The crystal structure described by Li4Fe5Sn3O16 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 Sn(1)O6 octahedra, corners with two equivalent Sn(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 54-64°. 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(4)O6 octahedra, corners with three equivalent Fe(3)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra, and edges with two equivalent Sn(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-64°. 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 Fe(2)O6 octahedra, corners with two equivalent Sn(1)O6 octahedra, corners with three equivalent Fe(1)O6 octahedra,  an edgeedge with one Sn(2)O6 octahedra, and edges with two equivalent Fe(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-62°. 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(2)O6 octahedra, corners with two equivalent Fe(4)O6 octahedra, corners with three equivalent Fe(1)O6 octahedra, and corners with four equivalent Sn(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-62°. 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 Sn(2)O6 octahedra, corners with four equivalent Fe(4)O6 octahedra, corners with three equivalent Li(3)O4 tetrahedra, corners with three equivalent Li(4)O4 tetrahedra,  an edgeedge with one Fe(2)O6 octahedra, and edges with two equivalent Sn(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-55°. 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,  a cornercorner with one Li(3)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Fe(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 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 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(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,  a cornercorner with one Li(2)O4 trigonal pyramid,  an edgeedge with one Fe(3)O6 octahedra, edges with two equivalent Fe(4)O6 octahedra, edges with two equivalent Sn(2)O6 octahedra, and  an edgeedge with one Li(3)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 51-52°. 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 Fe(3)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 Fe(1)O6 octahedra, edges with two equivalent Fe(2)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 are 53°. 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 Fe(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 Fe(3)O6 octahedra, edges with four equivalent Fe(4)O6 octahedra, and  an edgeedge with one Li(3)O4 tetrahedra. 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 distorted rectangular see-saw-like geometry to one Li(3), one Fe(1), one Fe(4), and one Sn(2) atom. In the second O site, O(2) is bonded in a distorted rectangular see-saw-like geometry to one Li(4), one Fe(1), and two equivalent Sn(1) atoms. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Li(1), one Fe(2), and two equivalent Sn(1) atoms. In the fourth O site, O(4) is bonded to one Li(3), one Fe(2), and two equivalent Sn(1) atoms to form distorted corner-sharing OLiFeSn2 tetrahedra. In the fifth O site, O(5) is bonded to one Li(2), two equivalent Fe(4), and one Sn(2) atom to form distorted corner-sharing OLiFe2Sn tetrahedra. In the sixth O site, O(6) is bonded to one Li(4), one Fe(1), one Fe(2), and one Sn(1) atom to form distorted OLiFe2Sn tetrahedra that share  a cornercorner with one O(6)LiFe2Sn tetrahedra, corners with two equivalent O(4)LiFeSn2 tetrahedra, and  an edgeedge with one O(6)LiFe2Sn tetrahedra. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), one Fe(3), 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 Fe(1), and two equivalent Fe(4) atoms. In the ninth O site, O(9) is bonded in a distorted rectangular see-saw-like geometry to one Li(1), one Fe(3), one Fe(4), and one Sn(2) atom. In the tenth O site, O(10) is bonded in a rectangular see-saw-like geometry to one Li(4), two equivalent Fe(4), and one Sn(2) atom. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one Fe(2), one Fe(3), and one Sn(1) 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 distorted corner-sharing OLiFe3 tetrahedra. is represented by the CIF card [CIF]
data_Li4Fe5Sn3O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.125
_cell_length_b   6.125
_cell_length_c   9.684
_cell_angle_alpha   89.432
_cell_angle_beta   89.432
_cell_angle_gamma   60.040
_symmetry_Int_Tables_number   1
_cell_volume   314.736
_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  0.331  0.331  0.113  1.0
  Li  Li1  1  0.010  0.010  0.008  1.0
  Li  Li2  1  0.007  0.007  0.499  1.0
  Li  Li3  1  0.666  0.666  0.604  1.0
  Fe  Fe4  1  0.329  0.329  0.504  1.0
  Fe  Fe5  1  0.170  0.170  0.784  1.0
  Fe  Fe6  1  0.661  0.661  0.013  1.0
  Fe  Fe7  1  0.829  0.340  0.285  1.0
  Fe  Fe8  1  0.340  0.829  0.285  1.0
  Sn  Sn9  1  0.661  0.169  0.786  1.0
  Sn  Sn10  1  0.169  0.661  0.786  1.0
  Sn  Sn11  1  0.829  0.829  0.287  1.0
  O  O12  1  0.672  0.167  0.403  1.0
  O  O13  1  0.483  0.483  0.655  1.0
  O  O14  1  0.329  0.329  0.903  1.0
  O  O15  1  0.004  0.004  0.685  1.0
  O  O16  1  0.004  0.004  0.191  1.0
  O  O17  1  0.167  0.672  0.403  1.0
  O  O18  1  0.477  0.038  0.657  1.0
  O  O19  1  0.038  0.477  0.657  1.0
  O  O20  1  0.838  0.838  0.907  1.0
  O  O21  1  0.166  0.166  0.396  1.0
  O  O22  1  0.959  0.514  0.157  1.0
  O  O23  1  0.514  0.959  0.157  1.0
  O  O24  1  0.661  0.661  0.398  1.0
  O  O25  1  0.838  0.328  0.902  1.0
  O  O26  1  0.519  0.519  0.163  1.0
  O  O27  1  0.328  0.838  0.902  1.0
[/CIF]
.
The crystal structure described by Li4Fe5Sn3O16 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 Sn(1)O6 octahedra, corners with two equivalent Sn(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 54-64°. 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(4)O6 octahedra, corners with three equivalent Fe(3)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra, and edges with two equivalent Sn(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-64°. 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 Fe(2)O6 octahedra, corners with two equivalent Sn(1)O6 octahedra, corners with three equivalent Fe(1)O6 octahedra,  an edgeedge with one Sn(2)O6 octahedra, and edges with two equivalent Fe(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-62°. 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(2)O6 octahedra, corners with two equivalent Fe(4)O6 octahedra, corners with three equivalent Fe(1)O6 octahedra, and corners with four equivalent Sn(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-62°. 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 Sn(2)O6 octahedra, corners with four equivalent Fe(4)O6 octahedra, corners with three equivalent Li(3)O4 tetrahedra, corners with three equivalent Li(4)O4 tetrahedra,  an edgeedge with one Fe(2)O6 octahedra, and edges with two equivalent Sn(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-55°. 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,  a cornercorner with one Li(3)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Fe(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 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 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(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,  a cornercorner with one Li(2)O4 trigonal pyramid,  an edgeedge with one Fe(3)O6 octahedra, edges with two equivalent Fe(4)O6 octahedra, edges with two equivalent Sn(2)O6 octahedra, and  an edgeedge with one Li(3)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 51-52°. 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 Fe(3)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 Fe(1)O6 octahedra, edges with two equivalent Fe(2)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 are 53°. 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 Fe(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 Fe(3)O6 octahedra, edges with four equivalent Fe(4)O6 octahedra, and  an edgeedge with one Li(3)O4 tetrahedra. 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 distorted rectangular see-saw-like geometry to one Li(3), one Fe(1), one Fe(4), and one Sn(2) atom. In the second O site, O(2) is bonded in a distorted rectangular see-saw-like geometry to one Li(4), one Fe(1), and two equivalent Sn(1) atoms. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Li(1), one Fe(2), and two equivalent Sn(1) atoms. In the fourth O site, O(4) is bonded to one Li(3), one Fe(2), and two equivalent Sn(1) atoms to form distorted corner-sharing OLiFeSn2 tetrahedra. In the fifth O site, O(5) is bonded to one Li(2), two equivalent Fe(4), and one Sn(2) atom to form distorted corner-sharing OLiFe2Sn tetrahedra. In the sixth O site, O(6) is bonded to one Li(4), one Fe(1), one Fe(2), and one Sn(1) atom to form distorted OLiFe2Sn tetrahedra that share  a cornercorner with one O(6)LiFe2Sn tetrahedra, corners with two equivalent O(4)LiFeSn2 tetrahedra, and  an edgeedge with one O(6)LiFe2Sn tetrahedra. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), one Fe(3), 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 Fe(1), and two equivalent Fe(4) atoms. In the ninth O site, O(9) is bonded in a distorted rectangular see-saw-like geometry to one Li(1), one Fe(3), one Fe(4), and one Sn(2) atom. In the tenth O site, O(10) is bonded in a rectangular see-saw-like geometry to one Li(4), two equivalent Fe(4), and one Sn(2) atom. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one Fe(2), one Fe(3), and one Sn(1) 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 distorted corner-sharing OLiFe3 tetrahedra. is represented by the CIF card [CIF]
data_Li4Fe5Sn3O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.125
_cell_length_b   6.125
_cell_length_c   9.684
_cell_angle_alpha   89.432
_cell_angle_beta   89.432
_cell_angle_gamma   60.040
_symmetry_Int_Tables_number   1
_cell_volume   314.736
_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  0.331  0.331  0.113  1.0
  Li  Li1  1  0.010  0.010  0.008  1.0
  Li  Li2  1  0.007  0.007  0.499  1.0
  Li  Li3  1  0.666  0.666  0.604  1.0
  Fe  Fe4  1  0.329  0.329  0.504  1.0
  Fe  Fe5  1  0.170  0.170  0.784  1.0
  Fe  Fe6  1  0.661  0.661  0.013  1.0
  Fe  Fe7  1  0.829  0.340  0.285  1.0
  Fe  Fe8  1  0.340  0.829  0.285  1.0
  Sn  Sn9  1  0.661  0.169  0.786  1.0
  Sn  Sn10  1  0.169  0.661  0.786  1.0
  Sn  Sn11  1  0.829  0.829  0.287  1.0
  O  O12  1  0.672  0.167  0.403  1.0
  O  O13  1  0.483  0.483  0.655  1.0
  O  O14  1  0.329  0.329  0.903  1.0
  O  O15  1  0.004  0.004  0.685  1.0
  O  O16  1  0.004  0.004  0.191  1.0
  O  O17  1  0.167  0.672  0.403  1.0
  O  O18  1  0.477  0.038  0.657  1.0
  O  O19  1  0.038  0.477  0.657  1.0
  O  O20  1  0.838  0.838  0.907  1.0
  O  O21  1  0.166  0.166  0.396  1.0
  O  O22  1  0.959  0.514  0.157  1.0
  O  O23  1  0.514  0.959  0.157  1.0
  O  O24  1  0.661  0.661  0.398  1.0
  O  O25  1  0.838  0.328  0.902  1.0
  O  O26  1  0.519  0.519  0.163  1.0
  O  O27  1  0.328  0.838  0.902  1.0
[/CIF]
.