The structure described by Li3CrFe3O8 crystallizes in the orthorhombic Cmc2_1 space group. There are two inequivalent Li sites. In the first Li site, Li(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 LiO6 octahedra that share corners with two equivalent Fe(2)O6 octahedra, corners with five equivalent Fe(1)O6 octahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(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, and  a faceface with one Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 10-46°. In the second Li site, Li(2) is bonded to one O(3), one O(6), two equivalent O(1), and two equivalent O(4) atoms to form distorted LiO6 octahedra that share corners with three equivalent Fe(2)O6 octahedra, corners with four equivalent Fe(1)O6 octahedra, edges with two equivalent Cr(1)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, edges with four equivalent Li(1)O6 octahedra, and  a faceface with one Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 10-46°. Cr(1) is bonded to one O(2), one O(5), two equivalent O(1), and two equivalent O(4) atoms to form CrO6 octahedra that share corners with two equivalent Fe(2)O6 octahedra, corners with four equivalent Fe(1)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, and edges with four equivalent Li(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-55°. There are two inequivalent Fe sites. In the first Fe site, Fe(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 FeO6 octahedra that share corners with two equivalent Li(2)O6 octahedra, corners with two equivalent Cr(1)O6 octahedra, corners with five equivalent Li(1)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Cr(1)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, and  a faceface with one Li(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 10-53°. In the second Fe site, Fe(2) is bonded to one O(3), one O(6), two equivalent O(1), and two equivalent O(4) atoms to form FeO6 octahedra that share corners with two equivalent Cr(1)O6 octahedra, corners with three equivalent Li(2)O6 octahedra, corners with four equivalent Li(1)O6 octahedra,  an edgeedge with one Cr(1)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with four equivalent Fe(1)O6 octahedra, and  a faceface with one Li(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 10-55°. There are six inequivalent O sites. In the first O site, O(5) is bonded to two equivalent Li(1), one Cr(1), and two equivalent Fe(1) atoms to form distorted OLi2CrFe2 square pyramids that share corners with two equivalent O(1)Li2CrFe2 square pyramids, corners with two equivalent O(4)Li2CrFe2 square pyramids, corners with five equivalent O(2)Li2CrFe2 square pyramids, edges with two equivalent O(6)Li3Fe3 octahedra, edges with two equivalent O(3)Li3Fe3 pentagonal pyramids, edges with two equivalent O(1)Li2CrFe2 square pyramids, and edges with two equivalent O(4)Li2CrFe2 square pyramids. In the second O site, O(6) is bonded to one Li(2), two equivalent Li(1), one Fe(2), and two equivalent Fe(1) atoms to form OLi3Fe3 octahedra that share corners with six equivalent O(3)Li3Fe3 pentagonal pyramids, edges with two equivalent O(2)Li2CrFe2 square pyramids, edges with two equivalent O(5)Li2CrFe2 square pyramids, edges with four equivalent O(1)Li2CrFe2 square pyramids, and edges with four equivalent O(4)Li2CrFe2 square pyramids. In the third O site, O(1) is bonded to one Li(1), one Li(2), one Cr(1), one Fe(1), and one Fe(2) atom to form distorted OLi2CrFe2 square pyramids that share  a cornercorner with one O(1)Li2CrFe2 square pyramid,  a cornercorner with one O(2)Li2CrFe2 square pyramid,  a cornercorner with one O(5)Li2CrFe2 square pyramid, corners with six equivalent O(4)Li2CrFe2 square pyramids, edges with two equivalent O(6)Li3Fe3 octahedra, edges with two equivalent O(3)Li3Fe3 pentagonal pyramids,  an edgeedge with one O(1)Li2CrFe2 square pyramid,  an edgeedge with one O(2)Li2CrFe2 square pyramid,  an edgeedge with one O(4)Li2CrFe2 square pyramid, and  an edgeedge with one O(5)Li2CrFe2 square pyramid. In the fourth O site, O(2) is bonded to two equivalent Li(1), one Cr(1), and two equivalent Fe(1) atoms to form OLi2CrFe2 square pyramids that share corners with two equivalent O(1)Li2CrFe2 square pyramids, corners with two equivalent O(4)Li2CrFe2 square pyramids, corners with five equivalent O(5)Li2CrFe2 square pyramids, edges with two equivalent O(6)Li3Fe3 octahedra, edges with two equivalent O(3)Li3Fe3 pentagonal pyramids, edges with two equivalent O(1)Li2CrFe2 square pyramids, and edges with two equivalent O(4)Li2CrFe2 square pyramids. In the fifth O site, O(3) is bonded to one Li(2), two equivalent Li(1), one Fe(2), and two equivalent Fe(1) atoms to form distorted OLi3Fe3 pentagonal pyramids that share corners with six equivalent O(6)Li3Fe3 octahedra, edges with two equivalent O(2)Li2CrFe2 square pyramids, edges with two equivalent O(5)Li2CrFe2 square pyramids, edges with four equivalent O(1)Li2CrFe2 square pyramids, and edges with four equivalent O(4)Li2CrFe2 square pyramids. The corner-sharing octahedral tilt angles range from 2-11°. In the sixth O site, O(4) is bonded to one Li(1), one Li(2), one Cr(1), one Fe(1), and one Fe(2) atom to form OLi2CrFe2 square pyramids that share  a cornercorner with one O(2)Li2CrFe2 square pyramid,  a cornercorner with one O(4)Li2CrFe2 square pyramid,  a cornercorner with one O(5)Li2CrFe2 square pyramid, corners with six equivalent O(1)Li2CrFe2 square pyramids, edges with two equivalent O(6)Li3Fe3 octahedra, edges with two equivalent O(3)Li3Fe3 pentagonal pyramids,  an edgeedge with one O(1)Li2CrFe2 square pyramid,  an edgeedge with one O(2)Li2CrFe2 square pyramid,  an edgeedge with one O(4)Li2CrFe2 square pyramid, and  an edgeedge with one O(5)Li2CrFe2 square pyramid. is represented by the CIF card [CIF]
data_Li3CrFe3O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.711
_cell_length_b   5.711
_cell_length_c   9.503
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   119.896
_symmetry_Int_Tables_number   1
_cell_volume   268.748
_cell_formula_units_Z   2
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  0.167  0.335  0.946  1.0
  Li  Li1  1  0.665  0.833  0.946  1.0
  Li  Li2  1  0.168  0.832  0.945  1.0
  Li  Li3  1  0.832  0.168  0.445  1.0
  Li  Li4  1  0.335  0.167  0.446  1.0
  Li  Li5  1  0.833  0.665  0.446  1.0
  Cr  Cr6  1  0.335  0.665  0.496  1.0
  Cr  Cr7  1  0.665  0.335  0.996  1.0
  Fe  Fe8  1  0.177  0.356  0.214  1.0
  Fe  Fe9  1  0.644  0.823  0.214  1.0
  Fe  Fe10  1  0.178  0.822  0.214  1.0
  Fe  Fe11  1  0.822  0.178  0.714  1.0
  Fe  Fe12  1  0.356  0.177  0.714  1.0
  Fe  Fe13  1  0.823  0.644  0.714  1.0
  O  O14  1  0.174  0.333  0.595  1.0
  O  O15  1  0.484  0.516  0.348  1.0
  O  O16  1  0.333  0.667  0.086  1.0
  O  O17  1  0.030  0.508  0.347  1.0
  O  O18  1  0.667  0.826  0.595  1.0
  O  O19  1  0.492  0.970  0.347  1.0
  O  O20  1  0.167  0.833  0.594  1.0
  O  O21  1  0.833  0.167  0.094  1.0
  O  O22  1  0.508  0.030  0.847  1.0
  O  O23  1  0.667  0.333  0.586  1.0
  O  O24  1  0.970  0.492  0.847  1.0
  O  O25  1  0.333  0.174  0.095  1.0
  O  O26  1  0.999  0.001  0.311  1.0
  O  O27  1  0.001  0.999  0.811  1.0
  O  O28  1  0.516  0.484  0.848  1.0
  O  O29  1  0.826  0.667  0.095  1.0
[/CIF]
.
The structure described by Li3CrFe3O8 crystallizes in the orthorhombic Cmc2_1 space group. There are two inequivalent Li sites. In the first Li site, Li(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 LiO6 octahedra that share corners with two equivalent Fe(2)O6 octahedra, corners with five equivalent Fe(1)O6 octahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(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, and  a faceface with one Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 10-46°. In the second Li site, Li(2) is bonded to one O(3), one O(6), two equivalent O(1), and two equivalent O(4) atoms to form distorted LiO6 octahedra that share corners with three equivalent Fe(2)O6 octahedra, corners with four equivalent Fe(1)O6 octahedra, edges with two equivalent Cr(1)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, edges with four equivalent Li(1)O6 octahedra, and  a faceface with one Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 10-46°. Cr(1) is bonded to one O(2), one O(5), two equivalent O(1), and two equivalent O(4) atoms to form CrO6 octahedra that share corners with two equivalent Fe(2)O6 octahedra, corners with four equivalent Fe(1)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, and edges with four equivalent Li(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-55°. There are two inequivalent Fe sites. In the first Fe site, Fe(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 FeO6 octahedra that share corners with two equivalent Li(2)O6 octahedra, corners with two equivalent Cr(1)O6 octahedra, corners with five equivalent Li(1)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Cr(1)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, and  a faceface with one Li(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 10-53°. In the second Fe site, Fe(2) is bonded to one O(3), one O(6), two equivalent O(1), and two equivalent O(4) atoms to form FeO6 octahedra that share corners with two equivalent Cr(1)O6 octahedra, corners with three equivalent Li(2)O6 octahedra, corners with four equivalent Li(1)O6 octahedra,  an edgeedge with one Cr(1)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with four equivalent Fe(1)O6 octahedra, and  a faceface with one Li(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 10-55°. There are six inequivalent O sites. In the first O site, O(5) is bonded to two equivalent Li(1), one Cr(1), and two equivalent Fe(1) atoms to form distorted OLi2CrFe2 square pyramids that share corners with two equivalent O(1)Li2CrFe2 square pyramids, corners with two equivalent O(4)Li2CrFe2 square pyramids, corners with five equivalent O(2)Li2CrFe2 square pyramids, edges with two equivalent O(6)Li3Fe3 octahedra, edges with two equivalent O(3)Li3Fe3 pentagonal pyramids, edges with two equivalent O(1)Li2CrFe2 square pyramids, and edges with two equivalent O(4)Li2CrFe2 square pyramids. In the second O site, O(6) is bonded to one Li(2), two equivalent Li(1), one Fe(2), and two equivalent Fe(1) atoms to form OLi3Fe3 octahedra that share corners with six equivalent O(3)Li3Fe3 pentagonal pyramids, edges with two equivalent O(2)Li2CrFe2 square pyramids, edges with two equivalent O(5)Li2CrFe2 square pyramids, edges with four equivalent O(1)Li2CrFe2 square pyramids, and edges with four equivalent O(4)Li2CrFe2 square pyramids. In the third O site, O(1) is bonded to one Li(1), one Li(2), one Cr(1), one Fe(1), and one Fe(2) atom to form distorted OLi2CrFe2 square pyramids that share  a cornercorner with one O(1)Li2CrFe2 square pyramid,  a cornercorner with one O(2)Li2CrFe2 square pyramid,  a cornercorner with one O(5)Li2CrFe2 square pyramid, corners with six equivalent O(4)Li2CrFe2 square pyramids, edges with two equivalent O(6)Li3Fe3 octahedra, edges with two equivalent O(3)Li3Fe3 pentagonal pyramids,  an edgeedge with one O(1)Li2CrFe2 square pyramid,  an edgeedge with one O(2)Li2CrFe2 square pyramid,  an edgeedge with one O(4)Li2CrFe2 square pyramid, and  an edgeedge with one O(5)Li2CrFe2 square pyramid. In the fourth O site, O(2) is bonded to two equivalent Li(1), one Cr(1), and two equivalent Fe(1) atoms to form OLi2CrFe2 square pyramids that share corners with two equivalent O(1)Li2CrFe2 square pyramids, corners with two equivalent O(4)Li2CrFe2 square pyramids, corners with five equivalent O(5)Li2CrFe2 square pyramids, edges with two equivalent O(6)Li3Fe3 octahedra, edges with two equivalent O(3)Li3Fe3 pentagonal pyramids, edges with two equivalent O(1)Li2CrFe2 square pyramids, and edges with two equivalent O(4)Li2CrFe2 square pyramids. In the fifth O site, O(3) is bonded to one Li(2), two equivalent Li(1), one Fe(2), and two equivalent Fe(1) atoms to form distorted OLi3Fe3 pentagonal pyramids that share corners with six equivalent O(6)Li3Fe3 octahedra, edges with two equivalent O(2)Li2CrFe2 square pyramids, edges with two equivalent O(5)Li2CrFe2 square pyramids, edges with four equivalent O(1)Li2CrFe2 square pyramids, and edges with four equivalent O(4)Li2CrFe2 square pyramids. The corner-sharing octahedral tilt angles range from 2-11°. In the sixth O site, O(4) is bonded to one Li(1), one Li(2), one Cr(1), one Fe(1), and one Fe(2) atom to form OLi2CrFe2 square pyramids that share  a cornercorner with one O(2)Li2CrFe2 square pyramid,  a cornercorner with one O(4)Li2CrFe2 square pyramid,  a cornercorner with one O(5)Li2CrFe2 square pyramid, corners with six equivalent O(1)Li2CrFe2 square pyramids, edges with two equivalent O(6)Li3Fe3 octahedra, edges with two equivalent O(3)Li3Fe3 pentagonal pyramids,  an edgeedge with one O(1)Li2CrFe2 square pyramid,  an edgeedge with one O(2)Li2CrFe2 square pyramid,  an edgeedge with one O(4)Li2CrFe2 square pyramid, and  an edgeedge with one O(5)Li2CrFe2 square pyramid. is represented by the CIF card [CIF]
data_Li3CrFe3O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.711
_cell_length_b   5.711
_cell_length_c   9.503
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   119.896
_symmetry_Int_Tables_number   1
_cell_volume   268.748
_cell_formula_units_Z   2
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  0.167  0.335  0.946  1.0
  Li  Li1  1  0.665  0.833  0.946  1.0
  Li  Li2  1  0.168  0.832  0.945  1.0
  Li  Li3  1  0.832  0.168  0.445  1.0
  Li  Li4  1  0.335  0.167  0.446  1.0
  Li  Li5  1  0.833  0.665  0.446  1.0
  Cr  Cr6  1  0.335  0.665  0.496  1.0
  Cr  Cr7  1  0.665  0.335  0.996  1.0
  Fe  Fe8  1  0.177  0.356  0.214  1.0
  Fe  Fe9  1  0.644  0.823  0.214  1.0
  Fe  Fe10  1  0.178  0.822  0.214  1.0
  Fe  Fe11  1  0.822  0.178  0.714  1.0
  Fe  Fe12  1  0.356  0.177  0.714  1.0
  Fe  Fe13  1  0.823  0.644  0.714  1.0
  O  O14  1  0.174  0.333  0.595  1.0
  O  O15  1  0.484  0.516  0.348  1.0
  O  O16  1  0.333  0.667  0.086  1.0
  O  O17  1  0.030  0.508  0.347  1.0
  O  O18  1  0.667  0.826  0.595  1.0
  O  O19  1  0.492  0.970  0.347  1.0
  O  O20  1  0.167  0.833  0.594  1.0
  O  O21  1  0.833  0.167  0.094  1.0
  O  O22  1  0.508  0.030  0.847  1.0
  O  O23  1  0.667  0.333  0.586  1.0
  O  O24  1  0.970  0.492  0.847  1.0
  O  O25  1  0.333  0.174  0.095  1.0
  O  O26  1  0.999  0.001  0.311  1.0
  O  O27  1  0.001  0.999  0.811  1.0
  O  O28  1  0.516  0.484  0.848  1.0
  O  O29  1  0.826  0.667  0.095  1.0
[/CIF]
.