The crystal structure described by Li3Cr3FeO8 crystallizes in the monoclinic C2/m space group. There are two inequivalent Li sites. In the first Li site, Li(1) is bonded to two equivalent O(1) and four equivalent O(3) atoms to form LiO6 octahedra that share corners with six equivalent Cr(1)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, edges with four equivalent Li(2)O6 octahedra, and edges with four equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 6-7°. In the second Li site, Li(2) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(3) atoms to form LiO6 octahedra that share corners with six equivalent Cr(2)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Cr(1)O6 octahedra, edges with two equivalent Cr(2)O6 octahedra, and edges with two equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 5-9°. There are two inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to two equivalent O(1) and four equivalent O(3) atoms to form CrO6 octahedra that share corners with six equivalent Li(1)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, edges with four equivalent Li(2)O6 octahedra, and edges with four equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 6-7°. In the second Cr site, Cr(2) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(3) atoms to form CrO6 octahedra that share corners with six equivalent Li(2)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Cr(1)O6 octahedra, edges with two equivalent Cr(2)O6 octahedra, and edges with two equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 5-9°. Fe(1) is bonded to two equivalent O(2) and four equivalent O(3) atoms to form FeO6 octahedra that share edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Cr(1)O6 octahedra, edges with four equivalent Li(2)O6 octahedra, and edges with four equivalent Cr(2)O6 octahedra. There are three inequivalent O sites. In the first O site, O(1) is bonded to one Li(1), two equivalent Li(2), one Cr(1), and two equivalent Cr(2) atoms to form OLi3Cr3 octahedra that share corners with six equivalent O(1)Li3Cr3 octahedra, edges with four equivalent O(2)Li2Cr2Fe square pyramids, and edges with eight equivalent O(3)Li2Cr2Fe square pyramids. The corner-sharing octahedra are not tilted. In the second O site, O(2) is bonded to two equivalent Li(2), two equivalent Cr(2), and one Fe(1) atom to form OLi2Cr2Fe square pyramids that share corners with four equivalent O(3)Li2Cr2Fe square pyramids, corners with five equivalent O(2)Li2Cr2Fe square pyramids, edges with four equivalent O(1)Li3Cr3 octahedra, and edges with four equivalent O(3)Li2Cr2Fe square pyramids. In the third O site, O(3) is bonded to one Li(1), one Li(2), one Cr(1), one Cr(2), and one Fe(1) atom to form OLi2Cr2Fe square pyramids that share corners with two equivalent O(2)Li2Cr2Fe square pyramids, corners with seven equivalent O(3)Li2Cr2Fe square pyramids, edges with four equivalent O(1)Li3Cr3 octahedra, edges with two equivalent O(2)Li2Cr2Fe square pyramids, and edges with two equivalent O(3)Li2Cr2Fe square pyramids. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li3Cr3FeO8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.912
_cell_length_b   5.912
_cell_length_c   5.944
_cell_angle_alpha   59.706
_cell_angle_beta   59.706
_cell_angle_gamma   60.712
_symmetry_Int_Tables_number   1
_cell_volume   147.024
_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  1.000  0.000  0.500  1.0
  Li  Li1  1  1.000  0.500  1.000  1.0
  Li  Li2  1  0.500  0.000  1.000  1.0
  Cr  Cr3  1  0.500  0.500  0.000  1.0
  Cr  Cr4  1  0.000  0.500  0.500  1.0
  Cr  Cr5  1  0.500  0.000  0.500  1.0
  Fe  Fe6  1  0.500  0.500  0.500  1.0
  O  O7  1  0.255  0.255  0.263  1.0
  O  O8  1  0.745  0.745  0.737  1.0
  O  O9  1  0.270  0.269  0.715  1.0
  O  O10  1  0.267  0.720  0.258  1.0
  O  O11  1  0.720  0.267  0.258  1.0
  O  O12  1  0.280  0.733  0.742  1.0
  O  O13  1  0.733  0.280  0.742  1.0
  O  O14  1  0.731  0.730  0.285  1.0
[/CIF]
.
The crystal structure described by Li3Cr3FeO8 crystallizes in the monoclinic C2/m space group. There are two inequivalent Li sites. In the first Li site, Li(1) is bonded to two equivalent O(1) and four equivalent O(3) atoms to form LiO6 octahedra that share corners with six equivalent Cr(1)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, edges with four equivalent Li(2)O6 octahedra, and edges with four equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 6-7°. In the second Li site, Li(2) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(3) atoms to form LiO6 octahedra that share corners with six equivalent Cr(2)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Cr(1)O6 octahedra, edges with two equivalent Cr(2)O6 octahedra, and edges with two equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 5-9°. There are two inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to two equivalent O(1) and four equivalent O(3) atoms to form CrO6 octahedra that share corners with six equivalent Li(1)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, edges with four equivalent Li(2)O6 octahedra, and edges with four equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 6-7°. In the second Cr site, Cr(2) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(3) atoms to form CrO6 octahedra that share corners with six equivalent Li(2)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Cr(1)O6 octahedra, edges with two equivalent Cr(2)O6 octahedra, and edges with two equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 5-9°. Fe(1) is bonded to two equivalent O(2) and four equivalent O(3) atoms to form FeO6 octahedra that share edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Cr(1)O6 octahedra, edges with four equivalent Li(2)O6 octahedra, and edges with four equivalent Cr(2)O6 octahedra. There are three inequivalent O sites. In the first O site, O(1) is bonded to one Li(1), two equivalent Li(2), one Cr(1), and two equivalent Cr(2) atoms to form OLi3Cr3 octahedra that share corners with six equivalent O(1)Li3Cr3 octahedra, edges with four equivalent O(2)Li2Cr2Fe square pyramids, and edges with eight equivalent O(3)Li2Cr2Fe square pyramids. The corner-sharing octahedra are not tilted. In the second O site, O(2) is bonded to two equivalent Li(2), two equivalent Cr(2), and one Fe(1) atom to form OLi2Cr2Fe square pyramids that share corners with four equivalent O(3)Li2Cr2Fe square pyramids, corners with five equivalent O(2)Li2Cr2Fe square pyramids, edges with four equivalent O(1)Li3Cr3 octahedra, and edges with four equivalent O(3)Li2Cr2Fe square pyramids. In the third O site, O(3) is bonded to one Li(1), one Li(2), one Cr(1), one Cr(2), and one Fe(1) atom to form OLi2Cr2Fe square pyramids that share corners with two equivalent O(2)Li2Cr2Fe square pyramids, corners with seven equivalent O(3)Li2Cr2Fe square pyramids, edges with four equivalent O(1)Li3Cr3 octahedra, edges with two equivalent O(2)Li2Cr2Fe square pyramids, and edges with two equivalent O(3)Li2Cr2Fe square pyramids. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li3Cr3FeO8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.912
_cell_length_b   5.912
_cell_length_c   5.944
_cell_angle_alpha   59.706
_cell_angle_beta   59.706
_cell_angle_gamma   60.712
_symmetry_Int_Tables_number   1
_cell_volume   147.024
_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  1.000  0.000  0.500  1.0
  Li  Li1  1  1.000  0.500  1.000  1.0
  Li  Li2  1  0.500  0.000  1.000  1.0
  Cr  Cr3  1  0.500  0.500  0.000  1.0
  Cr  Cr4  1  0.000  0.500  0.500  1.0
  Cr  Cr5  1  0.500  0.000  0.500  1.0
  Fe  Fe6  1  0.500  0.500  0.500  1.0
  O  O7  1  0.255  0.255  0.263  1.0
  O  O8  1  0.745  0.745  0.737  1.0
  O  O9  1  0.270  0.269  0.715  1.0
  O  O10  1  0.267  0.720  0.258  1.0
  O  O11  1  0.720  0.267  0.258  1.0
  O  O12  1  0.280  0.733  0.742  1.0
  O  O13  1  0.733  0.280  0.742  1.0
  O  O14  1  0.731  0.730  0.285  1.0
[/CIF]
.