The crystal structure described by Li4Ti3Nb3Cr2O16 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 Nb(1)O6 octahedra, corners with two equivalent Ti(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra, corners with three equivalent Cr(2)O6 octahedra, and corners with four equivalent Nb(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 54-64°. In the second Li site, Li(2) is bonded in a rectangular see-saw-like geometry to one O(5), one O(7), and two equivalent O(11) atoms. In the third Li site, Li(3) is bonded in a distorted rectangular see-saw-like geometry to one O(4), one O(8), and two equivalent O(1) atoms. In the fourth Li site, Li(4) is bonded to one O(10), one O(2), and two equivalent O(6) atoms to form LiO4 tetrahedra that share  a cornercorner with one Ti(2)O6 octahedra, corners with two equivalent Nb(1)O6 octahedra, corners with two equivalent Nb(2)O6 octahedra, corners with three equivalent Cr(1)O6 octahedra, and corners with four equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 45-62°. There are two inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(11), one O(2), one O(3), one O(4), one O(6), and one O(7) atom to form TiO6 octahedra that share corners with two equivalent Cr(2)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Cr(1)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, and edges with two equivalent Nb(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-51°. In the second Ti site, Ti(2) is bonded to one O(10), one O(5), two equivalent O(1), and two equivalent O(9) atoms to form TiO6 octahedra that share corners with two equivalent Cr(1)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one Cr(2)O6 octahedra, and edges with four equivalent Nb(2)O6 octahedra. The corner-sharing octahedral tilt angles are 50°. There are two inequivalent Nb sites. In the first Nb site, Nb(1) is bonded to one O(3), one O(4), two equivalent O(11), and two equivalent O(6) atoms to form NbO6 octahedra that share corners with two equivalent Cr(2)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Cr(1)O6 octahedra, and edges with four equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles are 53°. In the second Nb site, Nb(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 NbO6 octahedra that share corners with two equivalent Cr(1)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one Cr(2)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, and edges with two equivalent Nb(2)O6 octahedra. The corner-sharing octahedral tilt angles are 53°. There are two inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(2), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form CrO6 octahedra that share corners with two equivalent Ti(2)O6 octahedra, corners with four equivalent Nb(2)O6 octahedra, corners with three equivalent Li(4)O4 tetrahedra,  an edgeedge with one Nb(1)O6 octahedra, and edges with two equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-53°. In the second Cr site, Cr(2) is bonded to one O(12), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form CrO6 octahedra that share corners with two equivalent Nb(1)O6 octahedra, corners with four equivalent Ti(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra,  an edgeedge with one Ti(2)O6 octahedra, and edges with two equivalent Nb(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-53°. 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(2), one Nb(2), and one Cr(1) atom. In the second O site, O(2) is bonded to one Li(4), two equivalent Ti(1), and one Cr(1) atom to form distorted OLiTi2Cr tetrahedra that share corners with two equivalent O(4)LiTi2Nb tetrahedra, corners with two equivalent O(6)LiTiNbCr tetrahedra, and edges with two equivalent O(6)LiTiNbCr tetrahedra. In the third O site, O(3) is bonded in a distorted rectangular see-saw-like geometry to one Li(1), two equivalent Ti(1), and one Nb(1) atom. In the fourth O site, O(4) is bonded to one Li(3), two equivalent Ti(1), and one Nb(1) atom to form distorted OLiTi2Nb tetrahedra that share corners with two equivalent O(2)LiTi2Cr tetrahedra and corners with four equivalent O(6)LiTiNbCr tetrahedra. In the fifth O site, O(5) is bonded to one Li(2), one Ti(2), and two equivalent Nb(2) atoms to form distorted corner-sharing OLiTiNb2 tetrahedra. In the sixth O site, O(6) is bonded to one Li(4), one Ti(1), one Nb(1), and one Cr(1) atom to form distorted OLiTiNbCr tetrahedra that share  a cornercorner with one O(2)LiTi2Cr tetrahedra,  a cornercorner with one O(6)LiTiNbCr tetrahedra, corners with two equivalent O(4)LiTi2Nb tetrahedra,  an edgeedge with one O(2)LiTi2Cr tetrahedra, and  an edgeedge with one O(6)LiTiNbCr tetrahedra. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), two equivalent Ti(1), and one Cr(2) atom. In the eighth O site, O(8) is bonded in a distorted rectangular see-saw-like geometry to one Li(3), two equivalent Nb(2), and one Cr(1) atom. In the ninth O site, O(9) is bonded to one Li(1), one Ti(2), one Nb(2), and one Cr(2) atom to form distorted OLiTiNbCr tetrahedra that share  a cornercorner with one O(9)LiTiNbCr tetrahedra, corners with two equivalent O(5)LiTiNb2 tetrahedra, and  an edgeedge with one O(9)LiTiNbCr tetrahedra. In the tenth O site, O(10) is bonded in a distorted rectangular see-saw-like geometry to one Li(4), one Ti(2), and two equivalent Nb(2) atoms. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one Ti(1), one Nb(1), and one Cr(2) atom. In the twelfth O site, O(12) is bonded in a 4-coordinate geometry to one Li(1), two equivalent Nb(2), and one Cr(2) atom. is represented by the CIF file [CIF]
data_Li4Ti3Nb3Cr2O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.005
_cell_length_b   6.005
_cell_length_c   9.939
_cell_angle_alpha   89.486
_cell_angle_beta   89.486
_cell_angle_gamma   59.568
_symmetry_Int_Tables_number   1
_cell_volume   308.992
_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  0.666  0.666  0.900  1.0
  Li  Li1  1  0.011  0.011  0.993  1.0
  Li  Li2  1  0.006  0.006  0.497  1.0
  Li  Li3  1  0.331  0.331  0.391  1.0
  Ti  Ti4  1  0.831  0.338  0.217  1.0
  Ti  Ti5  1  0.338  0.831  0.217  1.0
  Ti  Ti6  1  0.165  0.165  0.718  1.0
  Nb  Nb7  1  0.834  0.834  0.211  1.0
  Nb  Nb8  1  0.641  0.187  0.710  1.0
  Nb  Nb9  1  0.187  0.641  0.710  1.0
  Cr  Cr10  1  0.669  0.669  0.484  1.0
  Cr  Cr11  1  0.332  0.332  0.989  1.0
  O  O12  1  0.833  0.331  0.602  1.0
  O  O13  1  0.521  0.521  0.335  1.0
  O  O14  1  0.665  0.665  0.105  1.0
  O  O15  1  0.006  0.006  0.316  1.0
  O  O16  1  0.001  0.001  0.812  1.0
  O  O17  1  0.331  0.833  0.602  1.0
  O  O18  1  0.961  0.518  0.339  1.0
  O  O19  1  0.518  0.961  0.339  1.0
  O  O20  1  0.163  0.163  0.107  1.0
  O  O21  1  0.837  0.837  0.596  1.0
  O  O22  1  0.478  0.034  0.834  1.0
  O  O23  1  0.034  0.478  0.834  1.0
  O  O24  1  0.313  0.313  0.588  1.0
  O  O25  1  0.678  0.166  0.104  1.0
  O  O26  1  0.483  0.483  0.854  1.0
  O  O27  1  0.166  0.678  0.104  1.0
[/CIF]
.
The crystal structure described by Li4Ti3Nb3Cr2O16 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 Nb(1)O6 octahedra, corners with two equivalent Ti(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra, corners with three equivalent Cr(2)O6 octahedra, and corners with four equivalent Nb(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 54-64°. In the second Li site, Li(2) is bonded in a rectangular see-saw-like geometry to one O(5), one O(7), and two equivalent O(11) atoms. In the third Li site, Li(3) is bonded in a distorted rectangular see-saw-like geometry to one O(4), one O(8), and two equivalent O(1) atoms. In the fourth Li site, Li(4) is bonded to one O(10), one O(2), and two equivalent O(6) atoms to form LiO4 tetrahedra that share  a cornercorner with one Ti(2)O6 octahedra, corners with two equivalent Nb(1)O6 octahedra, corners with two equivalent Nb(2)O6 octahedra, corners with three equivalent Cr(1)O6 octahedra, and corners with four equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 45-62°. There are two inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(11), one O(2), one O(3), one O(4), one O(6), and one O(7) atom to form TiO6 octahedra that share corners with two equivalent Cr(2)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Cr(1)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, and edges with two equivalent Nb(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-51°. In the second Ti site, Ti(2) is bonded to one O(10), one O(5), two equivalent O(1), and two equivalent O(9) atoms to form TiO6 octahedra that share corners with two equivalent Cr(1)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one Cr(2)O6 octahedra, and edges with four equivalent Nb(2)O6 octahedra. The corner-sharing octahedral tilt angles are 50°. There are two inequivalent Nb sites. In the first Nb site, Nb(1) is bonded to one O(3), one O(4), two equivalent O(11), and two equivalent O(6) atoms to form NbO6 octahedra that share corners with two equivalent Cr(2)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Cr(1)O6 octahedra, and edges with four equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles are 53°. In the second Nb site, Nb(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 NbO6 octahedra that share corners with two equivalent Cr(1)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one Cr(2)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, and edges with two equivalent Nb(2)O6 octahedra. The corner-sharing octahedral tilt angles are 53°. There are two inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(2), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form CrO6 octahedra that share corners with two equivalent Ti(2)O6 octahedra, corners with four equivalent Nb(2)O6 octahedra, corners with three equivalent Li(4)O4 tetrahedra,  an edgeedge with one Nb(1)O6 octahedra, and edges with two equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-53°. In the second Cr site, Cr(2) is bonded to one O(12), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form CrO6 octahedra that share corners with two equivalent Nb(1)O6 octahedra, corners with four equivalent Ti(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra,  an edgeedge with one Ti(2)O6 octahedra, and edges with two equivalent Nb(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-53°. 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(2), one Nb(2), and one Cr(1) atom. In the second O site, O(2) is bonded to one Li(4), two equivalent Ti(1), and one Cr(1) atom to form distorted OLiTi2Cr tetrahedra that share corners with two equivalent O(4)LiTi2Nb tetrahedra, corners with two equivalent O(6)LiTiNbCr tetrahedra, and edges with two equivalent O(6)LiTiNbCr tetrahedra. In the third O site, O(3) is bonded in a distorted rectangular see-saw-like geometry to one Li(1), two equivalent Ti(1), and one Nb(1) atom. In the fourth O site, O(4) is bonded to one Li(3), two equivalent Ti(1), and one Nb(1) atom to form distorted OLiTi2Nb tetrahedra that share corners with two equivalent O(2)LiTi2Cr tetrahedra and corners with four equivalent O(6)LiTiNbCr tetrahedra. In the fifth O site, O(5) is bonded to one Li(2), one Ti(2), and two equivalent Nb(2) atoms to form distorted corner-sharing OLiTiNb2 tetrahedra. In the sixth O site, O(6) is bonded to one Li(4), one Ti(1), one Nb(1), and one Cr(1) atom to form distorted OLiTiNbCr tetrahedra that share  a cornercorner with one O(2)LiTi2Cr tetrahedra,  a cornercorner with one O(6)LiTiNbCr tetrahedra, corners with two equivalent O(4)LiTi2Nb tetrahedra,  an edgeedge with one O(2)LiTi2Cr tetrahedra, and  an edgeedge with one O(6)LiTiNbCr tetrahedra. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), two equivalent Ti(1), and one Cr(2) atom. In the eighth O site, O(8) is bonded in a distorted rectangular see-saw-like geometry to one Li(3), two equivalent Nb(2), and one Cr(1) atom. In the ninth O site, O(9) is bonded to one Li(1), one Ti(2), one Nb(2), and one Cr(2) atom to form distorted OLiTiNbCr tetrahedra that share  a cornercorner with one O(9)LiTiNbCr tetrahedra, corners with two equivalent O(5)LiTiNb2 tetrahedra, and  an edgeedge with one O(9)LiTiNbCr tetrahedra. In the tenth O site, O(10) is bonded in a distorted rectangular see-saw-like geometry to one Li(4), one Ti(2), and two equivalent Nb(2) atoms. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one Ti(1), one Nb(1), and one Cr(2) atom. In the twelfth O site, O(12) is bonded in a 4-coordinate geometry to one Li(1), two equivalent Nb(2), and one Cr(2) atom. is represented by the CIF file [CIF]
data_Li4Ti3Nb3Cr2O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.005
_cell_length_b   6.005
_cell_length_c   9.939
_cell_angle_alpha   89.486
_cell_angle_beta   89.486
_cell_angle_gamma   59.568
_symmetry_Int_Tables_number   1
_cell_volume   308.992
_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  0.666  0.666  0.900  1.0
  Li  Li1  1  0.011  0.011  0.993  1.0
  Li  Li2  1  0.006  0.006  0.497  1.0
  Li  Li3  1  0.331  0.331  0.391  1.0
  Ti  Ti4  1  0.831  0.338  0.217  1.0
  Ti  Ti5  1  0.338  0.831  0.217  1.0
  Ti  Ti6  1  0.165  0.165  0.718  1.0
  Nb  Nb7  1  0.834  0.834  0.211  1.0
  Nb  Nb8  1  0.641  0.187  0.710  1.0
  Nb  Nb9  1  0.187  0.641  0.710  1.0
  Cr  Cr10  1  0.669  0.669  0.484  1.0
  Cr  Cr11  1  0.332  0.332  0.989  1.0
  O  O12  1  0.833  0.331  0.602  1.0
  O  O13  1  0.521  0.521  0.335  1.0
  O  O14  1  0.665  0.665  0.105  1.0
  O  O15  1  0.006  0.006  0.316  1.0
  O  O16  1  0.001  0.001  0.812  1.0
  O  O17  1  0.331  0.833  0.602  1.0
  O  O18  1  0.961  0.518  0.339  1.0
  O  O19  1  0.518  0.961  0.339  1.0
  O  O20  1  0.163  0.163  0.107  1.0
  O  O21  1  0.837  0.837  0.596  1.0
  O  O22  1  0.478  0.034  0.834  1.0
  O  O23  1  0.034  0.478  0.834  1.0
  O  O24  1  0.313  0.313  0.588  1.0
  O  O25  1  0.678  0.166  0.104  1.0
  O  O26  1  0.483  0.483  0.854  1.0
  O  O27  1  0.166  0.678  0.104  1.0
[/CIF]
.