The crystal structure described by MgHf8(N2O)4 crystallizes in the triclinic P1 space group. Mg(1) is bonded to one N(5), one N(7), one N(8), and one O(3) atom to form MgN3O tetrahedra that share  a cornercorner with one Hf(4)N4O2 octahedra,  a cornercorner with one Hf(5)N4O2 octahedra,  a cornercorner with one Hf(8)N4O2 octahedra, corners with three equivalent Hf(2)N3O tetrahedra, and corners with three equivalent Hf(3)N3O tetrahedra. The corner-sharing octahedral tilt angles range from 57-66°. There are eight inequivalent Hf sites. In the first Hf site, Hf(1) is bonded to one N(1), one N(2), one N(4), one N(6), one O(1), and one O(2) atom to form distorted HfN4O2 octahedra that share corners with three equivalent Hf(4)N4O2 octahedra, corners with three equivalent Hf(5)N4O2 octahedra,  a cornercorner with one Hf(3)N3O tetrahedra, edges with three equivalent Hf(6)N4O2 octahedra, edges with three equivalent Hf(7)N4O2 octahedra, and  a faceface with one Hf(8)N4O2 octahedra. The corner-sharing octahedral tilt angles range from 45-52°. In the second Hf site, Hf(2) is bonded to one N(3), one N(5), one N(8), and one O(3) atom to form HfN3O tetrahedra that share  a cornercorner with one Hf(4)N4O2 octahedra,  a cornercorner with one Hf(5)N4O2 octahedra,  a cornercorner with one Hf(8)N4O2 octahedra, corners with three equivalent Mg(1)N3O tetrahedra, and corners with three equivalent Hf(3)N3O tetrahedra. The corner-sharing octahedral tilt angles range from 63-65°. In the third Hf site, Hf(3) is bonded to one N(2), one N(5), one N(8), and one O(3) atom to form HfN3O tetrahedra that share  a cornercorner with one Hf(1)N4O2 octahedra,  a cornercorner with one Hf(6)N4O2 octahedra,  a cornercorner with one Hf(7)N4O2 octahedra, corners with three equivalent Mg(1)N3O tetrahedra, and corners with three equivalent Hf(2)N3O tetrahedra. The corner-sharing octahedral tilt angles range from 61-66°. In the fourth Hf site, Hf(4) is bonded to one N(1), one N(3), one N(4), one N(7), one O(2), and one O(4) atom to form distorted HfN4O2 octahedra that share corners with three equivalent Hf(1)N4O2 octahedra, corners with three equivalent Hf(7)N4O2 octahedra,  a cornercorner with one Mg(1)N3O tetrahedra,  a cornercorner with one Hf(2)N3O tetrahedra, edges with three equivalent Hf(5)N4O2 octahedra, edges with three equivalent Hf(8)N4O2 octahedra, and  a faceface with one Hf(6)N4O2 octahedra. The corner-sharing octahedral tilt angles range from 39-50°. In the fifth Hf site, Hf(5) is bonded to one N(1), one N(3), one N(4), one N(7), one O(2), and one O(4) atom to form distorted HfN4O2 octahedra that share corners with three equivalent Hf(1)N4O2 octahedra, corners with three equivalent Hf(6)N4O2 octahedra,  a cornercorner with one Mg(1)N3O tetrahedra,  a cornercorner with one Hf(2)N3O tetrahedra, edges with three equivalent Hf(4)N4O2 octahedra, edges with three equivalent Hf(8)N4O2 octahedra, and  a faceface with one Hf(7)N4O2 octahedra. The corner-sharing octahedral tilt angles range from 43-52°. In the sixth Hf site, Hf(6) is bonded to one N(1), one N(2), one N(4), one N(6), one O(1), and one O(2) atom to form distorted HfN4O2 octahedra that share corners with three equivalent Hf(5)N4O2 octahedra, corners with three equivalent Hf(8)N4O2 octahedra,  a cornercorner with one Hf(3)N3O tetrahedra, edges with three equivalent Hf(1)N4O2 octahedra, edges with three equivalent Hf(7)N4O2 octahedra, and  a faceface with one Hf(4)N4O2 octahedra. The corner-sharing octahedral tilt angles range from 43-49°. In the seventh Hf site, Hf(7) is bonded to one N(1), one N(2), one N(4), one N(6), one O(1), and one O(2) atom to form distorted HfN4O2 octahedra that share corners with three equivalent Hf(4)N4O2 octahedra, corners with three equivalent Hf(8)N4O2 octahedra,  a cornercorner with one Hf(3)N3O tetrahedra, edges with three equivalent Hf(1)N4O2 octahedra, edges with three equivalent Hf(6)N4O2 octahedra, and  a faceface with one Hf(5)N4O2 octahedra. The corner-sharing octahedral tilt angles range from 39-52°. In the eighth Hf site, Hf(8) is bonded to one N(1), one N(3), one N(4), one N(7), one O(2), and one O(4) atom to form distorted HfN4O2 octahedra that share corners with three equivalent Hf(6)N4O2 octahedra, corners with three equivalent Hf(7)N4O2 octahedra,  a cornercorner with one Mg(1)N3O tetrahedra,  a cornercorner with one Hf(2)N3O tetrahedra, edges with three equivalent Hf(4)N4O2 octahedra, edges with three equivalent Hf(5)N4O2 octahedra, and  a faceface with one Hf(1)N4O2 octahedra. The corner-sharing octahedral tilt angles range from 43-52°. There are eight inequivalent N sites. In the first N site, N(1) is bonded to one Hf(1), one Hf(4), one Hf(5), one Hf(6), one Hf(7), and one Hf(8) atom to form distorted NHf6 pentagonal pyramids that share  a cornercorner with one N(7)Hf3Mg tetrahedra,  a cornercorner with one N(2)Hf4 tetrahedra,  a cornercorner with one N(3)Hf4 tetrahedra, edges with three equivalent N(4)Hf6 pentagonal pyramids,  an edgeedge with one N(7)Hf3Mg tetrahedra,  an edgeedge with one N(2)Hf4 tetrahedra, and  an edgeedge with one N(3)Hf4 tetrahedra. In the second N site, N(2) is bonded to one Hf(1), one Hf(3), one Hf(6), and one Hf(7) atom to form a mixture of edge and corner-sharing NHf4 tetrahedra. In the third N site, N(3) is bonded to one Hf(2), one Hf(4), one Hf(5), and one Hf(8) atom to form NHf4 tetrahedra that share  a cornercorner with one N(1)Hf6 pentagonal pyramid,  a cornercorner with one N(4)Hf6 pentagonal pyramid, corners with three equivalent N(7)Hf3Mg tetrahedra,  an edgeedge with one N(1)Hf6 pentagonal pyramid, and  an edgeedge with one N(4)Hf6 pentagonal pyramid. In the fourth N site, N(4) is bonded to one Hf(1), one Hf(4), one Hf(5), one Hf(6), one Hf(7), and one Hf(8) atom to form distorted NHf6 pentagonal pyramids that share  a cornercorner with one N(7)Hf3Mg tetrahedra,  a cornercorner with one N(2)Hf4 tetrahedra,  a cornercorner with one N(3)Hf4 tetrahedra, edges with three equivalent N(1)Hf6 pentagonal pyramids,  an edgeedge with one N(7)Hf3Mg tetrahedra,  an edgeedge with one N(2)Hf4 tetrahedra, and  an edgeedge with one N(3)Hf4 tetrahedra. In the fifth N site, N(5) is bonded in a trigonal planar geometry to one Mg(1), one Hf(2), and one Hf(3) atom. In the sixth N site, N(6) is bonded in a trigonal non-coplanar geometry to one Hf(1), one Hf(6), and one Hf(7) atom. In the seventh N site, N(7) is bonded to one Mg(1), one Hf(4), one Hf(5), and one Hf(8) atom to form NHf3Mg tetrahedra that share  a cornercorner with one N(1)Hf6 pentagonal pyramid,  a cornercorner with one N(4)Hf6 pentagonal pyramid, corners with three equivalent N(3)Hf4 tetrahedra,  an edgeedge with one N(1)Hf6 pentagonal pyramid, and  an edgeedge with one N(4)Hf6 pentagonal pyramid. In the eighth N site, N(8) is bonded in a trigonal planar geometry to one Mg(1), one Hf(2), and one Hf(3) atom. There are four inequivalent O sites. In the first O site, O(1) is bonded in a trigonal non-coplanar geometry to one Hf(1), one Hf(6), and one Hf(7) atom. In the second O site, O(2) is bonded in a 6-coordinate geometry to one Hf(1), one Hf(4), one Hf(5), one Hf(6), one Hf(7), and one Hf(8) atom. In the third O site, O(3) is bonded in a trigonal planar geometry to one Mg(1), one Hf(2), and one Hf(3) atom. In the fourth O site, O(4) is bonded in a trigonal non-coplanar geometry to one Hf(4), one Hf(5), and one Hf(8) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_Hf8Mg(N2O)4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.743
_cell_length_b   5.736
_cell_length_c   10.866
_cell_angle_alpha   104.789
_cell_angle_beta   89.553
_cell_angle_gamma   59.470
_symmetry_Int_Tables_number   1
_cell_volume   294.061
_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
  Hf  Hf0  1  0.097  0.391  0.238  1.0
  Hf  Hf1  1  0.205  0.809  0.814  1.0
  Hf  Hf2  1  0.497  0.226  0.940  1.0
  Hf  Hf3  1  0.665  0.281  0.525  1.0
  Hf  Hf4  1  0.340  0.926  0.515  1.0
  Hf  Hf5  1  0.748  0.083  0.236  1.0
  Hf  Hf6  1  0.456  0.732  0.236  1.0
  Hf  Hf7  1  0.006  0.573  0.522  1.0
  Mg  Mg8  1  0.868  0.483  0.823  1.0
  N  N9  1  0.369  0.178  0.379  1.0
  N  N10  1  0.448  0.349  0.145  1.0
  N  N11  1  0.288  0.663  0.611  1.0
  N  N12  1  0.704  0.482  0.380  1.0
  N  N13  1  0.513  0.504  0.869  1.0
  N  N14  1  0.798  0.687  0.162  1.0
  N  N15  1  0.967  0.319  0.614  1.0
  N  N16  1  0.850  0.857  0.873  1.0
  O  O17  1  0.118  0.016  0.160  1.0
  O  O18  1  0.038  0.855  0.388  1.0
  O  O19  1  0.191  0.178  0.875  1.0
  O  O20  1  0.641  0.973  0.589  1.0
[/CIF]
.
The crystal structure described by MgHf8(N2O)4 crystallizes in the triclinic P1 space group. Mg(1) is bonded to one N(5), one N(7), one N(8), and one O(3) atom to form MgN3O tetrahedra that share  a cornercorner with one Hf(4)N4O2 octahedra,  a cornercorner with one Hf(5)N4O2 octahedra,  a cornercorner with one Hf(8)N4O2 octahedra, corners with three equivalent Hf(2)N3O tetrahedra, and corners with three equivalent Hf(3)N3O tetrahedra. The corner-sharing octahedral tilt angles range from 57-66°. There are eight inequivalent Hf sites. In the first Hf site, Hf(1) is bonded to one N(1), one N(2), one N(4), one N(6), one O(1), and one O(2) atom to form distorted HfN4O2 octahedra that share corners with three equivalent Hf(4)N4O2 octahedra, corners with three equivalent Hf(5)N4O2 octahedra,  a cornercorner with one Hf(3)N3O tetrahedra, edges with three equivalent Hf(6)N4O2 octahedra, edges with three equivalent Hf(7)N4O2 octahedra, and  a faceface with one Hf(8)N4O2 octahedra. The corner-sharing octahedral tilt angles range from 45-52°. In the second Hf site, Hf(2) is bonded to one N(3), one N(5), one N(8), and one O(3) atom to form HfN3O tetrahedra that share  a cornercorner with one Hf(4)N4O2 octahedra,  a cornercorner with one Hf(5)N4O2 octahedra,  a cornercorner with one Hf(8)N4O2 octahedra, corners with three equivalent Mg(1)N3O tetrahedra, and corners with three equivalent Hf(3)N3O tetrahedra. The corner-sharing octahedral tilt angles range from 63-65°. In the third Hf site, Hf(3) is bonded to one N(2), one N(5), one N(8), and one O(3) atom to form HfN3O tetrahedra that share  a cornercorner with one Hf(1)N4O2 octahedra,  a cornercorner with one Hf(6)N4O2 octahedra,  a cornercorner with one Hf(7)N4O2 octahedra, corners with three equivalent Mg(1)N3O tetrahedra, and corners with three equivalent Hf(2)N3O tetrahedra. The corner-sharing octahedral tilt angles range from 61-66°. In the fourth Hf site, Hf(4) is bonded to one N(1), one N(3), one N(4), one N(7), one O(2), and one O(4) atom to form distorted HfN4O2 octahedra that share corners with three equivalent Hf(1)N4O2 octahedra, corners with three equivalent Hf(7)N4O2 octahedra,  a cornercorner with one Mg(1)N3O tetrahedra,  a cornercorner with one Hf(2)N3O tetrahedra, edges with three equivalent Hf(5)N4O2 octahedra, edges with three equivalent Hf(8)N4O2 octahedra, and  a faceface with one Hf(6)N4O2 octahedra. The corner-sharing octahedral tilt angles range from 39-50°. In the fifth Hf site, Hf(5) is bonded to one N(1), one N(3), one N(4), one N(7), one O(2), and one O(4) atom to form distorted HfN4O2 octahedra that share corners with three equivalent Hf(1)N4O2 octahedra, corners with three equivalent Hf(6)N4O2 octahedra,  a cornercorner with one Mg(1)N3O tetrahedra,  a cornercorner with one Hf(2)N3O tetrahedra, edges with three equivalent Hf(4)N4O2 octahedra, edges with three equivalent Hf(8)N4O2 octahedra, and  a faceface with one Hf(7)N4O2 octahedra. The corner-sharing octahedral tilt angles range from 43-52°. In the sixth Hf site, Hf(6) is bonded to one N(1), one N(2), one N(4), one N(6), one O(1), and one O(2) atom to form distorted HfN4O2 octahedra that share corners with three equivalent Hf(5)N4O2 octahedra, corners with three equivalent Hf(8)N4O2 octahedra,  a cornercorner with one Hf(3)N3O tetrahedra, edges with three equivalent Hf(1)N4O2 octahedra, edges with three equivalent Hf(7)N4O2 octahedra, and  a faceface with one Hf(4)N4O2 octahedra. The corner-sharing octahedral tilt angles range from 43-49°. In the seventh Hf site, Hf(7) is bonded to one N(1), one N(2), one N(4), one N(6), one O(1), and one O(2) atom to form distorted HfN4O2 octahedra that share corners with three equivalent Hf(4)N4O2 octahedra, corners with three equivalent Hf(8)N4O2 octahedra,  a cornercorner with one Hf(3)N3O tetrahedra, edges with three equivalent Hf(1)N4O2 octahedra, edges with three equivalent Hf(6)N4O2 octahedra, and  a faceface with one Hf(5)N4O2 octahedra. The corner-sharing octahedral tilt angles range from 39-52°. In the eighth Hf site, Hf(8) is bonded to one N(1), one N(3), one N(4), one N(7), one O(2), and one O(4) atom to form distorted HfN4O2 octahedra that share corners with three equivalent Hf(6)N4O2 octahedra, corners with three equivalent Hf(7)N4O2 octahedra,  a cornercorner with one Mg(1)N3O tetrahedra,  a cornercorner with one Hf(2)N3O tetrahedra, edges with three equivalent Hf(4)N4O2 octahedra, edges with three equivalent Hf(5)N4O2 octahedra, and  a faceface with one Hf(1)N4O2 octahedra. The corner-sharing octahedral tilt angles range from 43-52°. There are eight inequivalent N sites. In the first N site, N(1) is bonded to one Hf(1), one Hf(4), one Hf(5), one Hf(6), one Hf(7), and one Hf(8) atom to form distorted NHf6 pentagonal pyramids that share  a cornercorner with one N(7)Hf3Mg tetrahedra,  a cornercorner with one N(2)Hf4 tetrahedra,  a cornercorner with one N(3)Hf4 tetrahedra, edges with three equivalent N(4)Hf6 pentagonal pyramids,  an edgeedge with one N(7)Hf3Mg tetrahedra,  an edgeedge with one N(2)Hf4 tetrahedra, and  an edgeedge with one N(3)Hf4 tetrahedra. In the second N site, N(2) is bonded to one Hf(1), one Hf(3), one Hf(6), and one Hf(7) atom to form a mixture of edge and corner-sharing NHf4 tetrahedra. In the third N site, N(3) is bonded to one Hf(2), one Hf(4), one Hf(5), and one Hf(8) atom to form NHf4 tetrahedra that share  a cornercorner with one N(1)Hf6 pentagonal pyramid,  a cornercorner with one N(4)Hf6 pentagonal pyramid, corners with three equivalent N(7)Hf3Mg tetrahedra,  an edgeedge with one N(1)Hf6 pentagonal pyramid, and  an edgeedge with one N(4)Hf6 pentagonal pyramid. In the fourth N site, N(4) is bonded to one Hf(1), one Hf(4), one Hf(5), one Hf(6), one Hf(7), and one Hf(8) atom to form distorted NHf6 pentagonal pyramids that share  a cornercorner with one N(7)Hf3Mg tetrahedra,  a cornercorner with one N(2)Hf4 tetrahedra,  a cornercorner with one N(3)Hf4 tetrahedra, edges with three equivalent N(1)Hf6 pentagonal pyramids,  an edgeedge with one N(7)Hf3Mg tetrahedra,  an edgeedge with one N(2)Hf4 tetrahedra, and  an edgeedge with one N(3)Hf4 tetrahedra. In the fifth N site, N(5) is bonded in a trigonal planar geometry to one Mg(1), one Hf(2), and one Hf(3) atom. In the sixth N site, N(6) is bonded in a trigonal non-coplanar geometry to one Hf(1), one Hf(6), and one Hf(7) atom. In the seventh N site, N(7) is bonded to one Mg(1), one Hf(4), one Hf(5), and one Hf(8) atom to form NHf3Mg tetrahedra that share  a cornercorner with one N(1)Hf6 pentagonal pyramid,  a cornercorner with one N(4)Hf6 pentagonal pyramid, corners with three equivalent N(3)Hf4 tetrahedra,  an edgeedge with one N(1)Hf6 pentagonal pyramid, and  an edgeedge with one N(4)Hf6 pentagonal pyramid. In the eighth N site, N(8) is bonded in a trigonal planar geometry to one Mg(1), one Hf(2), and one Hf(3) atom. There are four inequivalent O sites. In the first O site, O(1) is bonded in a trigonal non-coplanar geometry to one Hf(1), one Hf(6), and one Hf(7) atom. In the second O site, O(2) is bonded in a 6-coordinate geometry to one Hf(1), one Hf(4), one Hf(5), one Hf(6), one Hf(7), and one Hf(8) atom. In the third O site, O(3) is bonded in a trigonal planar geometry to one Mg(1), one Hf(2), and one Hf(3) atom. In the fourth O site, O(4) is bonded in a trigonal non-coplanar geometry to one Hf(4), one Hf(5), and one Hf(8) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_Hf8Mg(N2O)4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.743
_cell_length_b   5.736
_cell_length_c   10.866
_cell_angle_alpha   104.789
_cell_angle_beta   89.553
_cell_angle_gamma   59.470
_symmetry_Int_Tables_number   1
_cell_volume   294.061
_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
  Hf  Hf0  1  0.097  0.391  0.238  1.0
  Hf  Hf1  1  0.205  0.809  0.814  1.0
  Hf  Hf2  1  0.497  0.226  0.940  1.0
  Hf  Hf3  1  0.665  0.281  0.525  1.0
  Hf  Hf4  1  0.340  0.926  0.515  1.0
  Hf  Hf5  1  0.748  0.083  0.236  1.0
  Hf  Hf6  1  0.456  0.732  0.236  1.0
  Hf  Hf7  1  0.006  0.573  0.522  1.0
  Mg  Mg8  1  0.868  0.483  0.823  1.0
  N  N9  1  0.369  0.178  0.379  1.0
  N  N10  1  0.448  0.349  0.145  1.0
  N  N11  1  0.288  0.663  0.611  1.0
  N  N12  1  0.704  0.482  0.380  1.0
  N  N13  1  0.513  0.504  0.869  1.0
  N  N14  1  0.798  0.687  0.162  1.0
  N  N15  1  0.967  0.319  0.614  1.0
  N  N16  1  0.850  0.857  0.873  1.0
  O  O17  1  0.118  0.016  0.160  1.0
  O  O18  1  0.038  0.855  0.388  1.0
  O  O19  1  0.191  0.178  0.875  1.0
  O  O20  1  0.641  0.973  0.589  1.0
[/CIF]
.