The material described by Hf2ON2 crystallizes in the monoclinic Cm space group. There are six inequivalent Hf sites. In the first Hf site, Hf(1) is bonded to one N(2), one N(5), two equivalent N(1), and two equivalent O(3) atoms to form distorted HfN4O2 octahedra that share corners with two equivalent Hf(6)N2O4 octahedra,  an edgeedge with one Hf(6)N2O4 octahedra, and edges with two equivalent Hf(1)N4O2 octahedra. The corner-sharing octahedral tilt angles are 5°. In the second Hf site, Hf(2) is bonded in a 7-coordinate geometry to one N(1), one N(4), two equivalent N(3), one O(2), and two equivalent O(1) atoms. In the third Hf site, Hf(3) is bonded in a 7-coordinate geometry to one N(4), one N(6), two equivalent N(2), two equivalent N(3), and one O(3) atom. In the fourth Hf site, Hf(4) is bonded in a 7-coordinate geometry to one N(2), two equivalent N(5), two equivalent N(6), one O(1), and one O(3) atom. In the fifth Hf site, Hf(5) is bonded in a 7-coordinate geometry to one N(1), two equivalent N(4), two equivalent N(5), one O(1), and one O(2) atom. In the sixth Hf site, Hf(6) is bonded to one N(3), one N(6), two equivalent O(2), and two equivalent O(3) atoms to form distorted HfN2O4 octahedra that share corners with two equivalent Hf(1)N4O2 octahedra,  an edgeedge with one Hf(1)N4O2 octahedra, and edges with two equivalent Hf(6)N2O4 octahedra. The corner-sharing octahedral tilt angles are 5°. There are six inequivalent N sites. In the first N site, N(1) is bonded to one Hf(2), one Hf(5), and two equivalent Hf(1) atoms to form distorted NHf4 tetrahedra that share corners with two equivalent O(3)Hf6 octahedra, corners with two equivalent N(1)Hf4 tetrahedra, corners with two equivalent N(2)Hf4 tetrahedra, corners with two equivalent N(3)Hf5 trigonal bipyramids, corners with three equivalent N(4)Hf4 trigonal pyramids, corners with three equivalent O(1)Hf4 trigonal pyramids,  an edgeedge with one O(3)Hf6 octahedra,  an edgeedge with one O(2)Hf4 tetrahedra, and edges with two equivalent N(5)Hf5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 13°. In the second N site, N(2) is bonded to one Hf(1), one Hf(4), and two equivalent Hf(3) atoms to form NHf4 tetrahedra that share  a cornercorner with one O(3)Hf6 octahedra, corners with two equivalent N(1)Hf4 tetrahedra, corners with two equivalent N(2)Hf4 tetrahedra, corners with two equivalent N(3)Hf5 trigonal bipyramids, corners with three equivalent N(5)Hf5 trigonal bipyramids,  a cornercorner with one O(1)Hf4 trigonal pyramid, corners with two equivalent N(4)Hf4 trigonal pyramids, edges with two equivalent O(3)Hf6 octahedra, edges with two equivalent N(6)Hf4 tetrahedra, and  an edgeedge with one N(3)Hf5 trigonal bipyramid. The corner-sharing octahedral tilt angles are 47°. In the third N site, N(3) is bonded to one Hf(6), two equivalent Hf(2), and two equivalent Hf(3) atoms to form distorted NHf5 trigonal bipyramids that share corners with two equivalent N(1)Hf4 tetrahedra, corners with two equivalent N(2)Hf4 tetrahedra, corners with three equivalent N(6)Hf4 tetrahedra, corners with two equivalent O(1)Hf4 trigonal pyramids, edges with two equivalent O(3)Hf6 octahedra,  an edgeedge with one N(2)Hf4 tetrahedra, edges with two equivalent O(2)Hf4 tetrahedra, edges with two equivalent N(3)Hf5 trigonal bipyramids,  an edgeedge with one O(1)Hf4 trigonal pyramid, and edges with two equivalent N(4)Hf4 trigonal pyramids. In the fourth N site, N(4) is bonded to one Hf(2), one Hf(3), and two equivalent Hf(5) atoms to form distorted NHf4 trigonal pyramids that share  a cornercorner with one O(3)Hf6 octahedra,  a cornercorner with one N(6)Hf4 tetrahedra, corners with two equivalent N(2)Hf4 tetrahedra, corners with three equivalent N(1)Hf4 tetrahedra, corners with three equivalent O(2)Hf4 tetrahedra, corners with two equivalent N(5)Hf5 trigonal bipyramids, corners with two equivalent N(4)Hf4 trigonal pyramids,  an edgeedge with one N(5)Hf5 trigonal bipyramid, edges with two equivalent N(3)Hf5 trigonal bipyramids, and edges with two equivalent O(1)Hf4 trigonal pyramids. The corner-sharing octahedral tilt angles are 42°. In the fifth N site, N(5) is bonded to one Hf(1), two equivalent Hf(4), and two equivalent Hf(5) atoms to form distorted NHf5 trigonal bipyramids that share corners with two equivalent N(6)Hf4 tetrahedra, corners with two equivalent O(2)Hf4 tetrahedra, corners with three equivalent N(2)Hf4 tetrahedra, corners with two equivalent N(4)Hf4 trigonal pyramids, edges with two equivalent O(3)Hf6 octahedra,  an edgeedge with one N(6)Hf4 tetrahedra, edges with two equivalent N(1)Hf4 tetrahedra, edges with two equivalent N(5)Hf5 trigonal bipyramids,  an edgeedge with one N(4)Hf4 trigonal pyramid, and edges with two equivalent O(1)Hf4 trigonal pyramids. In the sixth N site, N(6) is bonded to one Hf(3), one Hf(6), and two equivalent Hf(4) atoms to form NHf4 tetrahedra that share  a cornercorner with one O(3)Hf6 octahedra, corners with two equivalent N(6)Hf4 tetrahedra, corners with two equivalent O(2)Hf4 tetrahedra, corners with two equivalent N(5)Hf5 trigonal bipyramids, corners with three equivalent N(3)Hf5 trigonal bipyramids,  a cornercorner with one N(4)Hf4 trigonal pyramid, corners with two equivalent O(1)Hf4 trigonal pyramids, edges with two equivalent O(3)Hf6 octahedra, edges with two equivalent N(2)Hf4 tetrahedra, and  an edgeedge with one N(5)Hf5 trigonal bipyramid. The corner-sharing octahedral tilt angles are 43°. There are three inequivalent O sites. In the first O site, O(1) is bonded to one Hf(4), one Hf(5), and two equivalent Hf(2) atoms to form distorted OHf4 trigonal pyramids that share  a cornercorner with one O(3)Hf6 octahedra,  a cornercorner with one N(2)Hf4 tetrahedra, corners with two equivalent N(6)Hf4 tetrahedra, corners with three equivalent N(1)Hf4 tetrahedra, corners with three equivalent O(2)Hf4 tetrahedra, corners with two equivalent N(3)Hf5 trigonal bipyramids, corners with two equivalent O(1)Hf4 trigonal pyramids,  an edgeedge with one N(3)Hf5 trigonal bipyramid, edges with two equivalent N(5)Hf5 trigonal bipyramids, and edges with two equivalent N(4)Hf4 trigonal pyramids. The corner-sharing octahedral tilt angles are 41°. In the second O site, O(2) is bonded to one Hf(2), one Hf(5), and two equivalent Hf(6) atoms to form distorted OHf4 tetrahedra that share corners with two equivalent O(3)Hf6 octahedra, corners with two equivalent N(6)Hf4 tetrahedra, corners with two equivalent O(2)Hf4 tetrahedra, corners with two equivalent N(5)Hf5 trigonal bipyramids, corners with three equivalent N(4)Hf4 trigonal pyramids, corners with three equivalent O(1)Hf4 trigonal pyramids,  an edgeedge with one O(3)Hf6 octahedra,  an edgeedge with one N(1)Hf4 tetrahedra, and edges with two equivalent N(3)Hf5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 13°. In the third O site, O(3) is bonded to one Hf(3), one Hf(4), two equivalent Hf(1), and two equivalent Hf(6) atoms to form OHf6 octahedra that share  a cornercorner with one N(2)Hf4 tetrahedra,  a cornercorner with one N(6)Hf4 tetrahedra, corners with two equivalent N(1)Hf4 tetrahedra, corners with two equivalent O(2)Hf4 tetrahedra,  a cornercorner with one N(4)Hf4 trigonal pyramid,  a cornercorner with one O(1)Hf4 trigonal pyramid, edges with two equivalent O(3)Hf6 octahedra,  an edgeedge with one N(1)Hf4 tetrahedra,  an edgeedge with one O(2)Hf4 tetrahedra, edges with two equivalent N(2)Hf4 tetrahedra, edges with two equivalent N(6)Hf4 tetrahedra, edges with two equivalent N(3)Hf5 trigonal bipyramids, and edges with two equivalent N(5)Hf5 trigonal bipyramids. is represented by the Crystallographic Information File (CIF) [CIF]
data_Hf2N2O
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   7.011
_cell_length_b   7.011
_cell_length_c   8.194
_cell_angle_alpha   80.181
_cell_angle_beta   80.181
_cell_angle_gamma   26.985
_symmetry_Int_Tables_number   1
_cell_volume   179.927
_cell_formula_units_Z   3
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  0.030  0.030  0.200  1.0
  Hf  Hf1  1  0.638  0.638  0.526  1.0
  Hf  Hf2  1  0.695  0.695  0.867  1.0
  Hf  Hf3  1  0.306  0.306  0.132  1.0
  Hf  Hf4  1  0.364  0.364  0.480  1.0
  Hf  Hf5  1  0.965  0.965  0.813  1.0
  N  N6  1  0.536  0.536  0.351  1.0
  N  N7  1  0.170  0.170  0.035  1.0
  N  N8  1  0.122  0.122  0.709  1.0
  N  N9  1  0.795  0.795  0.621  1.0
  N  N10  1  0.875  0.875  0.273  1.0
  N  N11  1  0.827  0.827  0.963  1.0
  O  O12  1  0.215  0.215  0.381  1.0
  O  O13  1  0.465  0.465  0.661  1.0
  O  O14  1  0.497  0.497  0.988  1.0
[/CIF]
.
The material described by Hf2ON2 crystallizes in the monoclinic Cm space group. There are six inequivalent Hf sites. In the first Hf site, Hf(1) is bonded to one N(2), one N(5), two equivalent N(1), and two equivalent O(3) atoms to form distorted HfN4O2 octahedra that share corners with two equivalent Hf(6)N2O4 octahedra,  an edgeedge with one Hf(6)N2O4 octahedra, and edges with two equivalent Hf(1)N4O2 octahedra. The corner-sharing octahedral tilt angles are 5°. In the second Hf site, Hf(2) is bonded in a 7-coordinate geometry to one N(1), one N(4), two equivalent N(3), one O(2), and two equivalent O(1) atoms. In the third Hf site, Hf(3) is bonded in a 7-coordinate geometry to one N(4), one N(6), two equivalent N(2), two equivalent N(3), and one O(3) atom. In the fourth Hf site, Hf(4) is bonded in a 7-coordinate geometry to one N(2), two equivalent N(5), two equivalent N(6), one O(1), and one O(3) atom. In the fifth Hf site, Hf(5) is bonded in a 7-coordinate geometry to one N(1), two equivalent N(4), two equivalent N(5), one O(1), and one O(2) atom. In the sixth Hf site, Hf(6) is bonded to one N(3), one N(6), two equivalent O(2), and two equivalent O(3) atoms to form distorted HfN2O4 octahedra that share corners with two equivalent Hf(1)N4O2 octahedra,  an edgeedge with one Hf(1)N4O2 octahedra, and edges with two equivalent Hf(6)N2O4 octahedra. The corner-sharing octahedral tilt angles are 5°. There are six inequivalent N sites. In the first N site, N(1) is bonded to one Hf(2), one Hf(5), and two equivalent Hf(1) atoms to form distorted NHf4 tetrahedra that share corners with two equivalent O(3)Hf6 octahedra, corners with two equivalent N(1)Hf4 tetrahedra, corners with two equivalent N(2)Hf4 tetrahedra, corners with two equivalent N(3)Hf5 trigonal bipyramids, corners with three equivalent N(4)Hf4 trigonal pyramids, corners with three equivalent O(1)Hf4 trigonal pyramids,  an edgeedge with one O(3)Hf6 octahedra,  an edgeedge with one O(2)Hf4 tetrahedra, and edges with two equivalent N(5)Hf5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 13°. In the second N site, N(2) is bonded to one Hf(1), one Hf(4), and two equivalent Hf(3) atoms to form NHf4 tetrahedra that share  a cornercorner with one O(3)Hf6 octahedra, corners with two equivalent N(1)Hf4 tetrahedra, corners with two equivalent N(2)Hf4 tetrahedra, corners with two equivalent N(3)Hf5 trigonal bipyramids, corners with three equivalent N(5)Hf5 trigonal bipyramids,  a cornercorner with one O(1)Hf4 trigonal pyramid, corners with two equivalent N(4)Hf4 trigonal pyramids, edges with two equivalent O(3)Hf6 octahedra, edges with two equivalent N(6)Hf4 tetrahedra, and  an edgeedge with one N(3)Hf5 trigonal bipyramid. The corner-sharing octahedral tilt angles are 47°. In the third N site, N(3) is bonded to one Hf(6), two equivalent Hf(2), and two equivalent Hf(3) atoms to form distorted NHf5 trigonal bipyramids that share corners with two equivalent N(1)Hf4 tetrahedra, corners with two equivalent N(2)Hf4 tetrahedra, corners with three equivalent N(6)Hf4 tetrahedra, corners with two equivalent O(1)Hf4 trigonal pyramids, edges with two equivalent O(3)Hf6 octahedra,  an edgeedge with one N(2)Hf4 tetrahedra, edges with two equivalent O(2)Hf4 tetrahedra, edges with two equivalent N(3)Hf5 trigonal bipyramids,  an edgeedge with one O(1)Hf4 trigonal pyramid, and edges with two equivalent N(4)Hf4 trigonal pyramids. In the fourth N site, N(4) is bonded to one Hf(2), one Hf(3), and two equivalent Hf(5) atoms to form distorted NHf4 trigonal pyramids that share  a cornercorner with one O(3)Hf6 octahedra,  a cornercorner with one N(6)Hf4 tetrahedra, corners with two equivalent N(2)Hf4 tetrahedra, corners with three equivalent N(1)Hf4 tetrahedra, corners with three equivalent O(2)Hf4 tetrahedra, corners with two equivalent N(5)Hf5 trigonal bipyramids, corners with two equivalent N(4)Hf4 trigonal pyramids,  an edgeedge with one N(5)Hf5 trigonal bipyramid, edges with two equivalent N(3)Hf5 trigonal bipyramids, and edges with two equivalent O(1)Hf4 trigonal pyramids. The corner-sharing octahedral tilt angles are 42°. In the fifth N site, N(5) is bonded to one Hf(1), two equivalent Hf(4), and two equivalent Hf(5) atoms to form distorted NHf5 trigonal bipyramids that share corners with two equivalent N(6)Hf4 tetrahedra, corners with two equivalent O(2)Hf4 tetrahedra, corners with three equivalent N(2)Hf4 tetrahedra, corners with two equivalent N(4)Hf4 trigonal pyramids, edges with two equivalent O(3)Hf6 octahedra,  an edgeedge with one N(6)Hf4 tetrahedra, edges with two equivalent N(1)Hf4 tetrahedra, edges with two equivalent N(5)Hf5 trigonal bipyramids,  an edgeedge with one N(4)Hf4 trigonal pyramid, and edges with two equivalent O(1)Hf4 trigonal pyramids. In the sixth N site, N(6) is bonded to one Hf(3), one Hf(6), and two equivalent Hf(4) atoms to form NHf4 tetrahedra that share  a cornercorner with one O(3)Hf6 octahedra, corners with two equivalent N(6)Hf4 tetrahedra, corners with two equivalent O(2)Hf4 tetrahedra, corners with two equivalent N(5)Hf5 trigonal bipyramids, corners with three equivalent N(3)Hf5 trigonal bipyramids,  a cornercorner with one N(4)Hf4 trigonal pyramid, corners with two equivalent O(1)Hf4 trigonal pyramids, edges with two equivalent O(3)Hf6 octahedra, edges with two equivalent N(2)Hf4 tetrahedra, and  an edgeedge with one N(5)Hf5 trigonal bipyramid. The corner-sharing octahedral tilt angles are 43°. There are three inequivalent O sites. In the first O site, O(1) is bonded to one Hf(4), one Hf(5), and two equivalent Hf(2) atoms to form distorted OHf4 trigonal pyramids that share  a cornercorner with one O(3)Hf6 octahedra,  a cornercorner with one N(2)Hf4 tetrahedra, corners with two equivalent N(6)Hf4 tetrahedra, corners with three equivalent N(1)Hf4 tetrahedra, corners with three equivalent O(2)Hf4 tetrahedra, corners with two equivalent N(3)Hf5 trigonal bipyramids, corners with two equivalent O(1)Hf4 trigonal pyramids,  an edgeedge with one N(3)Hf5 trigonal bipyramid, edges with two equivalent N(5)Hf5 trigonal bipyramids, and edges with two equivalent N(4)Hf4 trigonal pyramids. The corner-sharing octahedral tilt angles are 41°. In the second O site, O(2) is bonded to one Hf(2), one Hf(5), and two equivalent Hf(6) atoms to form distorted OHf4 tetrahedra that share corners with two equivalent O(3)Hf6 octahedra, corners with two equivalent N(6)Hf4 tetrahedra, corners with two equivalent O(2)Hf4 tetrahedra, corners with two equivalent N(5)Hf5 trigonal bipyramids, corners with three equivalent N(4)Hf4 trigonal pyramids, corners with three equivalent O(1)Hf4 trigonal pyramids,  an edgeedge with one O(3)Hf6 octahedra,  an edgeedge with one N(1)Hf4 tetrahedra, and edges with two equivalent N(3)Hf5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 13°. In the third O site, O(3) is bonded to one Hf(3), one Hf(4), two equivalent Hf(1), and two equivalent Hf(6) atoms to form OHf6 octahedra that share  a cornercorner with one N(2)Hf4 tetrahedra,  a cornercorner with one N(6)Hf4 tetrahedra, corners with two equivalent N(1)Hf4 tetrahedra, corners with two equivalent O(2)Hf4 tetrahedra,  a cornercorner with one N(4)Hf4 trigonal pyramid,  a cornercorner with one O(1)Hf4 trigonal pyramid, edges with two equivalent O(3)Hf6 octahedra,  an edgeedge with one N(1)Hf4 tetrahedra,  an edgeedge with one O(2)Hf4 tetrahedra, edges with two equivalent N(2)Hf4 tetrahedra, edges with two equivalent N(6)Hf4 tetrahedra, edges with two equivalent N(3)Hf5 trigonal bipyramids, and edges with two equivalent N(5)Hf5 trigonal bipyramids. is represented by the Crystallographic Information File (CIF) [CIF]
data_Hf2N2O
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   7.011
_cell_length_b   7.011
_cell_length_c   8.194
_cell_angle_alpha   80.181
_cell_angle_beta   80.181
_cell_angle_gamma   26.985
_symmetry_Int_Tables_number   1
_cell_volume   179.927
_cell_formula_units_Z   3
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  0.030  0.030  0.200  1.0
  Hf  Hf1  1  0.638  0.638  0.526  1.0
  Hf  Hf2  1  0.695  0.695  0.867  1.0
  Hf  Hf3  1  0.306  0.306  0.132  1.0
  Hf  Hf4  1  0.364  0.364  0.480  1.0
  Hf  Hf5  1  0.965  0.965  0.813  1.0
  N  N6  1  0.536  0.536  0.351  1.0
  N  N7  1  0.170  0.170  0.035  1.0
  N  N8  1  0.122  0.122  0.709  1.0
  N  N9  1  0.795  0.795  0.621  1.0
  N  N10  1  0.875  0.875  0.273  1.0
  N  N11  1  0.827  0.827  0.963  1.0
  O  O12  1  0.215  0.215  0.381  1.0
  O  O13  1  0.465  0.465  0.661  1.0
  O  O14  1  0.497  0.497  0.988  1.0
[/CIF]
.