The material structure described by Li4CrFe3O8 is alpha Po-derived structured and crystallizes in the triclinic P-1 space group. There are five inequivalent Li sites. In the first Li site, Li(1) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(8) atoms to form LiO6 octahedra that share corners with two equivalent Cr(1)O6 octahedra, corners with two equivalent Fe(1)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Li(3)O6 octahedra, edges with two equivalent Li(4)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, and edges with four equivalent Fe(3)O6 octahedra. The corner-sharing octahedral tilt angles are 5°. In the second Li site, Li(2) is bonded to one O(1), one O(2), one O(3), one O(4), one O(5), and one O(7) atom to form LiO6 octahedra that share  a cornercorner with one Fe(1)O6 octahedra,  a cornercorner with one Fe(2)O6 octahedra, corners with two equivalent Cr(1)O6 octahedra, corners with two equivalent Fe(3)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Li(5)O6 octahedra,  an edgeedge with one Cr(1)O6 octahedra,  an edgeedge with one Fe(3)O6 octahedra, edges with two equivalent Li(3)O6 octahedra, edges with two equivalent Li(4)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, and edges with two equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 4-5°. In the third Li site, Li(3) is bonded to one O(2), one O(6), one O(7), one O(8), and two equivalent O(3) atoms to form LiO6 octahedra that share  a cornercorner with one Fe(2)O6 octahedra,  a cornercorner with one Fe(3)O6 octahedra, corners with two equivalent Cr(1)O6 octahedra, corners with two equivalent Fe(1)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Li(3)O6 octahedra,  an edgeedge with one Li(4)O6 octahedra,  an edgeedge with one Li(5)O6 octahedra,  an edgeedge with one Cr(1)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Fe(3)O6 octahedra, and edges with three equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 4-5°. In the fourth Li site, Li(4) is bonded to one O(1), one O(5), one O(6), one O(8), and two equivalent O(4) atoms to form LiO6 octahedra that share  a cornercorner with one Cr(1)O6 octahedra,  a cornercorner with one Fe(1)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, corners with two equivalent Fe(3)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Li(3)O6 octahedra,  an edgeedge with one Li(4)O6 octahedra,  an edgeedge with one Li(5)O6 octahedra,  an edgeedge with one Fe(3)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Cr(1)O6 octahedra, and edges with three equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 4-6°. In the fifth Li site, Li(5) is bonded to two equivalent O(5), two equivalent O(6), and two equivalent O(7) atoms to form LiO6 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, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Li(3)O6 octahedra, edges with two equivalent Li(4)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, and edges with four equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 5-6°. Cr(1) is bonded to one O(4), one O(5), one O(6), one O(8), and two equivalent O(7) atoms to form CrO6 octahedra that share  a cornercorner with one Li(1)O6 octahedra,  a cornercorner with one Li(4)O6 octahedra, corners with two equivalent Li(2)O6 octahedra, corners with two equivalent Li(3)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Li(3)O6 octahedra,  an edgeedge with one Cr(1)O6 octahedra,  an edgeedge with one Fe(3)O6 octahedra, edges with two equivalent Li(4)O6 octahedra, edges with two equivalent Li(5)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, and edges with two equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 4-5°. There are three inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to one O(1), one O(2), one O(5), one O(8), and two equivalent O(4) atoms to form FeO6 octahedra that share  a cornercorner with one Li(1)O6 octahedra,  a cornercorner with one Li(2)O6 octahedra,  a cornercorner with one Li(4)O6 octahedra,  a cornercorner with one Li(5)O6 octahedra, corners with two equivalent Li(3)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Cr(1)O6 octahedra, edges with two equivalent Fe(3)O6 octahedra, and edges with three equivalent Li(4)O6 octahedra. The corner-sharing octahedral tilt angles are 5°. In the second Fe site, Fe(2) is bonded to one O(2), one O(5), one O(6), one O(7), and two equivalent O(3) atoms to form FeO6 octahedra that share  a cornercorner with one Li(1)O6 octahedra,  a cornercorner with one Li(2)O6 octahedra,  a cornercorner with one Li(3)O6 octahedra,  a cornercorner with one Li(5)O6 octahedra, corners with two equivalent Li(4)O6 octahedra,  an edgeedge with one Li(5)O6 octahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Cr(1)O6 octahedra, edges with two equivalent Fe(3)O6 octahedra, and edges with three equivalent Li(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 4-6°. In the third Fe site, Fe(3) is bonded to one O(2), one O(3), one O(6), one O(8), and two equivalent O(1) atoms to form FeO6 octahedra that share  a cornercorner with one Li(3)O6 octahedra,  a cornercorner with one Li(5)O6 octahedra, corners with two equivalent Li(2)O6 octahedra, corners with two equivalent Li(4)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Li(4)O6 octahedra,  an edgeedge with one Cr(1)O6 octahedra,  an edgeedge with one Fe(3)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(3)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, and edges with two equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 4-5°. There are eight inequivalent O sites. In the first O site, O(1) is bonded to one Li(1), one Li(2), one Li(4), one Fe(1), and two equivalent Fe(3) atoms to form OLi3Fe3 octahedra that share  a cornercorner with one O(7)Li3Cr2Fe octahedra,  a cornercorner with one O(4)Li3CrFe2 octahedra,  a cornercorner with one O(5)Li3CrFe2 octahedra,  a cornercorner with one O(6)Li3CrFe2 octahedra,  a cornercorner with one O(1)Li3Fe3 octahedra,  a cornercorner with one O(3)Li3Fe3 octahedra,  an edgeedge with one O(5)Li3CrFe2 octahedra,  an edgeedge with one O(6)Li3CrFe2 octahedra,  an edgeedge with one O(1)Li3Fe3 octahedra,  an edgeedge with one O(3)Li3Fe3 octahedra, edges with two equivalent O(4)Li3CrFe2 octahedra, edges with three equivalent O(8)Li3CrFe2 octahedra, and edges with three equivalent O(2)Li3Fe3 octahedra. The corner-sharing octahedral tilt angles range from 0-1°. In the second O site, O(2) is bonded to one Li(1), one Li(2), one Li(3), one Fe(1), one Fe(2), and one Fe(3) atom to form OLi3Fe3 octahedra that share  a cornercorner with one O(7)Li3Cr2Fe octahedra,  a cornercorner with one O(4)Li3CrFe2 octahedra,  a cornercorner with one O(5)Li3CrFe2 octahedra,  a cornercorner with one O(6)Li3CrFe2 octahedra,  a cornercorner with one O(8)Li3CrFe2 octahedra,  a cornercorner with one O(2)Li3Fe3 octahedra,  an edgeedge with one O(7)Li3Cr2Fe octahedra,  an edgeedge with one O(4)Li3CrFe2 octahedra,  an edgeedge with one O(5)Li3CrFe2 octahedra,  an edgeedge with one O(6)Li3CrFe2 octahedra, edges with two equivalent O(8)Li3CrFe2 octahedra, edges with three equivalent O(1)Li3Fe3 octahedra, and edges with three equivalent O(3)Li3Fe3 octahedra. The corner-sharing octahedral tilt angles range from 0-1°. In the third O site, O(3) is bonded to one Li(2), two equivalent Li(3), one Fe(3), and two equivalent Fe(2) atoms to form OLi3Fe3 octahedra that share  a cornercorner with one O(7)Li3Cr2Fe octahedra,  a cornercorner with one O(4)Li3CrFe2 octahedra,  a cornercorner with one O(5)Li3CrFe2 octahedra,  a cornercorner with one O(6)Li3CrFe2 octahedra,  a cornercorner with one O(8)Li3CrFe2 octahedra,  a cornercorner with one O(1)Li3Fe3 octahedra,  an edgeedge with one O(5)Li3CrFe2 octahedra,  an edgeedge with one O(8)Li3CrFe2 octahedra,  an edgeedge with one O(1)Li3Fe3 octahedra, edges with two equivalent O(7)Li3Cr2Fe octahedra, edges with two equivalent O(6)Li3CrFe2 octahedra, edges with two equivalent O(3)Li3Fe3 octahedra, and edges with three equivalent O(2)Li3Fe3 octahedra. The corner-sharing octahedral tilt angles range from 0-1°. In the fourth O site, O(4) is bonded to one Li(2), two equivalent Li(4), one Cr(1), and two equivalent Fe(1) atoms to form OLi3CrFe2 octahedra that share  a cornercorner with one O(7)Li3Cr2Fe octahedra,  a cornercorner with one O(6)Li3CrFe2 octahedra,  a cornercorner with one O(8)Li3CrFe2 octahedra,  a cornercorner with one O(1)Li3Fe3 octahedra,  a cornercorner with one O(2)Li3Fe3 octahedra,  a cornercorner with one O(3)Li3Fe3 octahedra,  an edgeedge with one O(7)Li3Cr2Fe octahedra,  an edgeedge with one O(6)Li3CrFe2 octahedra,  an edgeedge with one O(2)Li3Fe3 octahedra, edges with two equivalent O(4)Li3CrFe2 octahedra, edges with two equivalent O(8)Li3CrFe2 octahedra, edges with two equivalent O(1)Li3Fe3 octahedra, and edges with three equivalent O(5)Li3CrFe2 octahedra. The corner-sharing octahedral tilt angles range from 0-1°. In the fifth O site, O(5) is bonded to one Li(2), one Li(4), one Li(5), one Cr(1), one Fe(1), and one Fe(2) atom to form OLi3CrFe2 octahedra that share  a cornercorner with one O(5)Li3CrFe2 octahedra,  a cornercorner with one O(6)Li3CrFe2 octahedra,  a cornercorner with one O(8)Li3CrFe2 octahedra,  a cornercorner with one O(1)Li3Fe3 octahedra,  a cornercorner with one O(2)Li3Fe3 octahedra,  a cornercorner with one O(3)Li3Fe3 octahedra,  an edgeedge with one O(8)Li3CrFe2 octahedra,  an edgeedge with one O(1)Li3Fe3 octahedra,  an edgeedge with one O(2)Li3Fe3 octahedra,  an edgeedge with one O(3)Li3Fe3 octahedra, edges with two equivalent O(6)Li3CrFe2 octahedra, edges with three equivalent O(7)Li3Cr2Fe octahedra, and edges with three equivalent O(4)Li3CrFe2 octahedra. The corner-sharing octahedral tilt angles range from 0-1°. In the sixth O site, O(6) is bonded to one Li(3), one Li(4), one Li(5), one Cr(1), one Fe(2), and one Fe(3) atom to form OLi3CrFe2 octahedra that share  a cornercorner with one O(4)Li3CrFe2 octahedra,  a cornercorner with one O(5)Li3CrFe2 octahedra,  a cornercorner with one O(6)Li3CrFe2 octahedra,  a cornercorner with one O(1)Li3Fe3 octahedra,  a cornercorner with one O(2)Li3Fe3 octahedra,  a cornercorner with one O(3)Li3Fe3 octahedra,  an edgeedge with one O(4)Li3CrFe2 octahedra,  an edgeedge with one O(1)Li3Fe3 octahedra,  an edgeedge with one O(2)Li3Fe3 octahedra, edges with two equivalent O(5)Li3CrFe2 octahedra, edges with two equivalent O(8)Li3CrFe2 octahedra, edges with two equivalent O(3)Li3Fe3 octahedra, and edges with three equivalent O(7)Li3Cr2Fe octahedra. The corner-sharing octahedral tilt angles range from 0-1°. In the seventh O site, O(7) is bonded to one Li(2), one Li(3), one Li(5), two equivalent Cr(1), and one Fe(2) atom to form OLi3Cr2Fe octahedra that share  a cornercorner with one O(7)Li3Cr2Fe octahedra,  a cornercorner with one O(4)Li3CrFe2 octahedra,  a cornercorner with one O(8)Li3CrFe2 octahedra,  a cornercorner with one O(1)Li3Fe3 octahedra,  a cornercorner with one O(2)Li3Fe3 octahedra,  a cornercorner with one O(3)Li3Fe3 octahedra,  an edgeedge with one O(7)Li3Cr2Fe octahedra,  an edgeedge with one O(4)Li3CrFe2 octahedra,  an edgeedge with one O(8)Li3CrFe2 octahedra,  an edgeedge with one O(2)Li3Fe3 octahedra, edges with two equivalent O(3)Li3Fe3 octahedra, edges with three equivalent O(5)Li3CrFe2 octahedra, and edges with three equivalent O(6)Li3CrFe2 octahedra. The corner-sharing octahedral tilt angles range from 0-1°. In the eighth O site, O(8) is bonded to one Li(1), one Li(3), one Li(4), one Cr(1), one Fe(1), and one Fe(3) atom to form OLi3CrFe2 octahedra that share  a cornercorner with one O(7)Li3Cr2Fe octahedra,  a cornercorner with one O(4)Li3CrFe2 octahedra,  a cornercorner with one O(5)Li3CrFe2 octahedra,  a cornercorner with one O(8)Li3CrFe2 octahedra,  a cornercorner with one O(2)Li3Fe3 octahedra,  a cornercorner with one O(3)Li3Fe3 octahedra,  an edgeedge with one O(7)Li3Cr2Fe octahedra,  an edgeedge with one O(5)Li3CrFe2 octahedra,  an edgeedge with one O(3)Li3Fe3 octahedra, edges with two equivalent O(4)Li3CrFe2 octahedra, edges with two equivalent O(6)Li3CrFe2 octahedra, edges with two equivalent O(2)Li3Fe3 octahedra, and edges with three equivalent O(1)Li3Fe3 octahedra. The corner-sharing octahedral tilt angles range from 0-1°. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li4CrFe3O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.188
_cell_length_b   7.879
_cell_length_c   7.879
_cell_angle_alpha   81.787
_cell_angle_beta   83.759
_cell_angle_gamma   70.987
_symmetry_Int_Tables_number   1
_cell_volume   300.676
_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  0.000  0.000  0.000  1.0
  Li  Li1  1  0.001  0.750  0.750  1.0
  Li  Li2  1  0.001  0.875  0.375  1.0
  Li  Li3  1  0.000  0.375  0.874  1.0
  Li  Li4  1  0.000  0.500  0.500  1.0
  Li  Li5  1  1.000  0.625  0.126  1.0
  Li  Li6  1  0.999  0.125  0.625  1.0
  Li  Li7  1  0.999  0.250  0.250  1.0
  Cr  Cr8  1  0.500  0.438  0.687  1.0
  Cr  Cr9  1  0.500  0.562  0.313  1.0
  Fe  Fe10  1  0.500  0.687  0.938  1.0
  Fe  Fe11  1  0.500  0.812  0.563  1.0
  Fe  Fe12  1  0.500  0.937  0.188  1.0
  Fe  Fe13  1  0.500  0.063  0.812  1.0
  Fe  Fe14  1  0.500  0.188  0.437  1.0
  Fe  Fe15  1  0.500  0.313  0.062  1.0
  O  O16  1  0.729  0.848  0.969  1.0
  O  O17  1  0.271  0.902  0.781  1.0
  O  O18  1  0.730  0.972  0.594  1.0
  O  O19  1  0.273  0.526  0.903  1.0
  O  O20  1  0.726  0.597  0.720  1.0
  O  O21  1  0.725  0.722  0.345  1.0
  O  O22  1  0.275  0.650  0.530  1.0
  O  O23  1  0.727  0.225  0.843  1.0
  O  O24  1  0.725  0.350  0.470  1.0
  O  O25  1  0.273  0.775  0.157  1.0
  O  O26  1  0.275  0.278  0.655  1.0
  O  O27  1  0.727  0.474  0.097  1.0
  O  O28  1  0.274  0.403  0.280  1.0
  O  O29  1  0.729  0.098  0.219  1.0
  O  O30  1  0.270  0.028  0.406  1.0
  O  O31  1  0.271  0.152  0.031  1.0
[/CIF]
.
The material structure described by Li4CrFe3O8 is alpha Po-derived structured and crystallizes in the triclinic P-1 space group. There are five inequivalent Li sites. In the first Li site, Li(1) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(8) atoms to form LiO6 octahedra that share corners with two equivalent Cr(1)O6 octahedra, corners with two equivalent Fe(1)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Li(3)O6 octahedra, edges with two equivalent Li(4)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, and edges with four equivalent Fe(3)O6 octahedra. The corner-sharing octahedral tilt angles are 5°. In the second Li site, Li(2) is bonded to one O(1), one O(2), one O(3), one O(4), one O(5), and one O(7) atom to form LiO6 octahedra that share  a cornercorner with one Fe(1)O6 octahedra,  a cornercorner with one Fe(2)O6 octahedra, corners with two equivalent Cr(1)O6 octahedra, corners with two equivalent Fe(3)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Li(5)O6 octahedra,  an edgeedge with one Cr(1)O6 octahedra,  an edgeedge with one Fe(3)O6 octahedra, edges with two equivalent Li(3)O6 octahedra, edges with two equivalent Li(4)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, and edges with two equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 4-5°. In the third Li site, Li(3) is bonded to one O(2), one O(6), one O(7), one O(8), and two equivalent O(3) atoms to form LiO6 octahedra that share  a cornercorner with one Fe(2)O6 octahedra,  a cornercorner with one Fe(3)O6 octahedra, corners with two equivalent Cr(1)O6 octahedra, corners with two equivalent Fe(1)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Li(3)O6 octahedra,  an edgeedge with one Li(4)O6 octahedra,  an edgeedge with one Li(5)O6 octahedra,  an edgeedge with one Cr(1)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Fe(3)O6 octahedra, and edges with three equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 4-5°. In the fourth Li site, Li(4) is bonded to one O(1), one O(5), one O(6), one O(8), and two equivalent O(4) atoms to form LiO6 octahedra that share  a cornercorner with one Cr(1)O6 octahedra,  a cornercorner with one Fe(1)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, corners with two equivalent Fe(3)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Li(3)O6 octahedra,  an edgeedge with one Li(4)O6 octahedra,  an edgeedge with one Li(5)O6 octahedra,  an edgeedge with one Fe(3)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Cr(1)O6 octahedra, and edges with three equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 4-6°. In the fifth Li site, Li(5) is bonded to two equivalent O(5), two equivalent O(6), and two equivalent O(7) atoms to form LiO6 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, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Li(3)O6 octahedra, edges with two equivalent Li(4)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, and edges with four equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 5-6°. Cr(1) is bonded to one O(4), one O(5), one O(6), one O(8), and two equivalent O(7) atoms to form CrO6 octahedra that share  a cornercorner with one Li(1)O6 octahedra,  a cornercorner with one Li(4)O6 octahedra, corners with two equivalent Li(2)O6 octahedra, corners with two equivalent Li(3)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Li(3)O6 octahedra,  an edgeedge with one Cr(1)O6 octahedra,  an edgeedge with one Fe(3)O6 octahedra, edges with two equivalent Li(4)O6 octahedra, edges with two equivalent Li(5)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, and edges with two equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 4-5°. There are three inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to one O(1), one O(2), one O(5), one O(8), and two equivalent O(4) atoms to form FeO6 octahedra that share  a cornercorner with one Li(1)O6 octahedra,  a cornercorner with one Li(2)O6 octahedra,  a cornercorner with one Li(4)O6 octahedra,  a cornercorner with one Li(5)O6 octahedra, corners with two equivalent Li(3)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Cr(1)O6 octahedra, edges with two equivalent Fe(3)O6 octahedra, and edges with three equivalent Li(4)O6 octahedra. The corner-sharing octahedral tilt angles are 5°. In the second Fe site, Fe(2) is bonded to one O(2), one O(5), one O(6), one O(7), and two equivalent O(3) atoms to form FeO6 octahedra that share  a cornercorner with one Li(1)O6 octahedra,  a cornercorner with one Li(2)O6 octahedra,  a cornercorner with one Li(3)O6 octahedra,  a cornercorner with one Li(5)O6 octahedra, corners with two equivalent Li(4)O6 octahedra,  an edgeedge with one Li(5)O6 octahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Cr(1)O6 octahedra, edges with two equivalent Fe(3)O6 octahedra, and edges with three equivalent Li(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 4-6°. In the third Fe site, Fe(3) is bonded to one O(2), one O(3), one O(6), one O(8), and two equivalent O(1) atoms to form FeO6 octahedra that share  a cornercorner with one Li(3)O6 octahedra,  a cornercorner with one Li(5)O6 octahedra, corners with two equivalent Li(2)O6 octahedra, corners with two equivalent Li(4)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Li(4)O6 octahedra,  an edgeedge with one Cr(1)O6 octahedra,  an edgeedge with one Fe(3)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(3)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, and edges with two equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 4-5°. There are eight inequivalent O sites. In the first O site, O(1) is bonded to one Li(1), one Li(2), one Li(4), one Fe(1), and two equivalent Fe(3) atoms to form OLi3Fe3 octahedra that share  a cornercorner with one O(7)Li3Cr2Fe octahedra,  a cornercorner with one O(4)Li3CrFe2 octahedra,  a cornercorner with one O(5)Li3CrFe2 octahedra,  a cornercorner with one O(6)Li3CrFe2 octahedra,  a cornercorner with one O(1)Li3Fe3 octahedra,  a cornercorner with one O(3)Li3Fe3 octahedra,  an edgeedge with one O(5)Li3CrFe2 octahedra,  an edgeedge with one O(6)Li3CrFe2 octahedra,  an edgeedge with one O(1)Li3Fe3 octahedra,  an edgeedge with one O(3)Li3Fe3 octahedra, edges with two equivalent O(4)Li3CrFe2 octahedra, edges with three equivalent O(8)Li3CrFe2 octahedra, and edges with three equivalent O(2)Li3Fe3 octahedra. The corner-sharing octahedral tilt angles range from 0-1°. In the second O site, O(2) is bonded to one Li(1), one Li(2), one Li(3), one Fe(1), one Fe(2), and one Fe(3) atom to form OLi3Fe3 octahedra that share  a cornercorner with one O(7)Li3Cr2Fe octahedra,  a cornercorner with one O(4)Li3CrFe2 octahedra,  a cornercorner with one O(5)Li3CrFe2 octahedra,  a cornercorner with one O(6)Li3CrFe2 octahedra,  a cornercorner with one O(8)Li3CrFe2 octahedra,  a cornercorner with one O(2)Li3Fe3 octahedra,  an edgeedge with one O(7)Li3Cr2Fe octahedra,  an edgeedge with one O(4)Li3CrFe2 octahedra,  an edgeedge with one O(5)Li3CrFe2 octahedra,  an edgeedge with one O(6)Li3CrFe2 octahedra, edges with two equivalent O(8)Li3CrFe2 octahedra, edges with three equivalent O(1)Li3Fe3 octahedra, and edges with three equivalent O(3)Li3Fe3 octahedra. The corner-sharing octahedral tilt angles range from 0-1°. In the third O site, O(3) is bonded to one Li(2), two equivalent Li(3), one Fe(3), and two equivalent Fe(2) atoms to form OLi3Fe3 octahedra that share  a cornercorner with one O(7)Li3Cr2Fe octahedra,  a cornercorner with one O(4)Li3CrFe2 octahedra,  a cornercorner with one O(5)Li3CrFe2 octahedra,  a cornercorner with one O(6)Li3CrFe2 octahedra,  a cornercorner with one O(8)Li3CrFe2 octahedra,  a cornercorner with one O(1)Li3Fe3 octahedra,  an edgeedge with one O(5)Li3CrFe2 octahedra,  an edgeedge with one O(8)Li3CrFe2 octahedra,  an edgeedge with one O(1)Li3Fe3 octahedra, edges with two equivalent O(7)Li3Cr2Fe octahedra, edges with two equivalent O(6)Li3CrFe2 octahedra, edges with two equivalent O(3)Li3Fe3 octahedra, and edges with three equivalent O(2)Li3Fe3 octahedra. The corner-sharing octahedral tilt angles range from 0-1°. In the fourth O site, O(4) is bonded to one Li(2), two equivalent Li(4), one Cr(1), and two equivalent Fe(1) atoms to form OLi3CrFe2 octahedra that share  a cornercorner with one O(7)Li3Cr2Fe octahedra,  a cornercorner with one O(6)Li3CrFe2 octahedra,  a cornercorner with one O(8)Li3CrFe2 octahedra,  a cornercorner with one O(1)Li3Fe3 octahedra,  a cornercorner with one O(2)Li3Fe3 octahedra,  a cornercorner with one O(3)Li3Fe3 octahedra,  an edgeedge with one O(7)Li3Cr2Fe octahedra,  an edgeedge with one O(6)Li3CrFe2 octahedra,  an edgeedge with one O(2)Li3Fe3 octahedra, edges with two equivalent O(4)Li3CrFe2 octahedra, edges with two equivalent O(8)Li3CrFe2 octahedra, edges with two equivalent O(1)Li3Fe3 octahedra, and edges with three equivalent O(5)Li3CrFe2 octahedra. The corner-sharing octahedral tilt angles range from 0-1°. In the fifth O site, O(5) is bonded to one Li(2), one Li(4), one Li(5), one Cr(1), one Fe(1), and one Fe(2) atom to form OLi3CrFe2 octahedra that share  a cornercorner with one O(5)Li3CrFe2 octahedra,  a cornercorner with one O(6)Li3CrFe2 octahedra,  a cornercorner with one O(8)Li3CrFe2 octahedra,  a cornercorner with one O(1)Li3Fe3 octahedra,  a cornercorner with one O(2)Li3Fe3 octahedra,  a cornercorner with one O(3)Li3Fe3 octahedra,  an edgeedge with one O(8)Li3CrFe2 octahedra,  an edgeedge with one O(1)Li3Fe3 octahedra,  an edgeedge with one O(2)Li3Fe3 octahedra,  an edgeedge with one O(3)Li3Fe3 octahedra, edges with two equivalent O(6)Li3CrFe2 octahedra, edges with three equivalent O(7)Li3Cr2Fe octahedra, and edges with three equivalent O(4)Li3CrFe2 octahedra. The corner-sharing octahedral tilt angles range from 0-1°. In the sixth O site, O(6) is bonded to one Li(3), one Li(4), one Li(5), one Cr(1), one Fe(2), and one Fe(3) atom to form OLi3CrFe2 octahedra that share  a cornercorner with one O(4)Li3CrFe2 octahedra,  a cornercorner with one O(5)Li3CrFe2 octahedra,  a cornercorner with one O(6)Li3CrFe2 octahedra,  a cornercorner with one O(1)Li3Fe3 octahedra,  a cornercorner with one O(2)Li3Fe3 octahedra,  a cornercorner with one O(3)Li3Fe3 octahedra,  an edgeedge with one O(4)Li3CrFe2 octahedra,  an edgeedge with one O(1)Li3Fe3 octahedra,  an edgeedge with one O(2)Li3Fe3 octahedra, edges with two equivalent O(5)Li3CrFe2 octahedra, edges with two equivalent O(8)Li3CrFe2 octahedra, edges with two equivalent O(3)Li3Fe3 octahedra, and edges with three equivalent O(7)Li3Cr2Fe octahedra. The corner-sharing octahedral tilt angles range from 0-1°. In the seventh O site, O(7) is bonded to one Li(2), one Li(3), one Li(5), two equivalent Cr(1), and one Fe(2) atom to form OLi3Cr2Fe octahedra that share  a cornercorner with one O(7)Li3Cr2Fe octahedra,  a cornercorner with one O(4)Li3CrFe2 octahedra,  a cornercorner with one O(8)Li3CrFe2 octahedra,  a cornercorner with one O(1)Li3Fe3 octahedra,  a cornercorner with one O(2)Li3Fe3 octahedra,  a cornercorner with one O(3)Li3Fe3 octahedra,  an edgeedge with one O(7)Li3Cr2Fe octahedra,  an edgeedge with one O(4)Li3CrFe2 octahedra,  an edgeedge with one O(8)Li3CrFe2 octahedra,  an edgeedge with one O(2)Li3Fe3 octahedra, edges with two equivalent O(3)Li3Fe3 octahedra, edges with three equivalent O(5)Li3CrFe2 octahedra, and edges with three equivalent O(6)Li3CrFe2 octahedra. The corner-sharing octahedral tilt angles range from 0-1°. In the eighth O site, O(8) is bonded to one Li(1), one Li(3), one Li(4), one Cr(1), one Fe(1), and one Fe(3) atom to form OLi3CrFe2 octahedra that share  a cornercorner with one O(7)Li3Cr2Fe octahedra,  a cornercorner with one O(4)Li3CrFe2 octahedra,  a cornercorner with one O(5)Li3CrFe2 octahedra,  a cornercorner with one O(8)Li3CrFe2 octahedra,  a cornercorner with one O(2)Li3Fe3 octahedra,  a cornercorner with one O(3)Li3Fe3 octahedra,  an edgeedge with one O(7)Li3Cr2Fe octahedra,  an edgeedge with one O(5)Li3CrFe2 octahedra,  an edgeedge with one O(3)Li3Fe3 octahedra, edges with two equivalent O(4)Li3CrFe2 octahedra, edges with two equivalent O(6)Li3CrFe2 octahedra, edges with two equivalent O(2)Li3Fe3 octahedra, and edges with three equivalent O(1)Li3Fe3 octahedra. The corner-sharing octahedral tilt angles range from 0-1°. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li4CrFe3O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.188
_cell_length_b   7.879
_cell_length_c   7.879
_cell_angle_alpha   81.787
_cell_angle_beta   83.759
_cell_angle_gamma   70.987
_symmetry_Int_Tables_number   1
_cell_volume   300.676
_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  0.000  0.000  0.000  1.0
  Li  Li1  1  0.001  0.750  0.750  1.0
  Li  Li2  1  0.001  0.875  0.375  1.0
  Li  Li3  1  0.000  0.375  0.874  1.0
  Li  Li4  1  0.000  0.500  0.500  1.0
  Li  Li5  1  1.000  0.625  0.126  1.0
  Li  Li6  1  0.999  0.125  0.625  1.0
  Li  Li7  1  0.999  0.250  0.250  1.0
  Cr  Cr8  1  0.500  0.438  0.687  1.0
  Cr  Cr9  1  0.500  0.562  0.313  1.0
  Fe  Fe10  1  0.500  0.687  0.938  1.0
  Fe  Fe11  1  0.500  0.812  0.563  1.0
  Fe  Fe12  1  0.500  0.937  0.188  1.0
  Fe  Fe13  1  0.500  0.063  0.812  1.0
  Fe  Fe14  1  0.500  0.188  0.437  1.0
  Fe  Fe15  1  0.500  0.313  0.062  1.0
  O  O16  1  0.729  0.848  0.969  1.0
  O  O17  1  0.271  0.902  0.781  1.0
  O  O18  1  0.730  0.972  0.594  1.0
  O  O19  1  0.273  0.526  0.903  1.0
  O  O20  1  0.726  0.597  0.720  1.0
  O  O21  1  0.725  0.722  0.345  1.0
  O  O22  1  0.275  0.650  0.530  1.0
  O  O23  1  0.727  0.225  0.843  1.0
  O  O24  1  0.725  0.350  0.470  1.0
  O  O25  1  0.273  0.775  0.157  1.0
  O  O26  1  0.275  0.278  0.655  1.0
  O  O27  1  0.727  0.474  0.097  1.0
  O  O28  1  0.274  0.403  0.280  1.0
  O  O29  1  0.729  0.098  0.219  1.0
  O  O30  1  0.270  0.028  0.406  1.0
  O  O31  1  0.271  0.152  0.031  1.0
[/CIF]
.