The crystal structure described by Li4Ti2Co3Sn3O16 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 Co(1)O6 octahedra, corners with two equivalent Sn(1)O6 octahedra, corners with two equivalent Sn(2)O6 octahedra, corners with three equivalent Ti(2)O6 octahedra, and corners with four equivalent Co(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 trigonal pyramids that share  a cornercorner with one Sn(2)O6 octahedra, corners with two equivalent Co(2)O6 octahedra, corners with three equivalent Ti(2)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra, and edges with two equivalent Sn(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 54-68°. 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 Co(1)O6 octahedra, corners with two equivalent Sn(1)O6 octahedra, corners with three equivalent Ti(1)O6 octahedra,  an edgeedge with one Sn(2)O6 octahedra, and edges with two equivalent Co(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 54-66°. 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 Co(1)O6 octahedra, corners with two equivalent Co(2)O6 octahedra, corners with three equivalent Ti(1)O6 octahedra, and corners with four equivalent Sn(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-64°. There are two inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(2), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form distorted TiO6 octahedra that share corners with two equivalent Sn(2)O6 octahedra, corners with four equivalent Co(2)O6 octahedra, corners with three equivalent Li(3)O4 tetrahedra, corners with three equivalent Li(4)O4 tetrahedra,  an edgeedge with one Co(1)O6 octahedra, and edges with two equivalent Sn(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-55°. In the second Ti site, Ti(2) is bonded to one O(12), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form TiO6 octahedra that share corners with two equivalent Co(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 Co(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-53°. There are two inequivalent Co sites. In the first Co site, Co(1) is bonded to one O(3), one O(4), two equivalent O(11), and two equivalent O(6) atoms to form CoO6 octahedra that share corners with two equivalent Ti(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 Ti(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 second Co site, Co(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 CoO6 octahedra that share corners with two equivalent Ti(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 Ti(2)O6 octahedra, edges with two equivalent Co(2)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 are 50°. 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 Ti(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 Ti(1)O6 octahedra, edges with two equivalent Co(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 50-53°. 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 Ti(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 Ti(2)O6 octahedra, edges with four equivalent Co(2)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 rectangular see-saw-like geometry to one Li(3), one Ti(1), one Co(2), and one Sn(2) atom. In the second O site, O(2) is bonded to one Li(4), one Ti(1), and two equivalent Sn(1) atoms to form distorted OLiTiSn2 trigonal pyramids that share corners with two equivalent O(4)LiCoSn2 tetrahedra, corners with two equivalent O(6)LiTiCoSn tetrahedra, and edges with two equivalent O(6)LiTiCoSn tetrahedra. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Li(1), one Co(1), and two equivalent Sn(1) atoms. In the fourth O site, O(4) is bonded to one Li(3), one Co(1), and two equivalent Sn(1) atoms to form OLiCoSn2 tetrahedra that share corners with four equivalent O(6)LiTiCoSn tetrahedra and corners with two equivalent O(2)LiTiSn2 trigonal pyramids. In the fifth O site, O(5) is bonded to one Li(2), two equivalent Co(2), and one Sn(2) atom to form corner-sharing OLiCo2Sn tetrahedra. In the sixth O site, O(6) is bonded to one Li(4), one Ti(1), one Co(1), and one Sn(1) atom to form distorted OLiTiCoSn tetrahedra that share  a cornercorner with one O(6)LiTiCoSn tetrahedra, corners with two equivalent O(4)LiCoSn2 tetrahedra,  a cornercorner with one O(2)LiTiSn2 trigonal pyramid,  an edgeedge with one O(6)LiTiCoSn tetrahedra, and  an edgeedge with one O(2)LiTiSn2 trigonal pyramid. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), one Ti(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 Ti(1), and two equivalent Co(2) atoms. In the ninth O site, O(9) is bonded in a distorted rectangular see-saw-like geometry to one Li(1), one Ti(2), one Co(2), 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 Co(2), 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 Ti(2), one Co(1), and one Sn(1) atom. In the twelfth O site, O(12) is bonded to one Li(1), one Ti(2), and two equivalent Co(2) atoms to form corner-sharing OLiTiCo2 tetrahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li4Ti2Co3Sn3O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.103
_cell_length_b   6.114
_cell_length_c   9.668
_cell_angle_alpha   89.994
_cell_angle_beta   89.837
_cell_angle_gamma   120.080
_symmetry_Int_Tables_number   1
_cell_volume   312.198
_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  0.348  0.674  0.892  1.0
  Li  Li1  1  0.965  0.983  0.988  1.0
  Li  Li2  1  0.980  0.990  0.497  1.0
  Li  Li3  1  0.666  0.333  0.401  1.0
  Ti  Ti4  1  0.355  0.678  0.498  1.0
  Ti  Ti5  1  0.684  0.342  0.992  1.0
  Co  Co6  1  0.658  0.829  0.216  1.0
  Co  Co7  1  0.835  0.656  0.718  1.0
  Co  Co8  1  0.835  0.179  0.718  1.0
  Sn  Sn9  1  0.173  0.831  0.215  1.0
  Sn  Sn10  1  0.173  0.342  0.215  1.0
  Sn  Sn11  1  0.343  0.172  0.711  1.0
  O  O12  1  0.166  0.829  0.594  1.0
  O  O13  1  0.027  0.513  0.342  1.0
  O  O14  1  0.336  0.668  0.097  1.0
  O  O15  1  0.997  0.998  0.310  1.0
  O  O16  1  0.989  0.994  0.801  1.0
  O  O17  1  0.166  0.336  0.594  1.0
  O  O18  1  0.473  0.957  0.353  1.0
  O  O19  1  0.473  0.516  0.353  1.0
  O  O20  1  0.332  0.166  0.091  1.0
  O  O21  1  0.655  0.828  0.597  1.0
  O  O22  1  0.529  0.483  0.846  1.0
  O  O23  1  0.529  0.046  0.846  1.0
  O  O24  1  0.683  0.342  0.606  1.0
  O  O25  1  0.837  0.657  0.088  1.0
  O  O26  1  0.958  0.479  0.841  1.0
  O  O27  1  0.837  0.180  0.088  1.0
[/CIF]
.
The crystal structure described by Li4Ti2Co3Sn3O16 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 Co(1)O6 octahedra, corners with two equivalent Sn(1)O6 octahedra, corners with two equivalent Sn(2)O6 octahedra, corners with three equivalent Ti(2)O6 octahedra, and corners with four equivalent Co(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 trigonal pyramids that share  a cornercorner with one Sn(2)O6 octahedra, corners with two equivalent Co(2)O6 octahedra, corners with three equivalent Ti(2)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra, and edges with two equivalent Sn(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 54-68°. 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 Co(1)O6 octahedra, corners with two equivalent Sn(1)O6 octahedra, corners with three equivalent Ti(1)O6 octahedra,  an edgeedge with one Sn(2)O6 octahedra, and edges with two equivalent Co(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 54-66°. 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 Co(1)O6 octahedra, corners with two equivalent Co(2)O6 octahedra, corners with three equivalent Ti(1)O6 octahedra, and corners with four equivalent Sn(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-64°. There are two inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(2), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form distorted TiO6 octahedra that share corners with two equivalent Sn(2)O6 octahedra, corners with four equivalent Co(2)O6 octahedra, corners with three equivalent Li(3)O4 tetrahedra, corners with three equivalent Li(4)O4 tetrahedra,  an edgeedge with one Co(1)O6 octahedra, and edges with two equivalent Sn(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-55°. In the second Ti site, Ti(2) is bonded to one O(12), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form TiO6 octahedra that share corners with two equivalent Co(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 Co(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-53°. There are two inequivalent Co sites. In the first Co site, Co(1) is bonded to one O(3), one O(4), two equivalent O(11), and two equivalent O(6) atoms to form CoO6 octahedra that share corners with two equivalent Ti(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 Ti(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 second Co site, Co(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 CoO6 octahedra that share corners with two equivalent Ti(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 Ti(2)O6 octahedra, edges with two equivalent Co(2)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 are 50°. 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 Ti(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 Ti(1)O6 octahedra, edges with two equivalent Co(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 50-53°. 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 Ti(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 Ti(2)O6 octahedra, edges with four equivalent Co(2)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 rectangular see-saw-like geometry to one Li(3), one Ti(1), one Co(2), and one Sn(2) atom. In the second O site, O(2) is bonded to one Li(4), one Ti(1), and two equivalent Sn(1) atoms to form distorted OLiTiSn2 trigonal pyramids that share corners with two equivalent O(4)LiCoSn2 tetrahedra, corners with two equivalent O(6)LiTiCoSn tetrahedra, and edges with two equivalent O(6)LiTiCoSn tetrahedra. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Li(1), one Co(1), and two equivalent Sn(1) atoms. In the fourth O site, O(4) is bonded to one Li(3), one Co(1), and two equivalent Sn(1) atoms to form OLiCoSn2 tetrahedra that share corners with four equivalent O(6)LiTiCoSn tetrahedra and corners with two equivalent O(2)LiTiSn2 trigonal pyramids. In the fifth O site, O(5) is bonded to one Li(2), two equivalent Co(2), and one Sn(2) atom to form corner-sharing OLiCo2Sn tetrahedra. In the sixth O site, O(6) is bonded to one Li(4), one Ti(1), one Co(1), and one Sn(1) atom to form distorted OLiTiCoSn tetrahedra that share  a cornercorner with one O(6)LiTiCoSn tetrahedra, corners with two equivalent O(4)LiCoSn2 tetrahedra,  a cornercorner with one O(2)LiTiSn2 trigonal pyramid,  an edgeedge with one O(6)LiTiCoSn tetrahedra, and  an edgeedge with one O(2)LiTiSn2 trigonal pyramid. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), one Ti(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 Ti(1), and two equivalent Co(2) atoms. In the ninth O site, O(9) is bonded in a distorted rectangular see-saw-like geometry to one Li(1), one Ti(2), one Co(2), 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 Co(2), 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 Ti(2), one Co(1), and one Sn(1) atom. In the twelfth O site, O(12) is bonded to one Li(1), one Ti(2), and two equivalent Co(2) atoms to form corner-sharing OLiTiCo2 tetrahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li4Ti2Co3Sn3O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.103
_cell_length_b   6.114
_cell_length_c   9.668
_cell_angle_alpha   89.994
_cell_angle_beta   89.837
_cell_angle_gamma   120.080
_symmetry_Int_Tables_number   1
_cell_volume   312.198
_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  0.348  0.674  0.892  1.0
  Li  Li1  1  0.965  0.983  0.988  1.0
  Li  Li2  1  0.980  0.990  0.497  1.0
  Li  Li3  1  0.666  0.333  0.401  1.0
  Ti  Ti4  1  0.355  0.678  0.498  1.0
  Ti  Ti5  1  0.684  0.342  0.992  1.0
  Co  Co6  1  0.658  0.829  0.216  1.0
  Co  Co7  1  0.835  0.656  0.718  1.0
  Co  Co8  1  0.835  0.179  0.718  1.0
  Sn  Sn9  1  0.173  0.831  0.215  1.0
  Sn  Sn10  1  0.173  0.342  0.215  1.0
  Sn  Sn11  1  0.343  0.172  0.711  1.0
  O  O12  1  0.166  0.829  0.594  1.0
  O  O13  1  0.027  0.513  0.342  1.0
  O  O14  1  0.336  0.668  0.097  1.0
  O  O15  1  0.997  0.998  0.310  1.0
  O  O16  1  0.989  0.994  0.801  1.0
  O  O17  1  0.166  0.336  0.594  1.0
  O  O18  1  0.473  0.957  0.353  1.0
  O  O19  1  0.473  0.516  0.353  1.0
  O  O20  1  0.332  0.166  0.091  1.0
  O  O21  1  0.655  0.828  0.597  1.0
  O  O22  1  0.529  0.483  0.846  1.0
  O  O23  1  0.529  0.046  0.846  1.0
  O  O24  1  0.683  0.342  0.606  1.0
  O  O25  1  0.837  0.657  0.088  1.0
  O  O26  1  0.958  0.479  0.841  1.0
  O  O27  1  0.837  0.180  0.088  1.0
[/CIF]
.