The material described by Li4Ti3Co2Sn3O16 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 Ti(1)O6 octahedra, corners with two equivalent Sn(1)O6 octahedra, corners with two equivalent Sn(2)O6 octahedra, corners with three equivalent Co(2)O6 octahedra, and corners with four equivalent Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-64°. In the second Li site, Li(2) is bonded in a rectangular see-saw-like geometry to one O(5), one O(7), and two equivalent O(11) atoms. 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 trigonal pyramids that share  a cornercorner with one Ti(1)O6 octahedra, corners with two equivalent Sn(1)O6 octahedra, corners with three equivalent Co(1)O6 octahedra,  an edgeedge with one Sn(2)O6 octahedra, and edges with two equivalent Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 59-67°. 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 Ti(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra, corners with three equivalent Co(1)O6 octahedra, and corners with four equivalent Sn(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-63°. There are two inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(3), one O(4), two equivalent O(11), and two equivalent O(6) atoms to form TiO6 octahedra that share corners with two equivalent Co(2)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  a cornercorner with one Li(3)O4 trigonal pyramid,  an edgeedge with one Co(1)O6 octahedra, and edges with four equivalent Sn(1)O6 octahedra. The corner-sharing octahedral tilt angles are 50°. In the second Ti site, Ti(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 TiO6 octahedra that share corners with two equivalent Co(1)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one Co(2)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, edges with two equivalent Sn(2)O6 octahedra, and  an edgeedge with one Li(3)O4 trigonal pyramid. The corner-sharing octahedral tilt angles range from 52-54°. There are two inequivalent Co sites. In the first Co site, Co(1) is bonded to one O(2), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form CoO6 octahedra that share corners with two equivalent Sn(2)O6 octahedra, corners with four equivalent Ti(2)O6 octahedra, corners with three equivalent Li(4)O4 tetrahedra, corners with three equivalent Li(3)O4 trigonal pyramids,  an edgeedge with one Ti(1)O6 octahedra, and edges with two equivalent Sn(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-55°. In the second Co site, Co(2) is bonded to one O(12), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form CoO6 octahedra that share corners with two equivalent Ti(1)O6 octahedra, corners with four equivalent Sn(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra,  an edgeedge with one Sn(2)O6 octahedra, and edges with two equivalent Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-56°. 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 Co(2)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  a cornercorner with one Li(3)O4 trigonal pyramid,  an edgeedge with one Co(1)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, and edges with two equivalent Sn(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 54-56°. 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 Co(1)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one Co(2)O6 octahedra, edges with four equivalent Ti(2)O6 octahedra, and  an edgeedge with one Li(3)O4 trigonal pyramid. 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 Ti(2), one Co(1), and one Sn(2) atom. In the second O site, O(2) is bonded to one Li(4), one Co(1), and two equivalent Sn(1) atoms to form distorted OLiCoSn2 tetrahedra that share corners with two equivalent O(6)LiTiCoSn tetrahedra, corners with two equivalent O(4)LiTiSn2 tetrahedra,  a cornercorner with one O(8)LiTi2Co trigonal pyramid, 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 Ti(1), and two equivalent Sn(1) atoms. In the fourth O site, O(4) is bonded to one Li(3), one Ti(1), and two equivalent Sn(1) atoms to form distorted OLiTiSn2 tetrahedra that share corners with two equivalent O(2)LiCoSn2 tetrahedra, corners with four equivalent O(6)LiTiCoSn tetrahedra, and  a cornercorner with one O(8)LiTi2Co trigonal pyramid. In the fifth O site, O(5) is bonded to one Li(2), two equivalent Ti(2), and one Sn(2) atom to form distorted OLiTi2Sn tetrahedra that share corners with two equivalent O(12)LiTi2Co tetrahedra, corners with four equivalent O(9)LiTiCoSn tetrahedra, and  an edgeedge with one O(8)LiTi2Co trigonal pyramid. 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(2)LiCoSn2 tetrahedra,  a cornercorner with one O(6)LiTiCoSn tetrahedra, corners with two equivalent O(4)LiTiSn2 tetrahedra,  a cornercorner with one O(8)LiTi2Co trigonal pyramid,  an edgeedge with one O(2)LiCoSn2 tetrahedra, and  an edgeedge with one O(6)LiTiCoSn tetrahedra. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), one Co(2), and two equivalent Sn(1) atoms. In the eighth O site, O(8) is bonded to one Li(3), two equivalent Ti(2), and one Co(1) atom to form distorted OLiTi2Co trigonal pyramids that share  a cornercorner with one O(2)LiCoSn2 tetrahedra,  a cornercorner with one O(4)LiTiSn2 tetrahedra, corners with two equivalent O(12)LiTi2Co tetrahedra, corners with two equivalent O(6)LiTiCoSn tetrahedra, corners with two equivalent O(9)LiTiCoSn tetrahedra, and  an edgeedge with one O(5)LiTi2Sn tetrahedra. In the ninth O site, O(9) is bonded to one Li(1), one Ti(2), one Co(2), and one Sn(2) atom to form distorted OLiTiCoSn tetrahedra that share  a cornercorner with one O(12)LiTi2Co tetrahedra,  a cornercorner with one O(9)LiTiCoSn tetrahedra, corners with two equivalent O(5)LiTi2Sn tetrahedra,  a cornercorner with one O(8)LiTi2Co trigonal pyramid,  an edgeedge with one O(12)LiTi2Co tetrahedra, and  an edgeedge with one O(9)LiTiCoSn tetrahedra. In the tenth O site, O(10) is bonded in a rectangular see-saw-like geometry to one Li(4), two equivalent Ti(2), and one Sn(2) atom. In the eleventh O site, O(11) is bonded in a distorted rectangular see-saw-like geometry to one Li(2), one Ti(1), one Co(2), and one Sn(1) atom. In the twelfth O site, O(12) is bonded to one Li(1), two equivalent Ti(2), and one Co(2) atom to form distorted OLiTi2Co tetrahedra that share corners with two equivalent O(5)LiTi2Sn tetrahedra, corners with two equivalent O(9)LiTiCoSn tetrahedra, corners with two equivalent O(8)LiTi2Co trigonal pyramids, and edges with two equivalent O(9)LiTiCoSn tetrahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li4Ti3Co2Sn3O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.139
_cell_length_b   6.107
_cell_length_c   9.845
_cell_angle_alpha   89.996
_cell_angle_beta   89.229
_cell_angle_gamma   119.833
_symmetry_Int_Tables_number   1
_cell_volume   320.134
_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  0.337  0.669  0.886  1.0
  Li  Li1  1  0.980  0.990  0.996  1.0
  Li  Li2  1  0.988  0.994  0.502  1.0
  Li  Li3  1  0.670  0.335  0.393  1.0
  Ti  Ti4  1  0.661  0.831  0.217  1.0
  Ti  Ti5  1  0.830  0.167  0.716  1.0
  Ti  Ti6  1  0.831  0.662  0.717  1.0
  Co  Co7  1  0.330  0.665  0.494  1.0
  Co  Co8  1  0.673  0.337  0.993  1.0
  Sn  Sn9  1  0.169  0.831  0.214  1.0
  Sn  Sn10  1  0.169  0.338  0.214  1.0
  Sn  Sn11  1  0.341  0.171  0.713  1.0
  O  O12  1  0.153  0.836  0.602  1.0
  O  O13  1  0.030  0.515  0.337  1.0
  O  O14  1  0.351  0.675  0.098  1.0
  O  O15  1  0.987  0.993  0.319  1.0
  O  O16  1  0.990  0.995  0.815  1.0
  O  O17  1  0.153  0.317  0.602  1.0
  O  O18  1  0.491  0.964  0.335  1.0
  O  O19  1  0.491  0.527  0.335  1.0
  O  O20  1  0.313  0.157  0.095  1.0
  O  O21  1  0.690  0.845  0.614  1.0
  O  O22  1  0.529  0.493  0.832  1.0
  O  O23  1  0.529  0.036  0.832  1.0
  O  O24  1  0.690  0.345  0.603  1.0
  O  O25  1  0.830  0.682  0.105  1.0
  O  O26  1  0.962  0.481  0.826  1.0
  O  O27  1  0.830  0.149  0.105  1.0
[/CIF]
.
The material described by Li4Ti3Co2Sn3O16 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 Ti(1)O6 octahedra, corners with two equivalent Sn(1)O6 octahedra, corners with two equivalent Sn(2)O6 octahedra, corners with three equivalent Co(2)O6 octahedra, and corners with four equivalent Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-64°. In the second Li site, Li(2) is bonded in a rectangular see-saw-like geometry to one O(5), one O(7), and two equivalent O(11) atoms. 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 trigonal pyramids that share  a cornercorner with one Ti(1)O6 octahedra, corners with two equivalent Sn(1)O6 octahedra, corners with three equivalent Co(1)O6 octahedra,  an edgeedge with one Sn(2)O6 octahedra, and edges with two equivalent Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 59-67°. 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 Ti(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra, corners with three equivalent Co(1)O6 octahedra, and corners with four equivalent Sn(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-63°. There are two inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(3), one O(4), two equivalent O(11), and two equivalent O(6) atoms to form TiO6 octahedra that share corners with two equivalent Co(2)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  a cornercorner with one Li(3)O4 trigonal pyramid,  an edgeedge with one Co(1)O6 octahedra, and edges with four equivalent Sn(1)O6 octahedra. The corner-sharing octahedral tilt angles are 50°. In the second Ti site, Ti(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 TiO6 octahedra that share corners with two equivalent Co(1)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one Co(2)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, edges with two equivalent Sn(2)O6 octahedra, and  an edgeedge with one Li(3)O4 trigonal pyramid. The corner-sharing octahedral tilt angles range from 52-54°. There are two inequivalent Co sites. In the first Co site, Co(1) is bonded to one O(2), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form CoO6 octahedra that share corners with two equivalent Sn(2)O6 octahedra, corners with four equivalent Ti(2)O6 octahedra, corners with three equivalent Li(4)O4 tetrahedra, corners with three equivalent Li(3)O4 trigonal pyramids,  an edgeedge with one Ti(1)O6 octahedra, and edges with two equivalent Sn(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-55°. In the second Co site, Co(2) is bonded to one O(12), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form CoO6 octahedra that share corners with two equivalent Ti(1)O6 octahedra, corners with four equivalent Sn(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra,  an edgeedge with one Sn(2)O6 octahedra, and edges with two equivalent Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-56°. 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 Co(2)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  a cornercorner with one Li(3)O4 trigonal pyramid,  an edgeedge with one Co(1)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, and edges with two equivalent Sn(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 54-56°. 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 Co(1)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one Co(2)O6 octahedra, edges with four equivalent Ti(2)O6 octahedra, and  an edgeedge with one Li(3)O4 trigonal pyramid. 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 Ti(2), one Co(1), and one Sn(2) atom. In the second O site, O(2) is bonded to one Li(4), one Co(1), and two equivalent Sn(1) atoms to form distorted OLiCoSn2 tetrahedra that share corners with two equivalent O(6)LiTiCoSn tetrahedra, corners with two equivalent O(4)LiTiSn2 tetrahedra,  a cornercorner with one O(8)LiTi2Co trigonal pyramid, 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 Ti(1), and two equivalent Sn(1) atoms. In the fourth O site, O(4) is bonded to one Li(3), one Ti(1), and two equivalent Sn(1) atoms to form distorted OLiTiSn2 tetrahedra that share corners with two equivalent O(2)LiCoSn2 tetrahedra, corners with four equivalent O(6)LiTiCoSn tetrahedra, and  a cornercorner with one O(8)LiTi2Co trigonal pyramid. In the fifth O site, O(5) is bonded to one Li(2), two equivalent Ti(2), and one Sn(2) atom to form distorted OLiTi2Sn tetrahedra that share corners with two equivalent O(12)LiTi2Co tetrahedra, corners with four equivalent O(9)LiTiCoSn tetrahedra, and  an edgeedge with one O(8)LiTi2Co trigonal pyramid. 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(2)LiCoSn2 tetrahedra,  a cornercorner with one O(6)LiTiCoSn tetrahedra, corners with two equivalent O(4)LiTiSn2 tetrahedra,  a cornercorner with one O(8)LiTi2Co trigonal pyramid,  an edgeedge with one O(2)LiCoSn2 tetrahedra, and  an edgeedge with one O(6)LiTiCoSn tetrahedra. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), one Co(2), and two equivalent Sn(1) atoms. In the eighth O site, O(8) is bonded to one Li(3), two equivalent Ti(2), and one Co(1) atom to form distorted OLiTi2Co trigonal pyramids that share  a cornercorner with one O(2)LiCoSn2 tetrahedra,  a cornercorner with one O(4)LiTiSn2 tetrahedra, corners with two equivalent O(12)LiTi2Co tetrahedra, corners with two equivalent O(6)LiTiCoSn tetrahedra, corners with two equivalent O(9)LiTiCoSn tetrahedra, and  an edgeedge with one O(5)LiTi2Sn tetrahedra. In the ninth O site, O(9) is bonded to one Li(1), one Ti(2), one Co(2), and one Sn(2) atom to form distorted OLiTiCoSn tetrahedra that share  a cornercorner with one O(12)LiTi2Co tetrahedra,  a cornercorner with one O(9)LiTiCoSn tetrahedra, corners with two equivalent O(5)LiTi2Sn tetrahedra,  a cornercorner with one O(8)LiTi2Co trigonal pyramid,  an edgeedge with one O(12)LiTi2Co tetrahedra, and  an edgeedge with one O(9)LiTiCoSn tetrahedra. In the tenth O site, O(10) is bonded in a rectangular see-saw-like geometry to one Li(4), two equivalent Ti(2), and one Sn(2) atom. In the eleventh O site, O(11) is bonded in a distorted rectangular see-saw-like geometry to one Li(2), one Ti(1), one Co(2), and one Sn(1) atom. In the twelfth O site, O(12) is bonded to one Li(1), two equivalent Ti(2), and one Co(2) atom to form distorted OLiTi2Co tetrahedra that share corners with two equivalent O(5)LiTi2Sn tetrahedra, corners with two equivalent O(9)LiTiCoSn tetrahedra, corners with two equivalent O(8)LiTi2Co trigonal pyramids, and edges with two equivalent O(9)LiTiCoSn tetrahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li4Ti3Co2Sn3O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.139
_cell_length_b   6.107
_cell_length_c   9.845
_cell_angle_alpha   89.996
_cell_angle_beta   89.229
_cell_angle_gamma   119.833
_symmetry_Int_Tables_number   1
_cell_volume   320.134
_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  0.337  0.669  0.886  1.0
  Li  Li1  1  0.980  0.990  0.996  1.0
  Li  Li2  1  0.988  0.994  0.502  1.0
  Li  Li3  1  0.670  0.335  0.393  1.0
  Ti  Ti4  1  0.661  0.831  0.217  1.0
  Ti  Ti5  1  0.830  0.167  0.716  1.0
  Ti  Ti6  1  0.831  0.662  0.717  1.0
  Co  Co7  1  0.330  0.665  0.494  1.0
  Co  Co8  1  0.673  0.337  0.993  1.0
  Sn  Sn9  1  0.169  0.831  0.214  1.0
  Sn  Sn10  1  0.169  0.338  0.214  1.0
  Sn  Sn11  1  0.341  0.171  0.713  1.0
  O  O12  1  0.153  0.836  0.602  1.0
  O  O13  1  0.030  0.515  0.337  1.0
  O  O14  1  0.351  0.675  0.098  1.0
  O  O15  1  0.987  0.993  0.319  1.0
  O  O16  1  0.990  0.995  0.815  1.0
  O  O17  1  0.153  0.317  0.602  1.0
  O  O18  1  0.491  0.964  0.335  1.0
  O  O19  1  0.491  0.527  0.335  1.0
  O  O20  1  0.313  0.157  0.095  1.0
  O  O21  1  0.690  0.845  0.614  1.0
  O  O22  1  0.529  0.493  0.832  1.0
  O  O23  1  0.529  0.036  0.832  1.0
  O  O24  1  0.690  0.345  0.603  1.0
  O  O25  1  0.830  0.682  0.105  1.0
  O  O26  1  0.962  0.481  0.826  1.0
  O  O27  1  0.830  0.149  0.105  1.0
[/CIF]
.