The structure described by Li4Ti2Co3Ni3O16 is Hausmannite-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 Ni(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 Ni(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-66°. 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 Ni(2)O6 octahedra, corners with three equivalent Ti(2)O6 octahedra,  an edgeedge with one Ni(1)O6 octahedra, and edges with two equivalent Co(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-66°. 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 tetrahedra that share  a cornercorner with one Ni(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 Ni(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-69°. 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 Ni(1)O6 octahedra, corners with two equivalent Ni(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 56-68°. 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 Ni(2)O6 octahedra, corners with three equivalent Li(3)O4 tetrahedra, corners with three equivalent Li(4)O4 tetrahedra,  an edgeedge with one Ni(1)O6 octahedra, and edges with two equivalent Co(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 48-54°. 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 distorted TiO6 octahedra that share corners with two equivalent Ni(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 Ni(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 47-58°. 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,  a cornercorner with one Li(3)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Ti(1)O6 octahedra, edges with two equivalent Co(1)O6 octahedra, edges with two equivalent Ni(1)O6 octahedra, and  an edgeedge with one Li(2)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 47-51°. 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 Ni(2)O6 octahedra, and  an edgeedge with one Li(3)O4 tetrahedra. The corner-sharing octahedral tilt angles are 48°. There are two inequivalent Ni sites. In the first Ni site, Ni(1) is bonded to one O(3), one O(4), two equivalent O(11), and two equivalent O(6) atoms to form NiO6 octahedra that share corners with two equivalent Ti(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,  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 58°. In the second Ni site, Ni(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 NiO6 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 Co(2)O6 octahedra, edges with two equivalent Ni(2)O6 octahedra, and  an edgeedge with one Li(3)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 52-54°. 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 Co(2), and one Ni(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  a cornercorner with one O(10)LiCoNi2 tetrahedra, corners with two equivalent O(4)LiCo2Ni tetrahedra, corners with two equivalent O(6)LiTiCoNi tetrahedra, and edges with two equivalent O(6)LiTiCoNi tetrahedra. In the third O site, O(3) is bonded in a distorted rectangular see-saw-like geometry to one Li(1), two equivalent Co(1), and one Ni(1) atom. In the fourth O site, O(4) is bonded to one Li(3), two equivalent Co(1), and one Ni(1) atom to form OLiCo2Ni tetrahedra that share corners with four equivalent O(6)LiTiCoNi tetrahedra and corners with two equivalent O(2)LiTiCo2 trigonal pyramids. In the fifth O site, O(5) is bonded to one Li(2), one Co(2), and two equivalent Ni(2) atoms to form OLiCoNi2 tetrahedra that share corners with two equivalent O(12)LiTiNi2 tetrahedra, corners with three equivalent O(10)LiCoNi2 tetrahedra, and corners with four equivalent O(9)LiTiCoNi trigonal pyramids. In the sixth O site, O(6) is bonded to one Li(4), one Ti(1), one Co(1), and one Ni(1) atom to form distorted OLiTiCoNi tetrahedra that share  a cornercorner with one O(10)LiCoNi2 tetrahedra,  a cornercorner with one O(6)LiTiCoNi tetrahedra, corners with two equivalent O(4)LiCo2Ni tetrahedra,  a cornercorner with one O(2)LiTiCo2 trigonal pyramid,  an edgeedge with one O(6)LiTiCoNi 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 Ni(2) atoms. In the ninth O site, O(9) is bonded to one Li(1), one Ti(2), one Co(2), and one Ni(2) atom to form distorted OLiTiCoNi trigonal pyramids that share  a cornercorner with one O(12)LiTiNi2 tetrahedra, corners with two equivalent O(5)LiCoNi2 tetrahedra,  a cornercorner with one O(9)LiTiCoNi trigonal pyramid,  an edgeedge with one O(10)LiCoNi2 tetrahedra,  an edgeedge with one O(12)LiTiNi2 tetrahedra, and  an edgeedge with one O(9)LiTiCoNi trigonal pyramid. In the tenth O site, O(10) is bonded to one Li(4), one Co(2), and two equivalent Ni(2) atoms to form distorted OLiCoNi2 tetrahedra that share corners with two equivalent O(6)LiTiCoNi tetrahedra, corners with three equivalent O(5)LiCoNi2 tetrahedra,  a cornercorner with one O(2)LiTiCo2 trigonal pyramid,  an edgeedge with one O(12)LiTiNi2 tetrahedra, and edges with two equivalent O(9)LiTiCoNi trigonal pyramids. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one Ti(2), one Co(1), and one Ni(1) atom. In the twelfth O site, O(12) is bonded to one Li(1), one Ti(2), and two equivalent Ni(2) atoms to form distorted OLiTiNi2 tetrahedra that share corners with two equivalent O(5)LiCoNi2 tetrahedra, corners with two equivalent O(9)LiTiCoNi trigonal pyramids,  an edgeedge with one O(10)LiCoNi2 tetrahedra, and edges with two equivalent O(9)LiTiCoNi trigonal pyramids. is represented by the CIF file [CIF]
data_Li4Ti2Co3Ni3O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.841
_cell_length_b   5.841
_cell_length_c   9.402
_cell_angle_alpha   87.719
_cell_angle_beta   87.719
_cell_angle_gamma   58.260
_symmetry_Int_Tables_number   1
_cell_volume   272.499
_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  0.658  0.658  0.103  1.0
  Li  Li1  1  1.000  1.000  0.005  1.0
  Li  Li2  1  0.005  0.005  0.503  1.0
  Li  Li3  1  0.332  0.332  0.606  1.0
  Ti  Ti4  1  0.670  0.670  0.505  1.0
  Ti  Ti5  1  0.331  0.331  0.004  1.0
  Co  Co6  1  0.343  0.834  0.784  1.0
  Co  Co7  1  0.834  0.343  0.784  1.0
  Co  Co8  1  0.171  0.171  0.284  1.0
  Ni  Ni9  1  0.832  0.832  0.789  1.0
  Ni  Ni10  1  0.168  0.663  0.286  1.0
  Ni  Ni11  1  0.663  0.168  0.286  1.0
  O  O12  1  0.340  0.847  0.402  1.0
  O  O13  1  0.519  0.519  0.667  1.0
  O  O14  1  0.654  0.654  0.890  1.0
  O  O15  1  0.012  0.012  0.695  1.0
  O  O16  1  0.007  0.007  0.196  1.0
  O  O17  1  0.847  0.340  0.402  1.0
  O  O18  1  0.502  0.960  0.659  1.0
  O  O19  1  0.960  0.502  0.659  1.0
  O  O20  1  0.165  0.165  0.896  1.0
  O  O21  1  0.841  0.841  0.409  1.0
  O  O22  1  0.031  0.469  0.158  1.0
  O  O23  1  0.469  0.031  0.158  1.0
  O  O24  1  0.328  0.328  0.386  1.0
  O  O25  1  0.181  0.668  0.908  1.0
  O  O26  1  0.476  0.476  0.161  1.0
  O  O27  1  0.668  0.181  0.908  1.0
[/CIF]
.
The structure described by Li4Ti2Co3Ni3O16 is Hausmannite-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 Ni(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 Ni(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-66°. 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 Ni(2)O6 octahedra, corners with three equivalent Ti(2)O6 octahedra,  an edgeedge with one Ni(1)O6 octahedra, and edges with two equivalent Co(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-66°. 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 tetrahedra that share  a cornercorner with one Ni(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 Ni(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-69°. 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 Ni(1)O6 octahedra, corners with two equivalent Ni(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 56-68°. 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 Ni(2)O6 octahedra, corners with three equivalent Li(3)O4 tetrahedra, corners with three equivalent Li(4)O4 tetrahedra,  an edgeedge with one Ni(1)O6 octahedra, and edges with two equivalent Co(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 48-54°. 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 distorted TiO6 octahedra that share corners with two equivalent Ni(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 Ni(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 47-58°. 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,  a cornercorner with one Li(3)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Ti(1)O6 octahedra, edges with two equivalent Co(1)O6 octahedra, edges with two equivalent Ni(1)O6 octahedra, and  an edgeedge with one Li(2)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 47-51°. 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 Ni(2)O6 octahedra, and  an edgeedge with one Li(3)O4 tetrahedra. The corner-sharing octahedral tilt angles are 48°. There are two inequivalent Ni sites. In the first Ni site, Ni(1) is bonded to one O(3), one O(4), two equivalent O(11), and two equivalent O(6) atoms to form NiO6 octahedra that share corners with two equivalent Ti(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,  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 58°. In the second Ni site, Ni(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 NiO6 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 Co(2)O6 octahedra, edges with two equivalent Ni(2)O6 octahedra, and  an edgeedge with one Li(3)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 52-54°. 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 Co(2), and one Ni(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  a cornercorner with one O(10)LiCoNi2 tetrahedra, corners with two equivalent O(4)LiCo2Ni tetrahedra, corners with two equivalent O(6)LiTiCoNi tetrahedra, and edges with two equivalent O(6)LiTiCoNi tetrahedra. In the third O site, O(3) is bonded in a distorted rectangular see-saw-like geometry to one Li(1), two equivalent Co(1), and one Ni(1) atom. In the fourth O site, O(4) is bonded to one Li(3), two equivalent Co(1), and one Ni(1) atom to form OLiCo2Ni tetrahedra that share corners with four equivalent O(6)LiTiCoNi tetrahedra and corners with two equivalent O(2)LiTiCo2 trigonal pyramids. In the fifth O site, O(5) is bonded to one Li(2), one Co(2), and two equivalent Ni(2) atoms to form OLiCoNi2 tetrahedra that share corners with two equivalent O(12)LiTiNi2 tetrahedra, corners with three equivalent O(10)LiCoNi2 tetrahedra, and corners with four equivalent O(9)LiTiCoNi trigonal pyramids. In the sixth O site, O(6) is bonded to one Li(4), one Ti(1), one Co(1), and one Ni(1) atom to form distorted OLiTiCoNi tetrahedra that share  a cornercorner with one O(10)LiCoNi2 tetrahedra,  a cornercorner with one O(6)LiTiCoNi tetrahedra, corners with two equivalent O(4)LiCo2Ni tetrahedra,  a cornercorner with one O(2)LiTiCo2 trigonal pyramid,  an edgeedge with one O(6)LiTiCoNi 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 Ni(2) atoms. In the ninth O site, O(9) is bonded to one Li(1), one Ti(2), one Co(2), and one Ni(2) atom to form distorted OLiTiCoNi trigonal pyramids that share  a cornercorner with one O(12)LiTiNi2 tetrahedra, corners with two equivalent O(5)LiCoNi2 tetrahedra,  a cornercorner with one O(9)LiTiCoNi trigonal pyramid,  an edgeedge with one O(10)LiCoNi2 tetrahedra,  an edgeedge with one O(12)LiTiNi2 tetrahedra, and  an edgeedge with one O(9)LiTiCoNi trigonal pyramid. In the tenth O site, O(10) is bonded to one Li(4), one Co(2), and two equivalent Ni(2) atoms to form distorted OLiCoNi2 tetrahedra that share corners with two equivalent O(6)LiTiCoNi tetrahedra, corners with three equivalent O(5)LiCoNi2 tetrahedra,  a cornercorner with one O(2)LiTiCo2 trigonal pyramid,  an edgeedge with one O(12)LiTiNi2 tetrahedra, and edges with two equivalent O(9)LiTiCoNi trigonal pyramids. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one Ti(2), one Co(1), and one Ni(1) atom. In the twelfth O site, O(12) is bonded to one Li(1), one Ti(2), and two equivalent Ni(2) atoms to form distorted OLiTiNi2 tetrahedra that share corners with two equivalent O(5)LiCoNi2 tetrahedra, corners with two equivalent O(9)LiTiCoNi trigonal pyramids,  an edgeedge with one O(10)LiCoNi2 tetrahedra, and edges with two equivalent O(9)LiTiCoNi trigonal pyramids. is represented by the CIF file [CIF]
data_Li4Ti2Co3Ni3O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.841
_cell_length_b   5.841
_cell_length_c   9.402
_cell_angle_alpha   87.719
_cell_angle_beta   87.719
_cell_angle_gamma   58.260
_symmetry_Int_Tables_number   1
_cell_volume   272.499
_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  0.658  0.658  0.103  1.0
  Li  Li1  1  1.000  1.000  0.005  1.0
  Li  Li2  1  0.005  0.005  0.503  1.0
  Li  Li3  1  0.332  0.332  0.606  1.0
  Ti  Ti4  1  0.670  0.670  0.505  1.0
  Ti  Ti5  1  0.331  0.331  0.004  1.0
  Co  Co6  1  0.343  0.834  0.784  1.0
  Co  Co7  1  0.834  0.343  0.784  1.0
  Co  Co8  1  0.171  0.171  0.284  1.0
  Ni  Ni9  1  0.832  0.832  0.789  1.0
  Ni  Ni10  1  0.168  0.663  0.286  1.0
  Ni  Ni11  1  0.663  0.168  0.286  1.0
  O  O12  1  0.340  0.847  0.402  1.0
  O  O13  1  0.519  0.519  0.667  1.0
  O  O14  1  0.654  0.654  0.890  1.0
  O  O15  1  0.012  0.012  0.695  1.0
  O  O16  1  0.007  0.007  0.196  1.0
  O  O17  1  0.847  0.340  0.402  1.0
  O  O18  1  0.502  0.960  0.659  1.0
  O  O19  1  0.960  0.502  0.659  1.0
  O  O20  1  0.165  0.165  0.896  1.0
  O  O21  1  0.841  0.841  0.409  1.0
  O  O22  1  0.031  0.469  0.158  1.0
  O  O23  1  0.469  0.031  0.158  1.0
  O  O24  1  0.328  0.328  0.386  1.0
  O  O25  1  0.181  0.668  0.908  1.0
  O  O26  1  0.476  0.476  0.161  1.0
  O  O27  1  0.668  0.181  0.908  1.0
[/CIF]
.