The material described by K4HfO4 crystallizes in the triclinic P-1 space group. There are four inequivalent K sites. In the first K site, K(1) is bonded to one O(3), two equivalent O(1), and two equivalent O(2) atoms to form distorted KO5 square pyramids that share  a cornercorner with one Hf(1)O4 tetrahedra, corners with three equivalent K(4)O5 trigonal bipyramids, corners with two equivalent K(3)O4 trigonal pyramids, edges with two equivalent K(1)O5 square pyramids, edges with two equivalent Hf(1)O4 tetrahedra, and edges with three equivalent K(4)O5 trigonal bipyramids. In the second K site, K(2) is bonded in a 5-coordinate geometry to one O(1), one O(2), one O(3), and two equivalent O(4) atoms. In the third K site, K(3) is bonded to two equivalent O(3) and two equivalent O(4) atoms to form distorted KO4 trigonal pyramids that share corners with two equivalent K(1)O5 square pyramids, corners with four equivalent Hf(1)O4 tetrahedra, corners with two equivalent K(4)O5 trigonal bipyramids, and edges with two equivalent K(3)O4 trigonal pyramids. In the fourth K site, K(4) is bonded to one O(3), two equivalent O(1), and two equivalent O(2) atoms to form distorted KO5 trigonal bipyramids that share corners with three equivalent K(1)O5 square pyramids, corners with three equivalent Hf(1)O4 tetrahedra, corners with two equivalent K(3)O4 trigonal pyramids, edges with three equivalent K(1)O5 square pyramids,  an edgeedge with one Hf(1)O4 tetrahedra, and edges with two equivalent K(4)O5 trigonal bipyramids. Hf(1) is bonded to one O(1), one O(2), one O(3), and one O(4) atom to form HfO4 tetrahedra that share  a cornercorner with one K(1)O5 square pyramid, corners with three equivalent K(4)O5 trigonal bipyramids, corners with four equivalent K(3)O4 trigonal pyramids, edges with two equivalent K(1)O5 square pyramids, and  an edgeedge with one K(4)O5 trigonal bipyramid. There are four inequivalent O sites. In the first O site, O(1) is bonded to one K(2), two equivalent K(1), two equivalent K(4), and one Hf(1) atom to form distorted edge-sharing OK5Hf octahedra. In the second O site, O(2) is bonded in a 6-coordinate geometry to one K(2), two equivalent K(1), two equivalent K(4), and one Hf(1) atom. In the third O site, O(3) is bonded in a 6-coordinate geometry to one K(1), one K(2), one K(4), two equivalent K(3), and one Hf(1) atom. In the fourth O site, O(4) is bonded in a 4-coordinate geometry to two equivalent K(2), two equivalent K(3), and one Hf(1) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_K4HfO4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.531
_cell_length_b   6.542
_cell_length_c   9.737
_cell_angle_alpha   72.097
_cell_angle_beta   80.040
_cell_angle_gamma   66.930
_symmetry_Int_Tables_number   1
_cell_volume   363.526
_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
  K  K0  1  0.777  0.041  0.384  1.0
  K  K1  1  0.223  0.959  0.616  1.0
  K  K2  1  0.740  0.587  0.169  1.0
  K  K3  1  0.260  0.413  0.831  1.0
  K  K4  1  0.241  0.761  0.026  1.0
  K  K5  1  0.759  0.239  0.974  1.0
  K  K6  1  0.274  0.514  0.441  1.0
  K  K7  1  0.726  0.486  0.559  1.0
  Hf  Hf8  1  0.279  0.154  0.245  1.0
  Hf  Hf9  1  0.721  0.846  0.755  1.0
  O  O10  1  0.039  0.290  0.378  1.0
  O  O11  1  0.961  0.710  0.622  1.0
  O  O12  1  0.541  0.157  0.647  1.0
  O  O13  1  0.459  0.843  0.353  1.0
  O  O14  1  0.465  0.342  0.193  1.0
  O  O15  1  0.535  0.658  0.807  1.0
  O  O16  1  0.138  0.161  0.082  1.0
  O  O17  1  0.862  0.839  0.918  1.0
[/CIF]
.
The material described by K4HfO4 crystallizes in the triclinic P-1 space group. There are four inequivalent K sites. In the first K site, K(1) is bonded to one O(3), two equivalent O(1), and two equivalent O(2) atoms to form distorted KO5 square pyramids that share  a cornercorner with one Hf(1)O4 tetrahedra, corners with three equivalent K(4)O5 trigonal bipyramids, corners with two equivalent K(3)O4 trigonal pyramids, edges with two equivalent K(1)O5 square pyramids, edges with two equivalent Hf(1)O4 tetrahedra, and edges with three equivalent K(4)O5 trigonal bipyramids. In the second K site, K(2) is bonded in a 5-coordinate geometry to one O(1), one O(2), one O(3), and two equivalent O(4) atoms. In the third K site, K(3) is bonded to two equivalent O(3) and two equivalent O(4) atoms to form distorted KO4 trigonal pyramids that share corners with two equivalent K(1)O5 square pyramids, corners with four equivalent Hf(1)O4 tetrahedra, corners with two equivalent K(4)O5 trigonal bipyramids, and edges with two equivalent K(3)O4 trigonal pyramids. In the fourth K site, K(4) is bonded to one O(3), two equivalent O(1), and two equivalent O(2) atoms to form distorted KO5 trigonal bipyramids that share corners with three equivalent K(1)O5 square pyramids, corners with three equivalent Hf(1)O4 tetrahedra, corners with two equivalent K(3)O4 trigonal pyramids, edges with three equivalent K(1)O5 square pyramids,  an edgeedge with one Hf(1)O4 tetrahedra, and edges with two equivalent K(4)O5 trigonal bipyramids. Hf(1) is bonded to one O(1), one O(2), one O(3), and one O(4) atom to form HfO4 tetrahedra that share  a cornercorner with one K(1)O5 square pyramid, corners with three equivalent K(4)O5 trigonal bipyramids, corners with four equivalent K(3)O4 trigonal pyramids, edges with two equivalent K(1)O5 square pyramids, and  an edgeedge with one K(4)O5 trigonal bipyramid. There are four inequivalent O sites. In the first O site, O(1) is bonded to one K(2), two equivalent K(1), two equivalent K(4), and one Hf(1) atom to form distorted edge-sharing OK5Hf octahedra. In the second O site, O(2) is bonded in a 6-coordinate geometry to one K(2), two equivalent K(1), two equivalent K(4), and one Hf(1) atom. In the third O site, O(3) is bonded in a 6-coordinate geometry to one K(1), one K(2), one K(4), two equivalent K(3), and one Hf(1) atom. In the fourth O site, O(4) is bonded in a 4-coordinate geometry to two equivalent K(2), two equivalent K(3), and one Hf(1) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_K4HfO4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.531
_cell_length_b   6.542
_cell_length_c   9.737
_cell_angle_alpha   72.097
_cell_angle_beta   80.040
_cell_angle_gamma   66.930
_symmetry_Int_Tables_number   1
_cell_volume   363.526
_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
  K  K0  1  0.777  0.041  0.384  1.0
  K  K1  1  0.223  0.959  0.616  1.0
  K  K2  1  0.740  0.587  0.169  1.0
  K  K3  1  0.260  0.413  0.831  1.0
  K  K4  1  0.241  0.761  0.026  1.0
  K  K5  1  0.759  0.239  0.974  1.0
  K  K6  1  0.274  0.514  0.441  1.0
  K  K7  1  0.726  0.486  0.559  1.0
  Hf  Hf8  1  0.279  0.154  0.245  1.0
  Hf  Hf9  1  0.721  0.846  0.755  1.0
  O  O10  1  0.039  0.290  0.378  1.0
  O  O11  1  0.961  0.710  0.622  1.0
  O  O12  1  0.541  0.157  0.647  1.0
  O  O13  1  0.459  0.843  0.353  1.0
  O  O14  1  0.465  0.342  0.193  1.0
  O  O15  1  0.535  0.658  0.807  1.0
  O  O16  1  0.138  0.161  0.082  1.0
  O  O17  1  0.862  0.839  0.918  1.0
[/CIF]
.