The material structure described by Hf2ON2 is beta indium sulfide-derived structured and crystallizes in the trigonal P-3m1 space group. There are six inequivalent Hf sites. In the first Hf site, Hf(1) is bonded to one N(1) and three equivalent N(3) atoms to form HfN4 tetrahedra that share corners with three equivalent Hf(6)N6 octahedra and corners with nine equivalent Hf(4)N4O2 octahedra. The corner-sharing octahedral tilt angles range from 56-58°. In the second Hf site, Hf(2) is bonded to three equivalent N(2) and three equivalent O(1) atoms to form HfN3O3 octahedra that share corners with three equivalent Hf(5)N4 tetrahedra, edges with three equivalent Hf(3)N4O2 octahedra, and edges with three equivalent Hf(4)N4O2 octahedra. In the third Hf site, Hf(3) is bonded to four equivalent N(2) and two equivalent O(2) atoms to form HfN4O2 octahedra that share corners with four equivalent Hf(5)N4 tetrahedra, edges with two equivalent Hf(2)N3O3 octahedra, and edges with four equivalent Hf(3)N4O2 octahedra. In the fourth Hf site, Hf(4) is bonded to one N(1), one N(4), two equivalent N(3), and two equivalent O(1) atoms to form HfN4O2 octahedra that share  a cornercorner with one Hf(5)N4 tetrahedra, corners with three equivalent Hf(1)N4 tetrahedra,  an edgeedge with one Hf(2)N3O3 octahedra,  an edgeedge with one Hf(6)N6 octahedra, and edges with four equivalent Hf(4)N4O2 octahedra. In the fifth Hf site, Hf(5) is bonded to one N(4) and three equivalent N(2) atoms to form HfN4 tetrahedra that share corners with three equivalent Hf(2)N3O3 octahedra, corners with three equivalent Hf(4)N4O2 octahedra, and corners with six equivalent Hf(3)N4O2 octahedra. The corner-sharing octahedral tilt angles range from 57-58°. In the sixth Hf site, Hf(6) is bonded to six equivalent N(3) atoms to form HfN6 octahedra that share corners with six equivalent Hf(1)N4 tetrahedra and edges with six equivalent Hf(4)N4O2 octahedra. There are four inequivalent N sites. In the first N site, N(1) is bonded in a distorted rectangular see-saw-like geometry to one Hf(1) and three equivalent Hf(4) atoms. In the second N site, N(2) is bonded in a distorted rectangular see-saw-like geometry to one Hf(2), one Hf(5), and two equivalent Hf(3) atoms. In the third N site, N(3) is bonded to one Hf(1), one Hf(6), and two equivalent Hf(4) atoms to form a mixture of distorted edge and corner-sharing NHf4 trigonal pyramids. In the fourth N site, N(4) is bonded to one Hf(5) and three equivalent Hf(4) atoms to form distorted edge-sharing NHf4 trigonal pyramids. There are two inequivalent O sites. In the first O site, O(1) is bonded in a distorted trigonal non-coplanar geometry to one Hf(2) and two equivalent Hf(4) atoms. In the second O site, O(2) is bonded in a trigonal non-coplanar geometry to three equivalent Hf(3) atoms. is represented by the CIF file [CIF]
data_Hf2N2O
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.430
_cell_length_b   6.430
_cell_length_c   15.731
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   563.228
_cell_formula_units_Z   8
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
  Hf  Hf0  1  0.667  0.333  0.955  1.0
  Hf  Hf1  1  0.667  0.333  0.332  1.0
  Hf  Hf2  1  0.500  0.000  0.500  1.0
  Hf  Hf3  1  0.833  0.167  0.166  1.0
  Hf  Hf4  1  0.666  0.833  0.834  1.0
  Hf  Hf5  1  0.167  0.334  0.834  1.0
  Hf  Hf6  1  0.000  0.000  0.628  1.0
  Hf  Hf7  1  0.500  0.500  0.500  1.0
  Hf  Hf8  1  0.000  0.000  0.372  1.0
  Hf  Hf9  1  0.000  0.000  0.000  1.0
  Hf  Hf10  1  0.334  0.167  0.166  1.0
  Hf  Hf11  1  0.833  0.666  0.166  1.0
  Hf  Hf12  1  0.167  0.833  0.834  1.0
  Hf  Hf13  1  0.000  0.500  0.500  1.0
  Hf  Hf14  1  0.333  0.667  0.668  1.0
  Hf  Hf15  1  0.333  0.667  0.045  1.0
  N  N16  1  0.667  0.333  0.087  1.0
  N  N17  1  0.823  0.177  0.417  1.0
  N  N18  1  0.844  0.156  0.913  1.0
  N  N19  1  0.646  0.823  0.583  1.0
  N  N20  1  0.177  0.354  0.583  1.0
  N  N21  1  0.156  0.312  0.087  1.0
  N  N22  1  0.688  0.844  0.087  1.0
  N  N23  1  0.000  0.000  0.760  1.0
  N  N24  1  0.000  0.000  0.240  1.0
  N  N25  1  0.844  0.688  0.913  1.0
  N  N26  1  0.312  0.156  0.913  1.0
  N  N27  1  0.823  0.646  0.417  1.0
  N  N28  1  0.354  0.177  0.417  1.0
  N  N29  1  0.156  0.844  0.087  1.0
  N  N30  1  0.177  0.823  0.583  1.0
  N  N31  1  0.333  0.667  0.913  1.0
  O  O32  1  0.527  0.473  0.242  1.0
  O  O33  1  0.667  0.333  0.560  1.0
  O  O34  1  0.527  0.053  0.242  1.0
  O  O35  1  0.947  0.473  0.242  1.0
  O  O36  1  0.053  0.527  0.758  1.0
  O  O37  1  0.473  0.947  0.758  1.0
  O  O38  1  0.333  0.667  0.440  1.0
  O  O39  1  0.473  0.527  0.758  1.0
[/CIF]
.
The material structure described by Hf2ON2 is beta indium sulfide-derived structured and crystallizes in the trigonal P-3m1 space group. There are six inequivalent Hf sites. In the first Hf site, Hf(1) is bonded to one N(1) and three equivalent N(3) atoms to form HfN4 tetrahedra that share corners with three equivalent Hf(6)N6 octahedra and corners with nine equivalent Hf(4)N4O2 octahedra. The corner-sharing octahedral tilt angles range from 56-58°. In the second Hf site, Hf(2) is bonded to three equivalent N(2) and three equivalent O(1) atoms to form HfN3O3 octahedra that share corners with three equivalent Hf(5)N4 tetrahedra, edges with three equivalent Hf(3)N4O2 octahedra, and edges with three equivalent Hf(4)N4O2 octahedra. In the third Hf site, Hf(3) is bonded to four equivalent N(2) and two equivalent O(2) atoms to form HfN4O2 octahedra that share corners with four equivalent Hf(5)N4 tetrahedra, edges with two equivalent Hf(2)N3O3 octahedra, and edges with four equivalent Hf(3)N4O2 octahedra. In the fourth Hf site, Hf(4) is bonded to one N(1), one N(4), two equivalent N(3), and two equivalent O(1) atoms to form HfN4O2 octahedra that share  a cornercorner with one Hf(5)N4 tetrahedra, corners with three equivalent Hf(1)N4 tetrahedra,  an edgeedge with one Hf(2)N3O3 octahedra,  an edgeedge with one Hf(6)N6 octahedra, and edges with four equivalent Hf(4)N4O2 octahedra. In the fifth Hf site, Hf(5) is bonded to one N(4) and three equivalent N(2) atoms to form HfN4 tetrahedra that share corners with three equivalent Hf(2)N3O3 octahedra, corners with three equivalent Hf(4)N4O2 octahedra, and corners with six equivalent Hf(3)N4O2 octahedra. The corner-sharing octahedral tilt angles range from 57-58°. In the sixth Hf site, Hf(6) is bonded to six equivalent N(3) atoms to form HfN6 octahedra that share corners with six equivalent Hf(1)N4 tetrahedra and edges with six equivalent Hf(4)N4O2 octahedra. There are four inequivalent N sites. In the first N site, N(1) is bonded in a distorted rectangular see-saw-like geometry to one Hf(1) and three equivalent Hf(4) atoms. In the second N site, N(2) is bonded in a distorted rectangular see-saw-like geometry to one Hf(2), one Hf(5), and two equivalent Hf(3) atoms. In the third N site, N(3) is bonded to one Hf(1), one Hf(6), and two equivalent Hf(4) atoms to form a mixture of distorted edge and corner-sharing NHf4 trigonal pyramids. In the fourth N site, N(4) is bonded to one Hf(5) and three equivalent Hf(4) atoms to form distorted edge-sharing NHf4 trigonal pyramids. There are two inequivalent O sites. In the first O site, O(1) is bonded in a distorted trigonal non-coplanar geometry to one Hf(2) and two equivalent Hf(4) atoms. In the second O site, O(2) is bonded in a trigonal non-coplanar geometry to three equivalent Hf(3) atoms. is represented by the CIF file [CIF]
data_Hf2N2O
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.430
_cell_length_b   6.430
_cell_length_c   15.731
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   563.228
_cell_formula_units_Z   8
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
  Hf  Hf0  1  0.667  0.333  0.955  1.0
  Hf  Hf1  1  0.667  0.333  0.332  1.0
  Hf  Hf2  1  0.500  0.000  0.500  1.0
  Hf  Hf3  1  0.833  0.167  0.166  1.0
  Hf  Hf4  1  0.666  0.833  0.834  1.0
  Hf  Hf5  1  0.167  0.334  0.834  1.0
  Hf  Hf6  1  0.000  0.000  0.628  1.0
  Hf  Hf7  1  0.500  0.500  0.500  1.0
  Hf  Hf8  1  0.000  0.000  0.372  1.0
  Hf  Hf9  1  0.000  0.000  0.000  1.0
  Hf  Hf10  1  0.334  0.167  0.166  1.0
  Hf  Hf11  1  0.833  0.666  0.166  1.0
  Hf  Hf12  1  0.167  0.833  0.834  1.0
  Hf  Hf13  1  0.000  0.500  0.500  1.0
  Hf  Hf14  1  0.333  0.667  0.668  1.0
  Hf  Hf15  1  0.333  0.667  0.045  1.0
  N  N16  1  0.667  0.333  0.087  1.0
  N  N17  1  0.823  0.177  0.417  1.0
  N  N18  1  0.844  0.156  0.913  1.0
  N  N19  1  0.646  0.823  0.583  1.0
  N  N20  1  0.177  0.354  0.583  1.0
  N  N21  1  0.156  0.312  0.087  1.0
  N  N22  1  0.688  0.844  0.087  1.0
  N  N23  1  0.000  0.000  0.760  1.0
  N  N24  1  0.000  0.000  0.240  1.0
  N  N25  1  0.844  0.688  0.913  1.0
  N  N26  1  0.312  0.156  0.913  1.0
  N  N27  1  0.823  0.646  0.417  1.0
  N  N28  1  0.354  0.177  0.417  1.0
  N  N29  1  0.156  0.844  0.087  1.0
  N  N30  1  0.177  0.823  0.583  1.0
  N  N31  1  0.333  0.667  0.913  1.0
  O  O32  1  0.527  0.473  0.242  1.0
  O  O33  1  0.667  0.333  0.560  1.0
  O  O34  1  0.527  0.053  0.242  1.0
  O  O35  1  0.947  0.473  0.242  1.0
  O  O36  1  0.053  0.527  0.758  1.0
  O  O37  1  0.473  0.947  0.758  1.0
  O  O38  1  0.333  0.667  0.440  1.0
  O  O39  1  0.473  0.527  0.758  1.0
[/CIF]
.