The compound described by K4Hf5O12 crystallizes in the trigonal P-3m1 space group. There are two inequivalent K sites. In the first K site, K(1) is bonded in a 9-coordinate geometry to three equivalent O(1) and six equivalent O(2) atoms. In the second K site, K(2) is bonded to three equivalent O(2) and nine equivalent O(1) atoms to form KO12 cuboctahedra that share corners with six equivalent K(2)O12 cuboctahedra, faces with three equivalent K(2)O12 cuboctahedra, faces with three equivalent Hf(2)O6 octahedra, and faces with four equivalent Hf(3)O6 octahedra. There are three inequivalent Hf sites. In the first Hf site, Hf(1) is bonded in a 6-coordinate geometry to six equivalent O(2) atoms. In the second Hf site, Hf(2) is bonded to six equivalent O(1) atoms to form HfO6 octahedra that share corners with six equivalent Hf(3)O6 octahedra and faces with six equivalent K(2)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 7°. In the third Hf site, Hf(3) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form distorted HfO6 octahedra that share corners with three equivalent Hf(2)O6 octahedra and faces with four equivalent K(2)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 7°. There are two inequivalent O sites. In the first O site, O(1) is bonded in a 6-coordinate geometry to one K(1), three equivalent K(2), one Hf(2), and one Hf(3) atom. In the second O site, O(2) is bonded in a 3-coordinate geometry to one K(2), two equivalent K(1), one Hf(3), and two equivalent Hf(1) atoms. is represented by the CIF file [CIF]
data_K4Hf5O12
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.766
_cell_length_b   5.766
_cell_length_c   10.324
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   297.237
_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
  K  K0  1  0.000  0.000  0.323  1.0
  K  K1  1  1.000  1.000  0.677  1.0
  K  K2  1  0.333  0.667  0.113  1.0
  K  K3  1  0.667  0.333  0.887  1.0
  Hf  Hf4  1  0.333  0.667  0.476  1.0
  Hf  Hf5  1  0.667  0.333  0.524  1.0
  Hf  Hf6  1  1.000  1.000  1.000  1.0
  Hf  Hf7  1  0.333  0.667  0.784  1.0
  Hf  Hf8  1  0.667  0.333  0.216  1.0
  O  O9  1  0.835  0.165  0.121  1.0
  O  O10  1  0.835  0.670  0.121  1.0
  O  O11  1  0.330  0.165  0.121  1.0
  O  O12  1  0.670  0.835  0.879  1.0
  O  O13  1  0.165  0.330  0.879  1.0
  O  O14  1  0.165  0.835  0.879  1.0
  O  O15  1  0.510  0.490  0.377  1.0
  O  O16  1  0.510  0.019  0.377  1.0
  O  O17  1  0.981  0.490  0.377  1.0
  O  O18  1  0.019  0.510  0.623  1.0
  O  O19  1  0.490  0.981  0.623  1.0
  O  O20  1  0.490  0.510  0.623  1.0
[/CIF]
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The compound described by K4Hf5O12 crystallizes in the trigonal P-3m1 space group. There are two inequivalent K sites. In the first K site, K(1) is bonded in a 9-coordinate geometry to three equivalent O(1) and six equivalent O(2) atoms. In the second K site, K(2) is bonded to three equivalent O(2) and nine equivalent O(1) atoms to form KO12 cuboctahedra that share corners with six equivalent K(2)O12 cuboctahedra, faces with three equivalent K(2)O12 cuboctahedra, faces with three equivalent Hf(2)O6 octahedra, and faces with four equivalent Hf(3)O6 octahedra. There are three inequivalent Hf sites. In the first Hf site, Hf(1) is bonded in a 6-coordinate geometry to six equivalent O(2) atoms. In the second Hf site, Hf(2) is bonded to six equivalent O(1) atoms to form HfO6 octahedra that share corners with six equivalent Hf(3)O6 octahedra and faces with six equivalent K(2)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 7°. In the third Hf site, Hf(3) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form distorted HfO6 octahedra that share corners with three equivalent Hf(2)O6 octahedra and faces with four equivalent K(2)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 7°. There are two inequivalent O sites. In the first O site, O(1) is bonded in a 6-coordinate geometry to one K(1), three equivalent K(2), one Hf(2), and one Hf(3) atom. In the second O site, O(2) is bonded in a 3-coordinate geometry to one K(2), two equivalent K(1), one Hf(3), and two equivalent Hf(1) atoms. is represented by the CIF file [CIF]
data_K4Hf5O12
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.766
_cell_length_b   5.766
_cell_length_c   10.324
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   297.237
_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
  K  K0  1  0.000  0.000  0.323  1.0
  K  K1  1  1.000  1.000  0.677  1.0
  K  K2  1  0.333  0.667  0.113  1.0
  K  K3  1  0.667  0.333  0.887  1.0
  Hf  Hf4  1  0.333  0.667  0.476  1.0
  Hf  Hf5  1  0.667  0.333  0.524  1.0
  Hf  Hf6  1  1.000  1.000  1.000  1.0
  Hf  Hf7  1  0.333  0.667  0.784  1.0
  Hf  Hf8  1  0.667  0.333  0.216  1.0
  O  O9  1  0.835  0.165  0.121  1.0
  O  O10  1  0.835  0.670  0.121  1.0
  O  O11  1  0.330  0.165  0.121  1.0
  O  O12  1  0.670  0.835  0.879  1.0
  O  O13  1  0.165  0.330  0.879  1.0
  O  O14  1  0.165  0.835  0.879  1.0
  O  O15  1  0.510  0.490  0.377  1.0
  O  O16  1  0.510  0.019  0.377  1.0
  O  O17  1  0.981  0.490  0.377  1.0
  O  O18  1  0.019  0.510  0.623  1.0
  O  O19  1  0.490  0.981  0.623  1.0
  O  O20  1  0.490  0.510  0.623  1.0
[/CIF]
.