The crystal structure described by Li4Ti5Cr3O16 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 Cr(1)O6 octahedra, corners with two equivalent Ti(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra, corners with three equivalent Ti(4)O6 octahedra, and corners with four equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-62°. 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 Ti(1)O6 octahedra, corners with two equivalent Cr(2)O6 octahedra, corners with three equivalent Ti(4)O6 octahedra,  an edgeedge with one Cr(1)O6 octahedra, and edges with two equivalent Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 60-65°. In the third Li site, Li(3) is bonded to one O(4), one O(8), and two equivalent O(1) atoms to form distorted LiO4 tetrahedra that share  a cornercorner with one Cr(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra, corners with three equivalent Ti(3)O6 octahedra,  an edgeedge with one Ti(1)O6 octahedra, and edges with two equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-64°. 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(1)O6 octahedra, corners with two equivalent Cr(1)O6 octahedra, corners with two equivalent Cr(2)O6 octahedra, corners with three equivalent Ti(3)O6 octahedra, and corners with four equivalent Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-62°. There are four inequivalent Ti sites. In the first Ti site, Ti(1) 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 Ti(3)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(4)O6 octahedra, edges with four equivalent Cr(2)O6 octahedra, and  an edgeedge with one Li(3)O4 tetrahedra. The corner-sharing octahedral tilt angles are 51°. In the second Ti site, Ti(2) 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 Ti(4)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(3)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, edges with two equivalent Cr(1)O6 octahedra, and  an edgeedge with one Li(2)O4 tetrahedra. The corner-sharing octahedral tilt angles are 52°. In the third Ti site, Ti(3) 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 Ti(1)O6 octahedra, corners with four equivalent Cr(2)O6 octahedra, corners with three equivalent Li(3)O4 tetrahedra, corners with three equivalent Li(4)O4 tetrahedra,  an edgeedge with one Cr(1)O6 octahedra, and edges with two equivalent Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-52°. In the fourth Ti site, Ti(4) is bonded to one O(12), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form TiO6 octahedra that share corners with two equivalent Cr(1)O6 octahedra, corners with four equivalent Ti(2)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra, corners with three equivalent Li(2)O4 tetrahedra,  an edgeedge with one Ti(1)O6 octahedra, and edges with two equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-52°. There are two inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(3), one O(4), two equivalent O(11), and two equivalent O(6) atoms to form CrO6 octahedra that share corners with two equivalent Ti(4)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(3)O6 octahedra, edges with four equivalent Ti(2)O6 octahedra, and  an edgeedge with one Li(2)O4 tetrahedra. The corner-sharing octahedral tilt angles are 51°. In the second Cr site, Cr(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 CrO6 octahedra that share corners with two equivalent Ti(3)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(4)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, edges with two equivalent Cr(2)O6 octahedra, and  an edgeedge with one Li(3)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 51-52°. 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 Ti(3), and one Cr(2) atom. In the second O site, O(2) is bonded to one Li(4), one Ti(3), and two equivalent Ti(2) atoms to form a mixture of distorted edge and corner-sharing OLiTi3 tetrahedra. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Li(1), two equivalent Ti(2), and one Cr(1) atom. In the fourth O site, O(4) is bonded to one Li(3), two equivalent Ti(2), and one Cr(1) atom to form OLiTi2Cr tetrahedra that share corners with two equivalent O(2)LiTi3 tetrahedra and corners with four equivalent O(6)LiTi2Cr tetrahedra. In the fifth O site, O(5) is bonded to one Li(2), one Ti(1), and two equivalent Cr(2) atoms to form corner-sharing OLiTiCr2 tetrahedra. In the sixth O site, O(6) is bonded to one Li(4), one Ti(2), one Ti(3), and one Cr(1) atom to form distorted OLiTi2Cr tetrahedra that share  a cornercorner with one O(6)LiTi2Cr tetrahedra,  a cornercorner with one O(2)LiTi3 tetrahedra, corners with two equivalent O(4)LiTi2Cr tetrahedra,  an edgeedge with one O(6)LiTi2Cr tetrahedra, and  an edgeedge with one O(2)LiTi3 tetrahedra. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), one Ti(4), and two equivalent Ti(2) atoms. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Li(3), one Ti(3), and two equivalent Cr(2) atoms. In the ninth O site, O(9) is bonded in a distorted rectangular see-saw-like geometry to one Li(1), one Ti(1), one Ti(4), and one Cr(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), and two equivalent Cr(2) atoms. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one Ti(2), one Ti(4), and one Cr(1) atom. In the twelfth O site, O(12) is bonded to one Li(1), one Ti(4), and two equivalent Cr(2) atoms to form corner-sharing OLiTiCr2 tetrahedra. is represented by the CIF card [CIF]
data_Li4Ti5Cr3O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.925
_cell_length_b   5.925
_cell_length_c   9.560
_cell_angle_alpha   89.914
_cell_angle_beta   89.914
_cell_angle_gamma   60.014
_symmetry_Int_Tables_number   1
_cell_volume   290.717
_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  0.336  0.336  0.105  1.0
  Li  Li1  1  0.001  0.001  0.007  1.0
  Li  Li2  1  0.001  0.001  0.503  1.0
  Li  Li3  1  0.666  0.666  0.602  1.0
  Ti  Ti4  1  0.826  0.826  0.277  1.0
  Ti  Ti5  1  0.656  0.165  0.781  1.0
  Ti  Ti6  1  0.332  0.332  0.503  1.0
  Ti  Ti7  1  0.165  0.656  0.781  1.0
  Ti  Ti8  1  0.659  0.659  0.008  1.0
  Cr  Cr9  1  0.171  0.171  0.789  1.0
  Cr  Cr10  1  0.830  0.340  0.288  1.0
  Cr  Cr11  1  0.340  0.830  0.288  1.0
  O  O12  1  0.663  0.166  0.404  1.0
  O  O13  1  0.480  0.480  0.659  1.0
  O  O14  1  0.337  0.337  0.897  1.0
  O  O15  1  0.001  0.001  0.691  1.0
  O  O16  1  0.998  0.998  0.193  1.0
  O  O17  1  0.166  0.663  0.404  1.0
  O  O18  1  0.484  0.040  0.661  1.0
  O  O19  1  0.040  0.484  0.661  1.0
  O  O20  1  0.833  0.833  0.903  1.0
  O  O21  1  0.168  0.168  0.406  1.0
  O  O22  1  0.963  0.524  0.159  1.0
  O  O23  1  0.524  0.963  0.159  1.0
  O  O24  1  0.672  0.672  0.396  1.0
  O  O25  1  0.829  0.334  0.905  1.0
  O  O26  1  0.523  0.523  0.158  1.0
  O  O27  1  0.334  0.829  0.905  1.0
[/CIF]
.
The crystal structure described by Li4Ti5Cr3O16 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 Cr(1)O6 octahedra, corners with two equivalent Ti(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra, corners with three equivalent Ti(4)O6 octahedra, and corners with four equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-62°. 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 Ti(1)O6 octahedra, corners with two equivalent Cr(2)O6 octahedra, corners with three equivalent Ti(4)O6 octahedra,  an edgeedge with one Cr(1)O6 octahedra, and edges with two equivalent Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 60-65°. In the third Li site, Li(3) is bonded to one O(4), one O(8), and two equivalent O(1) atoms to form distorted LiO4 tetrahedra that share  a cornercorner with one Cr(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra, corners with three equivalent Ti(3)O6 octahedra,  an edgeedge with one Ti(1)O6 octahedra, and edges with two equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-64°. 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(1)O6 octahedra, corners with two equivalent Cr(1)O6 octahedra, corners with two equivalent Cr(2)O6 octahedra, corners with three equivalent Ti(3)O6 octahedra, and corners with four equivalent Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-62°. There are four inequivalent Ti sites. In the first Ti site, Ti(1) 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 Ti(3)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(4)O6 octahedra, edges with four equivalent Cr(2)O6 octahedra, and  an edgeedge with one Li(3)O4 tetrahedra. The corner-sharing octahedral tilt angles are 51°. In the second Ti site, Ti(2) 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 Ti(4)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(3)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, edges with two equivalent Cr(1)O6 octahedra, and  an edgeedge with one Li(2)O4 tetrahedra. The corner-sharing octahedral tilt angles are 52°. In the third Ti site, Ti(3) 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 Ti(1)O6 octahedra, corners with four equivalent Cr(2)O6 octahedra, corners with three equivalent Li(3)O4 tetrahedra, corners with three equivalent Li(4)O4 tetrahedra,  an edgeedge with one Cr(1)O6 octahedra, and edges with two equivalent Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-52°. In the fourth Ti site, Ti(4) is bonded to one O(12), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form TiO6 octahedra that share corners with two equivalent Cr(1)O6 octahedra, corners with four equivalent Ti(2)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra, corners with three equivalent Li(2)O4 tetrahedra,  an edgeedge with one Ti(1)O6 octahedra, and edges with two equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-52°. There are two inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(3), one O(4), two equivalent O(11), and two equivalent O(6) atoms to form CrO6 octahedra that share corners with two equivalent Ti(4)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(3)O6 octahedra, edges with four equivalent Ti(2)O6 octahedra, and  an edgeedge with one Li(2)O4 tetrahedra. The corner-sharing octahedral tilt angles are 51°. In the second Cr site, Cr(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 CrO6 octahedra that share corners with two equivalent Ti(3)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(4)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, edges with two equivalent Cr(2)O6 octahedra, and  an edgeedge with one Li(3)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 51-52°. 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 Ti(3), and one Cr(2) atom. In the second O site, O(2) is bonded to one Li(4), one Ti(3), and two equivalent Ti(2) atoms to form a mixture of distorted edge and corner-sharing OLiTi3 tetrahedra. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Li(1), two equivalent Ti(2), and one Cr(1) atom. In the fourth O site, O(4) is bonded to one Li(3), two equivalent Ti(2), and one Cr(1) atom to form OLiTi2Cr tetrahedra that share corners with two equivalent O(2)LiTi3 tetrahedra and corners with four equivalent O(6)LiTi2Cr tetrahedra. In the fifth O site, O(5) is bonded to one Li(2), one Ti(1), and two equivalent Cr(2) atoms to form corner-sharing OLiTiCr2 tetrahedra. In the sixth O site, O(6) is bonded to one Li(4), one Ti(2), one Ti(3), and one Cr(1) atom to form distorted OLiTi2Cr tetrahedra that share  a cornercorner with one O(6)LiTi2Cr tetrahedra,  a cornercorner with one O(2)LiTi3 tetrahedra, corners with two equivalent O(4)LiTi2Cr tetrahedra,  an edgeedge with one O(6)LiTi2Cr tetrahedra, and  an edgeedge with one O(2)LiTi3 tetrahedra. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), one Ti(4), and two equivalent Ti(2) atoms. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Li(3), one Ti(3), and two equivalent Cr(2) atoms. In the ninth O site, O(9) is bonded in a distorted rectangular see-saw-like geometry to one Li(1), one Ti(1), one Ti(4), and one Cr(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), and two equivalent Cr(2) atoms. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one Ti(2), one Ti(4), and one Cr(1) atom. In the twelfth O site, O(12) is bonded to one Li(1), one Ti(4), and two equivalent Cr(2) atoms to form corner-sharing OLiTiCr2 tetrahedra. is represented by the CIF card [CIF]
data_Li4Ti5Cr3O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.925
_cell_length_b   5.925
_cell_length_c   9.560
_cell_angle_alpha   89.914
_cell_angle_beta   89.914
_cell_angle_gamma   60.014
_symmetry_Int_Tables_number   1
_cell_volume   290.717
_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  0.336  0.336  0.105  1.0
  Li  Li1  1  0.001  0.001  0.007  1.0
  Li  Li2  1  0.001  0.001  0.503  1.0
  Li  Li3  1  0.666  0.666  0.602  1.0
  Ti  Ti4  1  0.826  0.826  0.277  1.0
  Ti  Ti5  1  0.656  0.165  0.781  1.0
  Ti  Ti6  1  0.332  0.332  0.503  1.0
  Ti  Ti7  1  0.165  0.656  0.781  1.0
  Ti  Ti8  1  0.659  0.659  0.008  1.0
  Cr  Cr9  1  0.171  0.171  0.789  1.0
  Cr  Cr10  1  0.830  0.340  0.288  1.0
  Cr  Cr11  1  0.340  0.830  0.288  1.0
  O  O12  1  0.663  0.166  0.404  1.0
  O  O13  1  0.480  0.480  0.659  1.0
  O  O14  1  0.337  0.337  0.897  1.0
  O  O15  1  0.001  0.001  0.691  1.0
  O  O16  1  0.998  0.998  0.193  1.0
  O  O17  1  0.166  0.663  0.404  1.0
  O  O18  1  0.484  0.040  0.661  1.0
  O  O19  1  0.040  0.484  0.661  1.0
  O  O20  1  0.833  0.833  0.903  1.0
  O  O21  1  0.168  0.168  0.406  1.0
  O  O22  1  0.963  0.524  0.159  1.0
  O  O23  1  0.524  0.963  0.159  1.0
  O  O24  1  0.672  0.672  0.396  1.0
  O  O25  1  0.829  0.334  0.905  1.0
  O  O26  1  0.523  0.523  0.158  1.0
  O  O27  1  0.334  0.829  0.905  1.0
[/CIF]
.