The crystal structure described by Li4Ti3(CoO4)3 crystallizes in the triclinic P-1 space group. There are five inequivalent Li sites. In the first Li site, Li(1) is bonded to two equivalent O(1), two equivalent O(5), and two equivalent O(8) atoms to form LiO6 octahedra that share corners with two equivalent Co(1)O6 octahedra, corners with two equivalent Co(3)O6 octahedra, corners with two equivalent Co(4)O6 octahedra, edges with two equivalent Li(3)O6 octahedra, edges with two equivalent Li(5)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, edges with two equivalent Ti(3)O6 octahedra, and edges with two equivalent Co(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 9-14°. In the second Li site, Li(2) is bonded to two equivalent O(2), two equivalent O(6), and two equivalent O(7) atoms to form LiO6 octahedra that share corners with two equivalent Co(1)O6 octahedra, corners with two equivalent Co(2)O6 octahedra, corners with two equivalent Co(3)O6 octahedra, edges with two equivalent Li(3)O6 octahedra, edges with two equivalent Li(4)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, and edges with two equivalent Co(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 12-13°. In the third Li site, Li(3) is bonded to one O(3), one O(4), one O(5), one O(6), one O(7), and one O(8) atom to form LiO6 octahedra that share  a cornercorner with one Ti(2)O6 octahedra,  a cornercorner with one Ti(3)O6 octahedra, corners with four equivalent Ti(1)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Li(4)O6 octahedra,  an edgeedge with one Li(5)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra,  an edgeedge with one Ti(3)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra,  an edgeedge with one Co(3)O6 octahedra, and  an edgeedge with one Co(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 2-15°. In the fourth Li site, Li(4) is bonded to one O(10), one O(2), one O(4), one O(6), and two equivalent O(11) atoms to form LiO6 octahedra that share  a cornercorner with one Co(3)O6 octahedra, corners with two equivalent Co(4)O6 octahedra, corners with three equivalent Co(2)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Li(3)O6 octahedra,  an edgeedge with one Li(4)O6 octahedra,  an edgeedge with one Ti(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra,  an edgeedge with one Co(3)O6 octahedra, and edges with two equivalent Ti(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 3-17°. In the fifth Li site, Li(5) is bonded to one O(1), one O(3), one O(5), one O(9), and two equivalent O(12) atoms to form distorted LiO6 octahedra that share  a cornercorner with one Co(1)O6 octahedra, corners with two equivalent Co(2)O6 octahedra, corners with three equivalent Co(4)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Li(3)O6 octahedra,  an edgeedge with one Li(5)O6 octahedra,  an edgeedge with one Ti(1)O6 octahedra,  an edgeedge with one Ti(3)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra, and edges with two equivalent Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 5-16°. There are three inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(10), one O(5), one O(6), one O(7), one O(8), and one O(9) atom to form TiO6 octahedra that share corners with four equivalent Li(3)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Li(4)O6 octahedra,  an edgeedge with one Li(5)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra,  an edgeedge with one Ti(3)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra,  an edgeedge with one Co(3)O6 octahedra, and  an edgeedge with one Co(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 2-11°. In the second Ti site, Ti(2) is bonded to one O(12), one O(2), one O(3), one O(4), one O(7), and one O(9) atom to form TiO6 octahedra that share  a cornercorner with one Li(3)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Li(3)O6 octahedra,  an edgeedge with one Li(4)O6 octahedra,  an edgeedge with one Ti(1)O6 octahedra,  an edgeedge with one Ti(3)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra, edges with two equivalent Li(5)O6 octahedra, and edges with two equivalent Co(2)O6 octahedra. The corner-sharing octahedral tilt angles are 15°. In the third Ti site, Ti(3) is bonded to one O(1), one O(10), one O(11), one O(3), one O(4), and one O(8) atom to form TiO6 octahedra that share  a cornercorner with one Li(3)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Li(3)O6 octahedra,  an edgeedge with one Li(5)O6 octahedra,  an edgeedge with one Ti(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra,  an edgeedge with one Co(3)O6 octahedra, edges with two equivalent Li(4)O6 octahedra, and edges with two equivalent Co(4)O6 octahedra. The corner-sharing octahedral tilt angles are 11°. There are four inequivalent Co sites. In the first Co site, Co(1) is bonded to two equivalent O(12), two equivalent O(5), and two equivalent O(7) atoms to form CoO6 octahedra that share corners with two equivalent Li(1)O6 octahedra, corners with two equivalent Li(2)O6 octahedra, corners with two equivalent Li(5)O6 octahedra, edges with two equivalent Li(3)O6 octahedra, edges with two equivalent Li(5)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, and edges with two equivalent Co(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 9-14°. In the second Co site, Co(2) is bonded to one O(11), one O(3), one O(6), one O(9), and two equivalent O(2) atoms to form CoO6 octahedra that share  a cornercorner with one Li(2)O6 octahedra, corners with two equivalent Li(5)O6 octahedra, corners with three equivalent Li(4)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Li(3)O6 octahedra,  an edgeedge with one Li(4)O6 octahedra,  an edgeedge with one Ti(1)O6 octahedra,  an edgeedge with one Ti(3)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra,  an edgeedge with one Co(3)O6 octahedra, and edges with two equivalent Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 4-17°. In the third Co site, Co(3) is bonded to two equivalent O(11), two equivalent O(6), and two equivalent O(8) atoms to form CoO6 octahedra that share corners with two equivalent Li(1)O6 octahedra, corners with two equivalent Li(2)O6 octahedra, corners with two equivalent Li(4)O6 octahedra, edges with two equivalent Li(3)O6 octahedra, edges with two equivalent Li(4)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, edges with two equivalent Ti(3)O6 octahedra, and edges with two equivalent Co(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 10-15°. In the fourth Co site, Co(4) is bonded to one O(10), one O(12), one O(4), one O(5), and two equivalent O(1) atoms to form CoO6 octahedra that share  a cornercorner with one Li(1)O6 octahedra, corners with two equivalent Li(4)O6 octahedra, corners with three equivalent Li(5)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Li(3)O6 octahedra,  an edgeedge with one Li(5)O6 octahedra,  an edgeedge with one Ti(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra, and edges with two equivalent Ti(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 3-16°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded to one Li(1), one Li(5), one Ti(3), and two equivalent Co(4) atoms to form OLi2TiCo2 square pyramids that share  a cornercorner with one O(5)Li3TiCo2 octahedra,  a cornercorner with one O(4)Li2Ti2Co square pyramid,  a cornercorner with one O(8)Li2Ti2Co square pyramid,  a cornercorner with one O(1)Li2TiCo2 square pyramid,  a cornercorner with one O(11)Li2TiCo2 square pyramid, corners with two equivalent O(12)Li2TiCo2 square pyramids, edges with two equivalent O(5)Li3TiCo2 octahedra,  an edgeedge with one O(3)Li2Ti2Co square pyramid,  an edgeedge with one O(4)Li2Ti2Co square pyramid,  an edgeedge with one O(8)Li2Ti2Co square pyramid,  an edgeedge with one O(1)Li2TiCo2 square pyramid, and  an edgeedge with one O(12)Li2TiCo2 square pyramid. The corner-sharing octahedral tilt angles are 3°. In the second O site, O(2) is bonded to one Li(2), one Li(4), one Ti(2), and two equivalent Co(2) atoms to form OLi2TiCo2 square pyramids that share  a cornercorner with one O(6)Li3TiCo2 octahedra,  a cornercorner with one O(3)Li2Ti2Co square pyramid,  a cornercorner with one O(7)Li2Ti2Co square pyramid,  a cornercorner with one O(12)Li2TiCo2 square pyramid,  a cornercorner with one O(2)Li2TiCo2 square pyramid, corners with two equivalent O(11)Li2TiCo2 square pyramids, edges with two equivalent O(6)Li3TiCo2 octahedra,  an edgeedge with one O(3)Li2Ti2Co square pyramid,  an edgeedge with one O(4)Li2Ti2Co square pyramid,  an edgeedge with one O(7)Li2Ti2Co square pyramid,  an edgeedge with one O(11)Li2TiCo2 square pyramid, and  an edgeedge with one O(2)Li2TiCo2 square pyramid. The corner-sharing octahedral tilt angles are 3°. In the third O site, O(3) is bonded to one Li(3), one Li(5), one Ti(2), one Ti(3), and one Co(2) atom to form OLi2Ti2Co square pyramids that share  a cornercorner with one O(4)Li2Ti2Co square pyramid,  a cornercorner with one O(12)Li2TiCo2 square pyramid,  a cornercorner with one O(2)Li2TiCo2 square pyramid, corners with two equivalent O(7)Li2Ti2Co square pyramids,  an edgeedge with one O(5)Li3TiCo2 octahedra,  an edgeedge with one O(6)Li3TiCo2 octahedra,  an edgeedge with one O(4)Li2Ti2Co square pyramid,  an edgeedge with one O(8)Li2Ti2Co square pyramid,  an edgeedge with one O(1)Li2TiCo2 square pyramid,  an edgeedge with one O(11)Li2TiCo2 square pyramid,  an edgeedge with one O(12)Li2TiCo2 square pyramid, and  an edgeedge with one O(2)Li2TiCo2 square pyramid. In the fourth O site, O(4) is bonded to one Li(3), one Li(4), one Ti(2), one Ti(3), and one Co(4) atom to form OLi2Ti2Co square pyramids that share  a cornercorner with one O(3)Li2Ti2Co square pyramid,  a cornercorner with one O(1)Li2TiCo2 square pyramid,  a cornercorner with one O(11)Li2TiCo2 square pyramid, corners with two equivalent O(8)Li2Ti2Co square pyramids,  an edgeedge with one O(5)Li3TiCo2 octahedra,  an edgeedge with one O(6)Li3TiCo2 octahedra,  an edgeedge with one O(3)Li2Ti2Co square pyramid,  an edgeedge with one O(7)Li2Ti2Co square pyramid,  an edgeedge with one O(1)Li2TiCo2 square pyramid,  an edgeedge with one O(11)Li2TiCo2 square pyramid,  an edgeedge with one O(12)Li2TiCo2 square pyramid, and  an edgeedge with one O(2)Li2TiCo2 square pyramid. In the fifth O site, O(5) is bonded to one Li(1), one Li(3), one Li(5), one Ti(1), one Co(1), and one Co(4) atom to form OLi3TiCo2 octahedra that share corners with two equivalent O(5)Li3TiCo2 octahedra, corners with two equivalent O(6)Li3TiCo2 octahedra,  a cornercorner with one O(1)Li2TiCo2 square pyramid,  a cornercorner with one O(12)Li2TiCo2 square pyramid,  an edgeedge with one O(3)Li2Ti2Co square pyramid,  an edgeedge with one O(4)Li2Ti2Co square pyramid, edges with two equivalent O(7)Li2Ti2Co square pyramids, edges with two equivalent O(8)Li2Ti2Co square pyramids, edges with two equivalent O(1)Li2TiCo2 square pyramids, and edges with two equivalent O(12)Li2TiCo2 square pyramids. The corner-sharing octahedral tilt angles range from 0-5°. In the sixth O site, O(6) is bonded to one Li(2), one Li(3), one Li(4), one Ti(1), one Co(2), and one Co(3) atom to form OLi3TiCo2 octahedra that share corners with two equivalent O(5)Li3TiCo2 octahedra, corners with two equivalent O(6)Li3TiCo2 octahedra,  a cornercorner with one O(11)Li2TiCo2 square pyramid,  a cornercorner with one O(2)Li2TiCo2 square pyramid,  an edgeedge with one O(3)Li2Ti2Co square pyramid,  an edgeedge with one O(4)Li2Ti2Co square pyramid, edges with two equivalent O(7)Li2Ti2Co square pyramids, edges with two equivalent O(8)Li2Ti2Co square pyramids, edges with two equivalent O(11)Li2TiCo2 square pyramids, and edges with two equivalent O(2)Li2TiCo2 square pyramids. The corner-sharing octahedral tilt angles range from 0-5°. In the seventh O site, O(7) is bonded to one Li(2), one Li(3), one Ti(1), one Ti(2), and one Co(1) atom to form OLi2Ti2Co square pyramids that share  a cornercorner with one O(12)Li2TiCo2 square pyramid,  a cornercorner with one O(2)Li2TiCo2 square pyramid, corners with two equivalent O(3)Li2Ti2Co square pyramids, corners with two equivalent O(7)Li2Ti2Co square pyramids, corners with two equivalent O(8)Li2Ti2Co square pyramids, edges with two equivalent O(5)Li3TiCo2 octahedra, edges with two equivalent O(6)Li3TiCo2 octahedra,  an edgeedge with one O(4)Li2Ti2Co square pyramid,  an edgeedge with one O(12)Li2TiCo2 square pyramid, and  an edgeedge with one O(2)Li2TiCo2 square pyramid. In the eighth O site, O(8) is bonded to one Li(1), one Li(3), one Ti(1), one Ti(3), and one Co(3) atom to form OLi2Ti2Co square pyramids that share  a cornercorner with one O(1)Li2TiCo2 square pyramid,  a cornercorner with one O(11)Li2TiCo2 square pyramid, corners with two equivalent O(4)Li2Ti2Co square pyramids, corners with two equivalent O(7)Li2Ti2Co square pyramids, corners with two equivalent O(8)Li2Ti2Co square pyramids, edges with two equivalent O(5)Li3TiCo2 octahedra, edges with two equivalent O(6)Li3TiCo2 octahedra,  an edgeedge with one O(3)Li2Ti2Co square pyramid,  an edgeedge with one O(1)Li2TiCo2 square pyramid, and  an edgeedge with one O(11)Li2TiCo2 square pyramid. In the ninth O site, O(9) is bonded in a see-saw-like geometry to one Li(5), one Ti(1), one Ti(2), and one Co(2) atom. In the tenth O site, O(10) is bonded in a rectangular see-saw-like geometry to one Li(4), one Ti(1), one Ti(3), and one Co(4) atom. In the eleventh O site, O(11) is bonded to two equivalent Li(4), one Ti(3), one Co(2), and one Co(3) atom to form OLi2TiCo2 square pyramids that share  a cornercorner with one O(6)Li3TiCo2 octahedra,  a cornercorner with one O(4)Li2Ti2Co square pyramid,  a cornercorner with one O(8)Li2Ti2Co square pyramid,  a cornercorner with one O(1)Li2TiCo2 square pyramid,  a cornercorner with one O(11)Li2TiCo2 square pyramid, corners with two equivalent O(2)Li2TiCo2 square pyramids, edges with two equivalent O(6)Li3TiCo2 octahedra,  an edgeedge with one O(3)Li2Ti2Co square pyramid,  an edgeedge with one O(4)Li2Ti2Co square pyramid,  an edgeedge with one O(8)Li2Ti2Co square pyramid,  an edgeedge with one O(11)Li2TiCo2 square pyramid, and  an edgeedge with one O(2)Li2TiCo2 square pyramid. The corner-sharing octahedral tilt angles are 11°. In the twelfth O site, O(12) is bonded to two equivalent Li(5), one Ti(2), one Co(1), and one Co(4) atom to form distorted OLi2TiCo2 square pyramids that share  a cornercorner with one O(5)Li3TiCo2 octahedra,  a cornercorner with one O(3)Li2Ti2Co square pyramid,  a cornercorner with one O(7)Li2Ti2Co square pyramid,  a cornercorner with one O(12)Li2TiCo2 square pyramid,  a cornercorner with one O(2)Li2TiCo2 square pyramid, corners with two equivalent O(1)Li2TiCo2 square pyramids, edges with two equivalent O(5)Li3TiCo2 octahedra,  an edgeedge with one O(3)Li2Ti2Co square pyramid,  an edgeedge with one O(4)Li2Ti2Co square pyramid,  an edgeedge with one O(7)Li2Ti2Co square pyramid,  an edgeedge with one O(1)Li2TiCo2 square pyramid, and  an edgeedge with one O(12)Li2TiCo2 square pyramid. The corner-sharing octahedral tilt angles are 11°. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li4Ti3(CoO4)3
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.616
_cell_length_b   8.405
_cell_length_c   8.646
_cell_angle_alpha   88.669
_cell_angle_beta   91.432
_cell_angle_gamma   108.560
_symmetry_Int_Tables_number   1
_cell_volume   455.572
_cell_formula_units_Z   2
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  0.333  0.583  0.750  1.0
  Li  Li1  1  0.333  0.083  0.250  1.0
  Li  Li2  1  0.329  0.332  1.000  1.0
  Li  Li3  1  0.337  0.834  0.500  1.0
  Li  Li4  1  0.989  0.760  0.231  1.0
  Li  Li5  1  0.992  0.276  0.734  1.0
  Li  Li6  1  0.677  0.406  0.269  1.0
  Li  Li7  1  0.675  0.890  0.766  1.0
  Ti  Ti8  1  0.338  0.827  0.993  1.0
  Ti  Ti9  1  0.329  0.340  0.507  1.0
  Ti  Ti10  1  0.676  0.159  0.993  1.0
  Ti  Ti11  1  0.687  0.659  0.488  1.0
  Ti  Ti12  1  0.979  0.508  0.012  1.0
  Ti  Ti13  1  0.991  0.007  0.507  1.0
  Co  Co14  1  0.333  0.083  0.750  1.0
  Co  Co15  1  0.669  0.915  0.250  1.0
  Co  Co16  1  0.998  0.251  0.250  1.0
  Co  Co17  1  0.333  0.583  0.250  1.0
  Co  Co18  1  0.665  0.420  0.750  1.0
  Co  Co19  1  0.001  0.747  0.750  1.0
  O  O20  1  0.995  0.518  0.773  1.0
  O  O21  1  0.975  0.997  0.274  1.0
  O  O22  1  0.672  0.649  0.727  1.0
  O  O23  1  0.691  0.170  0.226  1.0
  O  O24  1  0.994  0.274  0.006  1.0
  O  O25  1  0.991  0.759  0.507  1.0
  O  O26  1  0.676  0.408  0.993  1.0
  O  O27  1  0.673  0.893  0.494  1.0
  O  O28  1  0.331  0.333  0.731  1.0
  O  O29  1  0.364  0.842  0.234  1.0
  O  O30  1  0.303  0.325  0.266  1.0
  O  O31  1  0.335  0.833  0.769  1.0
  O  O32  1  0.366  0.082  0.995  1.0
  O  O33  1  0.354  0.573  0.493  1.0
  O  O34  1  0.313  0.594  0.007  1.0
  O  O35  1  0.300  0.085  0.505  1.0
  O  O36  1  0.655  0.929  0.003  1.0
  O  O37  1  0.639  0.418  0.503  1.0
  O  O38  1  0.028  0.749  0.997  1.0
  O  O39  1  0.012  0.238  0.497  1.0
  O  O40  1  0.669  0.667  0.271  1.0
  O  O41  1  0.672  0.193  0.770  1.0
  O  O42  1  0.998  0.499  0.229  1.0
  O  O43  1  0.995  0.974  0.730  1.0
[/CIF]
.
The crystal structure described by Li4Ti3(CoO4)3 crystallizes in the triclinic P-1 space group. There are five inequivalent Li sites. In the first Li site, Li(1) is bonded to two equivalent O(1), two equivalent O(5), and two equivalent O(8) atoms to form LiO6 octahedra that share corners with two equivalent Co(1)O6 octahedra, corners with two equivalent Co(3)O6 octahedra, corners with two equivalent Co(4)O6 octahedra, edges with two equivalent Li(3)O6 octahedra, edges with two equivalent Li(5)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, edges with two equivalent Ti(3)O6 octahedra, and edges with two equivalent Co(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 9-14°. In the second Li site, Li(2) is bonded to two equivalent O(2), two equivalent O(6), and two equivalent O(7) atoms to form LiO6 octahedra that share corners with two equivalent Co(1)O6 octahedra, corners with two equivalent Co(2)O6 octahedra, corners with two equivalent Co(3)O6 octahedra, edges with two equivalent Li(3)O6 octahedra, edges with two equivalent Li(4)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, and edges with two equivalent Co(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 12-13°. In the third Li site, Li(3) is bonded to one O(3), one O(4), one O(5), one O(6), one O(7), and one O(8) atom to form LiO6 octahedra that share  a cornercorner with one Ti(2)O6 octahedra,  a cornercorner with one Ti(3)O6 octahedra, corners with four equivalent Ti(1)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Li(4)O6 octahedra,  an edgeedge with one Li(5)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra,  an edgeedge with one Ti(3)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra,  an edgeedge with one Co(3)O6 octahedra, and  an edgeedge with one Co(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 2-15°. In the fourth Li site, Li(4) is bonded to one O(10), one O(2), one O(4), one O(6), and two equivalent O(11) atoms to form LiO6 octahedra that share  a cornercorner with one Co(3)O6 octahedra, corners with two equivalent Co(4)O6 octahedra, corners with three equivalent Co(2)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Li(3)O6 octahedra,  an edgeedge with one Li(4)O6 octahedra,  an edgeedge with one Ti(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra,  an edgeedge with one Co(3)O6 octahedra, and edges with two equivalent Ti(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 3-17°. In the fifth Li site, Li(5) is bonded to one O(1), one O(3), one O(5), one O(9), and two equivalent O(12) atoms to form distorted LiO6 octahedra that share  a cornercorner with one Co(1)O6 octahedra, corners with two equivalent Co(2)O6 octahedra, corners with three equivalent Co(4)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Li(3)O6 octahedra,  an edgeedge with one Li(5)O6 octahedra,  an edgeedge with one Ti(1)O6 octahedra,  an edgeedge with one Ti(3)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra, and edges with two equivalent Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 5-16°. There are three inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(10), one O(5), one O(6), one O(7), one O(8), and one O(9) atom to form TiO6 octahedra that share corners with four equivalent Li(3)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Li(4)O6 octahedra,  an edgeedge with one Li(5)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra,  an edgeedge with one Ti(3)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra,  an edgeedge with one Co(3)O6 octahedra, and  an edgeedge with one Co(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 2-11°. In the second Ti site, Ti(2) is bonded to one O(12), one O(2), one O(3), one O(4), one O(7), and one O(9) atom to form TiO6 octahedra that share  a cornercorner with one Li(3)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Li(3)O6 octahedra,  an edgeedge with one Li(4)O6 octahedra,  an edgeedge with one Ti(1)O6 octahedra,  an edgeedge with one Ti(3)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra, edges with two equivalent Li(5)O6 octahedra, and edges with two equivalent Co(2)O6 octahedra. The corner-sharing octahedral tilt angles are 15°. In the third Ti site, Ti(3) is bonded to one O(1), one O(10), one O(11), one O(3), one O(4), and one O(8) atom to form TiO6 octahedra that share  a cornercorner with one Li(3)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Li(3)O6 octahedra,  an edgeedge with one Li(5)O6 octahedra,  an edgeedge with one Ti(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra,  an edgeedge with one Co(3)O6 octahedra, edges with two equivalent Li(4)O6 octahedra, and edges with two equivalent Co(4)O6 octahedra. The corner-sharing octahedral tilt angles are 11°. There are four inequivalent Co sites. In the first Co site, Co(1) is bonded to two equivalent O(12), two equivalent O(5), and two equivalent O(7) atoms to form CoO6 octahedra that share corners with two equivalent Li(1)O6 octahedra, corners with two equivalent Li(2)O6 octahedra, corners with two equivalent Li(5)O6 octahedra, edges with two equivalent Li(3)O6 octahedra, edges with two equivalent Li(5)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, and edges with two equivalent Co(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 9-14°. In the second Co site, Co(2) is bonded to one O(11), one O(3), one O(6), one O(9), and two equivalent O(2) atoms to form CoO6 octahedra that share  a cornercorner with one Li(2)O6 octahedra, corners with two equivalent Li(5)O6 octahedra, corners with three equivalent Li(4)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Li(3)O6 octahedra,  an edgeedge with one Li(4)O6 octahedra,  an edgeedge with one Ti(1)O6 octahedra,  an edgeedge with one Ti(3)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra,  an edgeedge with one Co(3)O6 octahedra, and edges with two equivalent Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 4-17°. In the third Co site, Co(3) is bonded to two equivalent O(11), two equivalent O(6), and two equivalent O(8) atoms to form CoO6 octahedra that share corners with two equivalent Li(1)O6 octahedra, corners with two equivalent Li(2)O6 octahedra, corners with two equivalent Li(4)O6 octahedra, edges with two equivalent Li(3)O6 octahedra, edges with two equivalent Li(4)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, edges with two equivalent Ti(3)O6 octahedra, and edges with two equivalent Co(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 10-15°. In the fourth Co site, Co(4) is bonded to one O(10), one O(12), one O(4), one O(5), and two equivalent O(1) atoms to form CoO6 octahedra that share  a cornercorner with one Li(1)O6 octahedra, corners with two equivalent Li(4)O6 octahedra, corners with three equivalent Li(5)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Li(3)O6 octahedra,  an edgeedge with one Li(5)O6 octahedra,  an edgeedge with one Ti(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra, and edges with two equivalent Ti(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 3-16°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded to one Li(1), one Li(5), one Ti(3), and two equivalent Co(4) atoms to form OLi2TiCo2 square pyramids that share  a cornercorner with one O(5)Li3TiCo2 octahedra,  a cornercorner with one O(4)Li2Ti2Co square pyramid,  a cornercorner with one O(8)Li2Ti2Co square pyramid,  a cornercorner with one O(1)Li2TiCo2 square pyramid,  a cornercorner with one O(11)Li2TiCo2 square pyramid, corners with two equivalent O(12)Li2TiCo2 square pyramids, edges with two equivalent O(5)Li3TiCo2 octahedra,  an edgeedge with one O(3)Li2Ti2Co square pyramid,  an edgeedge with one O(4)Li2Ti2Co square pyramid,  an edgeedge with one O(8)Li2Ti2Co square pyramid,  an edgeedge with one O(1)Li2TiCo2 square pyramid, and  an edgeedge with one O(12)Li2TiCo2 square pyramid. The corner-sharing octahedral tilt angles are 3°. In the second O site, O(2) is bonded to one Li(2), one Li(4), one Ti(2), and two equivalent Co(2) atoms to form OLi2TiCo2 square pyramids that share  a cornercorner with one O(6)Li3TiCo2 octahedra,  a cornercorner with one O(3)Li2Ti2Co square pyramid,  a cornercorner with one O(7)Li2Ti2Co square pyramid,  a cornercorner with one O(12)Li2TiCo2 square pyramid,  a cornercorner with one O(2)Li2TiCo2 square pyramid, corners with two equivalent O(11)Li2TiCo2 square pyramids, edges with two equivalent O(6)Li3TiCo2 octahedra,  an edgeedge with one O(3)Li2Ti2Co square pyramid,  an edgeedge with one O(4)Li2Ti2Co square pyramid,  an edgeedge with one O(7)Li2Ti2Co square pyramid,  an edgeedge with one O(11)Li2TiCo2 square pyramid, and  an edgeedge with one O(2)Li2TiCo2 square pyramid. The corner-sharing octahedral tilt angles are 3°. In the third O site, O(3) is bonded to one Li(3), one Li(5), one Ti(2), one Ti(3), and one Co(2) atom to form OLi2Ti2Co square pyramids that share  a cornercorner with one O(4)Li2Ti2Co square pyramid,  a cornercorner with one O(12)Li2TiCo2 square pyramid,  a cornercorner with one O(2)Li2TiCo2 square pyramid, corners with two equivalent O(7)Li2Ti2Co square pyramids,  an edgeedge with one O(5)Li3TiCo2 octahedra,  an edgeedge with one O(6)Li3TiCo2 octahedra,  an edgeedge with one O(4)Li2Ti2Co square pyramid,  an edgeedge with one O(8)Li2Ti2Co square pyramid,  an edgeedge with one O(1)Li2TiCo2 square pyramid,  an edgeedge with one O(11)Li2TiCo2 square pyramid,  an edgeedge with one O(12)Li2TiCo2 square pyramid, and  an edgeedge with one O(2)Li2TiCo2 square pyramid. In the fourth O site, O(4) is bonded to one Li(3), one Li(4), one Ti(2), one Ti(3), and one Co(4) atom to form OLi2Ti2Co square pyramids that share  a cornercorner with one O(3)Li2Ti2Co square pyramid,  a cornercorner with one O(1)Li2TiCo2 square pyramid,  a cornercorner with one O(11)Li2TiCo2 square pyramid, corners with two equivalent O(8)Li2Ti2Co square pyramids,  an edgeedge with one O(5)Li3TiCo2 octahedra,  an edgeedge with one O(6)Li3TiCo2 octahedra,  an edgeedge with one O(3)Li2Ti2Co square pyramid,  an edgeedge with one O(7)Li2Ti2Co square pyramid,  an edgeedge with one O(1)Li2TiCo2 square pyramid,  an edgeedge with one O(11)Li2TiCo2 square pyramid,  an edgeedge with one O(12)Li2TiCo2 square pyramid, and  an edgeedge with one O(2)Li2TiCo2 square pyramid. In the fifth O site, O(5) is bonded to one Li(1), one Li(3), one Li(5), one Ti(1), one Co(1), and one Co(4) atom to form OLi3TiCo2 octahedra that share corners with two equivalent O(5)Li3TiCo2 octahedra, corners with two equivalent O(6)Li3TiCo2 octahedra,  a cornercorner with one O(1)Li2TiCo2 square pyramid,  a cornercorner with one O(12)Li2TiCo2 square pyramid,  an edgeedge with one O(3)Li2Ti2Co square pyramid,  an edgeedge with one O(4)Li2Ti2Co square pyramid, edges with two equivalent O(7)Li2Ti2Co square pyramids, edges with two equivalent O(8)Li2Ti2Co square pyramids, edges with two equivalent O(1)Li2TiCo2 square pyramids, and edges with two equivalent O(12)Li2TiCo2 square pyramids. The corner-sharing octahedral tilt angles range from 0-5°. In the sixth O site, O(6) is bonded to one Li(2), one Li(3), one Li(4), one Ti(1), one Co(2), and one Co(3) atom to form OLi3TiCo2 octahedra that share corners with two equivalent O(5)Li3TiCo2 octahedra, corners with two equivalent O(6)Li3TiCo2 octahedra,  a cornercorner with one O(11)Li2TiCo2 square pyramid,  a cornercorner with one O(2)Li2TiCo2 square pyramid,  an edgeedge with one O(3)Li2Ti2Co square pyramid,  an edgeedge with one O(4)Li2Ti2Co square pyramid, edges with two equivalent O(7)Li2Ti2Co square pyramids, edges with two equivalent O(8)Li2Ti2Co square pyramids, edges with two equivalent O(11)Li2TiCo2 square pyramids, and edges with two equivalent O(2)Li2TiCo2 square pyramids. The corner-sharing octahedral tilt angles range from 0-5°. In the seventh O site, O(7) is bonded to one Li(2), one Li(3), one Ti(1), one Ti(2), and one Co(1) atom to form OLi2Ti2Co square pyramids that share  a cornercorner with one O(12)Li2TiCo2 square pyramid,  a cornercorner with one O(2)Li2TiCo2 square pyramid, corners with two equivalent O(3)Li2Ti2Co square pyramids, corners with two equivalent O(7)Li2Ti2Co square pyramids, corners with two equivalent O(8)Li2Ti2Co square pyramids, edges with two equivalent O(5)Li3TiCo2 octahedra, edges with two equivalent O(6)Li3TiCo2 octahedra,  an edgeedge with one O(4)Li2Ti2Co square pyramid,  an edgeedge with one O(12)Li2TiCo2 square pyramid, and  an edgeedge with one O(2)Li2TiCo2 square pyramid. In the eighth O site, O(8) is bonded to one Li(1), one Li(3), one Ti(1), one Ti(3), and one Co(3) atom to form OLi2Ti2Co square pyramids that share  a cornercorner with one O(1)Li2TiCo2 square pyramid,  a cornercorner with one O(11)Li2TiCo2 square pyramid, corners with two equivalent O(4)Li2Ti2Co square pyramids, corners with two equivalent O(7)Li2Ti2Co square pyramids, corners with two equivalent O(8)Li2Ti2Co square pyramids, edges with two equivalent O(5)Li3TiCo2 octahedra, edges with two equivalent O(6)Li3TiCo2 octahedra,  an edgeedge with one O(3)Li2Ti2Co square pyramid,  an edgeedge with one O(1)Li2TiCo2 square pyramid, and  an edgeedge with one O(11)Li2TiCo2 square pyramid. In the ninth O site, O(9) is bonded in a see-saw-like geometry to one Li(5), one Ti(1), one Ti(2), and one Co(2) atom. In the tenth O site, O(10) is bonded in a rectangular see-saw-like geometry to one Li(4), one Ti(1), one Ti(3), and one Co(4) atom. In the eleventh O site, O(11) is bonded to two equivalent Li(4), one Ti(3), one Co(2), and one Co(3) atom to form OLi2TiCo2 square pyramids that share  a cornercorner with one O(6)Li3TiCo2 octahedra,  a cornercorner with one O(4)Li2Ti2Co square pyramid,  a cornercorner with one O(8)Li2Ti2Co square pyramid,  a cornercorner with one O(1)Li2TiCo2 square pyramid,  a cornercorner with one O(11)Li2TiCo2 square pyramid, corners with two equivalent O(2)Li2TiCo2 square pyramids, edges with two equivalent O(6)Li3TiCo2 octahedra,  an edgeedge with one O(3)Li2Ti2Co square pyramid,  an edgeedge with one O(4)Li2Ti2Co square pyramid,  an edgeedge with one O(8)Li2Ti2Co square pyramid,  an edgeedge with one O(11)Li2TiCo2 square pyramid, and  an edgeedge with one O(2)Li2TiCo2 square pyramid. The corner-sharing octahedral tilt angles are 11°. In the twelfth O site, O(12) is bonded to two equivalent Li(5), one Ti(2), one Co(1), and one Co(4) atom to form distorted OLi2TiCo2 square pyramids that share  a cornercorner with one O(5)Li3TiCo2 octahedra,  a cornercorner with one O(3)Li2Ti2Co square pyramid,  a cornercorner with one O(7)Li2Ti2Co square pyramid,  a cornercorner with one O(12)Li2TiCo2 square pyramid,  a cornercorner with one O(2)Li2TiCo2 square pyramid, corners with two equivalent O(1)Li2TiCo2 square pyramids, edges with two equivalent O(5)Li3TiCo2 octahedra,  an edgeedge with one O(3)Li2Ti2Co square pyramid,  an edgeedge with one O(4)Li2Ti2Co square pyramid,  an edgeedge with one O(7)Li2Ti2Co square pyramid,  an edgeedge with one O(1)Li2TiCo2 square pyramid, and  an edgeedge with one O(12)Li2TiCo2 square pyramid. The corner-sharing octahedral tilt angles are 11°. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li4Ti3(CoO4)3
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.616
_cell_length_b   8.405
_cell_length_c   8.646
_cell_angle_alpha   88.669
_cell_angle_beta   91.432
_cell_angle_gamma   108.560
_symmetry_Int_Tables_number   1
_cell_volume   455.572
_cell_formula_units_Z   2
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  0.333  0.583  0.750  1.0
  Li  Li1  1  0.333  0.083  0.250  1.0
  Li  Li2  1  0.329  0.332  1.000  1.0
  Li  Li3  1  0.337  0.834  0.500  1.0
  Li  Li4  1  0.989  0.760  0.231  1.0
  Li  Li5  1  0.992  0.276  0.734  1.0
  Li  Li6  1  0.677  0.406  0.269  1.0
  Li  Li7  1  0.675  0.890  0.766  1.0
  Ti  Ti8  1  0.338  0.827  0.993  1.0
  Ti  Ti9  1  0.329  0.340  0.507  1.0
  Ti  Ti10  1  0.676  0.159  0.993  1.0
  Ti  Ti11  1  0.687  0.659  0.488  1.0
  Ti  Ti12  1  0.979  0.508  0.012  1.0
  Ti  Ti13  1  0.991  0.007  0.507  1.0
  Co  Co14  1  0.333  0.083  0.750  1.0
  Co  Co15  1  0.669  0.915  0.250  1.0
  Co  Co16  1  0.998  0.251  0.250  1.0
  Co  Co17  1  0.333  0.583  0.250  1.0
  Co  Co18  1  0.665  0.420  0.750  1.0
  Co  Co19  1  0.001  0.747  0.750  1.0
  O  O20  1  0.995  0.518  0.773  1.0
  O  O21  1  0.975  0.997  0.274  1.0
  O  O22  1  0.672  0.649  0.727  1.0
  O  O23  1  0.691  0.170  0.226  1.0
  O  O24  1  0.994  0.274  0.006  1.0
  O  O25  1  0.991  0.759  0.507  1.0
  O  O26  1  0.676  0.408  0.993  1.0
  O  O27  1  0.673  0.893  0.494  1.0
  O  O28  1  0.331  0.333  0.731  1.0
  O  O29  1  0.364  0.842  0.234  1.0
  O  O30  1  0.303  0.325  0.266  1.0
  O  O31  1  0.335  0.833  0.769  1.0
  O  O32  1  0.366  0.082  0.995  1.0
  O  O33  1  0.354  0.573  0.493  1.0
  O  O34  1  0.313  0.594  0.007  1.0
  O  O35  1  0.300  0.085  0.505  1.0
  O  O36  1  0.655  0.929  0.003  1.0
  O  O37  1  0.639  0.418  0.503  1.0
  O  O38  1  0.028  0.749  0.997  1.0
  O  O39  1  0.012  0.238  0.497  1.0
  O  O40  1  0.669  0.667  0.271  1.0
  O  O41  1  0.672  0.193  0.770  1.0
  O  O42  1  0.998  0.499  0.229  1.0
  O  O43  1  0.995  0.974  0.730  1.0
[/CIF]
.