The crystal structure described by Li4Mn2Fe3Ni3O16 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 Ni(1)O6 octahedra, corners with two equivalent Fe(1)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, corners with three equivalent Mn(2)O6 octahedra, and corners with four equivalent Ni(2)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 Ni(2)O6 octahedra, corners with three equivalent Mn(2)O6 octahedra,  an edgeedge with one Ni(1)O6 octahedra, and edges with two equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 61-64°. 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 tetrahedra that share  a cornercorner with one Ni(1)O6 octahedra, corners with two equivalent Fe(1)O6 octahedra, corners with three equivalent Mn(1)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra, and edges with two equivalent Ni(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 61-64°. 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 Ni(1)O6 octahedra, corners with two equivalent Ni(2)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 two 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 Ni(2)O6 octahedra, corners with three equivalent Li(3)O4 tetrahedra, corners with three equivalent Li(4)O4 tetrahedra,  an edgeedge with one Ni(1)O6 octahedra, and edges with two equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 48-53°. In the second Mn site, Mn(2) 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 Ni(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 tetrahedra,  an edgeedge with one Fe(2)O6 octahedra, and edges with two equivalent Ni(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 49-52°. 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(2)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(3)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Mn(1)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, edges with two equivalent Ni(1)O6 octahedra, and  an edgeedge with one Li(2)O4 tetrahedra. The corner-sharing octahedral tilt angles are 49°. 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(2)O6 octahedra, edges with four equivalent Ni(2)O6 octahedra, and  an edgeedge with one Li(3)O4 tetrahedra. The corner-sharing octahedral tilt angles are 48°. There are two inequivalent Ni sites. In the first Ni site, Ni(1) is bonded to one O(3), one O(4), two equivalent O(11), and two equivalent O(6) atoms to form NiO6 octahedra that share corners with two equivalent Mn(2)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(3)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 52°. In the second Ni site, Ni(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 NiO6 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(2)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, edges with two equivalent Ni(2)O6 octahedra, and  an edgeedge with one Li(3)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 52-53°. 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(1), one Fe(2), and one Ni(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), two equivalent Fe(1), and one Ni(1) atom. In the fourth O site, O(4) is bonded in a tetrahedral geometry to one Li(3), two equivalent Fe(1), and one Ni(1) atom. In the fifth O site, O(5) is bonded to one Li(2), one Fe(2), and two equivalent Ni(2) atoms to form OLiFeNi2 tetrahedra that share corners with two equivalent O(12)LiMnNi2 tetrahedra and corners with three equivalent O(10)LiFeNi2 trigonal pyramids. 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 Fe(1), and one Ni(1) atom. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), one Mn(2), 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 Ni(2) atoms. In the ninth O site, O(9) is bonded in a distorted rectangular see-saw-like geometry to one Li(1), one Mn(2), one Fe(2), and one Ni(2) atom. In the tenth O site, O(10) is bonded to one Li(4), one Fe(2), and two equivalent Ni(2) atoms to form distorted OLiFeNi2 trigonal pyramids that share corners with three equivalent O(5)LiFeNi2 tetrahedra and  an edgeedge with one O(12)LiMnNi2 tetrahedra. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one Mn(2), one Fe(1), and one Ni(1) atom. In the twelfth O site, O(12) is bonded to one Li(1), one Mn(2), and two equivalent Ni(2) atoms to form a mixture of distorted edge and corner-sharing OLiMnNi2 tetrahedra. is represented by the CIF file [CIF]
data_Li4Mn2Fe3Ni3O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.831
_cell_length_b   5.831
_cell_length_c   9.378
_cell_angle_alpha   88.511
_cell_angle_beta   88.511
_cell_angle_gamma   59.213
_symmetry_Int_Tables_number   1
_cell_volume   273.770
_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  0.662  0.662  0.105  1.0
  Li  Li1  1  0.997  0.997  0.008  1.0
  Li  Li2  1  0.998  0.998  0.505  1.0
  Li  Li3  1  0.334  0.334  0.599  1.0
  Mn  Mn4  1  0.672  0.672  0.513  1.0
  Mn  Mn5  1  0.332  0.332  0.016  1.0
  Fe  Fe6  1  0.339  0.830  0.787  1.0
  Fe  Fe7  1  0.830  0.339  0.787  1.0
  Fe  Fe8  1  0.169  0.169  0.286  1.0
  Ni  Ni9  1  0.829  0.829  0.789  1.0
  Ni  Ni10  1  0.167  0.659  0.287  1.0
  Ni  Ni11  1  0.659  0.167  0.287  1.0
  O  O12  1  0.339  0.845  0.404  1.0
  O  O13  1  0.520  0.520  0.652  1.0
  O  O14  1  0.672  0.672  0.894  1.0
  O  O15  1  0.993  0.993  0.696  1.0
  O  O16  1  0.994  0.994  0.197  1.0
  O  O17  1  0.845  0.339  0.404  1.0
  O  O18  1  0.519  0.961  0.651  1.0
  O  O19  1  0.961  0.519  0.651  1.0
  O  O20  1  0.170  0.170  0.900  1.0
  O  O21  1  0.838  0.838  0.405  1.0
  O  O22  1  0.035  0.469  0.153  1.0
  O  O23  1  0.469  0.035  0.153  1.0
  O  O24  1  0.338  0.338  0.389  1.0
  O  O25  1  0.171  0.664  0.908  1.0
  O  O26  1  0.475  0.475  0.157  1.0
  O  O27  1  0.664  0.171  0.908  1.0
[/CIF]
.
The crystal structure described by Li4Mn2Fe3Ni3O16 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 Ni(1)O6 octahedra, corners with two equivalent Fe(1)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, corners with three equivalent Mn(2)O6 octahedra, and corners with four equivalent Ni(2)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 Ni(2)O6 octahedra, corners with three equivalent Mn(2)O6 octahedra,  an edgeedge with one Ni(1)O6 octahedra, and edges with two equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 61-64°. 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 tetrahedra that share  a cornercorner with one Ni(1)O6 octahedra, corners with two equivalent Fe(1)O6 octahedra, corners with three equivalent Mn(1)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra, and edges with two equivalent Ni(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 61-64°. 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 Ni(1)O6 octahedra, corners with two equivalent Ni(2)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 two 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 Ni(2)O6 octahedra, corners with three equivalent Li(3)O4 tetrahedra, corners with three equivalent Li(4)O4 tetrahedra,  an edgeedge with one Ni(1)O6 octahedra, and edges with two equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 48-53°. In the second Mn site, Mn(2) 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 Ni(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 tetrahedra,  an edgeedge with one Fe(2)O6 octahedra, and edges with two equivalent Ni(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 49-52°. 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(2)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(3)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Mn(1)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, edges with two equivalent Ni(1)O6 octahedra, and  an edgeedge with one Li(2)O4 tetrahedra. The corner-sharing octahedral tilt angles are 49°. 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(2)O6 octahedra, edges with four equivalent Ni(2)O6 octahedra, and  an edgeedge with one Li(3)O4 tetrahedra. The corner-sharing octahedral tilt angles are 48°. There are two inequivalent Ni sites. In the first Ni site, Ni(1) is bonded to one O(3), one O(4), two equivalent O(11), and two equivalent O(6) atoms to form NiO6 octahedra that share corners with two equivalent Mn(2)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(3)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 52°. In the second Ni site, Ni(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 NiO6 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(2)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, edges with two equivalent Ni(2)O6 octahedra, and  an edgeedge with one Li(3)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 52-53°. 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(1), one Fe(2), and one Ni(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), two equivalent Fe(1), and one Ni(1) atom. In the fourth O site, O(4) is bonded in a tetrahedral geometry to one Li(3), two equivalent Fe(1), and one Ni(1) atom. In the fifth O site, O(5) is bonded to one Li(2), one Fe(2), and two equivalent Ni(2) atoms to form OLiFeNi2 tetrahedra that share corners with two equivalent O(12)LiMnNi2 tetrahedra and corners with three equivalent O(10)LiFeNi2 trigonal pyramids. 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 Fe(1), and one Ni(1) atom. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), one Mn(2), 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 Ni(2) atoms. In the ninth O site, O(9) is bonded in a distorted rectangular see-saw-like geometry to one Li(1), one Mn(2), one Fe(2), and one Ni(2) atom. In the tenth O site, O(10) is bonded to one Li(4), one Fe(2), and two equivalent Ni(2) atoms to form distorted OLiFeNi2 trigonal pyramids that share corners with three equivalent O(5)LiFeNi2 tetrahedra and  an edgeedge with one O(12)LiMnNi2 tetrahedra. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one Mn(2), one Fe(1), and one Ni(1) atom. In the twelfth O site, O(12) is bonded to one Li(1), one Mn(2), and two equivalent Ni(2) atoms to form a mixture of distorted edge and corner-sharing OLiMnNi2 tetrahedra. is represented by the CIF file [CIF]
data_Li4Mn2Fe3Ni3O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.831
_cell_length_b   5.831
_cell_length_c   9.378
_cell_angle_alpha   88.511
_cell_angle_beta   88.511
_cell_angle_gamma   59.213
_symmetry_Int_Tables_number   1
_cell_volume   273.770
_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  0.662  0.662  0.105  1.0
  Li  Li1  1  0.997  0.997  0.008  1.0
  Li  Li2  1  0.998  0.998  0.505  1.0
  Li  Li3  1  0.334  0.334  0.599  1.0
  Mn  Mn4  1  0.672  0.672  0.513  1.0
  Mn  Mn5  1  0.332  0.332  0.016  1.0
  Fe  Fe6  1  0.339  0.830  0.787  1.0
  Fe  Fe7  1  0.830  0.339  0.787  1.0
  Fe  Fe8  1  0.169  0.169  0.286  1.0
  Ni  Ni9  1  0.829  0.829  0.789  1.0
  Ni  Ni10  1  0.167  0.659  0.287  1.0
  Ni  Ni11  1  0.659  0.167  0.287  1.0
  O  O12  1  0.339  0.845  0.404  1.0
  O  O13  1  0.520  0.520  0.652  1.0
  O  O14  1  0.672  0.672  0.894  1.0
  O  O15  1  0.993  0.993  0.696  1.0
  O  O16  1  0.994  0.994  0.197  1.0
  O  O17  1  0.845  0.339  0.404  1.0
  O  O18  1  0.519  0.961  0.651  1.0
  O  O19  1  0.961  0.519  0.651  1.0
  O  O20  1  0.170  0.170  0.900  1.0
  O  O21  1  0.838  0.838  0.405  1.0
  O  O22  1  0.035  0.469  0.153  1.0
  O  O23  1  0.469  0.035  0.153  1.0
  O  O24  1  0.338  0.338  0.389  1.0
  O  O25  1  0.171  0.664  0.908  1.0
  O  O26  1  0.475  0.475  0.157  1.0
  O  O27  1  0.664  0.171  0.908  1.0
[/CIF]
.