The crystal structure described by LuFe2O4 is Aluminum carbonitride-like structured and crystallizes in the trigonal R-3m space group. Lu(1) is bonded to six equivalent O(1) atoms to form distorted LuO6 octahedra that share corners with six equivalent Fe(1)O5 trigonal bipyramids and edges with six equivalent Lu(1)O6 octahedra. Fe(1) is bonded to one O(1) and four equivalent O(2) atoms to form FeO5 trigonal bipyramids that share corners with three equivalent Lu(1)O6 octahedra, corners with six equivalent Fe(1)O5 trigonal bipyramids, and edges with three equivalent Fe(1)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 63°. There are two inequivalent O sites. In the first O site, O(1) is bonded to three equivalent Lu(1) and one Fe(1) atom to form OLu3Fe tetrahedra that share corners with nine equivalent O(1)Lu3Fe tetrahedra, corners with four equivalent O(2)Fe4 trigonal pyramids, and edges with three equivalent O(1)Lu3Fe tetrahedra. In the second O site, O(2) is bonded to four equivalent Fe(1) atoms to form OFe4 trigonal pyramids that share corners with four equivalent O(1)Lu3Fe tetrahedra, corners with six equivalent O(2)Fe4 trigonal pyramids, and edges with three equivalent O(2)Fe4 trigonal pyramids. is represented by the CIF file [CIF]
data_Lu(FeO2)2
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.690
_cell_length_b   8.690
_cell_length_c   8.690
_cell_angle_alpha   23.039
_cell_angle_beta   23.039
_cell_angle_gamma   23.039
_symmetry_Int_Tables_number   1
_cell_volume   88.217
_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
  Lu  Lu0  1  0.000  0.000  0.000  1.0
  Fe  Fe1  1  0.786  0.786  0.786  1.0
  Fe  Fe2  1  0.214  0.214  0.214  1.0
  O  O3  1  0.707  0.707  0.707  1.0
  O  O4  1  0.293  0.293  0.293  1.0
  O  O5  1  0.872  0.872  0.872  1.0
  O  O6  1  0.128  0.128  0.128  1.0
[/CIF]
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The crystal structure described by LuFe2O4 is Aluminum carbonitride-like structured and crystallizes in the trigonal R-3m space group. Lu(1) is bonded to six equivalent O(1) atoms to form distorted LuO6 octahedra that share corners with six equivalent Fe(1)O5 trigonal bipyramids and edges with six equivalent Lu(1)O6 octahedra. Fe(1) is bonded to one O(1) and four equivalent O(2) atoms to form FeO5 trigonal bipyramids that share corners with three equivalent Lu(1)O6 octahedra, corners with six equivalent Fe(1)O5 trigonal bipyramids, and edges with three equivalent Fe(1)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 63°. There are two inequivalent O sites. In the first O site, O(1) is bonded to three equivalent Lu(1) and one Fe(1) atom to form OLu3Fe tetrahedra that share corners with nine equivalent O(1)Lu3Fe tetrahedra, corners with four equivalent O(2)Fe4 trigonal pyramids, and edges with three equivalent O(1)Lu3Fe tetrahedra. In the second O site, O(2) is bonded to four equivalent Fe(1) atoms to form OFe4 trigonal pyramids that share corners with four equivalent O(1)Lu3Fe tetrahedra, corners with six equivalent O(2)Fe4 trigonal pyramids, and edges with three equivalent O(2)Fe4 trigonal pyramids. is represented by the CIF file [CIF]
data_Lu(FeO2)2
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.690
_cell_length_b   8.690
_cell_length_c   8.690
_cell_angle_alpha   23.039
_cell_angle_beta   23.039
_cell_angle_gamma   23.039
_symmetry_Int_Tables_number   1
_cell_volume   88.217
_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
  Lu  Lu0  1  0.000  0.000  0.000  1.0
  Fe  Fe1  1  0.786  0.786  0.786  1.0
  Fe  Fe2  1  0.214  0.214  0.214  1.0
  O  O3  1  0.707  0.707  0.707  1.0
  O  O4  1  0.293  0.293  0.293  1.0
  O  O5  1  0.872  0.872  0.872  1.0
  O  O6  1  0.128  0.128  0.128  1.0
[/CIF]
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