The material structure described by Li4Ti3Co5O16 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(2)O6 octahedra, corners with two equivalent Ti(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra, corners with three equivalent Co(3)O6 octahedra, and corners with four equivalent Co(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 Ti(2)O6 octahedra, corners with two equivalent Co(4)O6 octahedra, corners with three equivalent Co(3)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra, and edges with two equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 61-67°. 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 Co(2)O6 octahedra, corners with two equivalent Ti(1)O6 octahedra, corners with three equivalent Co(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra, and edges with two equivalent Co(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 62-68°. 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 Ti(2)O6 octahedra, corners with two equivalent Co(2)O6 octahedra, corners with two equivalent Co(4)O6 octahedra, corners with three equivalent Co(1)O6 octahedra, and corners with four equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-64°. There are two inequivalent Ti sites. In the first Ti site, Ti(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 TiO6 octahedra that share corners with two equivalent Co(3)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, edges with two equivalent Co(2)O6 octahedra, and  an edgeedge with one Li(2)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 50°. In the second Ti site, Ti(2) is bonded to one O(10), one O(5), two equivalent O(1), and two equivalent O(9) atoms 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,  a cornercorner with one Li(2)O4 trigonal pyramid,  an edgeedge with one Co(3)O6 octahedra, edges with four equivalent Co(4)O6 octahedra, and  an edgeedge with one Li(3)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 51°. There are four 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 Ti(2)O6 octahedra, corners with four equivalent Co(4)O6 octahedra, corners with three equivalent Li(4)O4 tetrahedra, corners with three equivalent Li(3)O4 trigonal pyramids,  an edgeedge with one Co(2)O6 octahedra, and edges with two equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-51°. In the second Co site, Co(2) 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 Co(3)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 four equivalent Ti(1)O6 octahedra, and  an edgeedge with one Li(2)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 51°. In the third Co site, Co(3) 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 Co(2)O6 octahedra, corners with four equivalent Ti(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra, corners with three equivalent Li(2)O4 trigonal pyramids,  an edgeedge with one Ti(2)O6 octahedra, and edges with two equivalent Co(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-51°. In the fourth Co site, Co(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 CoO6 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,  a cornercorner with one Li(2)O4 trigonal pyramid,  an edgeedge with one Co(3)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, edges with two equivalent Co(4)O6 octahedra, and  an edgeedge with one Li(3)O4 trigonal pyramid. The corner-sharing octahedral tilt angles range from 50-51°. 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 Co(4) atom. In the second O site, O(2) is bonded to one Li(4), two equivalent Ti(1), and one Co(1) atom to form distorted OLiTi2Co tetrahedra that share corners with two equivalent O(4)LiTi2Co tetrahedra,  a cornercorner with one O(8)LiCo3 trigonal pyramid, and  a cornercorner with one O(10)LiTiCo2 trigonal pyramid. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Li(1), two equivalent Ti(1), and one Co(2) atom. In the fourth O site, O(4) is bonded to one Li(3), two equivalent Ti(1), and one Co(2) atom to form distorted OLiTi2Co tetrahedra that share corners with two equivalent O(2)LiTi2Co tetrahedra and  a cornercorner with one O(8)LiCo3 trigonal pyramid. In the fifth O site, O(5) is bonded to one Li(2), one Ti(2), and two equivalent Co(4) atoms to form distorted OLiTiCo2 tetrahedra that share corners with two equivalent O(12)LiCo3 tetrahedra, corners with three equivalent O(10)LiTiCo2 trigonal pyramids, and  an edgeedge with one O(8)LiCo3 trigonal pyramid. In the sixth O site, O(6) is bonded in a distorted rectangular see-saw-like geometry to one Li(4), one Ti(1), one Co(1), and one Co(2) atom. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), two equivalent Ti(1), and one Co(3) atom. In the eighth O site, O(8) is bonded to one Li(3), one Co(1), and two equivalent Co(4) atoms to form distorted OLiCo3 trigonal pyramids that share  a cornercorner with one O(2)LiTi2Co tetrahedra,  a cornercorner with one O(4)LiTi2Co tetrahedra, corners with two equivalent O(12)LiCo3 tetrahedra, corners with two equivalent O(10)LiTiCo2 trigonal pyramids, and  an edgeedge with one O(5)LiTiCo2 tetrahedra. 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(3), and one Co(4) atom. In the tenth O site, O(10) is bonded to one Li(4), one Ti(2), and two equivalent Co(4) atoms to form distorted OLiTiCo2 trigonal pyramids that share  a cornercorner with one O(2)LiTi2Co tetrahedra, corners with three equivalent O(5)LiTiCo2 tetrahedra, corners with two equivalent O(8)LiCo3 trigonal pyramids, and  an edgeedge with one O(12)LiCo3 tetrahedra. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one Ti(1), one Co(2), and one Co(3) atom. In the twelfth O site, O(12) is bonded to one Li(1), one Co(3), and two equivalent Co(4) atoms to form distorted OLiCo3 tetrahedra that share corners with two equivalent O(5)LiTiCo2 tetrahedra, corners with two equivalent O(8)LiCo3 trigonal pyramids, and  an edgeedge with one O(10)LiTiCo2 trigonal pyramid. is represented by the CIF card [CIF]
data_Li4Ti3Co5O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.727
_cell_length_b   5.727
_cell_length_c   9.310
_cell_angle_alpha   89.687
_cell_angle_beta   89.687
_cell_angle_gamma   60.894
_symmetry_Int_Tables_number   1
_cell_volume   266.776
_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  0.671  0.671  0.888  1.0
  Li  Li1  1  0.988  0.988  0.995  1.0
  Li  Li2  1  0.994  0.994  0.499  1.0
  Li  Li3  1  0.337  0.337  0.396  1.0
  Ti  Ti4  1  0.833  0.339  0.212  1.0
  Ti  Ti5  1  0.339  0.833  0.212  1.0
  Ti  Ti6  1  0.170  0.170  0.713  1.0
  Co  Co7  1  0.667  0.667  0.485  1.0
  Co  Co8  1  0.827  0.827  0.214  1.0
  Co  Co9  1  0.336  0.336  0.979  1.0
  Co  Co10  1  0.662  0.167  0.709  1.0
  Co  Co11  1  0.167  0.662  0.709  1.0
  O  O12  1  0.829  0.336  0.603  1.0
  O  O13  1  0.524  0.524  0.345  1.0
  O  O14  1  0.665  0.665  0.098  1.0
  O  O15  1  0.995  0.995  0.311  1.0
  O  O16  1  0.994  0.994  0.807  1.0
  O  O17  1  0.336  0.829  0.603  1.0
  O  O18  1  0.958  0.527  0.347  1.0
  O  O19  1  0.527  0.958  0.347  1.0
  O  O20  1  0.171  0.171  0.101  1.0
  O  O21  1  0.833  0.833  0.608  1.0
  O  O22  1  0.485  0.045  0.843  1.0
  O  O23  1  0.045  0.485  0.843  1.0
  O  O24  1  0.337  0.337  0.602  1.0
  O  O25  1  0.665  0.172  0.103  1.0
  O  O26  1  0.480  0.480  0.833  1.0
  O  O27  1  0.172  0.665  0.103  1.0
[/CIF]
.
The material structure described by Li4Ti3Co5O16 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(2)O6 octahedra, corners with two equivalent Ti(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra, corners with three equivalent Co(3)O6 octahedra, and corners with four equivalent Co(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 Ti(2)O6 octahedra, corners with two equivalent Co(4)O6 octahedra, corners with three equivalent Co(3)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra, and edges with two equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 61-67°. 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 Co(2)O6 octahedra, corners with two equivalent Ti(1)O6 octahedra, corners with three equivalent Co(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra, and edges with two equivalent Co(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 62-68°. 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 Ti(2)O6 octahedra, corners with two equivalent Co(2)O6 octahedra, corners with two equivalent Co(4)O6 octahedra, corners with three equivalent Co(1)O6 octahedra, and corners with four equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-64°. There are two inequivalent Ti sites. In the first Ti site, Ti(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 TiO6 octahedra that share corners with two equivalent Co(3)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, edges with two equivalent Co(2)O6 octahedra, and  an edgeedge with one Li(2)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 50°. In the second Ti site, Ti(2) is bonded to one O(10), one O(5), two equivalent O(1), and two equivalent O(9) atoms 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,  a cornercorner with one Li(2)O4 trigonal pyramid,  an edgeedge with one Co(3)O6 octahedra, edges with four equivalent Co(4)O6 octahedra, and  an edgeedge with one Li(3)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 51°. There are four 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 Ti(2)O6 octahedra, corners with four equivalent Co(4)O6 octahedra, corners with three equivalent Li(4)O4 tetrahedra, corners with three equivalent Li(3)O4 trigonal pyramids,  an edgeedge with one Co(2)O6 octahedra, and edges with two equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-51°. In the second Co site, Co(2) 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 Co(3)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 four equivalent Ti(1)O6 octahedra, and  an edgeedge with one Li(2)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 51°. In the third Co site, Co(3) 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 Co(2)O6 octahedra, corners with four equivalent Ti(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra, corners with three equivalent Li(2)O4 trigonal pyramids,  an edgeedge with one Ti(2)O6 octahedra, and edges with two equivalent Co(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-51°. In the fourth Co site, Co(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 CoO6 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,  a cornercorner with one Li(2)O4 trigonal pyramid,  an edgeedge with one Co(3)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, edges with two equivalent Co(4)O6 octahedra, and  an edgeedge with one Li(3)O4 trigonal pyramid. The corner-sharing octahedral tilt angles range from 50-51°. 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 Co(4) atom. In the second O site, O(2) is bonded to one Li(4), two equivalent Ti(1), and one Co(1) atom to form distorted OLiTi2Co tetrahedra that share corners with two equivalent O(4)LiTi2Co tetrahedra,  a cornercorner with one O(8)LiCo3 trigonal pyramid, and  a cornercorner with one O(10)LiTiCo2 trigonal pyramid. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Li(1), two equivalent Ti(1), and one Co(2) atom. In the fourth O site, O(4) is bonded to one Li(3), two equivalent Ti(1), and one Co(2) atom to form distorted OLiTi2Co tetrahedra that share corners with two equivalent O(2)LiTi2Co tetrahedra and  a cornercorner with one O(8)LiCo3 trigonal pyramid. In the fifth O site, O(5) is bonded to one Li(2), one Ti(2), and two equivalent Co(4) atoms to form distorted OLiTiCo2 tetrahedra that share corners with two equivalent O(12)LiCo3 tetrahedra, corners with three equivalent O(10)LiTiCo2 trigonal pyramids, and  an edgeedge with one O(8)LiCo3 trigonal pyramid. In the sixth O site, O(6) is bonded in a distorted rectangular see-saw-like geometry to one Li(4), one Ti(1), one Co(1), and one Co(2) atom. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), two equivalent Ti(1), and one Co(3) atom. In the eighth O site, O(8) is bonded to one Li(3), one Co(1), and two equivalent Co(4) atoms to form distorted OLiCo3 trigonal pyramids that share  a cornercorner with one O(2)LiTi2Co tetrahedra,  a cornercorner with one O(4)LiTi2Co tetrahedra, corners with two equivalent O(12)LiCo3 tetrahedra, corners with two equivalent O(10)LiTiCo2 trigonal pyramids, and  an edgeedge with one O(5)LiTiCo2 tetrahedra. 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(3), and one Co(4) atom. In the tenth O site, O(10) is bonded to one Li(4), one Ti(2), and two equivalent Co(4) atoms to form distorted OLiTiCo2 trigonal pyramids that share  a cornercorner with one O(2)LiTi2Co tetrahedra, corners with three equivalent O(5)LiTiCo2 tetrahedra, corners with two equivalent O(8)LiCo3 trigonal pyramids, and  an edgeedge with one O(12)LiCo3 tetrahedra. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one Ti(1), one Co(2), and one Co(3) atom. In the twelfth O site, O(12) is bonded to one Li(1), one Co(3), and two equivalent Co(4) atoms to form distorted OLiCo3 tetrahedra that share corners with two equivalent O(5)LiTiCo2 tetrahedra, corners with two equivalent O(8)LiCo3 trigonal pyramids, and  an edgeedge with one O(10)LiTiCo2 trigonal pyramid. is represented by the CIF card [CIF]
data_Li4Ti3Co5O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.727
_cell_length_b   5.727
_cell_length_c   9.310
_cell_angle_alpha   89.687
_cell_angle_beta   89.687
_cell_angle_gamma   60.894
_symmetry_Int_Tables_number   1
_cell_volume   266.776
_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  0.671  0.671  0.888  1.0
  Li  Li1  1  0.988  0.988  0.995  1.0
  Li  Li2  1  0.994  0.994  0.499  1.0
  Li  Li3  1  0.337  0.337  0.396  1.0
  Ti  Ti4  1  0.833  0.339  0.212  1.0
  Ti  Ti5  1  0.339  0.833  0.212  1.0
  Ti  Ti6  1  0.170  0.170  0.713  1.0
  Co  Co7  1  0.667  0.667  0.485  1.0
  Co  Co8  1  0.827  0.827  0.214  1.0
  Co  Co9  1  0.336  0.336  0.979  1.0
  Co  Co10  1  0.662  0.167  0.709  1.0
  Co  Co11  1  0.167  0.662  0.709  1.0
  O  O12  1  0.829  0.336  0.603  1.0
  O  O13  1  0.524  0.524  0.345  1.0
  O  O14  1  0.665  0.665  0.098  1.0
  O  O15  1  0.995  0.995  0.311  1.0
  O  O16  1  0.994  0.994  0.807  1.0
  O  O17  1  0.336  0.829  0.603  1.0
  O  O18  1  0.958  0.527  0.347  1.0
  O  O19  1  0.527  0.958  0.347  1.0
  O  O20  1  0.171  0.171  0.101  1.0
  O  O21  1  0.833  0.833  0.608  1.0
  O  O22  1  0.485  0.045  0.843  1.0
  O  O23  1  0.045  0.485  0.843  1.0
  O  O24  1  0.337  0.337  0.602  1.0
  O  O25  1  0.665  0.172  0.103  1.0
  O  O26  1  0.480  0.480  0.833  1.0
  O  O27  1  0.172  0.665  0.103  1.0
[/CIF]
.