The structure described by Li2Cr3FeO8 is Spinel-derived structured and crystallizes in the monoclinic Cc space group. There are two inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(2), one O(3), one O(6), and one O(7) atom to form LiO4 tetrahedra that share corners with three equivalent Cr(1)O6 octahedra, corners with three equivalent Cr(2)O6 octahedra, corners with three equivalent Cr(3)O6 octahedra, and corners with three equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-62°. In the second Li site, Li(2) is bonded in a rectangular see-saw-like geometry to one O(1), one O(4), one O(5), and one O(8) atom. 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(6), and one O(8) atom to form CrO6 octahedra that share corners with two equivalent Fe(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra,  an edgeedge with one Fe(1)O6 octahedra, edges with two equivalent Cr(2)O6 octahedra, and edges with two equivalent Cr(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-52°. In the second Cr site, Cr(2) is bonded to one O(2), one O(3), one O(4), one O(5), one O(7), and one O(8) atom to form CrO6 octahedra that share corners with two equivalent Fe(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra,  an edgeedge with one Fe(1)O6 octahedra, edges with two equivalent Cr(1)O6 octahedra, and edges with two equivalent Cr(3)O6 octahedra. The corner-sharing octahedral tilt angles are 54°. In the third Cr site, Cr(3) is bonded to one O(1), one O(3), one O(4), one O(5), one O(6), and one O(7) atom to form CrO6 octahedra that share corners with two equivalent Fe(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra,  an edgeedge with one Fe(1)O6 octahedra, edges with two equivalent Cr(1)O6 octahedra, and edges with two equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-51°. Fe(1) is bonded to one O(1), one O(2), one O(5), one O(6), one O(7), and one O(8) atom to form FeO6 octahedra that share corners with two equivalent Cr(1)O6 octahedra, corners with two equivalent Cr(2)O6 octahedra, corners with two equivalent Cr(3)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra,  an edgeedge with one Cr(1)O6 octahedra,  an edgeedge with one Cr(2)O6 octahedra, and  an edgeedge with one Cr(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-54°. There are eight inequivalent O sites. In the first O site, O(8) is bonded in a rectangular see-saw-like geometry to one Li(2), one Cr(1), one Cr(2), and one Fe(1) atom. In the second O site, O(1) is bonded in a distorted rectangular see-saw-like geometry to one Li(2), one Cr(1), one Cr(3), and one Fe(1) atom. In the third O site, O(2) is bonded to one Li(1), one Cr(1), one Cr(2), and one Fe(1) atom to form distorted OLiCr2Fe tetrahedra that share  a cornercorner with one O(6)LiCr2Fe tetrahedra,  a cornercorner with one O(7)LiCr2Fe tetrahedra, corners with two equivalent O(4)LiCr3 tetrahedra,  a cornercorner with one O(3)LiCr3 trigonal pyramid,  an edgeedge with one O(6)LiCr2Fe tetrahedra,  an edgeedge with one O(7)LiCr2Fe tetrahedra, and  an edgeedge with one O(3)LiCr3 trigonal pyramid. In the fourth O site, O(3) is bonded to one Li(1), one Cr(1), one Cr(2), and one Cr(3) atom to form distorted OLiCr3 trigonal pyramids that share  a cornercorner with one O(2)LiCr2Fe tetrahedra,  a cornercorner with one O(6)LiCr2Fe tetrahedra,  a cornercorner with one O(7)LiCr2Fe tetrahedra, corners with three equivalent O(4)LiCr3 tetrahedra,  an edgeedge with one O(2)LiCr2Fe tetrahedra,  an edgeedge with one O(6)LiCr2Fe tetrahedra, and  an edgeedge with one O(7)LiCr2Fe tetrahedra. In the fifth O site, O(4) is bonded to one Li(2), one Cr(1), one Cr(2), and one Cr(3) atom to form distorted OLiCr3 tetrahedra that share corners with two equivalent O(2)LiCr2Fe tetrahedra, corners with two equivalent O(6)LiCr2Fe tetrahedra, corners with two equivalent O(7)LiCr2Fe tetrahedra, and corners with three equivalent O(3)LiCr3 trigonal pyramids. In the sixth O site, O(5) is bonded in a rectangular see-saw-like geometry to one Li(2), one Cr(2), one Cr(3), and one Fe(1) atom. In the seventh O site, O(6) is bonded to one Li(1), one Cr(1), one Cr(3), and one Fe(1) atom to form distorted OLiCr2Fe tetrahedra that share  a cornercorner with one O(2)LiCr2Fe tetrahedra,  a cornercorner with one O(7)LiCr2Fe tetrahedra, corners with two equivalent O(4)LiCr3 tetrahedra,  a cornercorner with one O(3)LiCr3 trigonal pyramid,  an edgeedge with one O(2)LiCr2Fe tetrahedra,  an edgeedge with one O(7)LiCr2Fe tetrahedra, and  an edgeedge with one O(3)LiCr3 trigonal pyramid. In the eighth O site, O(7) is bonded to one Li(1), one Cr(2), one Cr(3), and one Fe(1) atom to form distorted OLiCr2Fe tetrahedra that share  a cornercorner with one O(2)LiCr2Fe tetrahedra,  a cornercorner with one O(6)LiCr2Fe tetrahedra, corners with two equivalent O(4)LiCr3 tetrahedra,  a cornercorner with one O(3)LiCr3 trigonal pyramid,  an edgeedge with one O(2)LiCr2Fe tetrahedra,  an edgeedge with one O(6)LiCr2Fe tetrahedra, and  an edgeedge with one O(3)LiCr3 trigonal pyramid. is represented by the CIF file [CIF]
data_Li2Cr3FeO8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.876
_cell_length_b   5.880
_cell_length_c   9.535
_cell_angle_alpha   89.166
_cell_angle_beta   90.417
_cell_angle_gamma   120.017
_symmetry_Int_Tables_number   1
_cell_volume   285.228
_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  0.332  0.668  0.895  1.0
  Li  Li1  1  0.000  0.000  0.997  1.0
  Li  Li2  1  1.000  1.000  0.497  1.0
  Li  Li3  1  0.668  0.336  0.395  1.0
  Cr  Cr4  1  0.169  0.832  0.212  1.0
  Cr  Cr5  1  0.170  0.340  0.215  1.0
  Cr  Cr6  1  0.662  0.832  0.212  1.0
  Cr  Cr7  1  0.338  0.169  0.712  1.0
  Cr  Cr8  1  0.831  0.663  0.712  1.0
  Cr  Cr9  1  0.830  0.170  0.715  1.0
  Fe  Fe10  1  0.337  0.665  0.488  1.0
  Fe  Fe11  1  0.663  0.328  0.988  1.0
  O  O12  1  0.164  0.838  0.607  1.0
  O  O13  1  0.040  0.527  0.336  1.0
  O  O14  1  0.335  0.672  0.103  1.0
  O  O15  1  0.999  0.996  0.313  1.0
  O  O16  1  0.001  0.997  0.813  1.0
  O  O17  1  0.173  0.324  0.603  1.0
  O  O18  1  0.483  0.963  0.332  1.0
  O  O19  1  0.490  0.528  0.335  1.0
  O  O20  1  0.325  0.153  0.105  1.0
  O  O21  1  0.675  0.829  0.605  1.0
  O  O22  1  0.517  0.480  0.832  1.0
  O  O23  1  0.510  0.038  0.835  1.0
  O  O24  1  0.665  0.337  0.603  1.0
  O  O25  1  0.836  0.675  0.107  1.0
  O  O26  1  0.960  0.487  0.836  1.0
  O  O27  1  0.827  0.152  0.103  1.0
[/CIF]
.
The structure described by Li2Cr3FeO8 is Spinel-derived structured and crystallizes in the monoclinic Cc space group. There are two inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(2), one O(3), one O(6), and one O(7) atom to form LiO4 tetrahedra that share corners with three equivalent Cr(1)O6 octahedra, corners with three equivalent Cr(2)O6 octahedra, corners with three equivalent Cr(3)O6 octahedra, and corners with three equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-62°. In the second Li site, Li(2) is bonded in a rectangular see-saw-like geometry to one O(1), one O(4), one O(5), and one O(8) atom. 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(6), and one O(8) atom to form CrO6 octahedra that share corners with two equivalent Fe(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra,  an edgeedge with one Fe(1)O6 octahedra, edges with two equivalent Cr(2)O6 octahedra, and edges with two equivalent Cr(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-52°. In the second Cr site, Cr(2) is bonded to one O(2), one O(3), one O(4), one O(5), one O(7), and one O(8) atom to form CrO6 octahedra that share corners with two equivalent Fe(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra,  an edgeedge with one Fe(1)O6 octahedra, edges with two equivalent Cr(1)O6 octahedra, and edges with two equivalent Cr(3)O6 octahedra. The corner-sharing octahedral tilt angles are 54°. In the third Cr site, Cr(3) is bonded to one O(1), one O(3), one O(4), one O(5), one O(6), and one O(7) atom to form CrO6 octahedra that share corners with two equivalent Fe(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra,  an edgeedge with one Fe(1)O6 octahedra, edges with two equivalent Cr(1)O6 octahedra, and edges with two equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-51°. Fe(1) is bonded to one O(1), one O(2), one O(5), one O(6), one O(7), and one O(8) atom to form FeO6 octahedra that share corners with two equivalent Cr(1)O6 octahedra, corners with two equivalent Cr(2)O6 octahedra, corners with two equivalent Cr(3)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra,  an edgeedge with one Cr(1)O6 octahedra,  an edgeedge with one Cr(2)O6 octahedra, and  an edgeedge with one Cr(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-54°. There are eight inequivalent O sites. In the first O site, O(8) is bonded in a rectangular see-saw-like geometry to one Li(2), one Cr(1), one Cr(2), and one Fe(1) atom. In the second O site, O(1) is bonded in a distorted rectangular see-saw-like geometry to one Li(2), one Cr(1), one Cr(3), and one Fe(1) atom. In the third O site, O(2) is bonded to one Li(1), one Cr(1), one Cr(2), and one Fe(1) atom to form distorted OLiCr2Fe tetrahedra that share  a cornercorner with one O(6)LiCr2Fe tetrahedra,  a cornercorner with one O(7)LiCr2Fe tetrahedra, corners with two equivalent O(4)LiCr3 tetrahedra,  a cornercorner with one O(3)LiCr3 trigonal pyramid,  an edgeedge with one O(6)LiCr2Fe tetrahedra,  an edgeedge with one O(7)LiCr2Fe tetrahedra, and  an edgeedge with one O(3)LiCr3 trigonal pyramid. In the fourth O site, O(3) is bonded to one Li(1), one Cr(1), one Cr(2), and one Cr(3) atom to form distorted OLiCr3 trigonal pyramids that share  a cornercorner with one O(2)LiCr2Fe tetrahedra,  a cornercorner with one O(6)LiCr2Fe tetrahedra,  a cornercorner with one O(7)LiCr2Fe tetrahedra, corners with three equivalent O(4)LiCr3 tetrahedra,  an edgeedge with one O(2)LiCr2Fe tetrahedra,  an edgeedge with one O(6)LiCr2Fe tetrahedra, and  an edgeedge with one O(7)LiCr2Fe tetrahedra. In the fifth O site, O(4) is bonded to one Li(2), one Cr(1), one Cr(2), and one Cr(3) atom to form distorted OLiCr3 tetrahedra that share corners with two equivalent O(2)LiCr2Fe tetrahedra, corners with two equivalent O(6)LiCr2Fe tetrahedra, corners with two equivalent O(7)LiCr2Fe tetrahedra, and corners with three equivalent O(3)LiCr3 trigonal pyramids. In the sixth O site, O(5) is bonded in a rectangular see-saw-like geometry to one Li(2), one Cr(2), one Cr(3), and one Fe(1) atom. In the seventh O site, O(6) is bonded to one Li(1), one Cr(1), one Cr(3), and one Fe(1) atom to form distorted OLiCr2Fe tetrahedra that share  a cornercorner with one O(2)LiCr2Fe tetrahedra,  a cornercorner with one O(7)LiCr2Fe tetrahedra, corners with two equivalent O(4)LiCr3 tetrahedra,  a cornercorner with one O(3)LiCr3 trigonal pyramid,  an edgeedge with one O(2)LiCr2Fe tetrahedra,  an edgeedge with one O(7)LiCr2Fe tetrahedra, and  an edgeedge with one O(3)LiCr3 trigonal pyramid. In the eighth O site, O(7) is bonded to one Li(1), one Cr(2), one Cr(3), and one Fe(1) atom to form distorted OLiCr2Fe tetrahedra that share  a cornercorner with one O(2)LiCr2Fe tetrahedra,  a cornercorner with one O(6)LiCr2Fe tetrahedra, corners with two equivalent O(4)LiCr3 tetrahedra,  a cornercorner with one O(3)LiCr3 trigonal pyramid,  an edgeedge with one O(2)LiCr2Fe tetrahedra,  an edgeedge with one O(6)LiCr2Fe tetrahedra, and  an edgeedge with one O(3)LiCr3 trigonal pyramid. is represented by the CIF file [CIF]
data_Li2Cr3FeO8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.876
_cell_length_b   5.880
_cell_length_c   9.535
_cell_angle_alpha   89.166
_cell_angle_beta   90.417
_cell_angle_gamma   120.017
_symmetry_Int_Tables_number   1
_cell_volume   285.228
_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  0.332  0.668  0.895  1.0
  Li  Li1  1  0.000  0.000  0.997  1.0
  Li  Li2  1  1.000  1.000  0.497  1.0
  Li  Li3  1  0.668  0.336  0.395  1.0
  Cr  Cr4  1  0.169  0.832  0.212  1.0
  Cr  Cr5  1  0.170  0.340  0.215  1.0
  Cr  Cr6  1  0.662  0.832  0.212  1.0
  Cr  Cr7  1  0.338  0.169  0.712  1.0
  Cr  Cr8  1  0.831  0.663  0.712  1.0
  Cr  Cr9  1  0.830  0.170  0.715  1.0
  Fe  Fe10  1  0.337  0.665  0.488  1.0
  Fe  Fe11  1  0.663  0.328  0.988  1.0
  O  O12  1  0.164  0.838  0.607  1.0
  O  O13  1  0.040  0.527  0.336  1.0
  O  O14  1  0.335  0.672  0.103  1.0
  O  O15  1  0.999  0.996  0.313  1.0
  O  O16  1  0.001  0.997  0.813  1.0
  O  O17  1  0.173  0.324  0.603  1.0
  O  O18  1  0.483  0.963  0.332  1.0
  O  O19  1  0.490  0.528  0.335  1.0
  O  O20  1  0.325  0.153  0.105  1.0
  O  O21  1  0.675  0.829  0.605  1.0
  O  O22  1  0.517  0.480  0.832  1.0
  O  O23  1  0.510  0.038  0.835  1.0
  O  O24  1  0.665  0.337  0.603  1.0
  O  O25  1  0.836  0.675  0.107  1.0
  O  O26  1  0.960  0.487  0.836  1.0
  O  O27  1  0.827  0.152  0.103  1.0
[/CIF]
.