The crystal structure described by Li4Mn2Fe3Sn3O16 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(1)O6 octahedra, corners with two equivalent Sn(1)O6 octahedra, corners with two equivalent Sn(2)O6 octahedra, corners with three equivalent Mn(2)O6 octahedra, and corners with four equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-65°. 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 Sn(2)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, corners with three equivalent Mn(2)O6 octahedra,  an edgeedge with one Fe(1)O6 octahedra, and edges with two equivalent Sn(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-65°. In the third Li site, Li(3) is bonded in a distorted 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 Sn(2)O6 octahedra, corners with two equivalent Fe(1)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, corners with three equivalent Mn(1)O6 octahedra, and corners with four equivalent Sn(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(2), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form MnO6 octahedra that share corners with two equivalent Sn(2)O6 octahedra, corners with four equivalent Fe(2)O6 octahedra, corners with three equivalent Li(4)O4 tetrahedra,  an edgeedge with one Fe(1)O6 octahedra, and edges with two equivalent Sn(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 49-55°. 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 Fe(1)O6 octahedra, corners with four equivalent Sn(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra, corners with three equivalent Li(2)O4 trigonal pyramids,  an edgeedge with one Sn(2)O6 octahedra, and edges with two equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 48-54°. There are two inequivalent Fe sites. In the first Fe site, Fe(1) 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 Mn(2)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 Sn(1)O6 octahedra, and  an edgeedge with one Li(2)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 48°. In the second Fe site, Fe(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 FeO6 octahedra that share corners with two equivalent Mn(1)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 Mn(2)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, and edges with two equivalent Sn(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 49-51°. There are two inequivalent Sn sites. In the first Sn site, Sn(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 SnO6 octahedra that share corners with two equivalent Mn(2)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 Fe(1)O6 octahedra, edges with two equivalent Sn(1)O6 octahedra, and  an edgeedge with one Li(2)O4 trigonal pyramid. The corner-sharing octahedral tilt angles range from 53-54°. In the second Sn site, Sn(2) is bonded to one O(10), one O(5), two equivalent O(1), and two equivalent O(9) atoms to form SnO6 octahedra that share corners with two equivalent Mn(1)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 Mn(2)O6 octahedra, and edges with four equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles are 55°. 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 Sn(2) atom. In the second O site, O(2) is bonded to one Li(4), one Mn(1), and two equivalent Sn(1) atoms to form distorted OLiMnSn2 tetrahedra that share corners with two equivalent O(4)LiFeSn2 tetrahedra,  a cornercorner with one O(10)LiFe2Sn trigonal pyramid, corners with two equivalent O(6)LiMnFeSn trigonal pyramids, and edges with two equivalent O(6)LiMnFeSn trigonal pyramids. In the third O site, O(3) is bonded in a distorted rectangular see-saw-like geometry to one Li(1), one Fe(1), and two equivalent Sn(1) atoms. In the fourth O site, O(4) is bonded to one Li(3), one Fe(1), and two equivalent Sn(1) atoms to form OLiFeSn2 tetrahedra that share corners with two equivalent O(2)LiMnSn2 tetrahedra and corners with four equivalent O(6)LiMnFeSn trigonal pyramids. In the fifth O site, O(5) is bonded to one Li(2), two equivalent Fe(2), and one Sn(2) atom to form distorted OLiFe2Sn tetrahedra that share corners with two equivalent O(12)LiMnFe2 tetrahedra and corners with three equivalent O(10)LiFe2Sn trigonal pyramids. In the sixth O site, O(6) is bonded to one Li(4), one Mn(1), one Fe(1), and one Sn(1) atom to form distorted OLiMnFeSn trigonal pyramids that share  a cornercorner with one O(2)LiMnSn2 tetrahedra, corners with two equivalent O(4)LiFeSn2 tetrahedra,  a cornercorner with one O(10)LiFe2Sn trigonal pyramid,  a cornercorner with one O(6)LiMnFeSn trigonal pyramid,  an edgeedge with one O(2)LiMnSn2 tetrahedra, and  an edgeedge with one O(6)LiMnFeSn trigonal pyramid. 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 Sn(1) atoms. In the eighth O site, O(8) is bonded in a distorted rectangular see-saw-like geometry to one Li(3), one Mn(1), and two equivalent Fe(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 Sn(2) atom. In the tenth O site, O(10) is bonded to one Li(4), two equivalent Fe(2), and one Sn(2) atom to form distorted OLiFe2Sn trigonal pyramids that share  a cornercorner with one O(2)LiMnSn2 tetrahedra, corners with three equivalent O(5)LiFe2Sn tetrahedra, corners with two equivalent O(6)LiMnFeSn trigonal pyramids, and  an edgeedge with one O(12)LiMnFe2 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 Sn(1) atom. In the twelfth O site, O(12) is bonded to one Li(1), one Mn(2), and two equivalent Fe(2) atoms to form a mixture of distorted corner and edge-sharing OLiMnFe2 tetrahedra. is represented by the CIF file [CIF]
data_Li4Mn2Fe3Sn3O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.101
_cell_length_b   6.101
_cell_length_c   9.681
_cell_angle_alpha   88.983
_cell_angle_beta   88.983
_cell_angle_gamma   60.653
_symmetry_Int_Tables_number   1
_cell_volume   314.074
_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  0.675  0.675  0.107  1.0
  Li  Li1  1  0.985  0.985  0.010  1.0
  Li  Li2  1  0.986  0.986  0.502  1.0
  Li  Li3  1  0.340  0.340  0.601  1.0
  Mn  Mn4  1  0.672  0.672  0.508  1.0
  Mn  Mn5  1  0.344  0.344  0.020  1.0
  Fe  Fe6  1  0.834  0.834  0.781  1.0
  Fe  Fe7  1  0.169  0.668  0.287  1.0
  Fe  Fe8  1  0.668  0.169  0.287  1.0
  Sn  Sn9  1  0.342  0.843  0.790  1.0
  Sn  Sn10  1  0.843  0.342  0.790  1.0
  Sn  Sn11  1  0.171  0.171  0.288  1.0
  O  O12  1  0.318  0.839  0.399  1.0
  O  O13  1  0.529  0.529  0.654  1.0
  O  O14  1  0.675  0.675  0.903  1.0
  O  O15  1  0.004  0.004  0.689  1.0
  O  O16  1  0.998  0.998  0.191  1.0
  O  O17  1  0.839  0.318  0.399  1.0
  O  O18  1  0.529  0.973  0.661  1.0
  O  O19  1  0.973  0.529  0.661  1.0
  O  O20  1  0.167  0.167  0.912  1.0
  O  O21  1  0.828  0.828  0.395  1.0
  O  O22  1  0.050  0.484  0.150  1.0
  O  O23  1  0.484  0.050  0.150  1.0
  O  O24  1  0.339  0.339  0.395  1.0
  O  O25  1  0.166  0.673  0.905  1.0
  O  O26  1  0.482  0.482  0.150  1.0
  O  O27  1  0.673  0.166  0.905  1.0
[/CIF]
.
The crystal structure described by Li4Mn2Fe3Sn3O16 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(1)O6 octahedra, corners with two equivalent Sn(1)O6 octahedra, corners with two equivalent Sn(2)O6 octahedra, corners with three equivalent Mn(2)O6 octahedra, and corners with four equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-65°. 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 Sn(2)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, corners with three equivalent Mn(2)O6 octahedra,  an edgeedge with one Fe(1)O6 octahedra, and edges with two equivalent Sn(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-65°. In the third Li site, Li(3) is bonded in a distorted 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 Sn(2)O6 octahedra, corners with two equivalent Fe(1)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, corners with three equivalent Mn(1)O6 octahedra, and corners with four equivalent Sn(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(2), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form MnO6 octahedra that share corners with two equivalent Sn(2)O6 octahedra, corners with four equivalent Fe(2)O6 octahedra, corners with three equivalent Li(4)O4 tetrahedra,  an edgeedge with one Fe(1)O6 octahedra, and edges with two equivalent Sn(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 49-55°. 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 Fe(1)O6 octahedra, corners with four equivalent Sn(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra, corners with three equivalent Li(2)O4 trigonal pyramids,  an edgeedge with one Sn(2)O6 octahedra, and edges with two equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 48-54°. There are two inequivalent Fe sites. In the first Fe site, Fe(1) 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 Mn(2)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 Sn(1)O6 octahedra, and  an edgeedge with one Li(2)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 48°. In the second Fe site, Fe(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 FeO6 octahedra that share corners with two equivalent Mn(1)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 Mn(2)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, and edges with two equivalent Sn(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 49-51°. There are two inequivalent Sn sites. In the first Sn site, Sn(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 SnO6 octahedra that share corners with two equivalent Mn(2)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 Fe(1)O6 octahedra, edges with two equivalent Sn(1)O6 octahedra, and  an edgeedge with one Li(2)O4 trigonal pyramid. The corner-sharing octahedral tilt angles range from 53-54°. In the second Sn site, Sn(2) is bonded to one O(10), one O(5), two equivalent O(1), and two equivalent O(9) atoms to form SnO6 octahedra that share corners with two equivalent Mn(1)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 Mn(2)O6 octahedra, and edges with four equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles are 55°. 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 Sn(2) atom. In the second O site, O(2) is bonded to one Li(4), one Mn(1), and two equivalent Sn(1) atoms to form distorted OLiMnSn2 tetrahedra that share corners with two equivalent O(4)LiFeSn2 tetrahedra,  a cornercorner with one O(10)LiFe2Sn trigonal pyramid, corners with two equivalent O(6)LiMnFeSn trigonal pyramids, and edges with two equivalent O(6)LiMnFeSn trigonal pyramids. In the third O site, O(3) is bonded in a distorted rectangular see-saw-like geometry to one Li(1), one Fe(1), and two equivalent Sn(1) atoms. In the fourth O site, O(4) is bonded to one Li(3), one Fe(1), and two equivalent Sn(1) atoms to form OLiFeSn2 tetrahedra that share corners with two equivalent O(2)LiMnSn2 tetrahedra and corners with four equivalent O(6)LiMnFeSn trigonal pyramids. In the fifth O site, O(5) is bonded to one Li(2), two equivalent Fe(2), and one Sn(2) atom to form distorted OLiFe2Sn tetrahedra that share corners with two equivalent O(12)LiMnFe2 tetrahedra and corners with three equivalent O(10)LiFe2Sn trigonal pyramids. In the sixth O site, O(6) is bonded to one Li(4), one Mn(1), one Fe(1), and one Sn(1) atom to form distorted OLiMnFeSn trigonal pyramids that share  a cornercorner with one O(2)LiMnSn2 tetrahedra, corners with two equivalent O(4)LiFeSn2 tetrahedra,  a cornercorner with one O(10)LiFe2Sn trigonal pyramid,  a cornercorner with one O(6)LiMnFeSn trigonal pyramid,  an edgeedge with one O(2)LiMnSn2 tetrahedra, and  an edgeedge with one O(6)LiMnFeSn trigonal pyramid. 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 Sn(1) atoms. In the eighth O site, O(8) is bonded in a distorted rectangular see-saw-like geometry to one Li(3), one Mn(1), and two equivalent Fe(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 Sn(2) atom. In the tenth O site, O(10) is bonded to one Li(4), two equivalent Fe(2), and one Sn(2) atom to form distorted OLiFe2Sn trigonal pyramids that share  a cornercorner with one O(2)LiMnSn2 tetrahedra, corners with three equivalent O(5)LiFe2Sn tetrahedra, corners with two equivalent O(6)LiMnFeSn trigonal pyramids, and  an edgeedge with one O(12)LiMnFe2 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 Sn(1) atom. In the twelfth O site, O(12) is bonded to one Li(1), one Mn(2), and two equivalent Fe(2) atoms to form a mixture of distorted corner and edge-sharing OLiMnFe2 tetrahedra. is represented by the CIF file [CIF]
data_Li4Mn2Fe3Sn3O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.101
_cell_length_b   6.101
_cell_length_c   9.681
_cell_angle_alpha   88.983
_cell_angle_beta   88.983
_cell_angle_gamma   60.653
_symmetry_Int_Tables_number   1
_cell_volume   314.074
_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  0.675  0.675  0.107  1.0
  Li  Li1  1  0.985  0.985  0.010  1.0
  Li  Li2  1  0.986  0.986  0.502  1.0
  Li  Li3  1  0.340  0.340  0.601  1.0
  Mn  Mn4  1  0.672  0.672  0.508  1.0
  Mn  Mn5  1  0.344  0.344  0.020  1.0
  Fe  Fe6  1  0.834  0.834  0.781  1.0
  Fe  Fe7  1  0.169  0.668  0.287  1.0
  Fe  Fe8  1  0.668  0.169  0.287  1.0
  Sn  Sn9  1  0.342  0.843  0.790  1.0
  Sn  Sn10  1  0.843  0.342  0.790  1.0
  Sn  Sn11  1  0.171  0.171  0.288  1.0
  O  O12  1  0.318  0.839  0.399  1.0
  O  O13  1  0.529  0.529  0.654  1.0
  O  O14  1  0.675  0.675  0.903  1.0
  O  O15  1  0.004  0.004  0.689  1.0
  O  O16  1  0.998  0.998  0.191  1.0
  O  O17  1  0.839  0.318  0.399  1.0
  O  O18  1  0.529  0.973  0.661  1.0
  O  O19  1  0.973  0.529  0.661  1.0
  O  O20  1  0.167  0.167  0.912  1.0
  O  O21  1  0.828  0.828  0.395  1.0
  O  O22  1  0.050  0.484  0.150  1.0
  O  O23  1  0.484  0.050  0.150  1.0
  O  O24  1  0.339  0.339  0.395  1.0
  O  O25  1  0.166  0.673  0.905  1.0
  O  O26  1  0.482  0.482  0.150  1.0
  O  O27  1  0.673  0.166  0.905  1.0
[/CIF]
.