The material structure described by LuFeCuO4 crystallizes in the trigonal R3m space group. Lu(1) is bonded in a 6-coordinate geometry to three equivalent O(1) and three equivalent O(2) atoms. Fe(1) is bonded to one O(2), one O(4), and three equivalent O(3) atoms to form FeO5 trigonal bipyramids that share corners with six equivalent Fe(1)O5 trigonal bipyramids and edges with three equivalent Cu(1)O5 trigonal bipyramids. Cu(1) is bonded to one O(1), one O(3), and three equivalent O(4) atoms to form CuO5 trigonal bipyramids that share corners with six equivalent Cu(1)O5 trigonal bipyramids and edges with three equivalent Fe(1)O5 trigonal bipyramids. There are four inequivalent O sites. In the first O site, O(1) is bonded to three equivalent Lu(1) and one Cu(1) atom to form OLu3Cu tetrahedra that share corners with three equivalent O(2)Lu3Fe tetrahedra, corners with six equivalent O(1)Lu3Cu tetrahedra,  a cornercorner with one O(3)Fe3Cu trigonal pyramid, corners with three equivalent O(4)FeCu3 trigonal pyramids, and edges with three equivalent O(2)Lu3Fe tetrahedra. In the second O site, O(2) is bonded to three equivalent Lu(1) and one Fe(1) atom to form distorted OLu3Fe tetrahedra that share corners with three equivalent O(1)Lu3Cu tetrahedra, corners with six equivalent O(2)Lu3Fe tetrahedra,  a cornercorner with one O(4)FeCu3 trigonal pyramid, corners with three equivalent O(3)Fe3Cu trigonal pyramids, and edges with three equivalent O(1)Lu3Cu tetrahedra. In the third O site, O(3) is bonded to three equivalent Fe(1) and one Cu(1) atom to form OFe3Cu trigonal pyramids that share  a cornercorner with one O(1)Lu3Cu tetrahedra, corners with three equivalent O(2)Lu3Fe tetrahedra, corners with six equivalent O(3)Fe3Cu trigonal pyramids, and edges with three equivalent O(4)FeCu3 trigonal pyramids. In the fourth O site, O(4) is bonded to one Fe(1) and three equivalent Cu(1) atoms to form OFeCu3 trigonal pyramids that share  a cornercorner with one O(2)Lu3Fe tetrahedra, corners with three equivalent O(1)Lu3Cu tetrahedra, corners with six equivalent O(4)FeCu3 trigonal pyramids, and edges with three equivalent O(3)Fe3Cu trigonal pyramids. is represented by the CIF card [CIF]
data_LuFeCuO4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.285
_cell_length_b   8.285
_cell_length_c   8.285
_cell_angle_alpha   24.431
_cell_angle_beta   24.431
_cell_angle_gamma   24.431
_symmetry_Int_Tables_number   1
_cell_volume   85.531
_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  0.005  0.005  0.005  1.0
  Fe  Fe1  1  0.212  0.212  0.212  1.0
  Cu  Cu2  1  0.788  0.788  0.788  1.0
  O  O3  1  0.708  0.708  0.708  1.0
  O  O4  1  0.293  0.293  0.293  1.0
  O  O5  1  0.874  0.874  0.874  1.0
  O  O6  1  0.129  0.129  0.129  1.0
[/CIF]
.
The material structure described by LuFeCuO4 crystallizes in the trigonal R3m space group. Lu(1) is bonded in a 6-coordinate geometry to three equivalent O(1) and three equivalent O(2) atoms. Fe(1) is bonded to one O(2), one O(4), and three equivalent O(3) atoms to form FeO5 trigonal bipyramids that share corners with six equivalent Fe(1)O5 trigonal bipyramids and edges with three equivalent Cu(1)O5 trigonal bipyramids. Cu(1) is bonded to one O(1), one O(3), and three equivalent O(4) atoms to form CuO5 trigonal bipyramids that share corners with six equivalent Cu(1)O5 trigonal bipyramids and edges with three equivalent Fe(1)O5 trigonal bipyramids. There are four inequivalent O sites. In the first O site, O(1) is bonded to three equivalent Lu(1) and one Cu(1) atom to form OLu3Cu tetrahedra that share corners with three equivalent O(2)Lu3Fe tetrahedra, corners with six equivalent O(1)Lu3Cu tetrahedra,  a cornercorner with one O(3)Fe3Cu trigonal pyramid, corners with three equivalent O(4)FeCu3 trigonal pyramids, and edges with three equivalent O(2)Lu3Fe tetrahedra. In the second O site, O(2) is bonded to three equivalent Lu(1) and one Fe(1) atom to form distorted OLu3Fe tetrahedra that share corners with three equivalent O(1)Lu3Cu tetrahedra, corners with six equivalent O(2)Lu3Fe tetrahedra,  a cornercorner with one O(4)FeCu3 trigonal pyramid, corners with three equivalent O(3)Fe3Cu trigonal pyramids, and edges with three equivalent O(1)Lu3Cu tetrahedra. In the third O site, O(3) is bonded to three equivalent Fe(1) and one Cu(1) atom to form OFe3Cu trigonal pyramids that share  a cornercorner with one O(1)Lu3Cu tetrahedra, corners with three equivalent O(2)Lu3Fe tetrahedra, corners with six equivalent O(3)Fe3Cu trigonal pyramids, and edges with three equivalent O(4)FeCu3 trigonal pyramids. In the fourth O site, O(4) is bonded to one Fe(1) and three equivalent Cu(1) atoms to form OFeCu3 trigonal pyramids that share  a cornercorner with one O(2)Lu3Fe tetrahedra, corners with three equivalent O(1)Lu3Cu tetrahedra, corners with six equivalent O(4)FeCu3 trigonal pyramids, and edges with three equivalent O(3)Fe3Cu trigonal pyramids. is represented by the CIF card [CIF]
data_LuFeCuO4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.285
_cell_length_b   8.285
_cell_length_c   8.285
_cell_angle_alpha   24.431
_cell_angle_beta   24.431
_cell_angle_gamma   24.431
_symmetry_Int_Tables_number   1
_cell_volume   85.531
_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  0.005  0.005  0.005  1.0
  Fe  Fe1  1  0.212  0.212  0.212  1.0
  Cu  Cu2  1  0.788  0.788  0.788  1.0
  O  O3  1  0.708  0.708  0.708  1.0
  O  O4  1  0.293  0.293  0.293  1.0
  O  O5  1  0.874  0.874  0.874  1.0
  O  O6  1  0.129  0.129  0.129  1.0
[/CIF]
.