The compound described by Li2CrFe3O8 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 Fe(1)O6 octahedra, corners with three equivalent Fe(2)O6 octahedra, and corners with three equivalent Fe(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-63°. In the second Li site, Li(2) is bonded to one O(1), one O(4), one O(5), and one O(8) atom to form distorted LiO4 trigonal pyramids that share  a cornercorner with one Fe(1)O6 octahedra,  a cornercorner with one Fe(2)O6 octahedra,  a cornercorner with one Fe(3)O6 octahedra, corners with three equivalent Cr(1)O6 octahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra, and  an edgeedge with one Fe(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 61-64°. Cr(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 CrO6 octahedra that share corners with two equivalent Fe(1)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, corners with two equivalent Fe(3)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra, corners with three equivalent Li(2)O4 trigonal pyramids,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra, and  an edgeedge with one Fe(3)O6 octahedra. The corner-sharing octahedral tilt angles are 51°. There are three 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(6), and one O(8) atom to form FeO6 octahedra that share corners with two equivalent Cr(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 trigonal pyramid,  an edgeedge with one Cr(1)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, edges with two equivalent Fe(3)O6 octahedra, and  an edgeedge with one Li(2)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 51°. In the second Fe site, Fe(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 FeO6 octahedra that share corners with two equivalent Cr(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 trigonal pyramid,  an edgeedge with one Cr(1)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, edges with two equivalent Fe(3)O6 octahedra, and  an edgeedge with one Li(2)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 51°. In the third Fe site, Fe(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 FeO6 octahedra that share corners with two equivalent Cr(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 trigonal pyramid,  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  an edgeedge with one Li(2)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 51°. 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 Fe(1), and one Fe(2) atom. In the second O site, O(1) is bonded in a rectangular see-saw-like geometry to one Li(2), one Cr(1), one Fe(1), and one Fe(3) atom. In the third O site, O(2) is bonded to one Li(1), one Cr(1), one Fe(1), and one Fe(2) atom to form distorted OLiCrFe2 tetrahedra that share  a cornercorner with one O(6)LiCrFe2 tetrahedra,  a cornercorner with one O(7)LiCrFe2 tetrahedra, corners with two equivalent O(4)LiFe3 tetrahedra,  a cornercorner with one O(3)LiFe3 trigonal pyramid,  an edgeedge with one O(6)LiCrFe2 tetrahedra,  an edgeedge with one O(7)LiCrFe2 tetrahedra, and  an edgeedge with one O(3)LiFe3 trigonal pyramid. In the fourth O site, O(3) is bonded to one Li(1), one Fe(1), one Fe(2), and one Fe(3) atom to form distorted OLiFe3 trigonal pyramids that share  a cornercorner with one O(2)LiCrFe2 tetrahedra,  a cornercorner with one O(6)LiCrFe2 tetrahedra,  a cornercorner with one O(7)LiCrFe2 tetrahedra, corners with three equivalent O(4)LiFe3 tetrahedra,  an edgeedge with one O(2)LiCrFe2 tetrahedra,  an edgeedge with one O(6)LiCrFe2 tetrahedra, and  an edgeedge with one O(7)LiCrFe2 tetrahedra. In the fifth O site, O(4) is bonded to one Li(2), one Fe(1), one Fe(2), and one Fe(3) atom to form distorted OLiFe3 tetrahedra that share corners with two equivalent O(2)LiCrFe2 tetrahedra, corners with two equivalent O(6)LiCrFe2 tetrahedra, corners with two equivalent O(7)LiCrFe2 tetrahedra, and corners with three equivalent O(3)LiFe3 trigonal pyramids. In the sixth O site, O(5) is bonded in a rectangular see-saw-like geometry to one Li(2), one Cr(1), one Fe(2), and one Fe(3) atom. In the seventh O site, O(6) is bonded to one Li(1), one Cr(1), one Fe(1), and one Fe(3) atom to form distorted OLiCrFe2 tetrahedra that share  a cornercorner with one O(2)LiCrFe2 tetrahedra,  a cornercorner with one O(7)LiCrFe2 tetrahedra, corners with two equivalent O(4)LiFe3 tetrahedra,  a cornercorner with one O(3)LiFe3 trigonal pyramid,  an edgeedge with one O(2)LiCrFe2 tetrahedra,  an edgeedge with one O(7)LiCrFe2 tetrahedra, and  an edgeedge with one O(3)LiFe3 trigonal pyramid. In the eighth O site, O(7) is bonded to one Li(1), one Cr(1), one Fe(2), and one Fe(3) atom to form distorted OLiCrFe2 tetrahedra that share  a cornercorner with one O(2)LiCrFe2 tetrahedra,  a cornercorner with one O(6)LiCrFe2 tetrahedra, corners with two equivalent O(4)LiFe3 tetrahedra,  a cornercorner with one O(3)LiFe3 trigonal pyramid,  an edgeedge with one O(2)LiCrFe2 tetrahedra,  an edgeedge with one O(6)LiCrFe2 tetrahedra, and  an edgeedge with one O(3)LiFe3 trigonal pyramid. is represented by the CIF card [CIF]
data_Li2CrFe3O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.890
_cell_length_b   5.930
_cell_length_c   9.600
_cell_angle_alpha   90.058
_cell_angle_beta   89.971
_cell_angle_gamma   120.224
_symmetry_Int_Tables_number   1
_cell_volume   289.733
_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  0.336  0.668  0.894  1.0
  Li  Li1  1  0.001  0.000  0.997  1.0
  Li  Li2  1  0.999  1.000  0.497  1.0
  Li  Li3  1  0.664  0.332  0.394  1.0
  Cr  Cr4  1  0.328  0.664  0.485  1.0
  Cr  Cr5  1  0.672  0.336  0.985  1.0
  Fe  Fe6  1  0.169  0.831  0.213  1.0
  Fe  Fe7  1  0.169  0.338  0.213  1.0
  Fe  Fe8  1  0.663  0.831  0.213  1.0
  Fe  Fe9  1  0.337  0.169  0.713  1.0
  Fe  Fe10  1  0.831  0.662  0.713  1.0
  Fe  Fe11  1  0.831  0.169  0.713  1.0
  O  O12  1  0.160  0.833  0.601  1.0
  O  O13  1  0.038  0.518  0.341  1.0
  O  O14  1  0.333  0.668  0.102  1.0
  O  O15  1  0.001  0.999  0.310  1.0
  O  O16  1  0.999  0.998  0.810  1.0
  O  O17  1  0.158  0.327  0.601  1.0
  O  O18  1  0.474  0.958  0.342  1.0
  O  O19  1  0.472  0.515  0.341  1.0
  O  O20  1  0.332  0.166  0.099  1.0
  O  O21  1  0.668  0.834  0.599  1.0
  O  O22  1  0.526  0.483  0.842  1.0
  O  O23  1  0.528  0.043  0.841  1.0
  O  O24  1  0.667  0.334  0.602  1.0
  O  O25  1  0.840  0.673  0.101  1.0
  O  O26  1  0.962  0.481  0.841  1.0
  O  O27  1  0.842  0.169  0.101  1.0
[/CIF]
.
The compound described by Li2CrFe3O8 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 Fe(1)O6 octahedra, corners with three equivalent Fe(2)O6 octahedra, and corners with three equivalent Fe(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-63°. In the second Li site, Li(2) is bonded to one O(1), one O(4), one O(5), and one O(8) atom to form distorted LiO4 trigonal pyramids that share  a cornercorner with one Fe(1)O6 octahedra,  a cornercorner with one Fe(2)O6 octahedra,  a cornercorner with one Fe(3)O6 octahedra, corners with three equivalent Cr(1)O6 octahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra, and  an edgeedge with one Fe(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 61-64°. Cr(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 CrO6 octahedra that share corners with two equivalent Fe(1)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, corners with two equivalent Fe(3)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra, corners with three equivalent Li(2)O4 trigonal pyramids,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra, and  an edgeedge with one Fe(3)O6 octahedra. The corner-sharing octahedral tilt angles are 51°. There are three 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(6), and one O(8) atom to form FeO6 octahedra that share corners with two equivalent Cr(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 trigonal pyramid,  an edgeedge with one Cr(1)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, edges with two equivalent Fe(3)O6 octahedra, and  an edgeedge with one Li(2)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 51°. In the second Fe site, Fe(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 FeO6 octahedra that share corners with two equivalent Cr(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 trigonal pyramid,  an edgeedge with one Cr(1)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, edges with two equivalent Fe(3)O6 octahedra, and  an edgeedge with one Li(2)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 51°. In the third Fe site, Fe(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 FeO6 octahedra that share corners with two equivalent Cr(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 trigonal pyramid,  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  an edgeedge with one Li(2)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 51°. 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 Fe(1), and one Fe(2) atom. In the second O site, O(1) is bonded in a rectangular see-saw-like geometry to one Li(2), one Cr(1), one Fe(1), and one Fe(3) atom. In the third O site, O(2) is bonded to one Li(1), one Cr(1), one Fe(1), and one Fe(2) atom to form distorted OLiCrFe2 tetrahedra that share  a cornercorner with one O(6)LiCrFe2 tetrahedra,  a cornercorner with one O(7)LiCrFe2 tetrahedra, corners with two equivalent O(4)LiFe3 tetrahedra,  a cornercorner with one O(3)LiFe3 trigonal pyramid,  an edgeedge with one O(6)LiCrFe2 tetrahedra,  an edgeedge with one O(7)LiCrFe2 tetrahedra, and  an edgeedge with one O(3)LiFe3 trigonal pyramid. In the fourth O site, O(3) is bonded to one Li(1), one Fe(1), one Fe(2), and one Fe(3) atom to form distorted OLiFe3 trigonal pyramids that share  a cornercorner with one O(2)LiCrFe2 tetrahedra,  a cornercorner with one O(6)LiCrFe2 tetrahedra,  a cornercorner with one O(7)LiCrFe2 tetrahedra, corners with three equivalent O(4)LiFe3 tetrahedra,  an edgeedge with one O(2)LiCrFe2 tetrahedra,  an edgeedge with one O(6)LiCrFe2 tetrahedra, and  an edgeedge with one O(7)LiCrFe2 tetrahedra. In the fifth O site, O(4) is bonded to one Li(2), one Fe(1), one Fe(2), and one Fe(3) atom to form distorted OLiFe3 tetrahedra that share corners with two equivalent O(2)LiCrFe2 tetrahedra, corners with two equivalent O(6)LiCrFe2 tetrahedra, corners with two equivalent O(7)LiCrFe2 tetrahedra, and corners with three equivalent O(3)LiFe3 trigonal pyramids. In the sixth O site, O(5) is bonded in a rectangular see-saw-like geometry to one Li(2), one Cr(1), one Fe(2), and one Fe(3) atom. In the seventh O site, O(6) is bonded to one Li(1), one Cr(1), one Fe(1), and one Fe(3) atom to form distorted OLiCrFe2 tetrahedra that share  a cornercorner with one O(2)LiCrFe2 tetrahedra,  a cornercorner with one O(7)LiCrFe2 tetrahedra, corners with two equivalent O(4)LiFe3 tetrahedra,  a cornercorner with one O(3)LiFe3 trigonal pyramid,  an edgeedge with one O(2)LiCrFe2 tetrahedra,  an edgeedge with one O(7)LiCrFe2 tetrahedra, and  an edgeedge with one O(3)LiFe3 trigonal pyramid. In the eighth O site, O(7) is bonded to one Li(1), one Cr(1), one Fe(2), and one Fe(3) atom to form distorted OLiCrFe2 tetrahedra that share  a cornercorner with one O(2)LiCrFe2 tetrahedra,  a cornercorner with one O(6)LiCrFe2 tetrahedra, corners with two equivalent O(4)LiFe3 tetrahedra,  a cornercorner with one O(3)LiFe3 trigonal pyramid,  an edgeedge with one O(2)LiCrFe2 tetrahedra,  an edgeedge with one O(6)LiCrFe2 tetrahedra, and  an edgeedge with one O(3)LiFe3 trigonal pyramid. is represented by the CIF card [CIF]
data_Li2CrFe3O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.890
_cell_length_b   5.930
_cell_length_c   9.600
_cell_angle_alpha   90.058
_cell_angle_beta   89.971
_cell_angle_gamma   120.224
_symmetry_Int_Tables_number   1
_cell_volume   289.733
_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  0.336  0.668  0.894  1.0
  Li  Li1  1  0.001  0.000  0.997  1.0
  Li  Li2  1  0.999  1.000  0.497  1.0
  Li  Li3  1  0.664  0.332  0.394  1.0
  Cr  Cr4  1  0.328  0.664  0.485  1.0
  Cr  Cr5  1  0.672  0.336  0.985  1.0
  Fe  Fe6  1  0.169  0.831  0.213  1.0
  Fe  Fe7  1  0.169  0.338  0.213  1.0
  Fe  Fe8  1  0.663  0.831  0.213  1.0
  Fe  Fe9  1  0.337  0.169  0.713  1.0
  Fe  Fe10  1  0.831  0.662  0.713  1.0
  Fe  Fe11  1  0.831  0.169  0.713  1.0
  O  O12  1  0.160  0.833  0.601  1.0
  O  O13  1  0.038  0.518  0.341  1.0
  O  O14  1  0.333  0.668  0.102  1.0
  O  O15  1  0.001  0.999  0.310  1.0
  O  O16  1  0.999  0.998  0.810  1.0
  O  O17  1  0.158  0.327  0.601  1.0
  O  O18  1  0.474  0.958  0.342  1.0
  O  O19  1  0.472  0.515  0.341  1.0
  O  O20  1  0.332  0.166  0.099  1.0
  O  O21  1  0.668  0.834  0.599  1.0
  O  O22  1  0.526  0.483  0.842  1.0
  O  O23  1  0.528  0.043  0.841  1.0
  O  O24  1  0.667  0.334  0.602  1.0
  O  O25  1  0.840  0.673  0.101  1.0
  O  O26  1  0.962  0.481  0.841  1.0
  O  O27  1  0.842  0.169  0.101  1.0
[/CIF]
.