The material structure described by Li4Ti3Cr3Mn2O16 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 Mn(2)O6 octahedra, and corners with four equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-64°. 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 Mn(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 56-65°. In the third Li site, Li(3) is bonded in a 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(1)O6 octahedra, corners with two equivalent Cr(1)O6 octahedra, corners with two equivalent Cr(2)O6 octahedra, corners with three equivalent Mn(1)O6 octahedra, and corners with four equivalent Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-63°. 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 Mn(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 Mn(2)O6 octahedra, and edges with four equivalent Cr(2)O6 octahedra. 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 Mn(2)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Mn(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 50-51°. 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 Mn(2)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Mn(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 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 Mn(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 Mn(2)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, and edges with two equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles are 52°. There are two inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to one O(2), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form MnO6 octahedra that share corners with two equivalent Ti(1)O6 octahedra, corners with four equivalent Cr(2)O6 octahedra, 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 Mn site, Mn(2) is bonded to one O(12), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form MnO6 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 50-51°. 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 Cr(2), and one Mn(1) atom. In the second O site, O(2) is bonded to one Li(4), two equivalent Ti(2), and one Mn(1) atom to form distorted OLiTi2Mn tetrahedra that share corners with two equivalent O(4)LiTi2Cr tetrahedra, corners with two equivalent O(6)LiTiMnCr tetrahedra, and edges with two equivalent O(6)LiTiMnCr 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)LiTi2Mn tetrahedra and corners with four equivalent O(6)LiTiMnCr tetrahedra. In the fifth O site, O(5) is bonded in a distorted tetrahedral geometry to one Li(2), one Ti(1), and two equivalent Cr(2) atoms. In the sixth O site, O(6) is bonded to one Li(4), one Ti(2), one Cr(1), and one Mn(1) atom to form distorted OLiTiMnCr tetrahedra that share  a cornercorner with one O(2)LiTi2Mn tetrahedra,  a cornercorner with one O(6)LiTiMnCr tetrahedra, corners with two equivalent O(4)LiTi2Cr tetrahedra,  an edgeedge with one O(2)LiTi2Mn tetrahedra, and  an edgeedge with one O(6)LiTiMnCr tetrahedra. 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 Mn(2) atom. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Li(3), two equivalent Cr(2), and one Mn(1) atom. 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 Cr(2), and one Mn(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 Cr(1), and one Mn(2) atom. In the twelfth O site, O(12) is bonded in a distorted rectangular see-saw-like geometry to one Li(1), two equivalent Cr(2), and one Mn(2) atom. is represented by the CIF file [CIF]
data_Li4Ti3Mn2Cr3O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.900
_cell_length_b   5.900
_cell_length_c   9.582
_cell_angle_alpha   88.679
_cell_angle_beta   88.679
_cell_angle_gamma   60.455
_symmetry_Int_Tables_number   1
_cell_volume   290.130
_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  0.668  0.668  0.104  1.0
  Li  Li1  1  0.995  0.995  0.005  1.0
  Li  Li2  1  0.991  0.991  0.504  1.0
  Li  Li3  1  0.338  0.338  0.601  1.0
  Ti  Ti4  1  0.163  0.163  0.292  1.0
  Ti  Ti5  1  0.342  0.839  0.785  1.0
  Ti  Ti6  1  0.839  0.342  0.785  1.0
  Mn  Mn7  1  0.669  0.669  0.510  1.0
  Mn  Mn8  1  0.337  0.337  0.020  1.0
  Cr  Cr9  1  0.832  0.832  0.792  1.0
  Cr  Cr10  1  0.165  0.658  0.285  1.0
  Cr  Cr11  1  0.658  0.165  0.285  1.0
  O  O12  1  0.320  0.842  0.396  1.0
  O  O13  1  0.526  0.526  0.659  1.0
  O  O14  1  0.659  0.659  0.897  1.0
  O  O15  1  0.005  0.005  0.692  1.0
  O  O16  1  0.001  0.001  0.188  1.0
  O  O17  1  0.842  0.320  0.396  1.0
  O  O18  1  0.517  0.970  0.668  1.0
  O  O19  1  0.970  0.517  0.668  1.0
  O  O20  1  0.165  0.165  0.899  1.0
  O  O21  1  0.832  0.832  0.400  1.0
  O  O22  1  0.044  0.475  0.154  1.0
  O  O23  1  0.475  0.044  0.154  1.0
  O  O24  1  0.325  0.325  0.394  1.0
  O  O25  1  0.173  0.669  0.901  1.0
  O  O26  1  0.479  0.479  0.157  1.0
  O  O27  1  0.669  0.173  0.901  1.0
[/CIF]
.
The material structure described by Li4Ti3Cr3Mn2O16 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 Mn(2)O6 octahedra, and corners with four equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-64°. 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 Mn(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 56-65°. In the third Li site, Li(3) is bonded in a 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(1)O6 octahedra, corners with two equivalent Cr(1)O6 octahedra, corners with two equivalent Cr(2)O6 octahedra, corners with three equivalent Mn(1)O6 octahedra, and corners with four equivalent Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-63°. 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 Mn(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 Mn(2)O6 octahedra, and edges with four equivalent Cr(2)O6 octahedra. 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 Mn(2)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Mn(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 50-51°. 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 Mn(2)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Mn(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 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 Mn(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 Mn(2)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, and edges with two equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles are 52°. There are two inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to one O(2), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form MnO6 octahedra that share corners with two equivalent Ti(1)O6 octahedra, corners with four equivalent Cr(2)O6 octahedra, 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 Mn site, Mn(2) is bonded to one O(12), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form MnO6 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 50-51°. 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 Cr(2), and one Mn(1) atom. In the second O site, O(2) is bonded to one Li(4), two equivalent Ti(2), and one Mn(1) atom to form distorted OLiTi2Mn tetrahedra that share corners with two equivalent O(4)LiTi2Cr tetrahedra, corners with two equivalent O(6)LiTiMnCr tetrahedra, and edges with two equivalent O(6)LiTiMnCr 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)LiTi2Mn tetrahedra and corners with four equivalent O(6)LiTiMnCr tetrahedra. In the fifth O site, O(5) is bonded in a distorted tetrahedral geometry to one Li(2), one Ti(1), and two equivalent Cr(2) atoms. In the sixth O site, O(6) is bonded to one Li(4), one Ti(2), one Cr(1), and one Mn(1) atom to form distorted OLiTiMnCr tetrahedra that share  a cornercorner with one O(2)LiTi2Mn tetrahedra,  a cornercorner with one O(6)LiTiMnCr tetrahedra, corners with two equivalent O(4)LiTi2Cr tetrahedra,  an edgeedge with one O(2)LiTi2Mn tetrahedra, and  an edgeedge with one O(6)LiTiMnCr tetrahedra. 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 Mn(2) atom. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Li(3), two equivalent Cr(2), and one Mn(1) atom. 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 Cr(2), and one Mn(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 Cr(1), and one Mn(2) atom. In the twelfth O site, O(12) is bonded in a distorted rectangular see-saw-like geometry to one Li(1), two equivalent Cr(2), and one Mn(2) atom. is represented by the CIF file [CIF]
data_Li4Ti3Mn2Cr3O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.900
_cell_length_b   5.900
_cell_length_c   9.582
_cell_angle_alpha   88.679
_cell_angle_beta   88.679
_cell_angle_gamma   60.455
_symmetry_Int_Tables_number   1
_cell_volume   290.130
_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  0.668  0.668  0.104  1.0
  Li  Li1  1  0.995  0.995  0.005  1.0
  Li  Li2  1  0.991  0.991  0.504  1.0
  Li  Li3  1  0.338  0.338  0.601  1.0
  Ti  Ti4  1  0.163  0.163  0.292  1.0
  Ti  Ti5  1  0.342  0.839  0.785  1.0
  Ti  Ti6  1  0.839  0.342  0.785  1.0
  Mn  Mn7  1  0.669  0.669  0.510  1.0
  Mn  Mn8  1  0.337  0.337  0.020  1.0
  Cr  Cr9  1  0.832  0.832  0.792  1.0
  Cr  Cr10  1  0.165  0.658  0.285  1.0
  Cr  Cr11  1  0.658  0.165  0.285  1.0
  O  O12  1  0.320  0.842  0.396  1.0
  O  O13  1  0.526  0.526  0.659  1.0
  O  O14  1  0.659  0.659  0.897  1.0
  O  O15  1  0.005  0.005  0.692  1.0
  O  O16  1  0.001  0.001  0.188  1.0
  O  O17  1  0.842  0.320  0.396  1.0
  O  O18  1  0.517  0.970  0.668  1.0
  O  O19  1  0.970  0.517  0.668  1.0
  O  O20  1  0.165  0.165  0.899  1.0
  O  O21  1  0.832  0.832  0.400  1.0
  O  O22  1  0.044  0.475  0.154  1.0
  O  O23  1  0.475  0.044  0.154  1.0
  O  O24  1  0.325  0.325  0.394  1.0
  O  O25  1  0.173  0.669  0.901  1.0
  O  O26  1  0.479  0.479  0.157  1.0
  O  O27  1  0.669  0.173  0.901  1.0
[/CIF]
.