The compound described by LuFe2O4 is Aluminum carbonitride-like structured and crystallizes in the monoclinic C2/m space group. There are two inequivalent Lu sites. In the first Lu site, Lu(1) is bonded to one O(5), one O(6), two equivalent O(7), and two equivalent O(8) atoms to form distorted LuO6 octahedra that share  a cornercorner with one Fe(1)O5 trigonal bipyramid,  a cornercorner with one Fe(4)O5 trigonal bipyramid, corners with two equivalent Fe(2)O5 trigonal bipyramids, corners with two equivalent Fe(3)O5 trigonal bipyramids, and edges with six equivalent Lu(2)O6 octahedra. In the second Lu site, Lu(2) is bonded to one O(5), one O(6), two equivalent O(7), and two equivalent O(8) atoms to form distorted LuO6 octahedra that share  a cornercorner with one Fe(1)O5 trigonal bipyramid,  a cornercorner with one Fe(4)O5 trigonal bipyramid, corners with two equivalent Fe(2)O5 trigonal bipyramids, corners with two equivalent Fe(3)O5 trigonal bipyramids, edges with three equivalent Lu(1)O6 octahedra, and edges with three equivalent Lu(2)O6 octahedra. There are four inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to one O(6), two equivalent O(2), and two equivalent O(3) atoms to form FeO5 trigonal bipyramids that share  a cornercorner with one Lu(1)O6 octahedra, corners with two equivalent Lu(2)O6 octahedra, corners with six equivalent Fe(3)O5 trigonal bipyramids,  an edgeedge with one Fe(1)O5 trigonal bipyramid, and edges with two equivalent Fe(3)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 61-67°. In the second Fe site, Fe(2) is bonded to one O(1), one O(8), and three equivalent O(4) atoms to form FeO5 trigonal bipyramids that share  a cornercorner with one Lu(1)O6 octahedra, corners with two equivalent Lu(2)O6 octahedra, corners with three equivalent Fe(2)O5 trigonal bipyramids, corners with three equivalent Fe(4)O5 trigonal bipyramids,  an edgeedge with one Fe(4)O5 trigonal bipyramid, and edges with two equivalent Fe(2)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 60-65°. In the third Fe site, Fe(3) is bonded to one O(2), one O(7), and three equivalent O(3) atoms to form FeO5 trigonal bipyramids that share  a cornercorner with one Lu(1)O6 octahedra, corners with two equivalent Lu(2)O6 octahedra, corners with three equivalent Fe(1)O5 trigonal bipyramids, corners with three equivalent Fe(3)O5 trigonal bipyramids,  an edgeedge with one Fe(1)O5 trigonal bipyramid, and edges with two equivalent Fe(3)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 62-66°. In the fourth Fe site, Fe(4) is bonded to one O(5), two equivalent O(1), and two equivalent O(4) atoms to form FeO5 trigonal bipyramids that share  a cornercorner with one Lu(1)O6 octahedra, corners with two equivalent Lu(2)O6 octahedra, corners with six equivalent Fe(2)O5 trigonal bipyramids,  an edgeedge with one Fe(4)O5 trigonal bipyramid, and edges with two equivalent Fe(2)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 61-64°. There are eight inequivalent O sites. In the first O site, O(1) is bonded to two equivalent Fe(2) and two equivalent Fe(4) atoms to form OFe4 trigonal pyramids that share corners with two equivalent O(5)Lu3Fe tetrahedra, corners with two equivalent O(8)Lu3Fe tetrahedra, corners with six equivalent O(4)Fe4 trigonal pyramids,  an edgeedge with one O(1)Fe4 trigonal pyramid, and edges with two equivalent O(4)Fe4 trigonal pyramids. In the second O site, O(2) is bonded to two equivalent Fe(1) and two equivalent Fe(3) atoms to form distorted OFe4 trigonal pyramids that share corners with two equivalent O(6)Lu3Fe tetrahedra, corners with two equivalent O(7)Lu3Fe tetrahedra, corners with six equivalent O(3)Fe4 trigonal pyramids,  an edgeedge with one O(2)Fe4 trigonal pyramid, and edges with two equivalent O(3)Fe4 trigonal pyramids. In the third O site, O(3) is bonded to one Fe(1) and three equivalent Fe(3) atoms to form OFe4 trigonal pyramids that share  a cornercorner with one O(6)Lu3Fe tetrahedra, corners with three equivalent O(7)Lu3Fe tetrahedra, corners with three equivalent O(2)Fe4 trigonal pyramids, corners with three equivalent O(3)Fe4 trigonal pyramids,  an edgeedge with one O(2)Fe4 trigonal pyramid, and edges with two equivalent O(3)Fe4 trigonal pyramids. In the fourth O site, O(4) is bonded to one Fe(4) and three equivalent Fe(2) atoms to form OFe4 trigonal pyramids that share  a cornercorner with one O(5)Lu3Fe tetrahedra, corners with three equivalent O(8)Lu3Fe tetrahedra, corners with three equivalent O(1)Fe4 trigonal pyramids, corners with three equivalent O(4)Fe4 trigonal pyramids,  an edgeedge with one O(1)Fe4 trigonal pyramid, and edges with two equivalent O(4)Fe4 trigonal pyramids. In the fifth O site, O(5) is bonded to one Lu(1), two equivalent Lu(2), and one Fe(4) atom to form OLu3Fe tetrahedra that share  a cornercorner with one O(6)Lu3Fe tetrahedra, corners with two equivalent O(7)Lu3Fe tetrahedra, corners with six equivalent O(8)Lu3Fe tetrahedra, corners with two equivalent O(1)Fe4 trigonal pyramids, corners with two equivalent O(4)Fe4 trigonal pyramids,  an edgeedge with one O(6)Lu3Fe tetrahedra, and edges with two equivalent O(7)Lu3Fe tetrahedra. In the sixth O site, O(6) is bonded to one Lu(1), two equivalent Lu(2), and one Fe(1) atom to form OLu3Fe tetrahedra that share  a cornercorner with one O(5)Lu3Fe tetrahedra, corners with two equivalent O(8)Lu3Fe tetrahedra, corners with six equivalent O(7)Lu3Fe tetrahedra, corners with two equivalent O(2)Fe4 trigonal pyramids, corners with two equivalent O(3)Fe4 trigonal pyramids,  an edgeedge with one O(5)Lu3Fe tetrahedra, and edges with two equivalent O(8)Lu3Fe tetrahedra. In the seventh O site, O(7) is bonded to one Lu(1), two equivalent Lu(2), and one Fe(3) atom to form OLu3Fe tetrahedra that share  a cornercorner with one O(5)Lu3Fe tetrahedra, corners with two equivalent O(8)Lu3Fe tetrahedra, corners with three equivalent O(6)Lu3Fe tetrahedra, corners with three equivalent O(7)Lu3Fe tetrahedra,  a cornercorner with one O(2)Fe4 trigonal pyramid, corners with three equivalent O(3)Fe4 trigonal pyramids,  an edgeedge with one O(5)Lu3Fe tetrahedra, and edges with two equivalent O(8)Lu3Fe tetrahedra. In the eighth O site, O(8) is bonded to one Lu(1), two equivalent Lu(2), and one Fe(2) atom to form OLu3Fe tetrahedra that share  a cornercorner with one O(6)Lu3Fe tetrahedra, corners with two equivalent O(7)Lu3Fe tetrahedra, corners with three equivalent O(5)Lu3Fe tetrahedra, corners with three equivalent O(8)Lu3Fe tetrahedra,  a cornercorner with one O(1)Fe4 trigonal pyramid, corners with three equivalent O(4)Fe4 trigonal pyramids,  an edgeedge with one O(6)Lu3Fe tetrahedra, and edges with two equivalent O(7)Lu3Fe tetrahedra. is represented by the CIF card [CIF]
data_Lu(FeO2)2
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   3.476
_cell_length_b   3.476
_cell_length_c   16.969
_cell_angle_alpha   90.285
_cell_angle_beta   95.616
_cell_angle_gamma   119.861
_symmetry_Int_Tables_number   1
_cell_volume   176.600
_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
  Fe  Fe0  1  0.284  0.645  0.928  1.0
  Fe  Fe1  1  0.716  0.355  0.072  1.0
  Fe  Fe2  1  0.291  0.138  0.428  1.0
  Fe  Fe3  1  0.709  0.862  0.572  1.0
  Lu  Lu4  1  0.506  0.744  0.250  1.0
  Lu  Lu5  1  0.494  0.256  0.750  1.0
  O  O6  1  0.633  0.810  0.442  1.0
  O  O7  1  0.367  0.190  0.558  1.0
  O  O8  1  0.369  0.689  0.058  1.0
  O  O9  1  0.631  0.311  0.942  1.0
  O  O10  1  0.790  0.901  0.690  1.0
  O  O11  1  0.210  0.099  0.310  1.0
  O  O12  1  0.200  0.610  0.810  1.0
  O  O13  1  0.800  0.390  0.190  1.0
[/CIF]
.
The compound described by LuFe2O4 is Aluminum carbonitride-like structured and crystallizes in the monoclinic C2/m space group. There are two inequivalent Lu sites. In the first Lu site, Lu(1) is bonded to one O(5), one O(6), two equivalent O(7), and two equivalent O(8) atoms to form distorted LuO6 octahedra that share  a cornercorner with one Fe(1)O5 trigonal bipyramid,  a cornercorner with one Fe(4)O5 trigonal bipyramid, corners with two equivalent Fe(2)O5 trigonal bipyramids, corners with two equivalent Fe(3)O5 trigonal bipyramids, and edges with six equivalent Lu(2)O6 octahedra. In the second Lu site, Lu(2) is bonded to one O(5), one O(6), two equivalent O(7), and two equivalent O(8) atoms to form distorted LuO6 octahedra that share  a cornercorner with one Fe(1)O5 trigonal bipyramid,  a cornercorner with one Fe(4)O5 trigonal bipyramid, corners with two equivalent Fe(2)O5 trigonal bipyramids, corners with two equivalent Fe(3)O5 trigonal bipyramids, edges with three equivalent Lu(1)O6 octahedra, and edges with three equivalent Lu(2)O6 octahedra. There are four inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to one O(6), two equivalent O(2), and two equivalent O(3) atoms to form FeO5 trigonal bipyramids that share  a cornercorner with one Lu(1)O6 octahedra, corners with two equivalent Lu(2)O6 octahedra, corners with six equivalent Fe(3)O5 trigonal bipyramids,  an edgeedge with one Fe(1)O5 trigonal bipyramid, and edges with two equivalent Fe(3)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 61-67°. In the second Fe site, Fe(2) is bonded to one O(1), one O(8), and three equivalent O(4) atoms to form FeO5 trigonal bipyramids that share  a cornercorner with one Lu(1)O6 octahedra, corners with two equivalent Lu(2)O6 octahedra, corners with three equivalent Fe(2)O5 trigonal bipyramids, corners with three equivalent Fe(4)O5 trigonal bipyramids,  an edgeedge with one Fe(4)O5 trigonal bipyramid, and edges with two equivalent Fe(2)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 60-65°. In the third Fe site, Fe(3) is bonded to one O(2), one O(7), and three equivalent O(3) atoms to form FeO5 trigonal bipyramids that share  a cornercorner with one Lu(1)O6 octahedra, corners with two equivalent Lu(2)O6 octahedra, corners with three equivalent Fe(1)O5 trigonal bipyramids, corners with three equivalent Fe(3)O5 trigonal bipyramids,  an edgeedge with one Fe(1)O5 trigonal bipyramid, and edges with two equivalent Fe(3)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 62-66°. In the fourth Fe site, Fe(4) is bonded to one O(5), two equivalent O(1), and two equivalent O(4) atoms to form FeO5 trigonal bipyramids that share  a cornercorner with one Lu(1)O6 octahedra, corners with two equivalent Lu(2)O6 octahedra, corners with six equivalent Fe(2)O5 trigonal bipyramids,  an edgeedge with one Fe(4)O5 trigonal bipyramid, and edges with two equivalent Fe(2)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 61-64°. There are eight inequivalent O sites. In the first O site, O(1) is bonded to two equivalent Fe(2) and two equivalent Fe(4) atoms to form OFe4 trigonal pyramids that share corners with two equivalent O(5)Lu3Fe tetrahedra, corners with two equivalent O(8)Lu3Fe tetrahedra, corners with six equivalent O(4)Fe4 trigonal pyramids,  an edgeedge with one O(1)Fe4 trigonal pyramid, and edges with two equivalent O(4)Fe4 trigonal pyramids. In the second O site, O(2) is bonded to two equivalent Fe(1) and two equivalent Fe(3) atoms to form distorted OFe4 trigonal pyramids that share corners with two equivalent O(6)Lu3Fe tetrahedra, corners with two equivalent O(7)Lu3Fe tetrahedra, corners with six equivalent O(3)Fe4 trigonal pyramids,  an edgeedge with one O(2)Fe4 trigonal pyramid, and edges with two equivalent O(3)Fe4 trigonal pyramids. In the third O site, O(3) is bonded to one Fe(1) and three equivalent Fe(3) atoms to form OFe4 trigonal pyramids that share  a cornercorner with one O(6)Lu3Fe tetrahedra, corners with three equivalent O(7)Lu3Fe tetrahedra, corners with three equivalent O(2)Fe4 trigonal pyramids, corners with three equivalent O(3)Fe4 trigonal pyramids,  an edgeedge with one O(2)Fe4 trigonal pyramid, and edges with two equivalent O(3)Fe4 trigonal pyramids. In the fourth O site, O(4) is bonded to one Fe(4) and three equivalent Fe(2) atoms to form OFe4 trigonal pyramids that share  a cornercorner with one O(5)Lu3Fe tetrahedra, corners with three equivalent O(8)Lu3Fe tetrahedra, corners with three equivalent O(1)Fe4 trigonal pyramids, corners with three equivalent O(4)Fe4 trigonal pyramids,  an edgeedge with one O(1)Fe4 trigonal pyramid, and edges with two equivalent O(4)Fe4 trigonal pyramids. In the fifth O site, O(5) is bonded to one Lu(1), two equivalent Lu(2), and one Fe(4) atom to form OLu3Fe tetrahedra that share  a cornercorner with one O(6)Lu3Fe tetrahedra, corners with two equivalent O(7)Lu3Fe tetrahedra, corners with six equivalent O(8)Lu3Fe tetrahedra, corners with two equivalent O(1)Fe4 trigonal pyramids, corners with two equivalent O(4)Fe4 trigonal pyramids,  an edgeedge with one O(6)Lu3Fe tetrahedra, and edges with two equivalent O(7)Lu3Fe tetrahedra. In the sixth O site, O(6) is bonded to one Lu(1), two equivalent Lu(2), and one Fe(1) atom to form OLu3Fe tetrahedra that share  a cornercorner with one O(5)Lu3Fe tetrahedra, corners with two equivalent O(8)Lu3Fe tetrahedra, corners with six equivalent O(7)Lu3Fe tetrahedra, corners with two equivalent O(2)Fe4 trigonal pyramids, corners with two equivalent O(3)Fe4 trigonal pyramids,  an edgeedge with one O(5)Lu3Fe tetrahedra, and edges with two equivalent O(8)Lu3Fe tetrahedra. In the seventh O site, O(7) is bonded to one Lu(1), two equivalent Lu(2), and one Fe(3) atom to form OLu3Fe tetrahedra that share  a cornercorner with one O(5)Lu3Fe tetrahedra, corners with two equivalent O(8)Lu3Fe tetrahedra, corners with three equivalent O(6)Lu3Fe tetrahedra, corners with three equivalent O(7)Lu3Fe tetrahedra,  a cornercorner with one O(2)Fe4 trigonal pyramid, corners with three equivalent O(3)Fe4 trigonal pyramids,  an edgeedge with one O(5)Lu3Fe tetrahedra, and edges with two equivalent O(8)Lu3Fe tetrahedra. In the eighth O site, O(8) is bonded to one Lu(1), two equivalent Lu(2), and one Fe(2) atom to form OLu3Fe tetrahedra that share  a cornercorner with one O(6)Lu3Fe tetrahedra, corners with two equivalent O(7)Lu3Fe tetrahedra, corners with three equivalent O(5)Lu3Fe tetrahedra, corners with three equivalent O(8)Lu3Fe tetrahedra,  a cornercorner with one O(1)Fe4 trigonal pyramid, corners with three equivalent O(4)Fe4 trigonal pyramids,  an edgeedge with one O(6)Lu3Fe tetrahedra, and edges with two equivalent O(7)Lu3Fe tetrahedra. is represented by the CIF card [CIF]
data_Lu(FeO2)2
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   3.476
_cell_length_b   3.476
_cell_length_c   16.969
_cell_angle_alpha   90.285
_cell_angle_beta   95.616
_cell_angle_gamma   119.861
_symmetry_Int_Tables_number   1
_cell_volume   176.600
_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
  Fe  Fe0  1  0.284  0.645  0.928  1.0
  Fe  Fe1  1  0.716  0.355  0.072  1.0
  Fe  Fe2  1  0.291  0.138  0.428  1.0
  Fe  Fe3  1  0.709  0.862  0.572  1.0
  Lu  Lu4  1  0.506  0.744  0.250  1.0
  Lu  Lu5  1  0.494  0.256  0.750  1.0
  O  O6  1  0.633  0.810  0.442  1.0
  O  O7  1  0.367  0.190  0.558  1.0
  O  O8  1  0.369  0.689  0.058  1.0
  O  O9  1  0.631  0.311  0.942  1.0
  O  O10  1  0.790  0.901  0.690  1.0
  O  O11  1  0.210  0.099  0.310  1.0
  O  O12  1  0.200  0.610  0.810  1.0
  O  O13  1  0.800  0.390  0.190  1.0
[/CIF]
.