The structure described by Ba3TiFe2O9 is (Cubic) Perovskite-derived structured and crystallizes in the hexagonal P6_3mc space group. There are three inequivalent Ba sites. In the first Ba site, Ba(1) is bonded to three equivalent O(2), three equivalent O(3), and six equivalent O(1) atoms to form BaO12 cuboctahedra that share corners with three equivalent Ba(3)O12 cuboctahedra, corners with six equivalent Ba(1)O12 cuboctahedra, corners with three equivalent Ti(1)O6 octahedra, faces with three equivalent Ba(3)O12 cuboctahedra, faces with four equivalent Ba(2)O12 cuboctahedra,  a faceface with one Ti(1)O6 octahedra, faces with three equivalent Fe(1)O6 octahedra, and faces with three equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles are 2°. In the second Ba site, Ba(2) is bonded to three equivalent O(1), three equivalent O(3), and six equivalent O(2) atoms to form BaO12 cuboctahedra that share corners with three equivalent Ba(3)O12 cuboctahedra, corners with six equivalent Ba(2)O12 cuboctahedra, corners with three equivalent Fe(1)O6 octahedra, faces with three equivalent Ba(3)O12 cuboctahedra, faces with four equivalent Ba(1)O12 cuboctahedra,  a faceface with one Fe(1)O6 octahedra, faces with three equivalent Ti(1)O6 octahedra, and faces with three equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles are 13°. In the third Ba site, Ba(3) is bonded to three equivalent O(1), three equivalent O(2), and six equivalent O(3) atoms to form BaO12 cuboctahedra that share corners with three equivalent Ba(1)O12 cuboctahedra, corners with three equivalent Ba(2)O12 cuboctahedra, corners with six equivalent Ba(3)O12 cuboctahedra, faces with three equivalent Ba(1)O12 cuboctahedra, faces with three equivalent Ba(2)O12 cuboctahedra, faces with two equivalent Fe(2)O6 octahedra, faces with three equivalent Ti(1)O6 octahedra, and faces with three equivalent Fe(1)O6 octahedra. Ti(1) is bonded to three equivalent O(2) and three equivalent O(3) atoms to form distorted TiO6 octahedra that share corners with three equivalent Ba(1)O12 cuboctahedra, corners with three equivalent Fe(2)O6 octahedra,  a faceface with one Ba(1)O12 cuboctahedra, faces with three equivalent Ba(2)O12 cuboctahedra, faces with three equivalent Ba(3)O12 cuboctahedra, and  a faceface with one Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles are 7°. There are two inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to three equivalent O(1) and three equivalent O(3) atoms to form FeO6 octahedra that share corners with three equivalent Ba(2)O12 cuboctahedra, corners with three equivalent Fe(2)O6 octahedra,  a faceface with one Ba(2)O12 cuboctahedra, faces with three equivalent Ba(1)O12 cuboctahedra, faces with three equivalent Ba(3)O12 cuboctahedra, and  a faceface with one Ti(1)O6 octahedra. The corner-sharing octahedra are not tilted. In the second Fe site, Fe(2) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form FeO6 octahedra that share corners with three equivalent Ti(1)O6 octahedra, corners with three equivalent Fe(1)O6 octahedra, faces with two equivalent Ba(3)O12 cuboctahedra, faces with three equivalent Ba(1)O12 cuboctahedra, and faces with three equivalent Ba(2)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 0-7°. There are three inequivalent O sites. In the first O site, O(1) is bonded in a distorted linear geometry to one Ba(2), one Ba(3), two equivalent Ba(1), one Fe(1), and one Fe(2) atom. In the second O site, O(2) is bonded in a distorted linear geometry to one Ba(1), one Ba(3), two equivalent Ba(2), one Ti(1), and one Fe(2) atom. In the third O site, O(3) is bonded in a 6-coordinate geometry to one Ba(1), one Ba(2), two equivalent Ba(3), one Ti(1), and one Fe(1) atom. is represented by the CIF file [CIF]
data_Ba3TiFe2O9
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.775
_cell_length_b   5.775
_cell_length_c   14.119
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   407.713
_cell_formula_units_Z   2
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  0.667  0.333  0.597  1.0
  Ba  Ba1  1  0.333  0.667  0.417  1.0
  Ba  Ba2  1  0.333  0.667  0.097  1.0
  Ba  Ba3  1  0.667  0.333  0.917  1.0
  Ba  Ba4  1  0.000  0.000  0.748  1.0
  Ba  Ba5  1  0.000  0.000  0.247  1.0
  Ti  Ti6  1  0.667  0.333  0.352  1.0
  Ti  Ti7  1  0.333  0.667  0.852  1.0
  Fe  Fe8  1  0.333  0.667  0.658  1.0
  Fe  Fe9  1  0.667  0.333  0.158  1.0
  Fe  Fe10  1  0.000  0.000  0.502  1.0
  Fe  Fe11  1  0.000  0.000  0.002  1.0
  O  O12  1  0.171  0.342  0.581  1.0
  O  O13  1  0.171  0.829  0.581  1.0
  O  O14  1  0.658  0.829  0.581  1.0
  O  O15  1  0.832  0.665  0.416  1.0
  O  O16  1  0.832  0.168  0.416  1.0
  O  O17  1  0.335  0.168  0.416  1.0
  O  O18  1  0.829  0.658  0.081  1.0
  O  O19  1  0.829  0.171  0.081  1.0
  O  O20  1  0.342  0.171  0.081  1.0
  O  O21  1  0.168  0.335  0.916  1.0
  O  O22  1  0.168  0.832  0.916  1.0
  O  O23  1  0.665  0.832  0.916  1.0
  O  O24  1  0.480  0.960  0.745  1.0
  O  O25  1  0.480  0.520  0.745  1.0
  O  O26  1  0.040  0.520  0.745  1.0
  O  O27  1  0.520  0.040  0.245  1.0
  O  O28  1  0.520  0.480  0.245  1.0
  O  O29  1  0.960  0.480  0.245  1.0
[/CIF]
.
The structure described by Ba3TiFe2O9 is (Cubic) Perovskite-derived structured and crystallizes in the hexagonal P6_3mc space group. There are three inequivalent Ba sites. In the first Ba site, Ba(1) is bonded to three equivalent O(2), three equivalent O(3), and six equivalent O(1) atoms to form BaO12 cuboctahedra that share corners with three equivalent Ba(3)O12 cuboctahedra, corners with six equivalent Ba(1)O12 cuboctahedra, corners with three equivalent Ti(1)O6 octahedra, faces with three equivalent Ba(3)O12 cuboctahedra, faces with four equivalent Ba(2)O12 cuboctahedra,  a faceface with one Ti(1)O6 octahedra, faces with three equivalent Fe(1)O6 octahedra, and faces with three equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles are 2°. In the second Ba site, Ba(2) is bonded to three equivalent O(1), three equivalent O(3), and six equivalent O(2) atoms to form BaO12 cuboctahedra that share corners with three equivalent Ba(3)O12 cuboctahedra, corners with six equivalent Ba(2)O12 cuboctahedra, corners with three equivalent Fe(1)O6 octahedra, faces with three equivalent Ba(3)O12 cuboctahedra, faces with four equivalent Ba(1)O12 cuboctahedra,  a faceface with one Fe(1)O6 octahedra, faces with three equivalent Ti(1)O6 octahedra, and faces with three equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles are 13°. In the third Ba site, Ba(3) is bonded to three equivalent O(1), three equivalent O(2), and six equivalent O(3) atoms to form BaO12 cuboctahedra that share corners with three equivalent Ba(1)O12 cuboctahedra, corners with three equivalent Ba(2)O12 cuboctahedra, corners with six equivalent Ba(3)O12 cuboctahedra, faces with three equivalent Ba(1)O12 cuboctahedra, faces with three equivalent Ba(2)O12 cuboctahedra, faces with two equivalent Fe(2)O6 octahedra, faces with three equivalent Ti(1)O6 octahedra, and faces with three equivalent Fe(1)O6 octahedra. Ti(1) is bonded to three equivalent O(2) and three equivalent O(3) atoms to form distorted TiO6 octahedra that share corners with three equivalent Ba(1)O12 cuboctahedra, corners with three equivalent Fe(2)O6 octahedra,  a faceface with one Ba(1)O12 cuboctahedra, faces with three equivalent Ba(2)O12 cuboctahedra, faces with three equivalent Ba(3)O12 cuboctahedra, and  a faceface with one Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles are 7°. There are two inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to three equivalent O(1) and three equivalent O(3) atoms to form FeO6 octahedra that share corners with three equivalent Ba(2)O12 cuboctahedra, corners with three equivalent Fe(2)O6 octahedra,  a faceface with one Ba(2)O12 cuboctahedra, faces with three equivalent Ba(1)O12 cuboctahedra, faces with three equivalent Ba(3)O12 cuboctahedra, and  a faceface with one Ti(1)O6 octahedra. The corner-sharing octahedra are not tilted. In the second Fe site, Fe(2) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form FeO6 octahedra that share corners with three equivalent Ti(1)O6 octahedra, corners with three equivalent Fe(1)O6 octahedra, faces with two equivalent Ba(3)O12 cuboctahedra, faces with three equivalent Ba(1)O12 cuboctahedra, and faces with three equivalent Ba(2)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 0-7°. There are three inequivalent O sites. In the first O site, O(1) is bonded in a distorted linear geometry to one Ba(2), one Ba(3), two equivalent Ba(1), one Fe(1), and one Fe(2) atom. In the second O site, O(2) is bonded in a distorted linear geometry to one Ba(1), one Ba(3), two equivalent Ba(2), one Ti(1), and one Fe(2) atom. In the third O site, O(3) is bonded in a 6-coordinate geometry to one Ba(1), one Ba(2), two equivalent Ba(3), one Ti(1), and one Fe(1) atom. is represented by the CIF file [CIF]
data_Ba3TiFe2O9
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.775
_cell_length_b   5.775
_cell_length_c   14.119
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   407.713
_cell_formula_units_Z   2
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  0.667  0.333  0.597  1.0
  Ba  Ba1  1  0.333  0.667  0.417  1.0
  Ba  Ba2  1  0.333  0.667  0.097  1.0
  Ba  Ba3  1  0.667  0.333  0.917  1.0
  Ba  Ba4  1  0.000  0.000  0.748  1.0
  Ba  Ba5  1  0.000  0.000  0.247  1.0
  Ti  Ti6  1  0.667  0.333  0.352  1.0
  Ti  Ti7  1  0.333  0.667  0.852  1.0
  Fe  Fe8  1  0.333  0.667  0.658  1.0
  Fe  Fe9  1  0.667  0.333  0.158  1.0
  Fe  Fe10  1  0.000  0.000  0.502  1.0
  Fe  Fe11  1  0.000  0.000  0.002  1.0
  O  O12  1  0.171  0.342  0.581  1.0
  O  O13  1  0.171  0.829  0.581  1.0
  O  O14  1  0.658  0.829  0.581  1.0
  O  O15  1  0.832  0.665  0.416  1.0
  O  O16  1  0.832  0.168  0.416  1.0
  O  O17  1  0.335  0.168  0.416  1.0
  O  O18  1  0.829  0.658  0.081  1.0
  O  O19  1  0.829  0.171  0.081  1.0
  O  O20  1  0.342  0.171  0.081  1.0
  O  O21  1  0.168  0.335  0.916  1.0
  O  O22  1  0.168  0.832  0.916  1.0
  O  O23  1  0.665  0.832  0.916  1.0
  O  O24  1  0.480  0.960  0.745  1.0
  O  O25  1  0.480  0.520  0.745  1.0
  O  O26  1  0.040  0.520  0.745  1.0
  O  O27  1  0.520  0.040  0.245  1.0
  O  O28  1  0.520  0.480  0.245  1.0
  O  O29  1  0.960  0.480  0.245  1.0
[/CIF]
.