The structure described by Li4Ti2Fe3Co3O16 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 Co(1)O6 octahedra, corners with two equivalent Co(2)O6 octahedra, corners with three equivalent Ti(2)O6 octahedra, and corners with four equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-63°. 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 Co(2)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, corners with three equivalent Ti(2)O6 octahedra,  an edgeedge with one Fe(1)O6 octahedra, and edges with two equivalent Co(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-65°. 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 Fe(1)O6 octahedra, corners with two equivalent Co(1)O6 octahedra, corners with three equivalent Ti(1)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra, and edges with two equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-65°. 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 Co(2)O6 octahedra, corners with two equivalent Fe(1)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, corners with three equivalent Ti(1)O6 octahedra, and corners with four equivalent Co(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-62°. 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 TiO6 octahedra that share corners with two equivalent Co(2)O6 octahedra, corners with four equivalent Fe(2)O6 octahedra, corners with three equivalent Li(4)O4 tetrahedra, corners with three equivalent Li(3)O4 trigonal pyramids,  an edgeedge with one Fe(1)O6 octahedra, and edges with two equivalent Co(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 48-55°. 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 Fe(1)O6 octahedra, corners with four equivalent Co(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra, corners with three equivalent Li(2)O4 tetrahedra,  an edgeedge with one Co(2)O6 octahedra, and edges with two equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-53°. 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 Ti(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 Ti(1)O6 octahedra, edges with four equivalent Co(1)O6 octahedra, and  an edgeedge with one Li(2)O4 tetrahedra. The corner-sharing octahedral tilt angles are 51°. 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 Ti(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 Ti(2)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, edges with two equivalent Co(2)O6 octahedra, and  an edgeedge with one Li(3)O4 trigonal pyramid. The corner-sharing octahedral tilt angles range from 52-55°. There are two inequivalent Co sites. In the first Co site, Co(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 CoO6 octahedra that share corners with two equivalent Ti(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 Ti(1)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, edges with two equivalent Co(1)O6 octahedra, and  an edgeedge with one Li(2)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 51-53°. In the second Co site, Co(2) is bonded to one O(10), one O(5), two equivalent O(1), and two equivalent O(9) atoms to form CoO6 octahedra that share corners with two equivalent Ti(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 Ti(2)O6 octahedra, edges with four equivalent Fe(2)O6 octahedra, and  an edgeedge with one Li(3)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 48°. 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 Fe(2), and one Co(2) atom. In the second O site, O(2) is bonded to one Li(4), one Ti(1), and two equivalent Co(1) atoms to form distorted OLiTiCo2 trigonal pyramids that share corners with two equivalent O(4)LiFeCo2 tetrahedra, corners with two equivalent O(6)LiTiFeCo tetrahedra, and edges with two equivalent O(6)LiTiFeCo tetrahedra. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Li(1), one Fe(1), and two equivalent Co(1) atoms. In the fourth O site, O(4) is bonded to one Li(3), one Fe(1), and two equivalent Co(1) atoms to form OLiFeCo2 tetrahedra that share corners with four equivalent O(6)LiTiFeCo tetrahedra and corners with two equivalent O(2)LiTiCo2 trigonal pyramids. In the fifth O site, O(5) is bonded to one Li(2), two equivalent Fe(2), and one Co(2) atom to form OLiFe2Co tetrahedra that share corners with two equivalent O(12)LiTiFe2 tetrahedra and corners with four equivalent O(9)LiTiFeCo tetrahedra. In the sixth O site, O(6) is bonded to one Li(4), one Ti(1), one Fe(1), and one Co(1) atom to form distorted OLiTiFeCo tetrahedra that share  a cornercorner with one O(6)LiTiFeCo tetrahedra, corners with two equivalent O(4)LiFeCo2 tetrahedra,  a cornercorner with one O(2)LiTiCo2 trigonal pyramid,  an edgeedge with one O(6)LiTiFeCo tetrahedra, and  an edgeedge with one O(2)LiTiCo2 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 Co(1) atoms. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Li(3), one Ti(1), and two equivalent Fe(2) atoms. In the ninth O site, O(9) is bonded to one Li(1), one Ti(2), one Fe(2), and one Co(2) atom to form distorted OLiTiFeCo tetrahedra that share  a cornercorner with one O(12)LiTiFe2 tetrahedra,  a cornercorner with one O(9)LiTiFeCo tetrahedra, corners with two equivalent O(5)LiFe2Co tetrahedra,  an edgeedge with one O(12)LiTiFe2 tetrahedra, and  an edgeedge with one O(9)LiTiFeCo tetrahedra. In the tenth O site, O(10) is bonded in a rectangular see-saw-like geometry to one Li(4), two equivalent Fe(2), and one Co(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 Fe(1), and one Co(1) atom. In the twelfth O site, O(12) is bonded to one Li(1), one Ti(2), and two equivalent Fe(2) atoms to form distorted OLiTiFe2 tetrahedra that share corners with two equivalent O(5)LiFe2Co tetrahedra, corners with two equivalent O(9)LiTiFeCo tetrahedra, and edges with two equivalent O(9)LiTiFeCo tetrahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li4Ti2Fe3Co3O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.873
_cell_length_b   5.873
_cell_length_c   9.527
_cell_angle_alpha   88.977
_cell_angle_beta   88.977
_cell_angle_gamma   60.227
_symmetry_Int_Tables_number   1
_cell_volume   285.188
_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  0.340  0.340  0.897  1.0
  Li  Li1  1  0.998  0.998  0.994  1.0
  Li  Li2  1  0.999  0.999  0.493  1.0
  Li  Li3  1  0.672  0.672  0.397  1.0
  Ti  Ti4  1  0.336  0.336  0.497  1.0
  Ti  Ti5  1  0.668  0.668  0.995  1.0
  Fe  Fe6  1  0.173  0.173  0.212  1.0
  Fe  Fe7  1  0.341  0.836  0.715  1.0
  Fe  Fe8  1  0.836  0.341  0.715  1.0
  Co  Co9  1  0.166  0.661  0.217  1.0
  Co  Co10  1  0.661  0.166  0.217  1.0
  Co  Co11  1  0.831  0.831  0.714  1.0
  O  O12  1  0.154  0.670  0.600  1.0
  O  O13  1  0.483  0.483  0.346  1.0
  O  O14  1  0.342  0.342  0.106  1.0
  O  O15  1  0.997  0.997  0.304  1.0
  O  O16  1  0.995  0.995  0.807  1.0
  O  O17  1  0.670  0.154  0.600  1.0
  O  O18  1  0.042  0.488  0.343  1.0
  O  O19  1  0.488  0.042  0.343  1.0
  O  O20  1  0.833  0.833  0.097  1.0
  O  O21  1  0.169  0.169  0.591  1.0
  O  O22  1  0.535  0.968  0.835  1.0
  O  O23  1  0.968  0.535  0.835  1.0
  O  O24  1  0.676  0.676  0.606  1.0
  O  O25  1  0.335  0.840  0.093  1.0
  O  O26  1  0.525  0.525  0.848  1.0
  O  O27  1  0.840  0.335  0.093  1.0
[/CIF]
.
The structure described by Li4Ti2Fe3Co3O16 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 Co(1)O6 octahedra, corners with two equivalent Co(2)O6 octahedra, corners with three equivalent Ti(2)O6 octahedra, and corners with four equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-63°. 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 Co(2)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, corners with three equivalent Ti(2)O6 octahedra,  an edgeedge with one Fe(1)O6 octahedra, and edges with two equivalent Co(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-65°. 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 Fe(1)O6 octahedra, corners with two equivalent Co(1)O6 octahedra, corners with three equivalent Ti(1)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra, and edges with two equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-65°. 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 Co(2)O6 octahedra, corners with two equivalent Fe(1)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, corners with three equivalent Ti(1)O6 octahedra, and corners with four equivalent Co(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-62°. 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 TiO6 octahedra that share corners with two equivalent Co(2)O6 octahedra, corners with four equivalent Fe(2)O6 octahedra, corners with three equivalent Li(4)O4 tetrahedra, corners with three equivalent Li(3)O4 trigonal pyramids,  an edgeedge with one Fe(1)O6 octahedra, and edges with two equivalent Co(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 48-55°. 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 Fe(1)O6 octahedra, corners with four equivalent Co(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra, corners with three equivalent Li(2)O4 tetrahedra,  an edgeedge with one Co(2)O6 octahedra, and edges with two equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-53°. 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 Ti(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 Ti(1)O6 octahedra, edges with four equivalent Co(1)O6 octahedra, and  an edgeedge with one Li(2)O4 tetrahedra. The corner-sharing octahedral tilt angles are 51°. 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 Ti(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 Ti(2)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, edges with two equivalent Co(2)O6 octahedra, and  an edgeedge with one Li(3)O4 trigonal pyramid. The corner-sharing octahedral tilt angles range from 52-55°. There are two inequivalent Co sites. In the first Co site, Co(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 CoO6 octahedra that share corners with two equivalent Ti(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 Ti(1)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, edges with two equivalent Co(1)O6 octahedra, and  an edgeedge with one Li(2)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 51-53°. In the second Co site, Co(2) is bonded to one O(10), one O(5), two equivalent O(1), and two equivalent O(9) atoms to form CoO6 octahedra that share corners with two equivalent Ti(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 Ti(2)O6 octahedra, edges with four equivalent Fe(2)O6 octahedra, and  an edgeedge with one Li(3)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 48°. 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 Fe(2), and one Co(2) atom. In the second O site, O(2) is bonded to one Li(4), one Ti(1), and two equivalent Co(1) atoms to form distorted OLiTiCo2 trigonal pyramids that share corners with two equivalent O(4)LiFeCo2 tetrahedra, corners with two equivalent O(6)LiTiFeCo tetrahedra, and edges with two equivalent O(6)LiTiFeCo tetrahedra. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Li(1), one Fe(1), and two equivalent Co(1) atoms. In the fourth O site, O(4) is bonded to one Li(3), one Fe(1), and two equivalent Co(1) atoms to form OLiFeCo2 tetrahedra that share corners with four equivalent O(6)LiTiFeCo tetrahedra and corners with two equivalent O(2)LiTiCo2 trigonal pyramids. In the fifth O site, O(5) is bonded to one Li(2), two equivalent Fe(2), and one Co(2) atom to form OLiFe2Co tetrahedra that share corners with two equivalent O(12)LiTiFe2 tetrahedra and corners with four equivalent O(9)LiTiFeCo tetrahedra. In the sixth O site, O(6) is bonded to one Li(4), one Ti(1), one Fe(1), and one Co(1) atom to form distorted OLiTiFeCo tetrahedra that share  a cornercorner with one O(6)LiTiFeCo tetrahedra, corners with two equivalent O(4)LiFeCo2 tetrahedra,  a cornercorner with one O(2)LiTiCo2 trigonal pyramid,  an edgeedge with one O(6)LiTiFeCo tetrahedra, and  an edgeedge with one O(2)LiTiCo2 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 Co(1) atoms. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Li(3), one Ti(1), and two equivalent Fe(2) atoms. In the ninth O site, O(9) is bonded to one Li(1), one Ti(2), one Fe(2), and one Co(2) atom to form distorted OLiTiFeCo tetrahedra that share  a cornercorner with one O(12)LiTiFe2 tetrahedra,  a cornercorner with one O(9)LiTiFeCo tetrahedra, corners with two equivalent O(5)LiFe2Co tetrahedra,  an edgeedge with one O(12)LiTiFe2 tetrahedra, and  an edgeedge with one O(9)LiTiFeCo tetrahedra. In the tenth O site, O(10) is bonded in a rectangular see-saw-like geometry to one Li(4), two equivalent Fe(2), and one Co(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 Fe(1), and one Co(1) atom. In the twelfth O site, O(12) is bonded to one Li(1), one Ti(2), and two equivalent Fe(2) atoms to form distorted OLiTiFe2 tetrahedra that share corners with two equivalent O(5)LiFe2Co tetrahedra, corners with two equivalent O(9)LiTiFeCo tetrahedra, and edges with two equivalent O(9)LiTiFeCo tetrahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li4Ti2Fe3Co3O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.873
_cell_length_b   5.873
_cell_length_c   9.527
_cell_angle_alpha   88.977
_cell_angle_beta   88.977
_cell_angle_gamma   60.227
_symmetry_Int_Tables_number   1
_cell_volume   285.188
_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  0.340  0.340  0.897  1.0
  Li  Li1  1  0.998  0.998  0.994  1.0
  Li  Li2  1  0.999  0.999  0.493  1.0
  Li  Li3  1  0.672  0.672  0.397  1.0
  Ti  Ti4  1  0.336  0.336  0.497  1.0
  Ti  Ti5  1  0.668  0.668  0.995  1.0
  Fe  Fe6  1  0.173  0.173  0.212  1.0
  Fe  Fe7  1  0.341  0.836  0.715  1.0
  Fe  Fe8  1  0.836  0.341  0.715  1.0
  Co  Co9  1  0.166  0.661  0.217  1.0
  Co  Co10  1  0.661  0.166  0.217  1.0
  Co  Co11  1  0.831  0.831  0.714  1.0
  O  O12  1  0.154  0.670  0.600  1.0
  O  O13  1  0.483  0.483  0.346  1.0
  O  O14  1  0.342  0.342  0.106  1.0
  O  O15  1  0.997  0.997  0.304  1.0
  O  O16  1  0.995  0.995  0.807  1.0
  O  O17  1  0.670  0.154  0.600  1.0
  O  O18  1  0.042  0.488  0.343  1.0
  O  O19  1  0.488  0.042  0.343  1.0
  O  O20  1  0.833  0.833  0.097  1.0
  O  O21  1  0.169  0.169  0.591  1.0
  O  O22  1  0.535  0.968  0.835  1.0
  O  O23  1  0.968  0.535  0.835  1.0
  O  O24  1  0.676  0.676  0.606  1.0
  O  O25  1  0.335  0.840  0.093  1.0
  O  O26  1  0.525  0.525  0.848  1.0
  O  O27  1  0.840  0.335  0.093  1.0
[/CIF]
.