The material structure described by LuFeO3 crystallizes in the hexagonal P6_3cm space group. There are two inequivalent Lu sites. In the first Lu site, Lu(1) is bonded to one O(3), three equivalent O(1), and three equivalent O(2) atoms to form distorted LuO7 pentagonal bipyramids that share corners with three equivalent Fe(1)O5 trigonal bipyramids and edges with three equivalent Fe(1)O5 trigonal bipyramids. In the second Lu site, Lu(2) is bonded in a 7-coordinate geometry to one O(4), three equivalent O(1), and three equivalent O(2) atoms. Fe(1) is bonded to one O(1), one O(2), one O(3), and two equivalent O(4) atoms to form FeO5 trigonal bipyramids that share  a cornercorner with one Lu(1)O7 pentagonal bipyramid, corners with six equivalent Fe(1)O5 trigonal bipyramids, and  an edgeedge with one Lu(1)O7 pentagonal bipyramid. There are four inequivalent O sites. In the first O site, O(1) is bonded to one Lu(1), two equivalent Lu(2), and one Fe(1) atom to form OLu3Fe tetrahedra that share corners with four equivalent O(2)Lu3Fe tetrahedra, corners with six equivalent O(1)Lu3Fe tetrahedra, corners with two equivalent O(3)LuFe3 trigonal pyramids, edges with three equivalent O(2)Lu3Fe tetrahedra, and edges with two equivalent O(4)LuFe3 trigonal pyramids. In the second O site, O(2) is bonded to one Lu(1), two equivalent Lu(2), and one Fe(1) atom to form distorted OLu3Fe tetrahedra that share corners with four equivalent O(1)Lu3Fe tetrahedra, corners with six equivalent O(2)Lu3Fe tetrahedra, corners with four equivalent O(4)LuFe3 trigonal pyramids, edges with three equivalent O(1)Lu3Fe tetrahedra, and  an edgeedge with one O(3)LuFe3 trigonal pyramid. In the third O site, O(3) is bonded to one Lu(1) and three equivalent Fe(1) atoms to form OLuFe3 trigonal pyramids that share corners with six equivalent O(1)Lu3Fe tetrahedra, corners with six equivalent O(4)LuFe3 trigonal pyramids, and edges with three equivalent O(2)Lu3Fe tetrahedra. In the fourth O site, O(4) is bonded to one Lu(2) and three equivalent Fe(1) atoms to form OLuFe3 trigonal pyramids that share corners with six equivalent O(2)Lu3Fe tetrahedra, corners with three equivalent O(3)LuFe3 trigonal pyramids, corners with three equivalent O(4)LuFe3 trigonal pyramids, and edges with three equivalent O(1)Lu3Fe tetrahedra. is represented by the CIF card [CIF]
data_LuFeO3
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.962
_cell_length_b   5.962
_cell_length_c   11.582
_cell_angle_alpha   89.998
_cell_angle_beta   89.998
_cell_angle_gamma   119.996
_symmetry_Int_Tables_number   1
_cell_volume   356.536
_cell_formula_units_Z   6
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  1.000  1.000  0.224  1.0
  Lu  Lu1  1  0.000  0.000  0.723  1.0
  Lu  Lu2  1  0.666  0.333  0.268  1.0
  Lu  Lu3  1  0.333  0.666  0.268  1.0
  Lu  Lu4  1  0.334  0.667  0.768  1.0
  Lu  Lu5  1  0.667  0.334  0.768  1.0
  Fe  Fe6  1  0.666  1.000  0.499  1.0
  Fe  Fe7  1  0.334  0.334  0.499  1.0
  Fe  Fe8  1  1.000  0.666  0.499  1.0
  Fe  Fe9  1  0.334  1.000  0.999  1.0
  Fe  Fe10  1  0.666  0.666  0.999  1.0
  Fe  Fe11  1  1.000  0.334  0.999  1.0
  O  O12  1  0.696  1.000  0.332  1.0
  O  O13  1  0.304  0.304  0.332  1.0
  O  O14  1  1.000  0.696  0.332  1.0
  O  O15  1  0.304  0.000  0.832  1.0
  O  O16  1  0.697  0.697  0.832  1.0
  O  O17  1  0.000  0.304  0.832  1.0
  O  O18  1  0.363  1.000  0.164  1.0
  O  O19  1  0.636  0.636  0.164  1.0
  O  O20  1  1.000  0.363  0.164  1.0
  O  O21  1  0.637  0.000  0.664  1.0
  O  O22  1  0.364  0.364  0.664  1.0
  O  O23  1  0.000  0.637  0.664  1.0
  O  O24  1  0.000  0.000  0.026  1.0
  O  O25  1  0.000  0.000  0.526  1.0
  O  O26  1  0.667  0.333  0.475  1.0
  O  O27  1  0.333  0.667  0.475  1.0
  O  O28  1  0.333  0.667  0.975  1.0
  O  O29  1  0.667  0.333  0.975  1.0
[/CIF]
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The material structure described by LuFeO3 crystallizes in the hexagonal P6_3cm space group. There are two inequivalent Lu sites. In the first Lu site, Lu(1) is bonded to one O(3), three equivalent O(1), and three equivalent O(2) atoms to form distorted LuO7 pentagonal bipyramids that share corners with three equivalent Fe(1)O5 trigonal bipyramids and edges with three equivalent Fe(1)O5 trigonal bipyramids. In the second Lu site, Lu(2) is bonded in a 7-coordinate geometry to one O(4), three equivalent O(1), and three equivalent O(2) atoms. Fe(1) is bonded to one O(1), one O(2), one O(3), and two equivalent O(4) atoms to form FeO5 trigonal bipyramids that share  a cornercorner with one Lu(1)O7 pentagonal bipyramid, corners with six equivalent Fe(1)O5 trigonal bipyramids, and  an edgeedge with one Lu(1)O7 pentagonal bipyramid. There are four inequivalent O sites. In the first O site, O(1) is bonded to one Lu(1), two equivalent Lu(2), and one Fe(1) atom to form OLu3Fe tetrahedra that share corners with four equivalent O(2)Lu3Fe tetrahedra, corners with six equivalent O(1)Lu3Fe tetrahedra, corners with two equivalent O(3)LuFe3 trigonal pyramids, edges with three equivalent O(2)Lu3Fe tetrahedra, and edges with two equivalent O(4)LuFe3 trigonal pyramids. In the second O site, O(2) is bonded to one Lu(1), two equivalent Lu(2), and one Fe(1) atom to form distorted OLu3Fe tetrahedra that share corners with four equivalent O(1)Lu3Fe tetrahedra, corners with six equivalent O(2)Lu3Fe tetrahedra, corners with four equivalent O(4)LuFe3 trigonal pyramids, edges with three equivalent O(1)Lu3Fe tetrahedra, and  an edgeedge with one O(3)LuFe3 trigonal pyramid. In the third O site, O(3) is bonded to one Lu(1) and three equivalent Fe(1) atoms to form OLuFe3 trigonal pyramids that share corners with six equivalent O(1)Lu3Fe tetrahedra, corners with six equivalent O(4)LuFe3 trigonal pyramids, and edges with three equivalent O(2)Lu3Fe tetrahedra. In the fourth O site, O(4) is bonded to one Lu(2) and three equivalent Fe(1) atoms to form OLuFe3 trigonal pyramids that share corners with six equivalent O(2)Lu3Fe tetrahedra, corners with three equivalent O(3)LuFe3 trigonal pyramids, corners with three equivalent O(4)LuFe3 trigonal pyramids, and edges with three equivalent O(1)Lu3Fe tetrahedra. is represented by the CIF card [CIF]
data_LuFeO3
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.962
_cell_length_b   5.962
_cell_length_c   11.582
_cell_angle_alpha   89.998
_cell_angle_beta   89.998
_cell_angle_gamma   119.996
_symmetry_Int_Tables_number   1
_cell_volume   356.536
_cell_formula_units_Z   6
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  1.000  1.000  0.224  1.0
  Lu  Lu1  1  0.000  0.000  0.723  1.0
  Lu  Lu2  1  0.666  0.333  0.268  1.0
  Lu  Lu3  1  0.333  0.666  0.268  1.0
  Lu  Lu4  1  0.334  0.667  0.768  1.0
  Lu  Lu5  1  0.667  0.334  0.768  1.0
  Fe  Fe6  1  0.666  1.000  0.499  1.0
  Fe  Fe7  1  0.334  0.334  0.499  1.0
  Fe  Fe8  1  1.000  0.666  0.499  1.0
  Fe  Fe9  1  0.334  1.000  0.999  1.0
  Fe  Fe10  1  0.666  0.666  0.999  1.0
  Fe  Fe11  1  1.000  0.334  0.999  1.0
  O  O12  1  0.696  1.000  0.332  1.0
  O  O13  1  0.304  0.304  0.332  1.0
  O  O14  1  1.000  0.696  0.332  1.0
  O  O15  1  0.304  0.000  0.832  1.0
  O  O16  1  0.697  0.697  0.832  1.0
  O  O17  1  0.000  0.304  0.832  1.0
  O  O18  1  0.363  1.000  0.164  1.0
  O  O19  1  0.636  0.636  0.164  1.0
  O  O20  1  1.000  0.363  0.164  1.0
  O  O21  1  0.637  0.000  0.664  1.0
  O  O22  1  0.364  0.364  0.664  1.0
  O  O23  1  0.000  0.637  0.664  1.0
  O  O24  1  0.000  0.000  0.026  1.0
  O  O25  1  0.000  0.000  0.526  1.0
  O  O26  1  0.667  0.333  0.475  1.0
  O  O27  1  0.333  0.667  0.475  1.0
  O  O28  1  0.333  0.667  0.975  1.0
  O  O29  1  0.667  0.333  0.975  1.0
[/CIF]
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