The crystal structure described by Bi4Ti3O12 crystallizes in the monoclinic Cc space group. There are three inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(4), one O(6), two equivalent O(1), and two equivalent O(10) atoms to form corner-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 21-30°. In the second Ti site, Ti(2) is bonded to one O(4), one O(8), two equivalent O(3), and two equivalent O(7) atoms to form distorted corner-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 25-35°. In the third Ti site, Ti(3) is bonded in a 6-coordinate geometry to one O(2), one O(6), two equivalent O(11), and two equivalent O(9) atoms. There are four inequivalent Bi sites. In the first Bi site, Bi(1) is bonded in a 6-coordinate geometry to two equivalent O(12), two equivalent O(5), and two equivalent O(8) atoms. In the second Bi site, Bi(2) is bonded in a 6-coordinate geometry to two equivalent O(12), two equivalent O(2), and two equivalent O(5) atoms. In the third Bi site, Bi(3) is bonded in a 6-coordinate geometry to one O(10), one O(11), two equivalent O(6), and two equivalent O(9) atoms. In the fourth Bi site, Bi(4) is bonded in a 8-coordinate geometry to one O(10), one O(3), two equivalent O(1), two equivalent O(4), and two equivalent O(7) atoms. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a 4-coordinate geometry to two equivalent Ti(1) and two equivalent Bi(4) atoms. In the second O site, O(2) is bonded in a distorted single-bond geometry to one Ti(3) and two equivalent Bi(2) atoms. In the third O site, O(3) is bonded in a 3-coordinate geometry to two equivalent Ti(2) and one Bi(4) atom. In the fourth O site, O(4) is bonded in a distorted see-saw-like geometry to one Ti(1), one Ti(2), and two equivalent Bi(4) atoms. In the fifth O site, O(5) is bonded to two equivalent Bi(1) and two equivalent Bi(2) atoms to form a mixture of corner and edge-sharing OBi4 tetrahedra. In the sixth O site, O(6) is bonded in a distorted see-saw-like geometry to one Ti(1), one Ti(3), and two equivalent Bi(3) atoms. In the seventh O site, O(7) is bonded in a 4-coordinate geometry to two equivalent Ti(2) and two equivalent Bi(4) atoms. In the eighth O site, O(8) is bonded in a distorted single-bond geometry to one Ti(2) and two equivalent Bi(1) atoms. In the ninth O site, O(9) is bonded to two equivalent Ti(3) and two equivalent Bi(3) atoms to form distorted edge-sharing OTi2Bi2 tetrahedra. In the tenth O site, O(10) is bonded in a 4-coordinate geometry to two equivalent Ti(1), one Bi(3), and one Bi(4) atom. In the eleventh O site, O(11) is bonded in a distorted T-shaped geometry to two equivalent Ti(3) and one Bi(3) atom. In the twelfth O site, O(12) is bonded to two equivalent Bi(1) and two equivalent Bi(2) atoms to form a mixture of corner and edge-sharing OBi4 tetrahedra. is represented by the CIF file [CIF]
data_Ti3(BiO3)4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   16.788
_cell_length_b   16.788
_cell_length_c   5.440
_cell_angle_alpha   89.970
_cell_angle_beta   89.970
_cell_angle_gamma   18.465
_symmetry_Int_Tables_number   1
_cell_volume   485.564
_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
  Ti  Ti0  1  0.998  0.505  0.523  1.0
  Ti  Ti1  1  0.126  0.631  0.530  1.0
  Ti  Ti2  1  0.373  0.869  0.025  1.0
  Ti  Ti3  1  0.869  0.373  0.525  1.0
  Ti  Ti4  1  0.631  0.126  0.030  1.0
  Ti  Ti5  1  0.505  0.998  0.023  1.0
  Bi  Bi6  1  0.701  0.219  0.460  1.0
  Bi  Bi7  1  0.786  0.287  0.967  1.0
  Bi  Bi8  1  0.219  0.701  0.960  1.0
  Bi  Bi9  1  0.428  0.938  0.477  1.0
  Bi  Bi10  1  0.287  0.786  0.467  1.0
  Bi  Bi11  1  0.564  0.069  0.484  1.0
  Bi  Bi12  1  0.069  0.564  0.984  1.0
  Bi  Bi13  1  0.938  0.428  0.977  1.0
  O  O14  1  0.295  0.228  0.769  1.0
  O  O15  1  0.359  0.777  0.028  1.0
  O  O16  1  0.929  0.822  0.848  1.0
  O  O17  1  0.636  0.985  0.070  1.0
  O  O18  1  0.501  0.498  0.737  1.0
  O  O19  1  0.010  0.378  0.566  1.0
  O  O20  1  0.985  0.636  0.570  1.0
  O  O21  1  0.329  0.393  0.268  1.0
  O  O22  1  0.378  0.010  0.066  1.0
  O  O23  1  0.625  0.237  0.038  1.0
  O  O24  1  0.657  0.621  0.269  1.0
  O  O25  1  0.777  0.359  0.528  1.0
  O  O26  1  0.789  0.700  0.843  1.0
  O  O27  1  0.165  0.092  0.323  1.0
  O  O28  1  0.822  0.929  0.348  1.0
  O  O29  1  0.001  0.997  0.733  1.0
  O  O30  1  0.621  0.657  0.769  1.0
  O  O31  1  0.237  0.625  0.538  1.0
  O  O32  1  0.700  0.789  0.343  1.0
  O  O33  1  0.498  0.501  0.237  1.0
  O  O34  1  0.393  0.329  0.768  1.0
  O  O35  1  0.997  0.001  0.233  1.0
  O  O36  1  0.092  0.165  0.823  1.0
  O  O37  1  0.228  0.295  0.269  1.0
[/CIF]
.
The crystal structure described by Bi4Ti3O12 crystallizes in the monoclinic Cc space group. There are three inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(4), one O(6), two equivalent O(1), and two equivalent O(10) atoms to form corner-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 21-30°. In the second Ti site, Ti(2) is bonded to one O(4), one O(8), two equivalent O(3), and two equivalent O(7) atoms to form distorted corner-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 25-35°. In the third Ti site, Ti(3) is bonded in a 6-coordinate geometry to one O(2), one O(6), two equivalent O(11), and two equivalent O(9) atoms. There are four inequivalent Bi sites. In the first Bi site, Bi(1) is bonded in a 6-coordinate geometry to two equivalent O(12), two equivalent O(5), and two equivalent O(8) atoms. In the second Bi site, Bi(2) is bonded in a 6-coordinate geometry to two equivalent O(12), two equivalent O(2), and two equivalent O(5) atoms. In the third Bi site, Bi(3) is bonded in a 6-coordinate geometry to one O(10), one O(11), two equivalent O(6), and two equivalent O(9) atoms. In the fourth Bi site, Bi(4) is bonded in a 8-coordinate geometry to one O(10), one O(3), two equivalent O(1), two equivalent O(4), and two equivalent O(7) atoms. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a 4-coordinate geometry to two equivalent Ti(1) and two equivalent Bi(4) atoms. In the second O site, O(2) is bonded in a distorted single-bond geometry to one Ti(3) and two equivalent Bi(2) atoms. In the third O site, O(3) is bonded in a 3-coordinate geometry to two equivalent Ti(2) and one Bi(4) atom. In the fourth O site, O(4) is bonded in a distorted see-saw-like geometry to one Ti(1), one Ti(2), and two equivalent Bi(4) atoms. In the fifth O site, O(5) is bonded to two equivalent Bi(1) and two equivalent Bi(2) atoms to form a mixture of corner and edge-sharing OBi4 tetrahedra. In the sixth O site, O(6) is bonded in a distorted see-saw-like geometry to one Ti(1), one Ti(3), and two equivalent Bi(3) atoms. In the seventh O site, O(7) is bonded in a 4-coordinate geometry to two equivalent Ti(2) and two equivalent Bi(4) atoms. In the eighth O site, O(8) is bonded in a distorted single-bond geometry to one Ti(2) and two equivalent Bi(1) atoms. In the ninth O site, O(9) is bonded to two equivalent Ti(3) and two equivalent Bi(3) atoms to form distorted edge-sharing OTi2Bi2 tetrahedra. In the tenth O site, O(10) is bonded in a 4-coordinate geometry to two equivalent Ti(1), one Bi(3), and one Bi(4) atom. In the eleventh O site, O(11) is bonded in a distorted T-shaped geometry to two equivalent Ti(3) and one Bi(3) atom. In the twelfth O site, O(12) is bonded to two equivalent Bi(1) and two equivalent Bi(2) atoms to form a mixture of corner and edge-sharing OBi4 tetrahedra. is represented by the CIF file [CIF]
data_Ti3(BiO3)4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   16.788
_cell_length_b   16.788
_cell_length_c   5.440
_cell_angle_alpha   89.970
_cell_angle_beta   89.970
_cell_angle_gamma   18.465
_symmetry_Int_Tables_number   1
_cell_volume   485.564
_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
  Ti  Ti0  1  0.998  0.505  0.523  1.0
  Ti  Ti1  1  0.126  0.631  0.530  1.0
  Ti  Ti2  1  0.373  0.869  0.025  1.0
  Ti  Ti3  1  0.869  0.373  0.525  1.0
  Ti  Ti4  1  0.631  0.126  0.030  1.0
  Ti  Ti5  1  0.505  0.998  0.023  1.0
  Bi  Bi6  1  0.701  0.219  0.460  1.0
  Bi  Bi7  1  0.786  0.287  0.967  1.0
  Bi  Bi8  1  0.219  0.701  0.960  1.0
  Bi  Bi9  1  0.428  0.938  0.477  1.0
  Bi  Bi10  1  0.287  0.786  0.467  1.0
  Bi  Bi11  1  0.564  0.069  0.484  1.0
  Bi  Bi12  1  0.069  0.564  0.984  1.0
  Bi  Bi13  1  0.938  0.428  0.977  1.0
  O  O14  1  0.295  0.228  0.769  1.0
  O  O15  1  0.359  0.777  0.028  1.0
  O  O16  1  0.929  0.822  0.848  1.0
  O  O17  1  0.636  0.985  0.070  1.0
  O  O18  1  0.501  0.498  0.737  1.0
  O  O19  1  0.010  0.378  0.566  1.0
  O  O20  1  0.985  0.636  0.570  1.0
  O  O21  1  0.329  0.393  0.268  1.0
  O  O22  1  0.378  0.010  0.066  1.0
  O  O23  1  0.625  0.237  0.038  1.0
  O  O24  1  0.657  0.621  0.269  1.0
  O  O25  1  0.777  0.359  0.528  1.0
  O  O26  1  0.789  0.700  0.843  1.0
  O  O27  1  0.165  0.092  0.323  1.0
  O  O28  1  0.822  0.929  0.348  1.0
  O  O29  1  0.001  0.997  0.733  1.0
  O  O30  1  0.621  0.657  0.769  1.0
  O  O31  1  0.237  0.625  0.538  1.0
  O  O32  1  0.700  0.789  0.343  1.0
  O  O33  1  0.498  0.501  0.237  1.0
  O  O34  1  0.393  0.329  0.768  1.0
  O  O35  1  0.997  0.001  0.233  1.0
  O  O36  1  0.092  0.165  0.823  1.0
  O  O37  1  0.228  0.295  0.269  1.0
[/CIF]
.