The crystal structure described by Li4Mn3Fe5O16 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 Mn(1)O6 octahedra, corners with two equivalent Fe(1)O6 octahedra, corners with two equivalent Fe(3)O6 octahedra, corners with three equivalent Fe(4)O6 octahedra, and corners with four equivalent Mn(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-62°. In the second Li site, Li(2) is bonded to one O(5), one O(7), and two equivalent O(11) atoms to form distorted LiO4 trigonal pyramids that share  a cornercorner with one Fe(3)O6 octahedra, corners with two equivalent Mn(2)O6 octahedra, corners with three equivalent Fe(4)O6 octahedra,  an edgeedge with one Mn(1)O6 octahedra, and edges with two equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 62-63°. In the third Li site, Li(3) is bonded in a rectangular see-saw-like geometry to one O(4), one O(8), and two equivalent O(1) atoms. 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 Fe(3)O6 octahedra, corners with two equivalent Mn(1)O6 octahedra, corners with two equivalent Mn(2)O6 octahedra, corners with three equivalent Fe(2)O6 octahedra, and corners with four equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-62°. There are two inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to one O(3), one O(4), two equivalent O(11), and two equivalent O(6) atoms to form MnO6 octahedra that share corners with two equivalent Fe(4)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Fe(2)O6 octahedra, edges with four equivalent Fe(1)O6 octahedra, and  an edgeedge with one Li(2)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 50°. In the second Mn site, Mn(2) 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 MnO6 octahedra that share corners with two equivalent Fe(2)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 trigonal pyramid,  an edgeedge with one Fe(4)O6 octahedra, edges with two equivalent Mn(2)O6 octahedra, and edges with two equivalent Fe(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-53°. There are four inequivalent Fe sites. In the first Fe site, Fe(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 FeO6 octahedra that share corners with two equivalent Fe(4)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Fe(2)O6 octahedra, edges with two equivalent Mn(1)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, and  an edgeedge with one Li(2)O4 trigonal pyramid. The corner-sharing octahedral tilt angles range from 52-53°. In the second Fe site, Fe(2) 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 Fe(3)O6 octahedra, corners with four equivalent Mn(2)O6 octahedra, corners with three equivalent Li(4)O4 tetrahedra,  an edgeedge with one Mn(1)O6 octahedra, and edges with two equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-53°. In the third Fe site, Fe(3) is bonded to one O(10), one O(5), two equivalent O(1), and two equivalent O(9) atoms to form FeO6 octahedra that share corners with two equivalent Fe(2)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 trigonal pyramid,  an edgeedge with one Fe(4)O6 octahedra, and edges with four equivalent Mn(2)O6 octahedra. The corner-sharing octahedral tilt angles are 52°. In the fourth Fe site, Fe(4) 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 Mn(1)O6 octahedra, corners with four equivalent Fe(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra, corners with three equivalent Li(2)O4 trigonal pyramids,  an edgeedge with one Fe(3)O6 octahedra, and edges with two equivalent Mn(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-53°. 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 Mn(2), one Fe(2), and one Fe(3) atom. In the second O site, O(2) is bonded to one Li(4), one Fe(2), and two equivalent Fe(1) atoms to form distorted OLiFe3 tetrahedra that share corners with two equivalent O(4)LiMnFe2 tetrahedra,  a cornercorner with one O(10)LiMn2Fe trigonal pyramid, corners with two equivalent O(6)LiMnFe2 trigonal pyramids, and edges with two equivalent O(6)LiMnFe2 trigonal pyramids. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Li(1), one Mn(1), and two equivalent Fe(1) atoms. In the fourth O site, O(4) is bonded to one Li(3), one Mn(1), and two equivalent Fe(1) atoms to form distorted OLiMnFe2 tetrahedra that share corners with two equivalent O(2)LiFe3 tetrahedra and corners with four equivalent O(6)LiMnFe2 trigonal pyramids. In the fifth O site, O(5) is bonded to one Li(2), two equivalent Mn(2), and one Fe(3) atom to form distorted OLiMn2Fe tetrahedra that share corners with two equivalent O(12)LiMn2Fe tetrahedra, corners with four equivalent O(9)LiMnFe2 tetrahedra, and corners with three equivalent O(10)LiMn2Fe trigonal pyramids. In the sixth O site, O(6) is bonded to one Li(4), one Mn(1), one Fe(1), and one Fe(2) atom to form distorted OLiMnFe2 trigonal pyramids that share  a cornercorner with one O(2)LiFe3 tetrahedra, corners with two equivalent O(4)LiMnFe2 tetrahedra,  a cornercorner with one O(10)LiMn2Fe trigonal pyramid,  a cornercorner with one O(6)LiMnFe2 trigonal pyramid,  an edgeedge with one O(2)LiFe3 tetrahedra, and  an edgeedge with one O(6)LiMnFe2 trigonal pyramid. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), one Fe(4), and two equivalent Fe(1) atoms. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Li(3), two equivalent Mn(2), and one Fe(2) atom. In the ninth O site, O(9) is bonded to one Li(1), one Mn(2), one Fe(3), and one Fe(4) atom to form distorted OLiMnFe2 tetrahedra that share  a cornercorner with one O(12)LiMn2Fe tetrahedra,  a cornercorner with one O(9)LiMnFe2 tetrahedra, corners with two equivalent O(5)LiMn2Fe tetrahedra,  an edgeedge with one O(12)LiMn2Fe tetrahedra,  an edgeedge with one O(9)LiMnFe2 tetrahedra, and  an edgeedge with one O(10)LiMn2Fe trigonal pyramid. In the tenth O site, O(10) is bonded to one Li(4), two equivalent Mn(2), and one Fe(3) atom to form distorted OLiMn2Fe trigonal pyramids that share  a cornercorner with one O(2)LiFe3 tetrahedra, corners with three equivalent O(5)LiMn2Fe tetrahedra, corners with two equivalent O(6)LiMnFe2 trigonal pyramids,  an edgeedge with one O(12)LiMn2Fe tetrahedra, and edges with two equivalent O(9)LiMnFe2 tetrahedra. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one Mn(1), one Fe(1), and one Fe(4) atom. In the twelfth O site, O(12) is bonded to one Li(1), two equivalent Mn(2), and one Fe(4) atom to form distorted OLiMn2Fe tetrahedra that share corners with two equivalent O(5)LiMn2Fe tetrahedra, corners with two equivalent O(9)LiMnFe2 tetrahedra, edges with two equivalent O(9)LiMnFe2 tetrahedra, and  an edgeedge with one O(10)LiMn2Fe trigonal pyramid. is represented by the CIF file [CIF]
data_Li4Mn3Fe5O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.852
_cell_length_b   5.852
_cell_length_c   9.540
_cell_angle_alpha   89.832
_cell_angle_beta   89.832
_cell_angle_gamma   59.968
_symmetry_Int_Tables_number   1
_cell_volume   282.891
_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  0.891  1.0
  Li  Li1  1  0.998  0.998  0.996  1.0
  Li  Li2  1  0.001  0.001  0.498  1.0
  Li  Li3  1  0.334  0.334  0.393  1.0
  Mn  Mn4  1  0.830  0.830  0.215  1.0
  Mn  Mn5  1  0.662  0.169  0.715  1.0
  Mn  Mn6  1  0.169  0.662  0.715  1.0
  Fe  Fe7  1  0.830  0.339  0.215  1.0
  Fe  Fe8  1  0.664  0.664  0.493  1.0
  Fe  Fe9  1  0.339  0.830  0.215  1.0
  Fe  Fe10  1  0.170  0.170  0.714  1.0
  Fe  Fe11  1  0.331  0.331  0.989  1.0
  O  O12  1  0.838  0.322  0.604  1.0
  O  O13  1  0.518  0.518  0.341  1.0
  O  O14  1  0.672  0.672  0.103  1.0
  O  O15  1  0.994  0.994  0.311  1.0
  O  O16  1  0.997  0.997  0.809  1.0
  O  O17  1  0.322  0.838  0.604  1.0
  O  O18  1  0.964  0.527  0.338  1.0
  O  O19  1  0.527  0.964  0.338  1.0
  O  O20  1  0.163  0.163  0.098  1.0
  O  O21  1  0.839  0.839  0.604  1.0
  O  O22  1  0.484  0.039  0.833  1.0
  O  O23  1  0.039  0.484  0.833  1.0
  O  O24  1  0.338  0.338  0.609  1.0
  O  O25  1  0.672  0.156  0.101  1.0
  O  O26  1  0.482  0.482  0.834  1.0
  O  O27  1  0.156  0.672  0.101  1.0
[/CIF]
.
The crystal structure described by Li4Mn3Fe5O16 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 Mn(1)O6 octahedra, corners with two equivalent Fe(1)O6 octahedra, corners with two equivalent Fe(3)O6 octahedra, corners with three equivalent Fe(4)O6 octahedra, and corners with four equivalent Mn(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-62°. In the second Li site, Li(2) is bonded to one O(5), one O(7), and two equivalent O(11) atoms to form distorted LiO4 trigonal pyramids that share  a cornercorner with one Fe(3)O6 octahedra, corners with two equivalent Mn(2)O6 octahedra, corners with three equivalent Fe(4)O6 octahedra,  an edgeedge with one Mn(1)O6 octahedra, and edges with two equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 62-63°. In the third Li site, Li(3) is bonded in a rectangular see-saw-like geometry to one O(4), one O(8), and two equivalent O(1) atoms. 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 Fe(3)O6 octahedra, corners with two equivalent Mn(1)O6 octahedra, corners with two equivalent Mn(2)O6 octahedra, corners with three equivalent Fe(2)O6 octahedra, and corners with four equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-62°. There are two inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to one O(3), one O(4), two equivalent O(11), and two equivalent O(6) atoms to form MnO6 octahedra that share corners with two equivalent Fe(4)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Fe(2)O6 octahedra, edges with four equivalent Fe(1)O6 octahedra, and  an edgeedge with one Li(2)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 50°. In the second Mn site, Mn(2) 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 MnO6 octahedra that share corners with two equivalent Fe(2)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 trigonal pyramid,  an edgeedge with one Fe(4)O6 octahedra, edges with two equivalent Mn(2)O6 octahedra, and edges with two equivalent Fe(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-53°. There are four inequivalent Fe sites. In the first Fe site, Fe(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 FeO6 octahedra that share corners with two equivalent Fe(4)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Fe(2)O6 octahedra, edges with two equivalent Mn(1)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, and  an edgeedge with one Li(2)O4 trigonal pyramid. The corner-sharing octahedral tilt angles range from 52-53°. In the second Fe site, Fe(2) 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 Fe(3)O6 octahedra, corners with four equivalent Mn(2)O6 octahedra, corners with three equivalent Li(4)O4 tetrahedra,  an edgeedge with one Mn(1)O6 octahedra, and edges with two equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-53°. In the third Fe site, Fe(3) is bonded to one O(10), one O(5), two equivalent O(1), and two equivalent O(9) atoms to form FeO6 octahedra that share corners with two equivalent Fe(2)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 trigonal pyramid,  an edgeedge with one Fe(4)O6 octahedra, and edges with four equivalent Mn(2)O6 octahedra. The corner-sharing octahedral tilt angles are 52°. In the fourth Fe site, Fe(4) 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 Mn(1)O6 octahedra, corners with four equivalent Fe(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra, corners with three equivalent Li(2)O4 trigonal pyramids,  an edgeedge with one Fe(3)O6 octahedra, and edges with two equivalent Mn(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-53°. 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 Mn(2), one Fe(2), and one Fe(3) atom. In the second O site, O(2) is bonded to one Li(4), one Fe(2), and two equivalent Fe(1) atoms to form distorted OLiFe3 tetrahedra that share corners with two equivalent O(4)LiMnFe2 tetrahedra,  a cornercorner with one O(10)LiMn2Fe trigonal pyramid, corners with two equivalent O(6)LiMnFe2 trigonal pyramids, and edges with two equivalent O(6)LiMnFe2 trigonal pyramids. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Li(1), one Mn(1), and two equivalent Fe(1) atoms. In the fourth O site, O(4) is bonded to one Li(3), one Mn(1), and two equivalent Fe(1) atoms to form distorted OLiMnFe2 tetrahedra that share corners with two equivalent O(2)LiFe3 tetrahedra and corners with four equivalent O(6)LiMnFe2 trigonal pyramids. In the fifth O site, O(5) is bonded to one Li(2), two equivalent Mn(2), and one Fe(3) atom to form distorted OLiMn2Fe tetrahedra that share corners with two equivalent O(12)LiMn2Fe tetrahedra, corners with four equivalent O(9)LiMnFe2 tetrahedra, and corners with three equivalent O(10)LiMn2Fe trigonal pyramids. In the sixth O site, O(6) is bonded to one Li(4), one Mn(1), one Fe(1), and one Fe(2) atom to form distorted OLiMnFe2 trigonal pyramids that share  a cornercorner with one O(2)LiFe3 tetrahedra, corners with two equivalent O(4)LiMnFe2 tetrahedra,  a cornercorner with one O(10)LiMn2Fe trigonal pyramid,  a cornercorner with one O(6)LiMnFe2 trigonal pyramid,  an edgeedge with one O(2)LiFe3 tetrahedra, and  an edgeedge with one O(6)LiMnFe2 trigonal pyramid. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), one Fe(4), and two equivalent Fe(1) atoms. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Li(3), two equivalent Mn(2), and one Fe(2) atom. In the ninth O site, O(9) is bonded to one Li(1), one Mn(2), one Fe(3), and one Fe(4) atom to form distorted OLiMnFe2 tetrahedra that share  a cornercorner with one O(12)LiMn2Fe tetrahedra,  a cornercorner with one O(9)LiMnFe2 tetrahedra, corners with two equivalent O(5)LiMn2Fe tetrahedra,  an edgeedge with one O(12)LiMn2Fe tetrahedra,  an edgeedge with one O(9)LiMnFe2 tetrahedra, and  an edgeedge with one O(10)LiMn2Fe trigonal pyramid. In the tenth O site, O(10) is bonded to one Li(4), two equivalent Mn(2), and one Fe(3) atom to form distorted OLiMn2Fe trigonal pyramids that share  a cornercorner with one O(2)LiFe3 tetrahedra, corners with three equivalent O(5)LiMn2Fe tetrahedra, corners with two equivalent O(6)LiMnFe2 trigonal pyramids,  an edgeedge with one O(12)LiMn2Fe tetrahedra, and edges with two equivalent O(9)LiMnFe2 tetrahedra. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one Mn(1), one Fe(1), and one Fe(4) atom. In the twelfth O site, O(12) is bonded to one Li(1), two equivalent Mn(2), and one Fe(4) atom to form distorted OLiMn2Fe tetrahedra that share corners with two equivalent O(5)LiMn2Fe tetrahedra, corners with two equivalent O(9)LiMnFe2 tetrahedra, edges with two equivalent O(9)LiMnFe2 tetrahedra, and  an edgeedge with one O(10)LiMn2Fe trigonal pyramid. is represented by the CIF file [CIF]
data_Li4Mn3Fe5O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.852
_cell_length_b   5.852
_cell_length_c   9.540
_cell_angle_alpha   89.832
_cell_angle_beta   89.832
_cell_angle_gamma   59.968
_symmetry_Int_Tables_number   1
_cell_volume   282.891
_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  0.891  1.0
  Li  Li1  1  0.998  0.998  0.996  1.0
  Li  Li2  1  0.001  0.001  0.498  1.0
  Li  Li3  1  0.334  0.334  0.393  1.0
  Mn  Mn4  1  0.830  0.830  0.215  1.0
  Mn  Mn5  1  0.662  0.169  0.715  1.0
  Mn  Mn6  1  0.169  0.662  0.715  1.0
  Fe  Fe7  1  0.830  0.339  0.215  1.0
  Fe  Fe8  1  0.664  0.664  0.493  1.0
  Fe  Fe9  1  0.339  0.830  0.215  1.0
  Fe  Fe10  1  0.170  0.170  0.714  1.0
  Fe  Fe11  1  0.331  0.331  0.989  1.0
  O  O12  1  0.838  0.322  0.604  1.0
  O  O13  1  0.518  0.518  0.341  1.0
  O  O14  1  0.672  0.672  0.103  1.0
  O  O15  1  0.994  0.994  0.311  1.0
  O  O16  1  0.997  0.997  0.809  1.0
  O  O17  1  0.322  0.838  0.604  1.0
  O  O18  1  0.964  0.527  0.338  1.0
  O  O19  1  0.527  0.964  0.338  1.0
  O  O20  1  0.163  0.163  0.098  1.0
  O  O21  1  0.839  0.839  0.604  1.0
  O  O22  1  0.484  0.039  0.833  1.0
  O  O23  1  0.039  0.484  0.833  1.0
  O  O24  1  0.338  0.338  0.609  1.0
  O  O25  1  0.672  0.156  0.101  1.0
  O  O26  1  0.482  0.482  0.834  1.0
  O  O27  1  0.156  0.672  0.101  1.0
[/CIF]
.