The material described by Li3Cr3FeO8 crystallizes in the monoclinic P2/m space group. There are three inequivalent Li sites. In the first Li site, Li(1) is bonded to two equivalent O(1) and four equivalent O(6) atoms to form LiO6 octahedra that share corners with two equivalent Cr(2)O6 octahedra, corners with four equivalent Cr(3)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, edges with four equivalent Li(3)O6 octahedra, and edges with four equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 5-7°. In the second Li site, Li(2) is bonded to two equivalent O(2) and four equivalent O(5) atoms to form LiO6 octahedra that share corners with two equivalent Cr(3)O6 octahedra, corners with four equivalent Cr(2)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, edges with four equivalent Li(3)O6 octahedra, and edges with four equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 6-9°. In the third Li site, Li(3) is bonded to one O(1), one O(2), one O(3), one O(4), one O(5), and one O(6) atom to form LiO6 octahedra that share corners with six equivalent Cr(1)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Cr(2)O6 octahedra,  an edgeedge with one Cr(3)O6 octahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra, edges with two equivalent Li(3)O6 octahedra, and edges with two equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 5-11°. There are three inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(1), one O(2), one O(3), one O(4), one O(5), and one O(6) atom to form CrO6 octahedra that share corners with six equivalent Li(3)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Cr(2)O6 octahedra,  an edgeedge with one Cr(3)O6 octahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra, edges with two equivalent Li(3)O6 octahedra, and edges with two equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 5-11°. In the second Cr site, Cr(2) is bonded to two equivalent O(1) and four equivalent O(5) atoms to form CrO6 octahedra that share corners with two equivalent Li(1)O6 octahedra, corners with four equivalent Li(2)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, edges with four equivalent Li(3)O6 octahedra, and edges with four equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 5-9°. In the third Cr site, Cr(3) is bonded to two equivalent O(2) and four equivalent O(6) atoms to form CrO6 octahedra that share corners with two equivalent Li(2)O6 octahedra, corners with four equivalent Li(1)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, edges with four equivalent Li(3)O6 octahedra, and edges with four equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 6-7°. There are two inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to two equivalent O(4) and four equivalent O(6) atoms to form FeO6 octahedra that share edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Cr(3)O6 octahedra, edges with four equivalent Li(3)O6 octahedra, and edges with four equivalent Cr(1)O6 octahedra. In the second Fe site, Fe(2) is bonded to two equivalent O(3) and four equivalent O(5) atoms to form FeO6 octahedra that share edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Cr(2)O6 octahedra, edges with four equivalent Li(3)O6 octahedra, and edges with four equivalent Cr(1)O6 octahedra. There are six inequivalent O sites. In the first O site, O(1) is bonded to one Li(1), two equivalent Li(3), one Cr(2), and two equivalent Cr(1) atoms to form OLi3Cr3 octahedra that share corners with two equivalent O(1)Li3Cr3 octahedra, corners with four equivalent O(2)Li3Cr3 octahedra, edges with two equivalent O(3)Li2Cr2Fe square pyramids, edges with two equivalent O(4)Li2Cr2Fe square pyramids, edges with four equivalent O(5)Li2Cr2Fe square pyramids, and edges with four equivalent O(6)Li2Cr2Fe square pyramids. The corner-sharing octahedral tilt angles range from 0-1°. In the second O site, O(2) is bonded to one Li(2), two equivalent Li(3), one Cr(3), and two equivalent Cr(1) atoms to form OLi3Cr3 octahedra that share corners with two equivalent O(2)Li3Cr3 octahedra, corners with four equivalent O(1)Li3Cr3 octahedra, edges with two equivalent O(3)Li2Cr2Fe square pyramids, edges with two equivalent O(4)Li2Cr2Fe square pyramids, edges with four equivalent O(5)Li2Cr2Fe square pyramids, and edges with four equivalent O(6)Li2Cr2Fe square pyramids. The corner-sharing octahedral tilt angles range from 0-1°. In the third O site, O(3) is bonded to two equivalent Li(3), two equivalent Cr(1), and one Fe(2) atom to form OLi2Cr2Fe square pyramids that share  a cornercorner with one O(3)Li2Cr2Fe square pyramid, corners with four equivalent O(4)Li2Cr2Fe square pyramids, corners with four equivalent O(6)Li2Cr2Fe square pyramids, edges with two equivalent O(1)Li3Cr3 octahedra, edges with two equivalent O(2)Li3Cr3 octahedra, and edges with four equivalent O(5)Li2Cr2Fe square pyramids. In the fourth O site, O(4) is bonded to two equivalent Li(3), two equivalent Cr(1), and one Fe(1) atom to form OLi2Cr2Fe square pyramids that share  a cornercorner with one O(4)Li2Cr2Fe square pyramid, corners with four equivalent O(3)Li2Cr2Fe square pyramids, corners with four equivalent O(5)Li2Cr2Fe square pyramids, edges with two equivalent O(1)Li3Cr3 octahedra, edges with two equivalent O(2)Li3Cr3 octahedra, and edges with four equivalent O(6)Li2Cr2Fe square pyramids. In the fifth O site, O(5) is bonded to one Li(2), one Li(3), one Cr(1), one Cr(2), and one Fe(2) atom to form OLi2Cr2Fe square pyramids that share corners with two equivalent O(4)Li2Cr2Fe square pyramids, corners with two equivalent O(6)Li2Cr2Fe square pyramids, corners with five equivalent O(5)Li2Cr2Fe square pyramids, edges with two equivalent O(1)Li3Cr3 octahedra, edges with two equivalent O(2)Li3Cr3 octahedra, edges with two equivalent O(3)Li2Cr2Fe square pyramids, and edges with two equivalent O(5)Li2Cr2Fe square pyramids. In the sixth O site, O(6) is bonded to one Li(1), one Li(3), one Cr(1), one Cr(3), and one Fe(1) atom to form OLi2Cr2Fe square pyramids that share corners with two equivalent O(3)Li2Cr2Fe square pyramids, corners with two equivalent O(5)Li2Cr2Fe square pyramids, corners with five equivalent O(6)Li2Cr2Fe square pyramids, edges with two equivalent O(1)Li3Cr3 octahedra, edges with two equivalent O(2)Li3Cr3 octahedra, edges with two equivalent O(4)Li2Cr2Fe square pyramids, and edges with two equivalent O(6)Li2Cr2Fe square pyramids. is represented by the CIF file [CIF]
data_Li3Cr3FeO8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.920
_cell_length_b   5.925
_cell_length_c   5.926
_cell_angle_alpha   60.229
_cell_angle_beta   60.309
_cell_angle_gamma   60.324
_symmetry_Int_Tables_number   1
_cell_volume   147.917
_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
  Cr  Cr0  1  0.500  0.000  0.500  1.0
  Cr  Cr1  1  0.500  0.500  0.000  1.0
  Cr  Cr2  1  1.000  0.500  0.500  1.0
  Fe  Fe3  1  0.500  0.500  0.500  1.0
  Li  Li4  1  0.500  0.000  1.000  1.0
  Li  Li5  1  0.000  1.000  0.500  1.0
  Li  Li6  1  0.000  0.500  1.000  1.0
  O  O7  1  0.258  0.258  0.258  1.0
  O  O8  1  0.742  0.742  0.742  1.0
  O  O9  1  0.717  0.265  0.265  1.0
  O  O10  1  0.264  0.265  0.718  1.0
  O  O11  1  0.264  0.718  0.265  1.0
  O  O12  1  0.736  0.282  0.735  1.0
  O  O13  1  0.736  0.735  0.282  1.0
  O  O14  1  0.283  0.735  0.735  1.0
[/CIF]
.
The material described by Li3Cr3FeO8 crystallizes in the monoclinic P2/m space group. There are three inequivalent Li sites. In the first Li site, Li(1) is bonded to two equivalent O(1) and four equivalent O(6) atoms to form LiO6 octahedra that share corners with two equivalent Cr(2)O6 octahedra, corners with four equivalent Cr(3)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, edges with four equivalent Li(3)O6 octahedra, and edges with four equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 5-7°. In the second Li site, Li(2) is bonded to two equivalent O(2) and four equivalent O(5) atoms to form LiO6 octahedra that share corners with two equivalent Cr(3)O6 octahedra, corners with four equivalent Cr(2)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, edges with four equivalent Li(3)O6 octahedra, and edges with four equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 6-9°. In the third Li site, Li(3) is bonded to one O(1), one O(2), one O(3), one O(4), one O(5), and one O(6) atom to form LiO6 octahedra that share corners with six equivalent Cr(1)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Cr(2)O6 octahedra,  an edgeedge with one Cr(3)O6 octahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra, edges with two equivalent Li(3)O6 octahedra, and edges with two equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 5-11°. There are three inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(1), one O(2), one O(3), one O(4), one O(5), and one O(6) atom to form CrO6 octahedra that share corners with six equivalent Li(3)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Cr(2)O6 octahedra,  an edgeedge with one Cr(3)O6 octahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra, edges with two equivalent Li(3)O6 octahedra, and edges with two equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 5-11°. In the second Cr site, Cr(2) is bonded to two equivalent O(1) and four equivalent O(5) atoms to form CrO6 octahedra that share corners with two equivalent Li(1)O6 octahedra, corners with four equivalent Li(2)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, edges with four equivalent Li(3)O6 octahedra, and edges with four equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 5-9°. In the third Cr site, Cr(3) is bonded to two equivalent O(2) and four equivalent O(6) atoms to form CrO6 octahedra that share corners with two equivalent Li(2)O6 octahedra, corners with four equivalent Li(1)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, edges with four equivalent Li(3)O6 octahedra, and edges with four equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 6-7°. There are two inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to two equivalent O(4) and four equivalent O(6) atoms to form FeO6 octahedra that share edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Cr(3)O6 octahedra, edges with four equivalent Li(3)O6 octahedra, and edges with four equivalent Cr(1)O6 octahedra. In the second Fe site, Fe(2) is bonded to two equivalent O(3) and four equivalent O(5) atoms to form FeO6 octahedra that share edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Cr(2)O6 octahedra, edges with four equivalent Li(3)O6 octahedra, and edges with four equivalent Cr(1)O6 octahedra. There are six inequivalent O sites. In the first O site, O(1) is bonded to one Li(1), two equivalent Li(3), one Cr(2), and two equivalent Cr(1) atoms to form OLi3Cr3 octahedra that share corners with two equivalent O(1)Li3Cr3 octahedra, corners with four equivalent O(2)Li3Cr3 octahedra, edges with two equivalent O(3)Li2Cr2Fe square pyramids, edges with two equivalent O(4)Li2Cr2Fe square pyramids, edges with four equivalent O(5)Li2Cr2Fe square pyramids, and edges with four equivalent O(6)Li2Cr2Fe square pyramids. The corner-sharing octahedral tilt angles range from 0-1°. In the second O site, O(2) is bonded to one Li(2), two equivalent Li(3), one Cr(3), and two equivalent Cr(1) atoms to form OLi3Cr3 octahedra that share corners with two equivalent O(2)Li3Cr3 octahedra, corners with four equivalent O(1)Li3Cr3 octahedra, edges with two equivalent O(3)Li2Cr2Fe square pyramids, edges with two equivalent O(4)Li2Cr2Fe square pyramids, edges with four equivalent O(5)Li2Cr2Fe square pyramids, and edges with four equivalent O(6)Li2Cr2Fe square pyramids. The corner-sharing octahedral tilt angles range from 0-1°. In the third O site, O(3) is bonded to two equivalent Li(3), two equivalent Cr(1), and one Fe(2) atom to form OLi2Cr2Fe square pyramids that share  a cornercorner with one O(3)Li2Cr2Fe square pyramid, corners with four equivalent O(4)Li2Cr2Fe square pyramids, corners with four equivalent O(6)Li2Cr2Fe square pyramids, edges with two equivalent O(1)Li3Cr3 octahedra, edges with two equivalent O(2)Li3Cr3 octahedra, and edges with four equivalent O(5)Li2Cr2Fe square pyramids. In the fourth O site, O(4) is bonded to two equivalent Li(3), two equivalent Cr(1), and one Fe(1) atom to form OLi2Cr2Fe square pyramids that share  a cornercorner with one O(4)Li2Cr2Fe square pyramid, corners with four equivalent O(3)Li2Cr2Fe square pyramids, corners with four equivalent O(5)Li2Cr2Fe square pyramids, edges with two equivalent O(1)Li3Cr3 octahedra, edges with two equivalent O(2)Li3Cr3 octahedra, and edges with four equivalent O(6)Li2Cr2Fe square pyramids. In the fifth O site, O(5) is bonded to one Li(2), one Li(3), one Cr(1), one Cr(2), and one Fe(2) atom to form OLi2Cr2Fe square pyramids that share corners with two equivalent O(4)Li2Cr2Fe square pyramids, corners with two equivalent O(6)Li2Cr2Fe square pyramids, corners with five equivalent O(5)Li2Cr2Fe square pyramids, edges with two equivalent O(1)Li3Cr3 octahedra, edges with two equivalent O(2)Li3Cr3 octahedra, edges with two equivalent O(3)Li2Cr2Fe square pyramids, and edges with two equivalent O(5)Li2Cr2Fe square pyramids. In the sixth O site, O(6) is bonded to one Li(1), one Li(3), one Cr(1), one Cr(3), and one Fe(1) atom to form OLi2Cr2Fe square pyramids that share corners with two equivalent O(3)Li2Cr2Fe square pyramids, corners with two equivalent O(5)Li2Cr2Fe square pyramids, corners with five equivalent O(6)Li2Cr2Fe square pyramids, edges with two equivalent O(1)Li3Cr3 octahedra, edges with two equivalent O(2)Li3Cr3 octahedra, edges with two equivalent O(4)Li2Cr2Fe square pyramids, and edges with two equivalent O(6)Li2Cr2Fe square pyramids. is represented by the CIF file [CIF]
data_Li3Cr3FeO8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.920
_cell_length_b   5.925
_cell_length_c   5.926
_cell_angle_alpha   60.229
_cell_angle_beta   60.309
_cell_angle_gamma   60.324
_symmetry_Int_Tables_number   1
_cell_volume   147.917
_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
  Cr  Cr0  1  0.500  0.000  0.500  1.0
  Cr  Cr1  1  0.500  0.500  0.000  1.0
  Cr  Cr2  1  1.000  0.500  0.500  1.0
  Fe  Fe3  1  0.500  0.500  0.500  1.0
  Li  Li4  1  0.500  0.000  1.000  1.0
  Li  Li5  1  0.000  1.000  0.500  1.0
  Li  Li6  1  0.000  0.500  1.000  1.0
  O  O7  1  0.258  0.258  0.258  1.0
  O  O8  1  0.742  0.742  0.742  1.0
  O  O9  1  0.717  0.265  0.265  1.0
  O  O10  1  0.264  0.265  0.718  1.0
  O  O11  1  0.264  0.718  0.265  1.0
  O  O12  1  0.736  0.282  0.735  1.0
  O  O13  1  0.736  0.735  0.282  1.0
  O  O14  1  0.283  0.735  0.735  1.0
[/CIF]
.