The material structure described by Li4Ti3V2Co3O16 is Hausmannite-derived structured and crystallizes in the triclinic P1 space group. There are four inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(11), one O(12), one O(15), and one O(3) atom to form LiO4 tetrahedra that share  a cornercorner with one Ti(1)O6 octahedra,  a cornercorner with one Ti(2)O6 octahedra,  a cornercorner with one Co(1)O6 octahedra, corners with two equivalent Ti(3)O6 octahedra, corners with two equivalent Co(2)O6 octahedra, corners with two equivalent Co(3)O6 octahedra, and corners with three equivalent V(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 53-65°. In the second Li site, Li(2) is bonded to one O(14), one O(16), one O(5), and one O(9) atom to form distorted LiO4 trigonal pyramids that share  a cornercorner with one Ti(3)O6 octahedra,  a cornercorner with one Co(2)O6 octahedra,  a cornercorner with one Co(3)O6 octahedra, corners with three equivalent V(2)O6 octahedra,  an edgeedge with one Ti(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra, and  an edgeedge with one Co(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 62-69°. In the third Li site, Li(3) is bonded to one O(1), one O(10), one O(4), and one O(6) atom to form LiO4 tetrahedra that share  a cornercorner with one Ti(1)O6 octahedra,  a cornercorner with one Ti(2)O6 octahedra,  a cornercorner with one Co(1)O6 octahedra,  an edgeedge with one Ti(3)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra, and  an edgeedge with one Co(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 61-68°. In the fourth Li site, Li(4) is bonded to one O(13), one O(2), one O(7), and one O(8) atom to form LiO4 tetrahedra that share  a cornercorner with one Ti(3)O6 octahedra,  a cornercorner with one Co(2)O6 octahedra,  a cornercorner with one Co(3)O6 octahedra, corners with two equivalent Ti(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra, and corners with two equivalent Co(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 46-64°. There are three inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(14), one O(2), one O(3), one O(4), one O(7), and one O(9) atom to form TiO6 octahedra that share corners with two equivalent V(2)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(3)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra, edges with two equivalent Ti(2)O6 octahedra, edges with two equivalent Co(1)O6 octahedra, and  an edgeedge with one Li(2)O4 trigonal pyramid. The corner-sharing octahedral tilt angles range from 54-55°. In the second Ti site, Ti(2) is bonded to one O(16), one O(2), one O(3), one O(4), one O(8), and one O(9) atom to form distorted TiO6 octahedra that share corners with two equivalent V(2)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(3)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra, edges with two equivalent Ti(1)O6 octahedra, edges with two equivalent Co(1)O6 octahedra, and  an edgeedge with one Li(2)O4 trigonal pyramid. The corner-sharing octahedral tilt angles range from 52-54°. In the third Ti site, Ti(3) is bonded to one O(1), one O(11), one O(12), one O(13), one O(5), and one O(6) atom to form distorted TiO6 octahedra that share  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 V(2)O6 octahedra, edges with two equivalent Co(2)O6 octahedra, edges with two equivalent Co(3)O6 octahedra, and  an edgeedge with one Li(3)O4 tetrahedra. There are two inequivalent V sites. In the first V site, V(1) is bonded in a 6-coordinate geometry to one O(1), one O(10), one O(2), one O(6), one O(7), and one O(8) atom. In the second V site, V(2) is bonded to one O(11), one O(12), one O(14), one O(15), one O(16), and one O(9) atom to form distorted VO6 octahedra that share corners with two equivalent Ti(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra, corners with two equivalent Co(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(3)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra, and  an edgeedge with one Co(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 43-55°. There are three inequivalent Co sites. In the first Co site, Co(1) is bonded to one O(14), one O(16), one O(3), one O(4), one O(7), and one O(8) atom to form CoO6 octahedra that share corners with two equivalent V(2)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(3)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra, edges with two equivalent Ti(1)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, and  an edgeedge with one Li(2)O4 trigonal pyramid. The corner-sharing octahedral tilt angles range from 43-44°. In the second Co site, Co(2) is bonded to one O(1), one O(10), one O(11), one O(13), one O(15), and one O(5) atom to form CoO6 octahedra that share  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 V(2)O6 octahedra, edges with two equivalent Ti(3)O6 octahedra, edges with two equivalent Co(3)O6 octahedra, and  an edgeedge with one Li(3)O4 tetrahedra. In the third Co site, Co(3) is bonded to one O(10), one O(12), one O(13), one O(15), one O(5), and one O(6) atom to form CoO6 octahedra that share  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 V(2)O6 octahedra, edges with two equivalent Ti(3)O6 octahedra, edges with two equivalent Co(2)O6 octahedra, and  an edgeedge with one Li(3)O4 tetrahedra. There are sixteen 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(3), one V(1), and one Co(2) atom. In the second O site, O(2) is bonded in a distorted rectangular see-saw-like geometry to one Li(4), one Ti(1), one Ti(2), and one V(1) atom. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Li(1), one Ti(1), one Ti(2), and one Co(1) atom. In the fourth O site, O(4) is bonded to one Li(3), one Ti(1), one Ti(2), and one Co(1) atom to form corner-sharing OLiTi2Co tetrahedra. In the fifth O site, O(5) is bonded to one Li(2), one Ti(3), one Co(2), and one Co(3) atom to form corner-sharing OLiTiCo2 tetrahedra. In the sixth O site, O(6) is bonded in a distorted rectangular see-saw-like geometry to one Li(3), one Ti(3), one V(1), and one Co(3) atom. In the seventh O site, O(7) is bonded to one Li(4), one Ti(1), one V(1), and one Co(1) atom to form distorted OLiTiVCo tetrahedra that share  a cornercorner with one O(8)LiTiVCo tetrahedra, corners with two equivalent O(4)LiTi2Co tetrahedra, and  an edgeedge with one O(8)LiTiVCo tetrahedra. In the eighth O site, O(8) is bonded to one Li(4), one Ti(2), one V(1), and one Co(1) atom to form distorted OLiTiVCo tetrahedra that share  a cornercorner with one O(7)LiTiVCo tetrahedra, corners with two equivalent O(4)LiTi2Co tetrahedra, and  an edgeedge with one O(7)LiTiVCo tetrahedra. In the ninth O site, O(9) is bonded in a rectangular see-saw-like geometry to one Li(2), one Ti(1), one Ti(2), and one V(2) atom. In the tenth O site, O(10) is bonded in a distorted rectangular see-saw-like geometry to one Li(3), one V(1), one Co(2), and one Co(3) atom. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(1), one Ti(3), one V(2), and one Co(2) atom. In the twelfth O site, O(12) is bonded in a distorted rectangular see-saw-like geometry to one Li(1), one Ti(3), one V(2), and one Co(3) atom. In the thirteenth O site, O(13) is bonded in a rectangular see-saw-like geometry to one Li(4), one Ti(3), one Co(2), and one Co(3) atom. In the fourteenth O site, O(14) is bonded in a rectangular see-saw-like geometry to one Li(2), one Ti(1), one V(2), and one Co(1) atom. In the fifteenth O site, O(15) is bonded to one Li(1), one V(2), one Co(2), and one Co(3) atom to form distorted corner-sharing OLiVCo2 tetrahedra. In the sixteenth O site, O(16) is bonded in a distorted rectangular see-saw-like geometry to one Li(2), one Ti(2), one V(2), and one Co(1) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li4Ti3V2Co3O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.913
_cell_length_b   5.913
_cell_length_c   9.632
_cell_angle_alpha   90.213
_cell_angle_beta   90.367
_cell_angle_gamma   119.783
_symmetry_Int_Tables_number   1
_cell_volume   292.275
_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  0.328  0.662  0.096  1.0
  Li  Li1  1  0.007  0.011  0.014  1.0
  Li  Li2  1  0.996  0.999  0.506  1.0
  Li  Li3  1  0.674  0.332  0.596  1.0
  Ti  Ti4  1  0.169  0.818  0.776  1.0
  Ti  Ti5  1  0.655  0.799  0.779  1.0
  Ti  Ti6  1  0.814  0.635  0.264  1.0
  V  V7  1  0.331  0.664  0.499  1.0
  V  V8  1  0.650  0.293  0.011  1.0
  Co  Co9  1  0.175  0.346  0.793  1.0
  Co  Co10  1  0.338  0.168  0.293  1.0
  Co  Co11  1  0.825  0.171  0.291  1.0
  O  O12  1  0.173  0.819  0.415  1.0
  O  O13  1  0.484  0.965  0.666  1.0
  O  O14  1  0.343  0.680  0.894  1.0
  O  O15  1  0.003  0.008  0.699  1.0
  O  O16  1  0.989  0.987  0.206  1.0
  O  O17  1  0.640  0.817  0.415  1.0
  O  O18  1  0.046  0.534  0.657  1.0
  O  O19  1  0.496  0.531  0.654  1.0
  O  O20  1  0.837  0.672  0.898  1.0
  O  O21  1  0.172  0.351  0.420  1.0
  O  O22  1  0.521  0.490  0.150  1.0
  O  O23  1  0.960  0.495  0.143  1.0
  O  O24  1  0.677  0.353  0.394  1.0
  O  O25  1  0.351  0.178  0.909  1.0
  O  O26  1  0.522  0.044  0.141  1.0
  O  O27  1  0.823  0.175  0.911  1.0
[/CIF]
.
The material structure described by Li4Ti3V2Co3O16 is Hausmannite-derived structured and crystallizes in the triclinic P1 space group. There are four inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(11), one O(12), one O(15), and one O(3) atom to form LiO4 tetrahedra that share  a cornercorner with one Ti(1)O6 octahedra,  a cornercorner with one Ti(2)O6 octahedra,  a cornercorner with one Co(1)O6 octahedra, corners with two equivalent Ti(3)O6 octahedra, corners with two equivalent Co(2)O6 octahedra, corners with two equivalent Co(3)O6 octahedra, and corners with three equivalent V(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 53-65°. In the second Li site, Li(2) is bonded to one O(14), one O(16), one O(5), and one O(9) atom to form distorted LiO4 trigonal pyramids that share  a cornercorner with one Ti(3)O6 octahedra,  a cornercorner with one Co(2)O6 octahedra,  a cornercorner with one Co(3)O6 octahedra, corners with three equivalent V(2)O6 octahedra,  an edgeedge with one Ti(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra, and  an edgeedge with one Co(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 62-69°. In the third Li site, Li(3) is bonded to one O(1), one O(10), one O(4), and one O(6) atom to form LiO4 tetrahedra that share  a cornercorner with one Ti(1)O6 octahedra,  a cornercorner with one Ti(2)O6 octahedra,  a cornercorner with one Co(1)O6 octahedra,  an edgeedge with one Ti(3)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra, and  an edgeedge with one Co(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 61-68°. In the fourth Li site, Li(4) is bonded to one O(13), one O(2), one O(7), and one O(8) atom to form LiO4 tetrahedra that share  a cornercorner with one Ti(3)O6 octahedra,  a cornercorner with one Co(2)O6 octahedra,  a cornercorner with one Co(3)O6 octahedra, corners with two equivalent Ti(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra, and corners with two equivalent Co(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 46-64°. There are three inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(14), one O(2), one O(3), one O(4), one O(7), and one O(9) atom to form TiO6 octahedra that share corners with two equivalent V(2)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(3)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra, edges with two equivalent Ti(2)O6 octahedra, edges with two equivalent Co(1)O6 octahedra, and  an edgeedge with one Li(2)O4 trigonal pyramid. The corner-sharing octahedral tilt angles range from 54-55°. In the second Ti site, Ti(2) is bonded to one O(16), one O(2), one O(3), one O(4), one O(8), and one O(9) atom to form distorted TiO6 octahedra that share corners with two equivalent V(2)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(3)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra, edges with two equivalent Ti(1)O6 octahedra, edges with two equivalent Co(1)O6 octahedra, and  an edgeedge with one Li(2)O4 trigonal pyramid. The corner-sharing octahedral tilt angles range from 52-54°. In the third Ti site, Ti(3) is bonded to one O(1), one O(11), one O(12), one O(13), one O(5), and one O(6) atom to form distorted TiO6 octahedra that share  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 V(2)O6 octahedra, edges with two equivalent Co(2)O6 octahedra, edges with two equivalent Co(3)O6 octahedra, and  an edgeedge with one Li(3)O4 tetrahedra. There are two inequivalent V sites. In the first V site, V(1) is bonded in a 6-coordinate geometry to one O(1), one O(10), one O(2), one O(6), one O(7), and one O(8) atom. In the second V site, V(2) is bonded to one O(11), one O(12), one O(14), one O(15), one O(16), and one O(9) atom to form distorted VO6 octahedra that share corners with two equivalent Ti(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra, corners with two equivalent Co(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(3)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra, and  an edgeedge with one Co(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 43-55°. There are three inequivalent Co sites. In the first Co site, Co(1) is bonded to one O(14), one O(16), one O(3), one O(4), one O(7), and one O(8) atom to form CoO6 octahedra that share corners with two equivalent V(2)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(3)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra, edges with two equivalent Ti(1)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, and  an edgeedge with one Li(2)O4 trigonal pyramid. The corner-sharing octahedral tilt angles range from 43-44°. In the second Co site, Co(2) is bonded to one O(1), one O(10), one O(11), one O(13), one O(15), and one O(5) atom to form CoO6 octahedra that share  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 V(2)O6 octahedra, edges with two equivalent Ti(3)O6 octahedra, edges with two equivalent Co(3)O6 octahedra, and  an edgeedge with one Li(3)O4 tetrahedra. In the third Co site, Co(3) is bonded to one O(10), one O(12), one O(13), one O(15), one O(5), and one O(6) atom to form CoO6 octahedra that share  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 V(2)O6 octahedra, edges with two equivalent Ti(3)O6 octahedra, edges with two equivalent Co(2)O6 octahedra, and  an edgeedge with one Li(3)O4 tetrahedra. There are sixteen 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(3), one V(1), and one Co(2) atom. In the second O site, O(2) is bonded in a distorted rectangular see-saw-like geometry to one Li(4), one Ti(1), one Ti(2), and one V(1) atom. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Li(1), one Ti(1), one Ti(2), and one Co(1) atom. In the fourth O site, O(4) is bonded to one Li(3), one Ti(1), one Ti(2), and one Co(1) atom to form corner-sharing OLiTi2Co tetrahedra. In the fifth O site, O(5) is bonded to one Li(2), one Ti(3), one Co(2), and one Co(3) atom to form corner-sharing OLiTiCo2 tetrahedra. In the sixth O site, O(6) is bonded in a distorted rectangular see-saw-like geometry to one Li(3), one Ti(3), one V(1), and one Co(3) atom. In the seventh O site, O(7) is bonded to one Li(4), one Ti(1), one V(1), and one Co(1) atom to form distorted OLiTiVCo tetrahedra that share  a cornercorner with one O(8)LiTiVCo tetrahedra, corners with two equivalent O(4)LiTi2Co tetrahedra, and  an edgeedge with one O(8)LiTiVCo tetrahedra. In the eighth O site, O(8) is bonded to one Li(4), one Ti(2), one V(1), and one Co(1) atom to form distorted OLiTiVCo tetrahedra that share  a cornercorner with one O(7)LiTiVCo tetrahedra, corners with two equivalent O(4)LiTi2Co tetrahedra, and  an edgeedge with one O(7)LiTiVCo tetrahedra. In the ninth O site, O(9) is bonded in a rectangular see-saw-like geometry to one Li(2), one Ti(1), one Ti(2), and one V(2) atom. In the tenth O site, O(10) is bonded in a distorted rectangular see-saw-like geometry to one Li(3), one V(1), one Co(2), and one Co(3) atom. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(1), one Ti(3), one V(2), and one Co(2) atom. In the twelfth O site, O(12) is bonded in a distorted rectangular see-saw-like geometry to one Li(1), one Ti(3), one V(2), and one Co(3) atom. In the thirteenth O site, O(13) is bonded in a rectangular see-saw-like geometry to one Li(4), one Ti(3), one Co(2), and one Co(3) atom. In the fourteenth O site, O(14) is bonded in a rectangular see-saw-like geometry to one Li(2), one Ti(1), one V(2), and one Co(1) atom. In the fifteenth O site, O(15) is bonded to one Li(1), one V(2), one Co(2), and one Co(3) atom to form distorted corner-sharing OLiVCo2 tetrahedra. In the sixteenth O site, O(16) is bonded in a distorted rectangular see-saw-like geometry to one Li(2), one Ti(2), one V(2), and one Co(1) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li4Ti3V2Co3O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.913
_cell_length_b   5.913
_cell_length_c   9.632
_cell_angle_alpha   90.213
_cell_angle_beta   90.367
_cell_angle_gamma   119.783
_symmetry_Int_Tables_number   1
_cell_volume   292.275
_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  0.328  0.662  0.096  1.0
  Li  Li1  1  0.007  0.011  0.014  1.0
  Li  Li2  1  0.996  0.999  0.506  1.0
  Li  Li3  1  0.674  0.332  0.596  1.0
  Ti  Ti4  1  0.169  0.818  0.776  1.0
  Ti  Ti5  1  0.655  0.799  0.779  1.0
  Ti  Ti6  1  0.814  0.635  0.264  1.0
  V  V7  1  0.331  0.664  0.499  1.0
  V  V8  1  0.650  0.293  0.011  1.0
  Co  Co9  1  0.175  0.346  0.793  1.0
  Co  Co10  1  0.338  0.168  0.293  1.0
  Co  Co11  1  0.825  0.171  0.291  1.0
  O  O12  1  0.173  0.819  0.415  1.0
  O  O13  1  0.484  0.965  0.666  1.0
  O  O14  1  0.343  0.680  0.894  1.0
  O  O15  1  0.003  0.008  0.699  1.0
  O  O16  1  0.989  0.987  0.206  1.0
  O  O17  1  0.640  0.817  0.415  1.0
  O  O18  1  0.046  0.534  0.657  1.0
  O  O19  1  0.496  0.531  0.654  1.0
  O  O20  1  0.837  0.672  0.898  1.0
  O  O21  1  0.172  0.351  0.420  1.0
  O  O22  1  0.521  0.490  0.150  1.0
  O  O23  1  0.960  0.495  0.143  1.0
  O  O24  1  0.677  0.353  0.394  1.0
  O  O25  1  0.351  0.178  0.909  1.0
  O  O26  1  0.522  0.044  0.141  1.0
  O  O27  1  0.823  0.175  0.911  1.0
[/CIF]
.