The material structure described by Li4Cr3Fe5O16 is Spinel-derived structured and crystallizes in the monoclinic Cm space group. There are four inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(12), one O(3), and two equivalent O(9) atoms to form LiO4 tetrahedra that share  a cornercorner with one Fe(2)O6 octahedra, corners with two equivalent Cr(1)O6 octahedra, corners with two equivalent Cr(2)O6 octahedra, corners with three equivalent Fe(3)O6 octahedra, and corners with four equivalent Fe(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-64°. In the second Li site, Li(2) is bonded in a distorted rectangular see-saw-like geometry to one O(5), one O(7), and two equivalent O(11) atoms. In the third Li site, Li(3) is bonded to one O(4), one O(8), and two equivalent O(1) atoms to form distorted LiO4 trigonal pyramids that share  a cornercorner with one Fe(2)O6 octahedra, corners with two equivalent Cr(1)O6 octahedra, corners with three equivalent Fe(1)O6 octahedra,  an edgeedge with one Cr(2)O6 octahedra, and edges with two equivalent Fe(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 60-66°. In the fourth Li site, Li(4) is bonded to one O(10), one O(2), and two equivalent O(6) atoms to form LiO4 tetrahedra that share  a cornercorner with one Cr(2)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, corners with two equivalent Fe(4)O6 octahedra, corners with three equivalent Fe(1)O6 octahedra, and corners with four equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-64°. There are two inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(11), one O(2), one O(3), one O(4), one O(6), and one O(7) atom to form CrO6 octahedra that share corners with two equivalent Fe(3)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  a cornercorner with one Li(3)O4 trigonal pyramid,  an edgeedge with one Fe(1)O6 octahedra, edges with two equivalent Cr(1)O6 octahedra, and edges with two equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles are 53°. In the second Cr site, Cr(2) is bonded to one O(10), one O(5), two equivalent O(1), and two equivalent O(9) atoms to form CrO6 octahedra that share corners with two equivalent Fe(1)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one Fe(3)O6 octahedra, edges with four equivalent Fe(4)O6 octahedra, and  an edgeedge with one Li(3)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 53°. There are four inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to one O(2), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form FeO6 octahedra that share corners with two equivalent Cr(2)O6 octahedra, corners with four equivalent Fe(4)O6 octahedra, corners with three equivalent Li(4)O4 tetrahedra, corners with three equivalent Li(3)O4 trigonal pyramids,  an edgeedge with one Fe(2)O6 octahedra, and edges with two equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-53°. In the second Fe site, Fe(2) is bonded to one O(3), one O(4), two equivalent O(11), and two equivalent O(6) atoms to form FeO6 octahedra that share corners with two equivalent Fe(3)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  a cornercorner with one Li(3)O4 trigonal pyramid,  an edgeedge with one Fe(1)O6 octahedra, and edges with four equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles are 50°. In the third Fe site, Fe(3) is bonded to one O(12), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form FeO6 octahedra that share corners with two equivalent Fe(2)O6 octahedra, corners with four equivalent Cr(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra,  an edgeedge with one Cr(2)O6 octahedra, and edges with two equivalent Fe(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-53°. In the fourth Fe site, Fe(4) is bonded to one O(1), one O(10), one O(12), one O(5), one O(8), and one O(9) atom to form FeO6 octahedra that share corners with two equivalent Fe(1)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one Fe(3)O6 octahedra, edges with two equivalent Cr(2)O6 octahedra, edges with two equivalent Fe(4)O6 octahedra, and  an edgeedge with one Li(3)O4 trigonal pyramid. The corner-sharing octahedral tilt angles range from 51-52°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a rectangular see-saw-like geometry to one Li(3), one Cr(2), one Fe(1), and one Fe(4) atom. In the second O site, O(2) is bonded to one Li(4), two equivalent Cr(1), and one Fe(1) atom to form distorted OLiCr2Fe tetrahedra that share corners with two equivalent O(4)LiCr2Fe tetrahedra, corners with two equivalent O(6)LiCrFe2 tetrahedra, and edges with two equivalent O(6)LiCrFe2 tetrahedra. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Li(1), two equivalent Cr(1), and one Fe(2) atom. In the fourth O site, O(4) is bonded to one Li(3), two equivalent Cr(1), and one Fe(2) atom to form distorted OLiCr2Fe tetrahedra that share corners with two equivalent O(2)LiCr2Fe tetrahedra and corners with four equivalent O(6)LiCrFe2 tetrahedra. In the fifth O site, O(5) is bonded to one Li(2), one Cr(2), and two equivalent Fe(4) atoms to form OLiCrFe2 tetrahedra that share corners with two equivalent O(12)LiFe3 tetrahedra and corners with four equivalent O(9)LiCrFe2 tetrahedra. In the sixth O site, O(6) is bonded to one Li(4), one Cr(1), one Fe(1), and one Fe(2) atom to form distorted OLiCrFe2 tetrahedra that share  a cornercorner with one O(2)LiCr2Fe tetrahedra,  a cornercorner with one O(6)LiCrFe2 tetrahedra, corners with two equivalent O(4)LiCr2Fe tetrahedra,  an edgeedge with one O(2)LiCr2Fe tetrahedra, and  an edgeedge with one O(6)LiCrFe2 tetrahedra. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), two equivalent Cr(1), and one Fe(3) atom. In the eighth O site, O(8) is bonded in a distorted rectangular see-saw-like geometry to one Li(3), one Fe(1), and two equivalent Fe(4) atoms. In the ninth O site, O(9) is bonded to one Li(1), one Cr(2), one Fe(3), and one Fe(4) atom to form distorted OLiCrFe2 tetrahedra that share  a cornercorner with one O(9)LiCrFe2 tetrahedra,  a cornercorner with one O(12)LiFe3 tetrahedra, corners with two equivalent O(5)LiCrFe2 tetrahedra,  an edgeedge with one O(9)LiCrFe2 tetrahedra, and  an edgeedge with one O(12)LiFe3 tetrahedra. In the tenth O site, O(10) is bonded in a rectangular see-saw-like geometry to one Li(4), one Cr(2), and two equivalent Fe(4) atoms. In the eleventh O site, O(11) 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 twelfth O site, O(12) is bonded to one Li(1), one Fe(3), and two equivalent Fe(4) atoms to form a mixture of distorted corner and edge-sharing OLiFe3 tetrahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li4Cr3Fe5O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.752
_cell_length_b   5.752
_cell_length_c   9.514
_cell_angle_alpha   89.171
_cell_angle_beta   89.171
_cell_angle_gamma   59.494
_symmetry_Int_Tables_number   1
_cell_volume   271.195
_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
  Li  Li0  1  0.669  0.669  0.892  1.0
  Li  Li1  1  0.997  0.997  0.994  1.0
  Li  Li2  1  0.998  0.998  0.498  1.0
  Li  Li3  1  0.332  0.332  0.394  1.0
  Cr  Cr4  1  0.344  0.826  0.214  1.0
  Cr  Cr5  1  0.826  0.344  0.214  1.0
  Cr  Cr6  1  0.169  0.169  0.715  1.0
  Fe  Fe7  1  0.669  0.669  0.495  1.0
  Fe  Fe8  1  0.832  0.832  0.214  1.0
  Fe  Fe9  1  0.335  0.335  0.993  1.0
  Fe  Fe10  1  0.176  0.655  0.715  1.0
  Fe  Fe11  1  0.655  0.176  0.715  1.0
  O  O12  1  0.329  0.833  0.602  1.0
  O  O13  1  0.515  0.515  0.332  1.0
  O  O14  1  0.672  0.672  0.104  1.0
  O  O15  1  0.998  0.998  0.310  1.0
  O  O16  1  0.993  0.993  0.808  1.0
  O  O17  1  0.833  0.329  0.602  1.0
  O  O18  1  0.522  0.959  0.335  1.0
  O  O19  1  0.959  0.522  0.335  1.0
  O  O20  1  0.161  0.161  0.103  1.0
  O  O21  1  0.839  0.839  0.609  1.0
  O  O22  1  0.038  0.481  0.830  1.0
  O  O23  1  0.481  0.038  0.830  1.0
  O  O24  1  0.337  0.337  0.605  1.0
  O  O25  1  0.159  0.674  0.104  1.0
  O  O26  1  0.481  0.481  0.840  1.0
  O  O27  1  0.674  0.159  0.104  1.0
[/CIF]
.
The material structure described by Li4Cr3Fe5O16 is Spinel-derived structured and crystallizes in the monoclinic Cm space group. There are four inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(12), one O(3), and two equivalent O(9) atoms to form LiO4 tetrahedra that share  a cornercorner with one Fe(2)O6 octahedra, corners with two equivalent Cr(1)O6 octahedra, corners with two equivalent Cr(2)O6 octahedra, corners with three equivalent Fe(3)O6 octahedra, and corners with four equivalent Fe(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-64°. In the second Li site, Li(2) is bonded in a distorted rectangular see-saw-like geometry to one O(5), one O(7), and two equivalent O(11) atoms. In the third Li site, Li(3) is bonded to one O(4), one O(8), and two equivalent O(1) atoms to form distorted LiO4 trigonal pyramids that share  a cornercorner with one Fe(2)O6 octahedra, corners with two equivalent Cr(1)O6 octahedra, corners with three equivalent Fe(1)O6 octahedra,  an edgeedge with one Cr(2)O6 octahedra, and edges with two equivalent Fe(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 60-66°. In the fourth Li site, Li(4) is bonded to one O(10), one O(2), and two equivalent O(6) atoms to form LiO4 tetrahedra that share  a cornercorner with one Cr(2)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, corners with two equivalent Fe(4)O6 octahedra, corners with three equivalent Fe(1)O6 octahedra, and corners with four equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-64°. There are two inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(11), one O(2), one O(3), one O(4), one O(6), and one O(7) atom to form CrO6 octahedra that share corners with two equivalent Fe(3)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  a cornercorner with one Li(3)O4 trigonal pyramid,  an edgeedge with one Fe(1)O6 octahedra, edges with two equivalent Cr(1)O6 octahedra, and edges with two equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles are 53°. In the second Cr site, Cr(2) is bonded to one O(10), one O(5), two equivalent O(1), and two equivalent O(9) atoms to form CrO6 octahedra that share corners with two equivalent Fe(1)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one Fe(3)O6 octahedra, edges with four equivalent Fe(4)O6 octahedra, and  an edgeedge with one Li(3)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 53°. There are four inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to one O(2), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form FeO6 octahedra that share corners with two equivalent Cr(2)O6 octahedra, corners with four equivalent Fe(4)O6 octahedra, corners with three equivalent Li(4)O4 tetrahedra, corners with three equivalent Li(3)O4 trigonal pyramids,  an edgeedge with one Fe(2)O6 octahedra, and edges with two equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-53°. In the second Fe site, Fe(2) is bonded to one O(3), one O(4), two equivalent O(11), and two equivalent O(6) atoms to form FeO6 octahedra that share corners with two equivalent Fe(3)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  a cornercorner with one Li(3)O4 trigonal pyramid,  an edgeedge with one Fe(1)O6 octahedra, and edges with four equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles are 50°. In the third Fe site, Fe(3) is bonded to one O(12), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form FeO6 octahedra that share corners with two equivalent Fe(2)O6 octahedra, corners with four equivalent Cr(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra,  an edgeedge with one Cr(2)O6 octahedra, and edges with two equivalent Fe(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-53°. In the fourth Fe site, Fe(4) is bonded to one O(1), one O(10), one O(12), one O(5), one O(8), and one O(9) atom to form FeO6 octahedra that share corners with two equivalent Fe(1)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one Fe(3)O6 octahedra, edges with two equivalent Cr(2)O6 octahedra, edges with two equivalent Fe(4)O6 octahedra, and  an edgeedge with one Li(3)O4 trigonal pyramid. The corner-sharing octahedral tilt angles range from 51-52°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a rectangular see-saw-like geometry to one Li(3), one Cr(2), one Fe(1), and one Fe(4) atom. In the second O site, O(2) is bonded to one Li(4), two equivalent Cr(1), and one Fe(1) atom to form distorted OLiCr2Fe tetrahedra that share corners with two equivalent O(4)LiCr2Fe tetrahedra, corners with two equivalent O(6)LiCrFe2 tetrahedra, and edges with two equivalent O(6)LiCrFe2 tetrahedra. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Li(1), two equivalent Cr(1), and one Fe(2) atom. In the fourth O site, O(4) is bonded to one Li(3), two equivalent Cr(1), and one Fe(2) atom to form distorted OLiCr2Fe tetrahedra that share corners with two equivalent O(2)LiCr2Fe tetrahedra and corners with four equivalent O(6)LiCrFe2 tetrahedra. In the fifth O site, O(5) is bonded to one Li(2), one Cr(2), and two equivalent Fe(4) atoms to form OLiCrFe2 tetrahedra that share corners with two equivalent O(12)LiFe3 tetrahedra and corners with four equivalent O(9)LiCrFe2 tetrahedra. In the sixth O site, O(6) is bonded to one Li(4), one Cr(1), one Fe(1), and one Fe(2) atom to form distorted OLiCrFe2 tetrahedra that share  a cornercorner with one O(2)LiCr2Fe tetrahedra,  a cornercorner with one O(6)LiCrFe2 tetrahedra, corners with two equivalent O(4)LiCr2Fe tetrahedra,  an edgeedge with one O(2)LiCr2Fe tetrahedra, and  an edgeedge with one O(6)LiCrFe2 tetrahedra. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), two equivalent Cr(1), and one Fe(3) atom. In the eighth O site, O(8) is bonded in a distorted rectangular see-saw-like geometry to one Li(3), one Fe(1), and two equivalent Fe(4) atoms. In the ninth O site, O(9) is bonded to one Li(1), one Cr(2), one Fe(3), and one Fe(4) atom to form distorted OLiCrFe2 tetrahedra that share  a cornercorner with one O(9)LiCrFe2 tetrahedra,  a cornercorner with one O(12)LiFe3 tetrahedra, corners with two equivalent O(5)LiCrFe2 tetrahedra,  an edgeedge with one O(9)LiCrFe2 tetrahedra, and  an edgeedge with one O(12)LiFe3 tetrahedra. In the tenth O site, O(10) is bonded in a rectangular see-saw-like geometry to one Li(4), one Cr(2), and two equivalent Fe(4) atoms. In the eleventh O site, O(11) 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 twelfth O site, O(12) is bonded to one Li(1), one Fe(3), and two equivalent Fe(4) atoms to form a mixture of distorted corner and edge-sharing OLiFe3 tetrahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li4Cr3Fe5O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.752
_cell_length_b   5.752
_cell_length_c   9.514
_cell_angle_alpha   89.171
_cell_angle_beta   89.171
_cell_angle_gamma   59.494
_symmetry_Int_Tables_number   1
_cell_volume   271.195
_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
  Li  Li0  1  0.669  0.669  0.892  1.0
  Li  Li1  1  0.997  0.997  0.994  1.0
  Li  Li2  1  0.998  0.998  0.498  1.0
  Li  Li3  1  0.332  0.332  0.394  1.0
  Cr  Cr4  1  0.344  0.826  0.214  1.0
  Cr  Cr5  1  0.826  0.344  0.214  1.0
  Cr  Cr6  1  0.169  0.169  0.715  1.0
  Fe  Fe7  1  0.669  0.669  0.495  1.0
  Fe  Fe8  1  0.832  0.832  0.214  1.0
  Fe  Fe9  1  0.335  0.335  0.993  1.0
  Fe  Fe10  1  0.176  0.655  0.715  1.0
  Fe  Fe11  1  0.655  0.176  0.715  1.0
  O  O12  1  0.329  0.833  0.602  1.0
  O  O13  1  0.515  0.515  0.332  1.0
  O  O14  1  0.672  0.672  0.104  1.0
  O  O15  1  0.998  0.998  0.310  1.0
  O  O16  1  0.993  0.993  0.808  1.0
  O  O17  1  0.833  0.329  0.602  1.0
  O  O18  1  0.522  0.959  0.335  1.0
  O  O19  1  0.959  0.522  0.335  1.0
  O  O20  1  0.161  0.161  0.103  1.0
  O  O21  1  0.839  0.839  0.609  1.0
  O  O22  1  0.038  0.481  0.830  1.0
  O  O23  1  0.481  0.038  0.830  1.0
  O  O24  1  0.337  0.337  0.605  1.0
  O  O25  1  0.159  0.674  0.104  1.0
  O  O26  1  0.481  0.481  0.840  1.0
  O  O27  1  0.674  0.159  0.104  1.0
[/CIF]
.