The compound described by K4Zr5O12 crystallizes in the trigonal P-3m1 space group. There are two inequivalent K sites. In the first K site, K(1) is bonded to three equivalent O(1) and nine equivalent O(2) atoms to form KO12 cuboctahedra that share corners with six equivalent K(1)O12 cuboctahedra, faces with three equivalent K(1)O12 cuboctahedra, faces with three equivalent Zr(3)O6 octahedra, and faces with four equivalent Zr(1)O6 octahedra. In the second K site, K(2) is bonded in a 9-coordinate geometry to three equivalent O(2) and six equivalent O(1) atoms. There are three inequivalent Zr sites. In the first Zr site, Zr(1) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form distorted ZrO6 octahedra that share corners with three equivalent Zr(3)O6 octahedra and faces with four equivalent K(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 7°. In the second Zr site, Zr(2) is bonded in a 6-coordinate geometry to six equivalent O(1) atoms. In the third Zr site, Zr(3) is bonded to six equivalent O(2) atoms to form ZrO6 octahedra that share corners with six equivalent Zr(1)O6 octahedra and faces with six equivalent K(1)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 3-coordinate geometry to one K(1), two equivalent K(2), one Zr(1), and two equivalent Zr(2) atoms. In the second O site, O(2) is bonded in a 6-coordinate geometry to one K(2), three equivalent K(1), one Zr(1), and one Zr(3) atom. is represented by the CIF card [CIF]
data_K4Zr5O12
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.831
_cell_length_b   5.831
_cell_length_c   10.464
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   308.094
_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  0.667  0.333  0.613  1.0
  K  K1  1  0.333  0.667  0.387  1.0
  K  K2  1  1.000  0.000  0.821  1.0
  K  K3  1  1.000  1.000  0.179  1.0
  Zr  Zr4  1  0.667  0.333  0.283  1.0
  Zr  Zr5  1  0.333  0.667  0.717  1.0
  Zr  Zr6  1  0.667  0.333  0.976  1.0
  Zr  Zr7  1  0.333  0.667  0.024  1.0
  Zr  Zr8  1  1.000  1.000  0.500  1.0
  O  O9  1  0.981  0.490  0.123  1.0
  O  O10  1  0.510  0.490  0.123  1.0
  O  O11  1  0.510  0.019  0.123  1.0
  O  O12  1  0.490  0.510  0.877  1.0
  O  O13  1  0.019  0.510  0.877  1.0
  O  O14  1  0.490  0.981  0.877  1.0
  O  O15  1  0.330  0.165  0.379  1.0
  O  O16  1  0.835  0.165  0.379  1.0
  O  O17  1  0.835  0.670  0.379  1.0
  O  O18  1  0.165  0.330  0.621  1.0
  O  O19  1  0.670  0.835  0.621  1.0
  O  O20  1  0.165  0.835  0.621  1.0
[/CIF]
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The compound described by K4Zr5O12 crystallizes in the trigonal P-3m1 space group. There are two inequivalent K sites. In the first K site, K(1) is bonded to three equivalent O(1) and nine equivalent O(2) atoms to form KO12 cuboctahedra that share corners with six equivalent K(1)O12 cuboctahedra, faces with three equivalent K(1)O12 cuboctahedra, faces with three equivalent Zr(3)O6 octahedra, and faces with four equivalent Zr(1)O6 octahedra. In the second K site, K(2) is bonded in a 9-coordinate geometry to three equivalent O(2) and six equivalent O(1) atoms. There are three inequivalent Zr sites. In the first Zr site, Zr(1) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form distorted ZrO6 octahedra that share corners with three equivalent Zr(3)O6 octahedra and faces with four equivalent K(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 7°. In the second Zr site, Zr(2) is bonded in a 6-coordinate geometry to six equivalent O(1) atoms. In the third Zr site, Zr(3) is bonded to six equivalent O(2) atoms to form ZrO6 octahedra that share corners with six equivalent Zr(1)O6 octahedra and faces with six equivalent K(1)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 3-coordinate geometry to one K(1), two equivalent K(2), one Zr(1), and two equivalent Zr(2) atoms. In the second O site, O(2) is bonded in a 6-coordinate geometry to one K(2), three equivalent K(1), one Zr(1), and one Zr(3) atom. is represented by the CIF card [CIF]
data_K4Zr5O12
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.831
_cell_length_b   5.831
_cell_length_c   10.464
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   308.094
_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  0.667  0.333  0.613  1.0
  K  K1  1  0.333  0.667  0.387  1.0
  K  K2  1  1.000  0.000  0.821  1.0
  K  K3  1  1.000  1.000  0.179  1.0
  Zr  Zr4  1  0.667  0.333  0.283  1.0
  Zr  Zr5  1  0.333  0.667  0.717  1.0
  Zr  Zr6  1  0.667  0.333  0.976  1.0
  Zr  Zr7  1  0.333  0.667  0.024  1.0
  Zr  Zr8  1  1.000  1.000  0.500  1.0
  O  O9  1  0.981  0.490  0.123  1.0
  O  O10  1  0.510  0.490  0.123  1.0
  O  O11  1  0.510  0.019  0.123  1.0
  O  O12  1  0.490  0.510  0.877  1.0
  O  O13  1  0.019  0.510  0.877  1.0
  O  O14  1  0.490  0.981  0.877  1.0
  O  O15  1  0.330  0.165  0.379  1.0
  O  O16  1  0.835  0.165  0.379  1.0
  O  O17  1  0.835  0.670  0.379  1.0
  O  O18  1  0.165  0.330  0.621  1.0
  O  O19  1  0.670  0.835  0.621  1.0
  O  O20  1  0.165  0.835  0.621  1.0
[/CIF]
.