The structure described by Ba7Ti2Nb4O21 crystallizes in the trigonal R-3m space group. There are four 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(4)O12 cuboctahedra, corners with six equivalent Ba(1)O12 cuboctahedra, faces with three equivalent Ba(3)O12 cuboctahedra,  a faceface with one Nb(2)O6 octahedra, faces with three equivalent Ti(1)O6 octahedra, and faces with three equivalent Nb(1)O6 octahedra. In the second Ba site, Ba(2) is bonded in a 12-coordinate geometry to three equivalent O(1) and nine equivalent O(3) atoms. In the third Ba site, Ba(3) is bonded to three equivalent O(1), three equivalent O(4), and six equivalent O(2) atoms to form BaO12 cuboctahedra that share corners with nine equivalent Ba(3)O12 cuboctahedra, faces with three equivalent Ba(1)O12 cuboctahedra, faces with three equivalent Ba(4)O12 cuboctahedra,  a faceface with one Nb(1)O6 octahedra, faces with three equivalent Ti(1)O6 octahedra, and faces with four equivalent Nb(2)O6 octahedra. In the fourth Ba site, Ba(4) is bonded to six equivalent O(2) and six equivalent O(4) atoms to form BaO12 cuboctahedra that share corners with six equivalent Ba(1)O12 cuboctahedra, corners with six equivalent Ba(4)O12 cuboctahedra, faces with six equivalent Ba(3)O12 cuboctahedra, faces with two equivalent Ti(1)O6 octahedra, and faces with six equivalent Nb(2)O6 octahedra. Ti(1) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form TiO6 octahedra that share corners with three equivalent Nb(1)O6 octahedra, corners with three equivalent Nb(2)O6 octahedra,  a faceface with one Ba(4)O12 cuboctahedra, faces with three equivalent Ba(1)O12 cuboctahedra, and faces with three equivalent Ba(3)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 8-12°. There are two inequivalent Nb sites. In the first Nb site, Nb(1) is bonded to three equivalent O(1) and three equivalent O(3) atoms to form distorted NbO6 octahedra that share corners with three equivalent Ti(1)O6 octahedra,  a faceface with one Ba(3)O12 cuboctahedra, and faces with three equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 12°. In the second Nb site, Nb(2) is bonded to three equivalent O(2) and three equivalent O(4) atoms to form NbO6 octahedra that share corners with three equivalent Ti(1)O6 octahedra, corners with three equivalent Nb(2)O6 octahedra,  a faceface with one Ba(1)O12 cuboctahedra, faces with three equivalent Ba(4)O12 cuboctahedra, and faces with four equivalent Ba(3)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 0-8°. There are four inequivalent O sites. In the first O site, O(1) is bonded in a 1-coordinate geometry to one Ba(2), one Ba(3), two equivalent Ba(1), one Ti(1), and one Nb(1) atom. In the second O site, O(2) is bonded in a 2-coordinate geometry to one Ba(1), one Ba(4), two equivalent Ba(3), one Ti(1), and one Nb(2) atom. In the third O site, O(3) is bonded in a distorted single-bond geometry to one Ba(1), three equivalent Ba(2), and one Nb(1) atom. In the fourth O site, O(4) is bonded to two equivalent Ba(3), two equivalent Ba(4), and two equivalent Nb(2) atoms to form a mixture of distorted face and corner-sharing OBa4Nb2 octahedra. The corner-sharing octahedral tilt angles range from 0-60°. is represented by the CIF file [CIF]
data_Ba7Ti2Nb4O21
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   17.049
_cell_length_b   17.049
_cell_length_c   17.049
_cell_angle_alpha   19.795
_cell_angle_beta   19.795
_cell_angle_gamma   19.795
_symmetry_Int_Tables_number   1
_cell_volume   497.142
_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  0.765  0.765  0.765  1.0
  Ba  Ba1  1  0.235  0.235  0.235  1.0
  Ba  Ba2  1  0.851  0.851  0.851  1.0
  Ba  Ba3  1  0.149  0.149  0.149  1.0
  Ba  Ba4  1  0.618  0.618  0.618  1.0
  Ba  Ba5  1  0.382  0.382  0.382  1.0
  Ba  Ba6  1  0.000  0.000  0.000  1.0
  Ti  Ti7  1  0.924  0.924  0.924  1.0
  Ti  Ti8  1  0.076  0.076  0.076  1.0
  Nb  Nb9  1  0.543  0.543  0.543  1.0
  Nb  Nb10  1  0.457  0.457  0.457  1.0
  Nb  Nb11  1  0.692  0.692  0.692  1.0
  Nb  Nb12  1  0.308  0.308  0.308  1.0
  O  O13  1  0.745  0.229  0.745  1.0
  O  O14  1  0.745  0.745  0.229  1.0
  O  O15  1  0.229  0.745  0.745  1.0
  O  O16  1  0.255  0.771  0.255  1.0
  O  O17  1  0.255  0.255  0.771  1.0
  O  O18  1  0.771  0.255  0.255  1.0
  O  O19  1  0.878  0.385  0.878  1.0
  O  O20  1  0.878  0.878  0.385  1.0
  O  O21  1  0.385  0.878  0.878  1.0
  O  O22  1  0.122  0.615  0.122  1.0
  O  O23  1  0.122  0.122  0.615  1.0
  O  O24  1  0.615  0.122  0.122  1.0
  O  O25  1  0.638  0.146  0.638  1.0
  O  O26  1  0.638  0.638  0.146  1.0
  O  O27  1  0.146  0.638  0.638  1.0
  O  O28  1  0.362  0.854  0.362  1.0
  O  O29  1  0.362  0.362  0.854  1.0
  O  O30  1  0.854  0.362  0.362  1.0
  O  O31  1  0.500  0.500  0.000  1.0
  O  O32  1  0.000  0.500  0.500  1.0
  O  O33  1  0.500  0.000  0.500  1.0
[/CIF]
.
The structure described by Ba7Ti2Nb4O21 crystallizes in the trigonal R-3m space group. There are four 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(4)O12 cuboctahedra, corners with six equivalent Ba(1)O12 cuboctahedra, faces with three equivalent Ba(3)O12 cuboctahedra,  a faceface with one Nb(2)O6 octahedra, faces with three equivalent Ti(1)O6 octahedra, and faces with three equivalent Nb(1)O6 octahedra. In the second Ba site, Ba(2) is bonded in a 12-coordinate geometry to three equivalent O(1) and nine equivalent O(3) atoms. In the third Ba site, Ba(3) is bonded to three equivalent O(1), three equivalent O(4), and six equivalent O(2) atoms to form BaO12 cuboctahedra that share corners with nine equivalent Ba(3)O12 cuboctahedra, faces with three equivalent Ba(1)O12 cuboctahedra, faces with three equivalent Ba(4)O12 cuboctahedra,  a faceface with one Nb(1)O6 octahedra, faces with three equivalent Ti(1)O6 octahedra, and faces with four equivalent Nb(2)O6 octahedra. In the fourth Ba site, Ba(4) is bonded to six equivalent O(2) and six equivalent O(4) atoms to form BaO12 cuboctahedra that share corners with six equivalent Ba(1)O12 cuboctahedra, corners with six equivalent Ba(4)O12 cuboctahedra, faces with six equivalent Ba(3)O12 cuboctahedra, faces with two equivalent Ti(1)O6 octahedra, and faces with six equivalent Nb(2)O6 octahedra. Ti(1) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form TiO6 octahedra that share corners with three equivalent Nb(1)O6 octahedra, corners with three equivalent Nb(2)O6 octahedra,  a faceface with one Ba(4)O12 cuboctahedra, faces with three equivalent Ba(1)O12 cuboctahedra, and faces with three equivalent Ba(3)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 8-12°. There are two inequivalent Nb sites. In the first Nb site, Nb(1) is bonded to three equivalent O(1) and three equivalent O(3) atoms to form distorted NbO6 octahedra that share corners with three equivalent Ti(1)O6 octahedra,  a faceface with one Ba(3)O12 cuboctahedra, and faces with three equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 12°. In the second Nb site, Nb(2) is bonded to three equivalent O(2) and three equivalent O(4) atoms to form NbO6 octahedra that share corners with three equivalent Ti(1)O6 octahedra, corners with three equivalent Nb(2)O6 octahedra,  a faceface with one Ba(1)O12 cuboctahedra, faces with three equivalent Ba(4)O12 cuboctahedra, and faces with four equivalent Ba(3)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 0-8°. There are four inequivalent O sites. In the first O site, O(1) is bonded in a 1-coordinate geometry to one Ba(2), one Ba(3), two equivalent Ba(1), one Ti(1), and one Nb(1) atom. In the second O site, O(2) is bonded in a 2-coordinate geometry to one Ba(1), one Ba(4), two equivalent Ba(3), one Ti(1), and one Nb(2) atom. In the third O site, O(3) is bonded in a distorted single-bond geometry to one Ba(1), three equivalent Ba(2), and one Nb(1) atom. In the fourth O site, O(4) is bonded to two equivalent Ba(3), two equivalent Ba(4), and two equivalent Nb(2) atoms to form a mixture of distorted face and corner-sharing OBa4Nb2 octahedra. The corner-sharing octahedral tilt angles range from 0-60°. is represented by the CIF file [CIF]
data_Ba7Ti2Nb4O21
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   17.049
_cell_length_b   17.049
_cell_length_c   17.049
_cell_angle_alpha   19.795
_cell_angle_beta   19.795
_cell_angle_gamma   19.795
_symmetry_Int_Tables_number   1
_cell_volume   497.142
_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  0.765  0.765  0.765  1.0
  Ba  Ba1  1  0.235  0.235  0.235  1.0
  Ba  Ba2  1  0.851  0.851  0.851  1.0
  Ba  Ba3  1  0.149  0.149  0.149  1.0
  Ba  Ba4  1  0.618  0.618  0.618  1.0
  Ba  Ba5  1  0.382  0.382  0.382  1.0
  Ba  Ba6  1  0.000  0.000  0.000  1.0
  Ti  Ti7  1  0.924  0.924  0.924  1.0
  Ti  Ti8  1  0.076  0.076  0.076  1.0
  Nb  Nb9  1  0.543  0.543  0.543  1.0
  Nb  Nb10  1  0.457  0.457  0.457  1.0
  Nb  Nb11  1  0.692  0.692  0.692  1.0
  Nb  Nb12  1  0.308  0.308  0.308  1.0
  O  O13  1  0.745  0.229  0.745  1.0
  O  O14  1  0.745  0.745  0.229  1.0
  O  O15  1  0.229  0.745  0.745  1.0
  O  O16  1  0.255  0.771  0.255  1.0
  O  O17  1  0.255  0.255  0.771  1.0
  O  O18  1  0.771  0.255  0.255  1.0
  O  O19  1  0.878  0.385  0.878  1.0
  O  O20  1  0.878  0.878  0.385  1.0
  O  O21  1  0.385  0.878  0.878  1.0
  O  O22  1  0.122  0.615  0.122  1.0
  O  O23  1  0.122  0.122  0.615  1.0
  O  O24  1  0.615  0.122  0.122  1.0
  O  O25  1  0.638  0.146  0.638  1.0
  O  O26  1  0.638  0.638  0.146  1.0
  O  O27  1  0.146  0.638  0.638  1.0
  O  O28  1  0.362  0.854  0.362  1.0
  O  O29  1  0.362  0.362  0.854  1.0
  O  O30  1  0.854  0.362  0.362  1.0
  O  O31  1  0.500  0.500  0.000  1.0
  O  O32  1  0.000  0.500  0.500  1.0
  O  O33  1  0.500  0.000  0.500  1.0
[/CIF]
.