0.571  1.0
  O  O22  1  0.641  0.201  0.571  1.0
  O  O23  1  0.799  0.359  0.429  1.0
  O  O24  1  0.359  0.799  0.429  1.0
  O  O25  1  0.331  0.331  0.925  1.0
  O  O26  1  0.669  0.669  0.075  1.0
  O  O27  1  0.013  0.013  0.753  1.0
  O  O28  1  0.987  0.987  0.247  1.0
  O  O29  1  0.358  0.358  0.424  1.0
  O  O30  1  0.642  0.642  0.576  1.0
  O  O31  1  0.835  0.835  0.925  1.0
  O  O32  1  0.165  0.165  0.075  1.0
[/CIF]
.
The crystal structure described by 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. is represented by the CIF file [CIF]
data_Ba4Fe9O20
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.975
_cell_length_b   5.975
_cell_length_c   14.548
_cell_angle_alpha   89.464
_cell_angle_beta   89.464
_cell_angle_gamma   60.129
_symmetry_Int_Tables_number   1
_cell_volume   450.403
_cell_formula_units_Z   1
loop_
 _symmetry_equiv_pos_site_id
 _symmetry_equiv_pos_as_xyz
  1  'x, y, z'
loop_
 _atom_site_type_symbol
 _atom_site_label
 _atom_site_symmetry_multiplicity
 _atom_site_fract_x
 _atom_site_fract_y
 _atom_site_fract_z
 _atom_site_occupancy
  Ba  Ba0  1  0.167  0.167  0.580  1.0
  Ba  Ba1  1  0.833  0.833  0.420  1.0
  Ba  Ba2  1  0.501  0.501  0.737  1.0
  Ba  Ba3  1  0.499  0.499  0.263  1.0
  Fe  Fe4  1  0.500  0.500  0.000  1.0
  Fe  Fe5  1  0.170  0.170  0.825  1.0
  Fe  Fe6  1  0.830  0.830  0.175  1.0
  Fe  Fe7  1  0.837  0.837  0.789  1.0
  Fe  Fe8  1  0.163  0.163  0.211  1.0
  Fe  Fe9  1  0.000  0.500  0.000  1.0
  Fe  Fe10  1  0.500  0.000  0.000  1.0
  Fe  Fe11  1  0.500  0.500  0.500  1.0
  Fe  Fe12  1  0.000  0.000  0.000  1.0
  O  O13  1  0.843  0.331  0.925  1.0
  O  O14  1  0.331  0.843  0.925  1.0
  O  O15  1  0.157  0.669  0.075  1.0
  O  O16  1  0.669  0.157  0.075  1.0
  O  O17  1  0.014  0.490  0.755  1.0
  O  O18  1  0.490  0.014  0.755  1.0
  O  O19  1  0.986  0.510  0.245  1.0
  O  O20  1  0.510  0.986  0.245  1.0
  O  O21  1  0.201  0.641  0.571  1.0
  O  O22  1  0.641  0.201  0.571  1.0
  O  O23  1  0.799  0.359  0.429  1.0
  O  O24  1  0.359  0.799  0.429  1.0
  O  O25  1  0.331  0.331  0.925  1.0
  O  O26  1  0.669  0.669  0.075  1.0
  O  O27  1  0.013  0.013  0.753  1.0
  O  O28  1  0.987  0.987  0.247  1.0
  O  O29  1  0.358  0.358  0.424  1.0
  O  O30  1  0.642  0.642  0.576  1.0
  O  O31  1  0.835  0.835  0.925  1.0
  O  O32  1  0.165  0.165  0.075  1.0
[/CIF]
.