The structure described by Ba3HfNb4O15 crystallizes in the tetragonal P4bm space group. There are two inequivalent Ba sites. In the first Ba site, Ba(1) is bonded to four equivalent O(3) and eight equivalent O(2) atoms to form BaO12 cuboctahedra that share faces with two equivalent Ba(1)O12 cuboctahedra and faces with eight equivalent Nb(1)O6 octahedra. In the second Ba site, Ba(2) is bonded in a 9-coordinate geometry to one O(4), two equivalent O(3), two equivalent O(5), and four equivalent O(1) atoms. Hf(1) is bonded to two equivalent O(4) and four equivalent O(1) atoms to form HfO6 octahedra that share corners with two equivalent Hf(1)O6 octahedra and corners with four equivalent Nb(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-39°. Nb(1) is bonded to one O(1), one O(5), two equivalent O(2), and two equivalent O(3) atoms to form NbO6 octahedra that share  a cornercorner with one Hf(1)O6 octahedra, corners with five equivalent Nb(1)O6 octahedra, and faces with two equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 7-39°. There are five inequivalent O sites. In the first O site, O(3) is bonded in a 2-coordinate geometry to one Ba(1), one Ba(2), and two equivalent Nb(1) atoms. In the second O site, O(4) is bonded in a linear geometry to two equivalent Ba(2) and two equivalent Hf(1) atoms. In the third O site, O(5) is bonded in a 4-coordinate geometry to two equivalent Ba(2) and two equivalent Nb(1) atoms. In the fourth O site, O(1) is bonded in a distorted rectangular see-saw-like geometry to two equivalent Ba(2), one Hf(1), and one Nb(1) atom. In the fifth O site, O(2) is bonded in a 2-coordinate geometry to two equivalent Ba(1) and two equivalent Nb(1) atoms. is represented by the Crystallographic Information File (CIF) [CIF]
data_Ba3HfNb4O15
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   4.113
_cell_length_b   12.813
_cell_length_c   12.813
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   675.148
_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  0.335  0.500  0.500  1.0
  Ba  Ba1  1  0.335  0.000  0.000  1.0
  Ba  Ba2  1  0.344  0.832  0.332  1.0
  Ba  Ba3  1  0.344  0.168  0.668  1.0
  Ba  Ba4  1  0.344  0.668  0.832  1.0
  Ba  Ba5  1  0.344  0.332  0.168  1.0
  Hf  Hf6  1  0.827  0.000  0.500  1.0
  Hf  Hf7  1  0.827  0.500  0.000  1.0
  Nb  Nb8  1  0.855  0.286  0.425  1.0
  Nb  Nb9  1  0.855  0.714  0.575  1.0
  Nb  Nb10  1  0.855  0.214  0.925  1.0
  Nb  Nb11  1  0.855  0.786  0.075  1.0
  Nb  Nb12  1  0.855  0.425  0.714  1.0
  Nb  Nb13  1  0.855  0.575  0.286  1.0
  Nb  Nb14  1  0.855  0.925  0.786  1.0
  Nb  Nb15  1  0.855  0.075  0.214  1.0
  O  O16  1  0.816  0.490  0.162  1.0
  O  O17  1  0.816  0.510  0.838  1.0
  O  O18  1  0.816  0.010  0.662  1.0
  O  O19  1  0.816  0.990  0.338  1.0
  O  O20  1  0.816  0.162  0.510  1.0
  O  O21  1  0.816  0.838  0.490  1.0
  O  O22  1  0.816  0.662  0.990  1.0
  O  O23  1  0.816  0.338  0.010  1.0
  O  O24  1  0.808  0.433  0.362  1.0
  O  O25  1  0.808  0.567  0.638  1.0
  O  O26  1  0.808  0.067  0.862  1.0
  O  O27  1  0.808  0.933  0.138  1.0
  O  O28  1  0.808  0.362  0.567  1.0
  O  O29  1  0.808  0.638  0.433  1.0
  O  O30  1  0.808  0.862  0.933  1.0
  O  O31  1  0.808  0.138  0.067  1.0
  O  O32  1  0.311  0.295  0.421  1.0
  O  O33  1  0.311  0.705  0.579  1.0
  O  O34  1  0.311  0.205  0.921  1.0
  O  O35  1  0.311  0.795  0.079  1.0
  O  O36  1  0.311  0.421  0.705  1.0
  O  O37  1  0.311  0.579  0.295  1.0
  O  O38  1  0.311  0.921  0.795  1.0
  O  O39  1  0.311  0.079  0.205  1.0
  O  O40  1  0.320  0.000  0.500  1.0
  O  O41  1  0.320  0.500  0.000  1.0
  O  O42  1  0.814  0.717  0.217  1.0
  O  O43  1  0.814  0.283  0.783  1.0
  O  O44  1  0.814  0.783  0.717  1.0
  O  O45  1  0.814  0.217  0.283  1.0
[/CIF]
.
The structure described by Ba3HfNb4O15 crystallizes in the tetragonal P4bm space group. There are two inequivalent Ba sites. In the first Ba site, Ba(1) is bonded to four equivalent O(3) and eight equivalent O(2) atoms to form BaO12 cuboctahedra that share faces with two equivalent Ba(1)O12 cuboctahedra and faces with eight equivalent Nb(1)O6 octahedra. In the second Ba site, Ba(2) is bonded in a 9-coordinate geometry to one O(4), two equivalent O(3), two equivalent O(5), and four equivalent O(1) atoms. Hf(1) is bonded to two equivalent O(4) and four equivalent O(1) atoms to form HfO6 octahedra that share corners with two equivalent Hf(1)O6 octahedra and corners with four equivalent Nb(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-39°. Nb(1) is bonded to one O(1), one O(5), two equivalent O(2), and two equivalent O(3) atoms to form NbO6 octahedra that share  a cornercorner with one Hf(1)O6 octahedra, corners with five equivalent Nb(1)O6 octahedra, and faces with two equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 7-39°. There are five inequivalent O sites. In the first O site, O(3) is bonded in a 2-coordinate geometry to one Ba(1), one Ba(2), and two equivalent Nb(1) atoms. In the second O site, O(4) is bonded in a linear geometry to two equivalent Ba(2) and two equivalent Hf(1) atoms. In the third O site, O(5) is bonded in a 4-coordinate geometry to two equivalent Ba(2) and two equivalent Nb(1) atoms. In the fourth O site, O(1) is bonded in a distorted rectangular see-saw-like geometry to two equivalent Ba(2), one Hf(1), and one Nb(1) atom. In the fifth O site, O(2) is bonded in a 2-coordinate geometry to two equivalent Ba(1) and two equivalent Nb(1) atoms. is represented by the Crystallographic Information File (CIF) [CIF]
data_Ba3HfNb4O15
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   4.113
_cell_length_b   12.813
_cell_length_c   12.813
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   675.148
_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  0.335  0.500  0.500  1.0
  Ba  Ba1  1  0.335  0.000  0.000  1.0
  Ba  Ba2  1  0.344  0.832  0.332  1.0
  Ba  Ba3  1  0.344  0.168  0.668  1.0
  Ba  Ba4  1  0.344  0.668  0.832  1.0
  Ba  Ba5  1  0.344  0.332  0.168  1.0
  Hf  Hf6  1  0.827  0.000  0.500  1.0
  Hf  Hf7  1  0.827  0.500  0.000  1.0
  Nb  Nb8  1  0.855  0.286  0.425  1.0
  Nb  Nb9  1  0.855  0.714  0.575  1.0
  Nb  Nb10  1  0.855  0.214  0.925  1.0
  Nb  Nb11  1  0.855  0.786  0.075  1.0
  Nb  Nb12  1  0.855  0.425  0.714  1.0
  Nb  Nb13  1  0.855  0.575  0.286  1.0
  Nb  Nb14  1  0.855  0.925  0.786  1.0
  Nb  Nb15  1  0.855  0.075  0.214  1.0
  O  O16  1  0.816  0.490  0.162  1.0
  O  O17  1  0.816  0.510  0.838  1.0
  O  O18  1  0.816  0.010  0.662  1.0
  O  O19  1  0.816  0.990  0.338  1.0
  O  O20  1  0.816  0.162  0.510  1.0
  O  O21  1  0.816  0.838  0.490  1.0
  O  O22  1  0.816  0.662  0.990  1.0
  O  O23  1  0.816  0.338  0.010  1.0
  O  O24  1  0.808  0.433  0.362  1.0
  O  O25  1  0.808  0.567  0.638  1.0
  O  O26  1  0.808  0.067  0.862  1.0
  O  O27  1  0.808  0.933  0.138  1.0
  O  O28  1  0.808  0.362  0.567  1.0
  O  O29  1  0.808  0.638  0.433  1.0
  O  O30  1  0.808  0.862  0.933  1.0
  O  O31  1  0.808  0.138  0.067  1.0
  O  O32  1  0.311  0.295  0.421  1.0
  O  O33  1  0.311  0.705  0.579  1.0
  O  O34  1  0.311  0.205  0.921  1.0
  O  O35  1  0.311  0.795  0.079  1.0
  O  O36  1  0.311  0.421  0.705  1.0
  O  O37  1  0.311  0.579  0.295  1.0
  O  O38  1  0.311  0.921  0.795  1.0
  O  O39  1  0.311  0.079  0.205  1.0
  O  O40  1  0.320  0.000  0.500  1.0
  O  O41  1  0.320  0.500  0.000  1.0
  O  O42  1  0.814  0.717  0.217  1.0
  O  O43  1  0.814  0.283  0.783  1.0
  O  O44  1  0.814  0.783  0.717  1.0
  O  O45  1  0.814  0.217  0.283  1.0
[/CIF]
.