The material structure described by Li4Mn5Fe3O16 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(2)O6 octahedra, corners with two equivalent Fe(1)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, corners with three equivalent Mn(3)O6 octahedra, and corners with four equivalent Mn(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-63°. 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 tetrahedra that share  a cornercorner with one Fe(2)O6 octahedra, corners with two equivalent Mn(4)O6 octahedra, corners with three equivalent Mn(3)O6 octahedra,  an edgeedge with one Mn(2)O6 octahedra, and edges with two equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 60-65°. 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(2)O6 octahedra, corners with two equivalent Mn(2)O6 octahedra, corners with two equivalent Mn(4)O6 octahedra, corners with three equivalent Mn(1)O6 octahedra, and corners with four equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-63°. There are four inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to one O(2), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form MnO6 octahedra that share corners with two equivalent Fe(2)O6 octahedra, corners with four equivalent Mn(4)O6 octahedra, corners with three equivalent Li(4)O4 tetrahedra,  an edgeedge with one Mn(2)O6 octahedra, and edges with two equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles are 51°. In the second Mn site, Mn(2) 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 Mn(3)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Mn(1)O6 octahedra, edges with four equivalent Fe(1)O6 octahedra, and  an edgeedge with one Li(2)O4 tetrahedra. The corner-sharing octahedral tilt angles are 50°. In the third Mn site, Mn(3) is bonded to one O(12), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form MnO6 octahedra that share corners with two equivalent Mn(2)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 tetrahedra,  an edgeedge with one Fe(2)O6 octahedra, and edges with two equivalent Mn(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-51°. In the fourth Mn site, Mn(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 MnO6 octahedra that share corners with two equivalent Mn(1)O6 octahedra,  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one Mn(3)O6 octahedra, edges with two equivalent Mn(4)O6 octahedra, and edges with two equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles are 51°. There are two 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 Mn(3)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Mn(1)O6 octahedra, edges with two equivalent Mn(2)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, and  an edgeedge with one Li(2)O4 tetrahedra. The corner-sharing octahedral tilt angles are 51°. In the second Fe site, Fe(2) 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 Mn(1)O6 octahedra,  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one Mn(3)O6 octahedra, and edges with four equivalent Mn(4)O6 octahedra. The corner-sharing octahedral tilt angles are 51°. 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(1), one Mn(4), and one Fe(2) atom. In the second O site, O(2) is bonded in a distorted rectangular see-saw-like geometry to one Li(4), one Mn(1), and two equivalent Fe(1) atoms. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Li(1), one Mn(2), and two equivalent Fe(1) atoms. In the fourth O site, O(4) is bonded in a distorted tetrahedral geometry to one Li(3), one Mn(2), and two equivalent Fe(1) atoms. In the fifth O site, O(5) is bonded to one Li(2), two equivalent Mn(4), and one Fe(2) atom to form distorted corner-sharing OLiMn2Fe tetrahedra. In the sixth O site, O(6) is bonded in a distorted rectangular see-saw-like geometry to one Li(4), one Mn(1), one Mn(2), and one Fe(1) atom. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), one Mn(3), 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), one Mn(1), and two equivalent Mn(4) atoms. In the ninth O site, O(9) is bonded to one Li(1), one Mn(3), one Mn(4), and one Fe(2) atom to form a mixture of distorted corner and edge-sharing OLiMn2Fe tetrahedra. In the tenth O site, O(10) is bonded in a distorted rectangular see-saw-like geometry to one Li(4), two equivalent Mn(4), and one Fe(2) atom. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one Mn(2), one Mn(3), and one Fe(1) atom. In the twelfth O site, O(12) is bonded in a distorted rectangular see-saw-like geometry to one Li(1), one Mn(3), and two equivalent Mn(4) atoms. is represented by the CIF file [CIF]
data_Li4Mn5Fe3O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.903
_cell_length_b   5.903
_cell_length_c   9.498
_cell_angle_alpha   88.892
_cell_angle_beta   88.892
_cell_angle_gamma   59.811
_symmetry_Int_Tables_number   1
_cell_volume   286.061
_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  0.670  0.670  0.897  1.0
  Li  Li1  1  0.998  0.998  0.996  1.0
  Li  Li2  1  1.000  1.000  0.492  1.0
  Li  Li3  1  0.337  0.337  0.396  1.0
  Mn  Mn4  1  0.666  0.666  0.485  1.0
  Mn  Mn5  1  0.827  0.827  0.213  1.0
  Mn  Mn6  1  0.331  0.331  0.985  1.0
  Mn  Mn7  1  0.662  0.171  0.713  1.0
  Mn  Mn8  1  0.171  0.662  0.713  1.0
  Fe  Fe9  1  0.826  0.338  0.212  1.0
  Fe  Fe10  1  0.338  0.826  0.212  1.0
  Fe  Fe11  1  0.170  0.170  0.712  1.0
  O  O12  1  0.834  0.330  0.600  1.0
  O  O13  1  0.519  0.519  0.344  1.0
  O  O14  1  0.673  0.673  0.104  1.0
  O  O15  1  0.991  0.991  0.306  1.0
  O  O16  1  0.995  0.995  0.808  1.0
  O  O17  1  0.330  0.834  0.600  1.0
  O  O18  1  0.959  0.527  0.343  1.0
  O  O19  1  0.527  0.959  0.343  1.0
  O  O20  1  0.166  0.166  0.094  1.0
  O  O21  1  0.837  0.837  0.605  1.0
  O  O22  1  0.486  0.044  0.842  1.0
  O  O23  1  0.044  0.486  0.842  1.0
  O  O24  1  0.341  0.341  0.608  1.0
  O  O25  1  0.664  0.161  0.100  1.0
  O  O26  1  0.481  0.481  0.841  1.0
  O  O27  1  0.161  0.664  0.100  1.0
[/CIF]
.
The material structure described by Li4Mn5Fe3O16 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(2)O6 octahedra, corners with two equivalent Fe(1)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, corners with three equivalent Mn(3)O6 octahedra, and corners with four equivalent Mn(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-63°. 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 tetrahedra that share  a cornercorner with one Fe(2)O6 octahedra, corners with two equivalent Mn(4)O6 octahedra, corners with three equivalent Mn(3)O6 octahedra,  an edgeedge with one Mn(2)O6 octahedra, and edges with two equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 60-65°. 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(2)O6 octahedra, corners with two equivalent Mn(2)O6 octahedra, corners with two equivalent Mn(4)O6 octahedra, corners with three equivalent Mn(1)O6 octahedra, and corners with four equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-63°. There are four inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to one O(2), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form MnO6 octahedra that share corners with two equivalent Fe(2)O6 octahedra, corners with four equivalent Mn(4)O6 octahedra, corners with three equivalent Li(4)O4 tetrahedra,  an edgeedge with one Mn(2)O6 octahedra, and edges with two equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles are 51°. In the second Mn site, Mn(2) 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 Mn(3)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Mn(1)O6 octahedra, edges with four equivalent Fe(1)O6 octahedra, and  an edgeedge with one Li(2)O4 tetrahedra. The corner-sharing octahedral tilt angles are 50°. In the third Mn site, Mn(3) is bonded to one O(12), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form MnO6 octahedra that share corners with two equivalent Mn(2)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 tetrahedra,  an edgeedge with one Fe(2)O6 octahedra, and edges with two equivalent Mn(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-51°. In the fourth Mn site, Mn(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 MnO6 octahedra that share corners with two equivalent Mn(1)O6 octahedra,  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one Mn(3)O6 octahedra, edges with two equivalent Mn(4)O6 octahedra, and edges with two equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles are 51°. There are two 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 Mn(3)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Mn(1)O6 octahedra, edges with two equivalent Mn(2)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, and  an edgeedge with one Li(2)O4 tetrahedra. The corner-sharing octahedral tilt angles are 51°. In the second Fe site, Fe(2) 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 Mn(1)O6 octahedra,  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one Mn(3)O6 octahedra, and edges with four equivalent Mn(4)O6 octahedra. The corner-sharing octahedral tilt angles are 51°. 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(1), one Mn(4), and one Fe(2) atom. In the second O site, O(2) is bonded in a distorted rectangular see-saw-like geometry to one Li(4), one Mn(1), and two equivalent Fe(1) atoms. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Li(1), one Mn(2), and two equivalent Fe(1) atoms. In the fourth O site, O(4) is bonded in a distorted tetrahedral geometry to one Li(3), one Mn(2), and two equivalent Fe(1) atoms. In the fifth O site, O(5) is bonded to one Li(2), two equivalent Mn(4), and one Fe(2) atom to form distorted corner-sharing OLiMn2Fe tetrahedra. In the sixth O site, O(6) is bonded in a distorted rectangular see-saw-like geometry to one Li(4), one Mn(1), one Mn(2), and one Fe(1) atom. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), one Mn(3), 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), one Mn(1), and two equivalent Mn(4) atoms. In the ninth O site, O(9) is bonded to one Li(1), one Mn(3), one Mn(4), and one Fe(2) atom to form a mixture of distorted corner and edge-sharing OLiMn2Fe tetrahedra. In the tenth O site, O(10) is bonded in a distorted rectangular see-saw-like geometry to one Li(4), two equivalent Mn(4), and one Fe(2) atom. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one Mn(2), one Mn(3), and one Fe(1) atom. In the twelfth O site, O(12) is bonded in a distorted rectangular see-saw-like geometry to one Li(1), one Mn(3), and two equivalent Mn(4) atoms. is represented by the CIF file [CIF]
data_Li4Mn5Fe3O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.903
_cell_length_b   5.903
_cell_length_c   9.498
_cell_angle_alpha   88.892
_cell_angle_beta   88.892
_cell_angle_gamma   59.811
_symmetry_Int_Tables_number   1
_cell_volume   286.061
_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  0.670  0.670  0.897  1.0
  Li  Li1  1  0.998  0.998  0.996  1.0
  Li  Li2  1  1.000  1.000  0.492  1.0
  Li  Li3  1  0.337  0.337  0.396  1.0
  Mn  Mn4  1  0.666  0.666  0.485  1.0
  Mn  Mn5  1  0.827  0.827  0.213  1.0
  Mn  Mn6  1  0.331  0.331  0.985  1.0
  Mn  Mn7  1  0.662  0.171  0.713  1.0
  Mn  Mn8  1  0.171  0.662  0.713  1.0
  Fe  Fe9  1  0.826  0.338  0.212  1.0
  Fe  Fe10  1  0.338  0.826  0.212  1.0
  Fe  Fe11  1  0.170  0.170  0.712  1.0
  O  O12  1  0.834  0.330  0.600  1.0
  O  O13  1  0.519  0.519  0.344  1.0
  O  O14  1  0.673  0.673  0.104  1.0
  O  O15  1  0.991  0.991  0.306  1.0
  O  O16  1  0.995  0.995  0.808  1.0
  O  O17  1  0.330  0.834  0.600  1.0
  O  O18  1  0.959  0.527  0.343  1.0
  O  O19  1  0.527  0.959  0.343  1.0
  O  O20  1  0.166  0.166  0.094  1.0
  O  O21  1  0.837  0.837  0.605  1.0
  O  O22  1  0.486  0.044  0.842  1.0
  O  O23  1  0.044  0.486  0.842  1.0
  O  O24  1  0.341  0.341  0.608  1.0
  O  O25  1  0.664  0.161  0.100  1.0
  O  O26  1  0.481  0.481  0.841  1.0
  O  O27  1  0.161  0.664  0.100  1.0
[/CIF]
.