The structure described by Li4Ti3Nb2Cr3O16 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 Nb(2)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 trigonal pyramids that share  a cornercorner with one Ti(1)O6 octahedra, corners with two equivalent Cr(2)O6 octahedra, corners with three equivalent Nb(2)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 61-64°. 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 Nb(1)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 59-63°. 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 Nb(1)O6 octahedra, and corners with four equivalent Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 53-63°. There are two 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 Nb(1)O6 octahedra,  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 Nb(2)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 Nb(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 Nb(1)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 trigonal pyramid. The corner-sharing octahedral tilt angles range from 51-52°. There are two inequivalent Nb sites. In the first Nb site, Nb(1) is bonded to one O(2), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form NbO6 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 second Nb site, Nb(2) is bonded to one O(12), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form NbO6 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 trigonal pyramids,  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 Nb(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 Nb(1)O6 octahedra, edges with four equivalent Ti(2)O6 octahedra, and  an edgeedge with one Li(2)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 52°. 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 Nb(1)O6 octahedra,  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 Nb(2)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 Nb(1), and one Cr(2) atom. In the second O site, O(2) is bonded to one Li(4), two equivalent Ti(2), and one Nb(1) atom to form distorted OLiTi2Nb trigonal pyramids that share corners with two equivalent O(4)LiTi2Cr 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 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 four equivalent O(6)LiTiNbCr tetrahedra and corners with two equivalent O(2)LiTi2Nb trigonal pyramids. In the fifth O site, O(5) is bonded to one Li(2), one Ti(1), and two equivalent Cr(2) atoms to form OLiTiCr2 tetrahedra that share corners with two equivalent O(12)LiNbCr2 tetrahedra and corners with four equivalent O(9)LiTiNbCr trigonal pyramids. In the sixth O site, O(6) is bonded to one Li(4), one Ti(2), one Nb(1), and one Cr(1) atom to form distorted OLiTiNbCr tetrahedra that share  a cornercorner with one O(6)LiTiNbCr tetrahedra, corners with two equivalent O(4)LiTi2Cr tetrahedra,  a cornercorner with one O(2)LiTi2Nb trigonal pyramid,  an edgeedge with one O(6)LiTiNbCr tetrahedra, and  an edgeedge with one O(2)LiTi2Nb trigonal pyramid. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), two equivalent Ti(2), and one Nb(2) atom. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Li(3), one Nb(1), and two equivalent Cr(2) atoms. In the ninth O site, O(9) is bonded to one Li(1), one Ti(1), one Nb(2), and one Cr(2) atom to form distorted OLiTiNbCr trigonal pyramids that share  a cornercorner with one O(12)LiNbCr2 tetrahedra, corners with two equivalent O(5)LiTiCr2 tetrahedra,  a cornercorner with one O(9)LiTiNbCr trigonal pyramid,  an edgeedge with one O(12)LiNbCr2 tetrahedra, and  an edgeedge with one O(9)LiTiNbCr trigonal pyramid. 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 Nb(2), and one Cr(1) atom. In the twelfth O site, O(12) is bonded to one Li(1), one Nb(2), and two equivalent Cr(2) atoms to form distorted OLiNbCr2 tetrahedra that share corners with two equivalent O(5)LiTiCr2 tetrahedra, corners with two equivalent O(9)LiTiNbCr trigonal pyramids, and edges with two equivalent O(9)LiTiNbCr trigonal pyramids. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li4Ti3Nb2Cr3O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.998
_cell_length_b   5.998
_cell_length_c   9.745
_cell_angle_alpha   89.439
_cell_angle_beta   89.439
_cell_angle_gamma   59.819
_symmetry_Int_Tables_number   1
_cell_volume   302.993
_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  0.665  0.665  0.102  1.0
  Li  Li1  1  1.000  1.000  0.008  1.0
  Li  Li2  1  0.998  0.998  0.505  1.0
  Li  Li3  1  0.333  0.333  0.598  1.0
  Ti  Ti4  1  0.171  0.171  0.279  1.0
  Ti  Ti5  1  0.342  0.835  0.781  1.0
  Ti  Ti6  1  0.835  0.342  0.781  1.0
  Nb  Nb7  1  0.667  0.667  0.507  1.0
  Nb  Nb8  1  0.338  0.338  0.009  1.0
  Cr  Cr9  1  0.832  0.832  0.789  1.0
  Cr  Cr10  1  0.170  0.661  0.287  1.0
  Cr  Cr11  1  0.661  0.170  0.287  1.0
  O  O12  1  0.330  0.838  0.403  1.0
  O  O13  1  0.518  0.518  0.660  1.0
  O  O14  1  0.662  0.662  0.892  1.0
  O  O15  1  0.001  0.001  0.691  1.0
  O  O16  1  0.004  0.004  0.193  1.0
  O  O17  1  0.838  0.330  0.403  1.0
  O  O18  1  0.514  0.962  0.662  1.0
  O  O19  1  0.962  0.514  0.662  1.0
  O  O20  1  0.164  0.164  0.900  1.0
  O  O21  1  0.833  0.833  0.406  1.0
  O  O22  1  0.037  0.476  0.160  1.0
  O  O23  1  0.476  0.037  0.160  1.0
  O  O24  1  0.326  0.326  0.393  1.0
  O  O25  1  0.171  0.670  0.906  1.0
  O  O26  1  0.480  0.480  0.160  1.0
  O  O27  1  0.670  0.171  0.906  1.0
[/CIF]
.
The structure described by Li4Ti3Nb2Cr3O16 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 Nb(2)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 trigonal pyramids that share  a cornercorner with one Ti(1)O6 octahedra, corners with two equivalent Cr(2)O6 octahedra, corners with three equivalent Nb(2)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 61-64°. 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 Nb(1)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 59-63°. 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 Nb(1)O6 octahedra, and corners with four equivalent Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 53-63°. There are two 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 Nb(1)O6 octahedra,  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 Nb(2)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 Nb(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 Nb(1)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 trigonal pyramid. The corner-sharing octahedral tilt angles range from 51-52°. There are two inequivalent Nb sites. In the first Nb site, Nb(1) is bonded to one O(2), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form NbO6 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 second Nb site, Nb(2) is bonded to one O(12), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form NbO6 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 trigonal pyramids,  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 Nb(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 Nb(1)O6 octahedra, edges with four equivalent Ti(2)O6 octahedra, and  an edgeedge with one Li(2)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 52°. 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 Nb(1)O6 octahedra,  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 Nb(2)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 Nb(1), and one Cr(2) atom. In the second O site, O(2) is bonded to one Li(4), two equivalent Ti(2), and one Nb(1) atom to form distorted OLiTi2Nb trigonal pyramids that share corners with two equivalent O(4)LiTi2Cr 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 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 four equivalent O(6)LiTiNbCr tetrahedra and corners with two equivalent O(2)LiTi2Nb trigonal pyramids. In the fifth O site, O(5) is bonded to one Li(2), one Ti(1), and two equivalent Cr(2) atoms to form OLiTiCr2 tetrahedra that share corners with two equivalent O(12)LiNbCr2 tetrahedra and corners with four equivalent O(9)LiTiNbCr trigonal pyramids. In the sixth O site, O(6) is bonded to one Li(4), one Ti(2), one Nb(1), and one Cr(1) atom to form distorted OLiTiNbCr tetrahedra that share  a cornercorner with one O(6)LiTiNbCr tetrahedra, corners with two equivalent O(4)LiTi2Cr tetrahedra,  a cornercorner with one O(2)LiTi2Nb trigonal pyramid,  an edgeedge with one O(6)LiTiNbCr tetrahedra, and  an edgeedge with one O(2)LiTi2Nb trigonal pyramid. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), two equivalent Ti(2), and one Nb(2) atom. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Li(3), one Nb(1), and two equivalent Cr(2) atoms. In the ninth O site, O(9) is bonded to one Li(1), one Ti(1), one Nb(2), and one Cr(2) atom to form distorted OLiTiNbCr trigonal pyramids that share  a cornercorner with one O(12)LiNbCr2 tetrahedra, corners with two equivalent O(5)LiTiCr2 tetrahedra,  a cornercorner with one O(9)LiTiNbCr trigonal pyramid,  an edgeedge with one O(12)LiNbCr2 tetrahedra, and  an edgeedge with one O(9)LiTiNbCr trigonal pyramid. 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 Nb(2), and one Cr(1) atom. In the twelfth O site, O(12) is bonded to one Li(1), one Nb(2), and two equivalent Cr(2) atoms to form distorted OLiNbCr2 tetrahedra that share corners with two equivalent O(5)LiTiCr2 tetrahedra, corners with two equivalent O(9)LiTiNbCr trigonal pyramids, and edges with two equivalent O(9)LiTiNbCr trigonal pyramids. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li4Ti3Nb2Cr3O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.998
_cell_length_b   5.998
_cell_length_c   9.745
_cell_angle_alpha   89.439
_cell_angle_beta   89.439
_cell_angle_gamma   59.819
_symmetry_Int_Tables_number   1
_cell_volume   302.993
_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  0.665  0.665  0.102  1.0
  Li  Li1  1  1.000  1.000  0.008  1.0
  Li  Li2  1  0.998  0.998  0.505  1.0
  Li  Li3  1  0.333  0.333  0.598  1.0
  Ti  Ti4  1  0.171  0.171  0.279  1.0
  Ti  Ti5  1  0.342  0.835  0.781  1.0
  Ti  Ti6  1  0.835  0.342  0.781  1.0
  Nb  Nb7  1  0.667  0.667  0.507  1.0
  Nb  Nb8  1  0.338  0.338  0.009  1.0
  Cr  Cr9  1  0.832  0.832  0.789  1.0
  Cr  Cr10  1  0.170  0.661  0.287  1.0
  Cr  Cr11  1  0.661  0.170  0.287  1.0
  O  O12  1  0.330  0.838  0.403  1.0
  O  O13  1  0.518  0.518  0.660  1.0
  O  O14  1  0.662  0.662  0.892  1.0
  O  O15  1  0.001  0.001  0.691  1.0
  O  O16  1  0.004  0.004  0.193  1.0
  O  O17  1  0.838  0.330  0.403  1.0
  O  O18  1  0.514  0.962  0.662  1.0
  O  O19  1  0.962  0.514  0.662  1.0
  O  O20  1  0.164  0.164  0.900  1.0
  O  O21  1  0.833  0.833  0.406  1.0
  O  O22  1  0.037  0.476  0.160  1.0
  O  O23  1  0.476  0.037  0.160  1.0
  O  O24  1  0.326  0.326  0.393  1.0
  O  O25  1  0.171  0.670  0.906  1.0
  O  O26  1  0.480  0.480  0.160  1.0
  O  O27  1  0.670  0.171  0.906  1.0
[/CIF]
.