The structure described by LiHf8(N2O)4 is Aluminum carbonitride-derived structured and crystallizes in the triclinic P1 space group. Li(1) is bonded to one N(1), one N(4), one O(1), and one O(2) atom to form distorted LiN2O2 tetrahedra that share  a cornercorner with one Hf(3)N4O2 octahedra, corners with three equivalent Hf(1)N4O trigonal bipyramids, and corners with three equivalent Hf(5)N4O trigonal bipyramids. The corner-sharing octahedral tilt angles are 68°. 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(7), and one O(2) atom to form HfN4O trigonal bipyramids that share  a cornercorner with one Hf(2)N4O2 octahedra,  a cornercorner with one Hf(3)N4O2 octahedra,  a cornercorner with one Hf(8)N4O2 octahedra, corners with three equivalent Li(1)N2O2 tetrahedra, and corners with three equivalent Hf(5)N4O trigonal bipyramids. The corner-sharing octahedral tilt angles range from 50-63°. In the second Hf site, Hf(2) is bonded to one N(3), one N(5), one N(7), one N(8), one O(3), and one O(4) atom to form HfN4O2 octahedra that share corners with three equivalent Hf(3)N4O2 octahedra,  a cornercorner with one Hf(1)N4O trigonal bipyramid,  a cornercorner with one Hf(5)N4O trigonal bipyramid, and edges with three equivalent Hf(8)N4O2 octahedra. The corner-sharing octahedral tilt angles range from 48-59°. In the third Hf site, Hf(3) is bonded to one N(2), one N(5), one N(6), one N(8), one O(1), and one O(3) atom to form distorted HfN4O2 octahedra that share corners with three equivalent Hf(2)N4O2 octahedra, corners with three equivalent Hf(8)N4O2 octahedra,  a cornercorner with one Li(1)N2O2 tetrahedra,  a cornercorner with one Hf(1)N4O trigonal bipyramid, and  a cornercorner with one Hf(5)N4O trigonal bipyramid. The corner-sharing octahedral tilt angles range from 46-59°. In the fourth Hf site, Hf(4) is bonded in a 5-coordinate geometry to one N(3), one N(4), one N(5), one N(7), and one O(4) atom. In the fifth Hf site, Hf(5) is bonded to one N(1), one N(3), one N(4), one N(6), and one O(2) atom to form HfN4O trigonal bipyramids that share  a cornercorner with one Hf(2)N4O2 octahedra,  a cornercorner with one Hf(3)N4O2 octahedra,  a cornercorner with one Hf(8)N4O2 octahedra, corners with three equivalent Li(1)N2O2 tetrahedra, and corners with three equivalent Hf(1)N4O trigonal bipyramids. The corner-sharing octahedral tilt angles range from 52-62°. In the sixth Hf site, Hf(6) is bonded in a 5-coordinate geometry to one N(1), one N(2), one N(5), one N(6), one N(8), and one O(1) atom. In the seventh Hf site, Hf(7) is bonded in a 6-coordinate geometry to one N(2), one N(5), one N(6), one N(8), one O(1), and one O(3) atom. In the eighth Hf site, Hf(8) is bonded to one N(3), one N(5), one N(7), one N(8), one O(3), and one O(4) atom to form distorted HfN4O2 octahedra that share corners with three equivalent Hf(3)N4O2 octahedra,  a cornercorner with one Hf(1)N4O trigonal bipyramid,  a cornercorner with one Hf(5)N4O trigonal bipyramid, and edges with three equivalent Hf(2)N4O2 octahedra. The corner-sharing octahedral tilt angles range from 46-57°. There are eight inequivalent N sites. In the first N site, N(1) is bonded to one Li(1), one Hf(1), one Hf(5), and one Hf(6) atom to form NLiHf3 tetrahedra that share  a cornercorner with one N(3)Hf4 tetrahedra,  a cornercorner with one N(7)Hf4 tetrahedra, corners with three equivalent N(4)LiHf3 tetrahedra,  an edgeedge with one N(2)Hf4 tetrahedra,  an edgeedge with one N(6)Hf4 tetrahedra, and  an edgeedge with one O(1)LiHf3 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 NHf4 tetrahedra that share  a cornercorner with one N(7)Hf4 tetrahedra,  a cornercorner with one N(4)LiHf3 tetrahedra, corners with three equivalent N(6)Hf4 tetrahedra, corners with three equivalent O(1)LiHf3 tetrahedra, and  an edgeedge with one N(1)LiHf3 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(6)Hf4 tetrahedra,  a cornercorner with one N(1)LiHf3 tetrahedra, corners with three equivalent N(7)Hf4 tetrahedra, and  an edgeedge with one N(4)LiHf3 tetrahedra. In the fourth N site, N(4) is bonded to one Li(1), one Hf(1), one Hf(4), and one Hf(5) atom to form NLiHf3 tetrahedra that share  a cornercorner with one N(2)Hf4 tetrahedra,  a cornercorner with one N(6)Hf4 tetrahedra,  a cornercorner with one O(1)LiHf3 tetrahedra, corners with three equivalent N(1)LiHf3 tetrahedra,  an edgeedge with one N(3)Hf4 tetrahedra, and  an edgeedge with one N(7)Hf4 tetrahedra. In the fifth N site, N(5) is bonded in a 6-coordinate geometry to one Hf(2), one Hf(3), one Hf(4), one Hf(6), one Hf(7), and one Hf(8) atom. In the sixth N site, N(6) is bonded to one Hf(3), one Hf(5), one Hf(6), and one Hf(7) atom to form NHf4 tetrahedra that share  a cornercorner with one N(3)Hf4 tetrahedra,  a cornercorner with one N(4)LiHf3 tetrahedra, corners with three equivalent N(2)Hf4 tetrahedra, corners with three equivalent O(1)LiHf3 tetrahedra, and  an edgeedge with one N(1)LiHf3 tetrahedra. In the seventh N site, N(7) is bonded to one Hf(1), one Hf(2), one Hf(4), and one Hf(8) atom to form NHf4 tetrahedra that share  a cornercorner with one N(2)Hf4 tetrahedra,  a cornercorner with one N(1)LiHf3 tetrahedra, corners with three equivalent N(3)Hf4 tetrahedra, and  an edgeedge with one N(4)LiHf3 tetrahedra. In the eighth N site, N(8) is bonded in a 5-coordinate geometry to one Hf(2), one Hf(3), one Hf(6), one Hf(7), and one Hf(8) atom. There are four inequivalent O sites. In the first O site, O(1) is bonded to one Li(1), one Hf(3), one Hf(6), and one Hf(7) atom to form OLiHf3 tetrahedra that share  a cornercorner with one N(4)LiHf3 tetrahedra, corners with three equivalent N(2)Hf4 tetrahedra, corners with three equivalent N(6)Hf4 tetrahedra, and  an edgeedge with one N(1)LiHf3 tetrahedra. In the second O site, O(2) is bonded in a trigonal planar geometry to one Li(1), one Hf(1), and one Hf(5) atom. In the third O site, O(3) is bonded in a 4-coordinate geometry to one Hf(2), one Hf(3), one Hf(7), and one Hf(8) atom. In the fourth O site, O(4) is bonded in a trigonal planar geometry to one Hf(2), one Hf(4), and one Hf(8) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_LiHf8(N2O)4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.878
_cell_length_b   5.835
_cell_length_c   10.873
_cell_angle_alpha   74.801
_cell_angle_beta   57.742
_cell_angle_gamma   59.338
_symmetry_Int_Tables_number   1
_cell_volume   271.258
_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
  Li  Li0  1  0.912  0.021  0.336  1.0
  Hf  Hf1  1  0.206  0.345  0.378  1.0
  Hf  Hf2  1  0.157  0.987  0.748  1.0
  Hf  Hf3  1  0.263  0.338  0.006  1.0
  Hf  Hf4  1  0.605  0.348  0.652  1.0
  Hf  Hf5  1  0.533  0.673  0.377  1.0
  Hf  Hf6  1  0.807  0.989  0.095  1.0
  Hf  Hf7  1  0.553  0.660  0.037  1.0
  Hf  Hf8  1  0.856  0.668  0.726  1.0
  N  N9  1  0.597  0.001  0.326  1.0
  N  N10  1  0.410  0.355  0.137  1.0
  N  N11  1  0.273  0.700  0.618  1.0
  N  N12  1  0.831  0.330  0.424  1.0
  N  N13  1  0.391  0.632  0.863  1.0
  N  N14  1  0.792  0.622  0.137  1.0
  N  N15  1  0.005  0.326  0.618  1.0
  N  N16  1  0.728  0.986  0.896  1.0
  O  O17  1  0.146  0.005  0.101  1.0
  O  O18  1  0.187  0.698  0.372  1.0
  O  O19  1  0.991  0.364  0.882  1.0
  O  O20  1  0.577  0.007  0.665  1.0
[/CIF]
.
The structure described by LiHf8(N2O)4 is Aluminum carbonitride-derived structured and crystallizes in the triclinic P1 space group. Li(1) is bonded to one N(1), one N(4), one O(1), and one O(2) atom to form distorted LiN2O2 tetrahedra that share  a cornercorner with one Hf(3)N4O2 octahedra, corners with three equivalent Hf(1)N4O trigonal bipyramids, and corners with three equivalent Hf(5)N4O trigonal bipyramids. The corner-sharing octahedral tilt angles are 68°. 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(7), and one O(2) atom to form HfN4O trigonal bipyramids that share  a cornercorner with one Hf(2)N4O2 octahedra,  a cornercorner with one Hf(3)N4O2 octahedra,  a cornercorner with one Hf(8)N4O2 octahedra, corners with three equivalent Li(1)N2O2 tetrahedra, and corners with three equivalent Hf(5)N4O trigonal bipyramids. The corner-sharing octahedral tilt angles range from 50-63°. In the second Hf site, Hf(2) is bonded to one N(3), one N(5), one N(7), one N(8), one O(3), and one O(4) atom to form HfN4O2 octahedra that share corners with three equivalent Hf(3)N4O2 octahedra,  a cornercorner with one Hf(1)N4O trigonal bipyramid,  a cornercorner with one Hf(5)N4O trigonal bipyramid, and edges with three equivalent Hf(8)N4O2 octahedra. The corner-sharing octahedral tilt angles range from 48-59°. In the third Hf site, Hf(3) is bonded to one N(2), one N(5), one N(6), one N(8), one O(1), and one O(3) atom to form distorted HfN4O2 octahedra that share corners with three equivalent Hf(2)N4O2 octahedra, corners with three equivalent Hf(8)N4O2 octahedra,  a cornercorner with one Li(1)N2O2 tetrahedra,  a cornercorner with one Hf(1)N4O trigonal bipyramid, and  a cornercorner with one Hf(5)N4O trigonal bipyramid. The corner-sharing octahedral tilt angles range from 46-59°. In the fourth Hf site, Hf(4) is bonded in a 5-coordinate geometry to one N(3), one N(4), one N(5), one N(7), and one O(4) atom. In the fifth Hf site, Hf(5) is bonded to one N(1), one N(3), one N(4), one N(6), and one O(2) atom to form HfN4O trigonal bipyramids that share  a cornercorner with one Hf(2)N4O2 octahedra,  a cornercorner with one Hf(3)N4O2 octahedra,  a cornercorner with one Hf(8)N4O2 octahedra, corners with three equivalent Li(1)N2O2 tetrahedra, and corners with three equivalent Hf(1)N4O trigonal bipyramids. The corner-sharing octahedral tilt angles range from 52-62°. In the sixth Hf site, Hf(6) is bonded in a 5-coordinate geometry to one N(1), one N(2), one N(5), one N(6), one N(8), and one O(1) atom. In the seventh Hf site, Hf(7) is bonded in a 6-coordinate geometry to one N(2), one N(5), one N(6), one N(8), one O(1), and one O(3) atom. In the eighth Hf site, Hf(8) is bonded to one N(3), one N(5), one N(7), one N(8), one O(3), and one O(4) atom to form distorted HfN4O2 octahedra that share corners with three equivalent Hf(3)N4O2 octahedra,  a cornercorner with one Hf(1)N4O trigonal bipyramid,  a cornercorner with one Hf(5)N4O trigonal bipyramid, and edges with three equivalent Hf(2)N4O2 octahedra. The corner-sharing octahedral tilt angles range from 46-57°. There are eight inequivalent N sites. In the first N site, N(1) is bonded to one Li(1), one Hf(1), one Hf(5), and one Hf(6) atom to form NLiHf3 tetrahedra that share  a cornercorner with one N(3)Hf4 tetrahedra,  a cornercorner with one N(7)Hf4 tetrahedra, corners with three equivalent N(4)LiHf3 tetrahedra,  an edgeedge with one N(2)Hf4 tetrahedra,  an edgeedge with one N(6)Hf4 tetrahedra, and  an edgeedge with one O(1)LiHf3 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 NHf4 tetrahedra that share  a cornercorner with one N(7)Hf4 tetrahedra,  a cornercorner with one N(4)LiHf3 tetrahedra, corners with three equivalent N(6)Hf4 tetrahedra, corners with three equivalent O(1)LiHf3 tetrahedra, and  an edgeedge with one N(1)LiHf3 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(6)Hf4 tetrahedra,  a cornercorner with one N(1)LiHf3 tetrahedra, corners with three equivalent N(7)Hf4 tetrahedra, and  an edgeedge with one N(4)LiHf3 tetrahedra. In the fourth N site, N(4) is bonded to one Li(1), one Hf(1), one Hf(4), and one Hf(5) atom to form NLiHf3 tetrahedra that share  a cornercorner with one N(2)Hf4 tetrahedra,  a cornercorner with one N(6)Hf4 tetrahedra,  a cornercorner with one O(1)LiHf3 tetrahedra, corners with three equivalent N(1)LiHf3 tetrahedra,  an edgeedge with one N(3)Hf4 tetrahedra, and  an edgeedge with one N(7)Hf4 tetrahedra. In the fifth N site, N(5) is bonded in a 6-coordinate geometry to one Hf(2), one Hf(3), one Hf(4), one Hf(6), one Hf(7), and one Hf(8) atom. In the sixth N site, N(6) is bonded to one Hf(3), one Hf(5), one Hf(6), and one Hf(7) atom to form NHf4 tetrahedra that share  a cornercorner with one N(3)Hf4 tetrahedra,  a cornercorner with one N(4)LiHf3 tetrahedra, corners with three equivalent N(2)Hf4 tetrahedra, corners with three equivalent O(1)LiHf3 tetrahedra, and  an edgeedge with one N(1)LiHf3 tetrahedra. In the seventh N site, N(7) is bonded to one Hf(1), one Hf(2), one Hf(4), and one Hf(8) atom to form NHf4 tetrahedra that share  a cornercorner with one N(2)Hf4 tetrahedra,  a cornercorner with one N(1)LiHf3 tetrahedra, corners with three equivalent N(3)Hf4 tetrahedra, and  an edgeedge with one N(4)LiHf3 tetrahedra. In the eighth N site, N(8) is bonded in a 5-coordinate geometry to one Hf(2), one Hf(3), one Hf(6), one Hf(7), and one Hf(8) atom. There are four inequivalent O sites. In the first O site, O(1) is bonded to one Li(1), one Hf(3), one Hf(6), and one Hf(7) atom to form OLiHf3 tetrahedra that share  a cornercorner with one N(4)LiHf3 tetrahedra, corners with three equivalent N(2)Hf4 tetrahedra, corners with three equivalent N(6)Hf4 tetrahedra, and  an edgeedge with one N(1)LiHf3 tetrahedra. In the second O site, O(2) is bonded in a trigonal planar geometry to one Li(1), one Hf(1), and one Hf(5) atom. In the third O site, O(3) is bonded in a 4-coordinate geometry to one Hf(2), one Hf(3), one Hf(7), and one Hf(8) atom. In the fourth O site, O(4) is bonded in a trigonal planar geometry to one Hf(2), one Hf(4), and one Hf(8) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_LiHf8(N2O)4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.878
_cell_length_b   5.835
_cell_length_c   10.873
_cell_angle_alpha   74.801
_cell_angle_beta   57.742
_cell_angle_gamma   59.338
_symmetry_Int_Tables_number   1
_cell_volume   271.258
_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
  Li  Li0  1  0.912  0.021  0.336  1.0
  Hf  Hf1  1  0.206  0.345  0.378  1.0
  Hf  Hf2  1  0.157  0.987  0.748  1.0
  Hf  Hf3  1  0.263  0.338  0.006  1.0
  Hf  Hf4  1  0.605  0.348  0.652  1.0
  Hf  Hf5  1  0.533  0.673  0.377  1.0
  Hf  Hf6  1  0.807  0.989  0.095  1.0
  Hf  Hf7  1  0.553  0.660  0.037  1.0
  Hf  Hf8  1  0.856  0.668  0.726  1.0
  N  N9  1  0.597  0.001  0.326  1.0
  N  N10  1  0.410  0.355  0.137  1.0
  N  N11  1  0.273  0.700  0.618  1.0
  N  N12  1  0.831  0.330  0.424  1.0
  N  N13  1  0.391  0.632  0.863  1.0
  N  N14  1  0.792  0.622  0.137  1.0
  N  N15  1  0.005  0.326  0.618  1.0
  N  N16  1  0.728  0.986  0.896  1.0
  O  O17  1  0.146  0.005  0.101  1.0
  O  O18  1  0.187  0.698  0.372  1.0
  O  O19  1  0.991  0.364  0.882  1.0
  O  O20  1  0.577  0.007  0.665  1.0
[/CIF]
.