The material described by Li4Ti3Cr3(WO8)2 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 W(2)O6 octahedra, and corners with four equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-61°. 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 to one O(4), one O(8), and two equivalent O(1) atoms to form distorted LiO4 trigonal pyramids that share  a cornercorner with one Cr(1)O6 octahedra, corners with two equivalent Ti(1)O6 octahedra, corners with three equivalent W(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra, and edges with two equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 61-65°. 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 Cr(1)O6 octahedra, corners with two equivalent Cr(2)O6 octahedra, corners with three equivalent W(1)O6 octahedra, and corners with four equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 54-62°. 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 W(2)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  a cornercorner with one Li(3)O4 trigonal pyramid,  an edgeedge with one W(1)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, and edges with two equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-52°. 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 W(1)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one W(2)O6 octahedra, edges with four equivalent Cr(2)O6 octahedra, and  an edgeedge with one Li(3)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 51°. There are two inequivalent W sites. In the first W site, W(1) is bonded to one O(2), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form WO6 octahedra that share corners with two equivalent Ti(2)O6 octahedra, corners with four equivalent Cr(2)O6 octahedra, corners with three equivalent Li(4)O4 tetrahedra, corners with three equivalent Li(3)O4 trigonal pyramids,  an edgeedge with one Cr(1)O6 octahedra, and edges with two equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-52°. In the second W site, W(2) is bonded to one O(12), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form WO6 octahedra that share corners with two equivalent Cr(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 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 W(2)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  a cornercorner with one Li(3)O4 trigonal pyramid,  an edgeedge with one W(1)O6 octahedra, and edges with four equivalent Ti(1)O6 octahedra. 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 W(1)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one W(2)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, edges with two equivalent Cr(2)O6 octahedra, and  an edgeedge with one Li(3)O4 trigonal pyramid. 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(2), one W(1), and one Cr(2) atom. In the second O site, O(2) is bonded to one Li(4), two equivalent Ti(1), and one W(1) atom to form distorted OLiTi2W trigonal pyramids that share corners with two equivalent O(4)LiTi2Cr tetrahedra, corners with two equivalent O(6)LiTiCrW tetrahedra, and edges with two equivalent O(6)LiTiCrW tetrahedra. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Li(1), two equivalent Ti(1), and one Cr(1) atom. In the fourth O site, O(4) is bonded to one Li(3), two equivalent Ti(1), and one Cr(1) atom to form distorted OLiTi2Cr tetrahedra that share corners with four equivalent O(6)LiTiCrW tetrahedra and corners with two equivalent O(2)LiTi2W trigonal pyramids. In the fifth O site, O(5) is bonded to one Li(2), one Ti(2), and two equivalent Cr(2) atoms to form distorted OLiTiCr2 tetrahedra that share corners with two equivalent O(12)LiCr2W tetrahedra and corners with four equivalent O(9)LiTiCrW tetrahedra. In the sixth O site, O(6) is bonded to one Li(4), one Ti(1), one W(1), and one Cr(1) atom to form distorted OLiTiCrW tetrahedra that share  a cornercorner with one O(6)LiTiCrW tetrahedra, corners with two equivalent O(4)LiTi2Cr tetrahedra,  a cornercorner with one O(2)LiTi2W trigonal pyramid,  an edgeedge with one O(6)LiTiCrW tetrahedra, and  an edgeedge with one O(2)LiTi2W 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(1), and one W(2) atom. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Li(3), one W(1), and two equivalent Cr(2) atoms. In the ninth O site, O(9) is bonded to one Li(1), one Ti(2), one W(2), and one Cr(2) atom to form distorted OLiTiCrW tetrahedra that share  a cornercorner with one O(12)LiCr2W tetrahedra,  a cornercorner with one O(9)LiTiCrW tetrahedra, corners with two equivalent O(5)LiTiCr2 tetrahedra,  an edgeedge with one O(12)LiCr2W tetrahedra, and  an edgeedge with one O(9)LiTiCrW tetrahedra. In the tenth O site, O(10) is bonded in a rectangular see-saw-like geometry to one Li(4), one Ti(2), 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(1), one W(2), and one Cr(1) atom. In the twelfth O site, O(12) is bonded to one Li(1), one W(2), and two equivalent Cr(2) atoms to form distorted OLiCr2W tetrahedra that share corners with two equivalent O(5)LiTiCr2 tetrahedra, corners with two equivalent O(9)LiTiCrW tetrahedra, and edges with two equivalent O(9)LiTiCrW tetrahedra. is represented by the CIF file [CIF]
data_Li4Ti3Cr3(WO8)2
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.974
_cell_length_b   5.974
_cell_length_c   9.843
_cell_angle_alpha   89.042
_cell_angle_beta   89.042
_cell_angle_gamma   59.899
_symmetry_Int_Tables_number   1
_cell_volume   303.897
_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  0.103  1.0
  Li  Li1  1  0.999  0.999  0.008  1.0
  Li  Li2  1  0.997  0.997  0.505  1.0
  Li  Li3  1  0.333  0.333  0.600  1.0
  Ti  Ti4  1  0.338  0.835  0.785  1.0
  Ti  Ti5  1  0.835  0.338  0.785  1.0
  Ti  Ti6  1  0.169  0.169  0.286  1.0
  Cr  Cr7  1  0.830  0.830  0.788  1.0
  Cr  Cr8  1  0.171  0.661  0.287  1.0
  Cr  Cr9  1  0.661  0.171  0.287  1.0
  W  W10  1  0.669  0.669  0.512  1.0
  W  W11  1  0.336  0.336  0.015  1.0
  O  O12  1  0.326  0.841  0.397  1.0
  O  O13  1  0.519  0.519  0.659  1.0
  O  O14  1  0.661  0.661  0.895  1.0
  O  O15  1  0.999  0.999  0.690  1.0
  O  O16  1  0.004  0.004  0.192  1.0
  O  O17  1  0.841  0.326  0.397  1.0
  O  O18  1  0.517  0.963  0.662  1.0
  O  O19  1  0.963  0.517  0.662  1.0
  O  O20  1  0.163  0.163  0.895  1.0
  O  O21  1  0.836  0.836  0.401  1.0
  O  O22  1  0.039  0.479  0.161  1.0
  O  O23  1  0.479  0.039  0.161  1.0
  O  O24  1  0.327  0.327  0.393  1.0
  O  O25  1  0.163  0.675  0.902  1.0
  O  O26  1  0.483  0.483  0.164  1.0
  O  O27  1  0.675  0.163  0.902  1.0
[/CIF]
.
The material described by Li4Ti3Cr3(WO8)2 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 W(2)O6 octahedra, and corners with four equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-61°. 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 to one O(4), one O(8), and two equivalent O(1) atoms to form distorted LiO4 trigonal pyramids that share  a cornercorner with one Cr(1)O6 octahedra, corners with two equivalent Ti(1)O6 octahedra, corners with three equivalent W(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra, and edges with two equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 61-65°. 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 Cr(1)O6 octahedra, corners with two equivalent Cr(2)O6 octahedra, corners with three equivalent W(1)O6 octahedra, and corners with four equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 54-62°. 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 W(2)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  a cornercorner with one Li(3)O4 trigonal pyramid,  an edgeedge with one W(1)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, and edges with two equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-52°. 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 W(1)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one W(2)O6 octahedra, edges with four equivalent Cr(2)O6 octahedra, and  an edgeedge with one Li(3)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 51°. There are two inequivalent W sites. In the first W site, W(1) is bonded to one O(2), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form WO6 octahedra that share corners with two equivalent Ti(2)O6 octahedra, corners with four equivalent Cr(2)O6 octahedra, corners with three equivalent Li(4)O4 tetrahedra, corners with three equivalent Li(3)O4 trigonal pyramids,  an edgeedge with one Cr(1)O6 octahedra, and edges with two equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-52°. In the second W site, W(2) is bonded to one O(12), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form WO6 octahedra that share corners with two equivalent Cr(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 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 W(2)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  a cornercorner with one Li(3)O4 trigonal pyramid,  an edgeedge with one W(1)O6 octahedra, and edges with four equivalent Ti(1)O6 octahedra. 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 W(1)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one W(2)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, edges with two equivalent Cr(2)O6 octahedra, and  an edgeedge with one Li(3)O4 trigonal pyramid. 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(2), one W(1), and one Cr(2) atom. In the second O site, O(2) is bonded to one Li(4), two equivalent Ti(1), and one W(1) atom to form distorted OLiTi2W trigonal pyramids that share corners with two equivalent O(4)LiTi2Cr tetrahedra, corners with two equivalent O(6)LiTiCrW tetrahedra, and edges with two equivalent O(6)LiTiCrW tetrahedra. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Li(1), two equivalent Ti(1), and one Cr(1) atom. In the fourth O site, O(4) is bonded to one Li(3), two equivalent Ti(1), and one Cr(1) atom to form distorted OLiTi2Cr tetrahedra that share corners with four equivalent O(6)LiTiCrW tetrahedra and corners with two equivalent O(2)LiTi2W trigonal pyramids. In the fifth O site, O(5) is bonded to one Li(2), one Ti(2), and two equivalent Cr(2) atoms to form distorted OLiTiCr2 tetrahedra that share corners with two equivalent O(12)LiCr2W tetrahedra and corners with four equivalent O(9)LiTiCrW tetrahedra. In the sixth O site, O(6) is bonded to one Li(4), one Ti(1), one W(1), and one Cr(1) atom to form distorted OLiTiCrW tetrahedra that share  a cornercorner with one O(6)LiTiCrW tetrahedra, corners with two equivalent O(4)LiTi2Cr tetrahedra,  a cornercorner with one O(2)LiTi2W trigonal pyramid,  an edgeedge with one O(6)LiTiCrW tetrahedra, and  an edgeedge with one O(2)LiTi2W 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(1), and one W(2) atom. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Li(3), one W(1), and two equivalent Cr(2) atoms. In the ninth O site, O(9) is bonded to one Li(1), one Ti(2), one W(2), and one Cr(2) atom to form distorted OLiTiCrW tetrahedra that share  a cornercorner with one O(12)LiCr2W tetrahedra,  a cornercorner with one O(9)LiTiCrW tetrahedra, corners with two equivalent O(5)LiTiCr2 tetrahedra,  an edgeedge with one O(12)LiCr2W tetrahedra, and  an edgeedge with one O(9)LiTiCrW tetrahedra. In the tenth O site, O(10) is bonded in a rectangular see-saw-like geometry to one Li(4), one Ti(2), 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(1), one W(2), and one Cr(1) atom. In the twelfth O site, O(12) is bonded to one Li(1), one W(2), and two equivalent Cr(2) atoms to form distorted OLiCr2W tetrahedra that share corners with two equivalent O(5)LiTiCr2 tetrahedra, corners with two equivalent O(9)LiTiCrW tetrahedra, and edges with two equivalent O(9)LiTiCrW tetrahedra. is represented by the CIF file [CIF]
data_Li4Ti3Cr3(WO8)2
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.974
_cell_length_b   5.974
_cell_length_c   9.843
_cell_angle_alpha   89.042
_cell_angle_beta   89.042
_cell_angle_gamma   59.899
_symmetry_Int_Tables_number   1
_cell_volume   303.897
_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  0.103  1.0
  Li  Li1  1  0.999  0.999  0.008  1.0
  Li  Li2  1  0.997  0.997  0.505  1.0
  Li  Li3  1  0.333  0.333  0.600  1.0
  Ti  Ti4  1  0.338  0.835  0.785  1.0
  Ti  Ti5  1  0.835  0.338  0.785  1.0
  Ti  Ti6  1  0.169  0.169  0.286  1.0
  Cr  Cr7  1  0.830  0.830  0.788  1.0
  Cr  Cr8  1  0.171  0.661  0.287  1.0
  Cr  Cr9  1  0.661  0.171  0.287  1.0
  W  W10  1  0.669  0.669  0.512  1.0
  W  W11  1  0.336  0.336  0.015  1.0
  O  O12  1  0.326  0.841  0.397  1.0
  O  O13  1  0.519  0.519  0.659  1.0
  O  O14  1  0.661  0.661  0.895  1.0
  O  O15  1  0.999  0.999  0.690  1.0
  O  O16  1  0.004  0.004  0.192  1.0
  O  O17  1  0.841  0.326  0.397  1.0
  O  O18  1  0.517  0.963  0.662  1.0
  O  O19  1  0.963  0.517  0.662  1.0
  O  O20  1  0.163  0.163  0.895  1.0
  O  O21  1  0.836  0.836  0.401  1.0
  O  O22  1  0.039  0.479  0.161  1.0
  O  O23  1  0.479  0.039  0.161  1.0
  O  O24  1  0.327  0.327  0.393  1.0
  O  O25  1  0.163  0.675  0.902  1.0
  O  O26  1  0.483  0.483  0.164  1.0
  O  O27  1  0.675  0.163  0.902  1.0
[/CIF]
.