The material described by Li4Ti3Cr2Fe3O16 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 Fe(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 Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-64°. In the second Li site, Li(2) is bonded in a distorted 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 Fe(1)O6 octahedra, corners with two equivalent Ti(1)O6 octahedra, corners with three equivalent Cr(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra, and edges with two equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 60-64°. 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(2)O6 octahedra, corners with two equivalent Fe(1)O6 octahedra, corners with two equivalent Fe(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 56-64°. 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,  a cornercorner with one Li(3)O4 trigonal pyramid,  an edgeedge with one Cr(1)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, and edges with two equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 49-51°. 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, edges with four equivalent Fe(2)O6 octahedra, and  an edgeedge with one Li(3)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 49°. 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 Fe(2)O6 octahedra, corners with three equivalent Li(4)O4 tetrahedra, corners with three equivalent Li(3)O4 trigonal pyramids,  an edgeedge with one Fe(1)O6 octahedra, and edges with two equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 49-53°. 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 Fe(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 Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 49-53°. There are two inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to one O(3), one O(4), two equivalent O(11), and two equivalent O(6) atoms to form FeO6 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,  a cornercorner with one Li(3)O4 trigonal pyramid,  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 Fe site, Fe(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 FeO6 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, edges with two equivalent Fe(2)O6 octahedra, and  an edgeedge with one Li(3)O4 trigonal pyramid. The corner-sharing octahedral tilt angles range from 51-53°. 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 Cr(1), and one Fe(2) 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)LiTi2Fe tetrahedra, corners with two equivalent O(6)LiTiCrFe tetrahedra,  a cornercorner with one O(10)LiTiFe2 trigonal pyramid, and edges with two equivalent O(6)LiTiCrFe 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 Fe(1) atom. In the fourth O site, O(4) is bonded to one Li(3), two equivalent Ti(1), and one Fe(1) atom to form distorted OLiTi2Fe tetrahedra that share corners with two equivalent O(2)LiTi2Cr tetrahedra and corners with four equivalent O(6)LiTiCrFe tetrahedra. In the fifth O site, O(5) is bonded to one Li(2), one Ti(2), and two equivalent Fe(2) atoms to form distorted OLiTiFe2 tetrahedra that share corners with three equivalent O(10)LiTiFe2 trigonal pyramids and corners with four equivalent O(9)LiTiCrFe trigonal pyramids. In the sixth O site, O(6) is bonded to one Li(4), one Ti(1), one Cr(1), and one Fe(1) atom to form distorted OLiTiCrFe tetrahedra that share  a cornercorner with one O(2)LiTi2Cr tetrahedra,  a cornercorner with one O(6)LiTiCrFe tetrahedra, corners with two equivalent O(4)LiTi2Fe tetrahedra,  a cornercorner with one O(10)LiTiFe2 trigonal pyramid,  an edgeedge with one O(2)LiTi2Cr tetrahedra, and  an edgeedge with one O(6)LiTiCrFe 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 rectangular see-saw-like geometry to one Li(3), one Cr(1), and two equivalent Fe(2) atoms. In the ninth O site, O(9) is bonded to one Li(1), one Ti(2), one Cr(2), and one Fe(2) atom to form distorted OLiTiCrFe trigonal pyramids that share corners with two equivalent O(5)LiTiFe2 tetrahedra,  a cornercorner with one O(9)LiTiCrFe trigonal pyramid,  an edgeedge with one O(9)LiTiCrFe trigonal pyramid, and  an edgeedge with one O(10)LiTiFe2 trigonal pyramid. In the tenth O site, O(10) is bonded to one Li(4), one Ti(2), and two equivalent Fe(2) atoms to form distorted OLiTiFe2 trigonal pyramids that share  a cornercorner with one O(2)LiTi2Cr tetrahedra, corners with two equivalent O(6)LiTiCrFe tetrahedra, corners with three equivalent O(5)LiTiFe2 tetrahedra, and edges with two equivalent O(9)LiTiCrFe trigonal pyramids. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one Ti(1), one Cr(2), and one Fe(1) atom. In the twelfth O site, O(12) is bonded in a distorted rectangular see-saw-like geometry to one Li(1), one Cr(2), and two equivalent Fe(2) atoms. is represented by the CIF file [CIF]
data_Li4Ti3Cr2Fe3O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.936
_cell_length_b   5.936
_cell_length_c   9.605
_cell_angle_alpha   89.622
_cell_angle_beta   89.622
_cell_angle_gamma   59.892
_symmetry_Int_Tables_number   1
_cell_volume   292.755
_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  0.669  0.669  0.108  1.0
  Li  Li1  1  0.996  0.996  0.005  1.0
  Li  Li2  1  0.997  0.997  0.503  1.0
  Li  Li3  1  0.333  0.333  0.604  1.0
  Ti  Ti4  1  0.337  0.832  0.786  1.0
  Ti  Ti5  1  0.832  0.337  0.786  1.0
  Ti  Ti6  1  0.169  0.169  0.286  1.0
  Cr  Cr7  1  0.666  0.666  0.514  1.0
  Cr  Cr8  1  0.336  0.336  0.017  1.0
  Fe  Fe9  1  0.831  0.831  0.786  1.0
  Fe  Fe10  1  0.170  0.661  0.287  1.0
  Fe  Fe11  1  0.661  0.170  0.287  1.0
  O  O12  1  0.330  0.841  0.399  1.0
  O  O13  1  0.519  0.519  0.663  1.0
  O  O14  1  0.663  0.663  0.896  1.0
  O  O15  1  0.002  0.002  0.689  1.0
  O  O16  1  0.001  0.001  0.191  1.0
  O  O17  1  0.841  0.330  0.399  1.0
  O  O18  1  0.513  0.957  0.658  1.0
  O  O19  1  0.957  0.513  0.658  1.0
  O  O20  1  0.165  0.165  0.894  1.0
  O  O21  1  0.834  0.834  0.400  1.0
  O  O22  1  0.041  0.473  0.159  1.0
  O  O23  1  0.473  0.041  0.159  1.0
  O  O24  1  0.330  0.330  0.397  1.0
  O  O25  1  0.173  0.672  0.898  1.0
  O  O26  1  0.481  0.481  0.159  1.0
  O  O27  1  0.672  0.173  0.898  1.0
[/CIF]
.
The material described by Li4Ti3Cr2Fe3O16 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 Fe(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 Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-64°. In the second Li site, Li(2) is bonded in a distorted 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 Fe(1)O6 octahedra, corners with two equivalent Ti(1)O6 octahedra, corners with three equivalent Cr(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra, and edges with two equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 60-64°. 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(2)O6 octahedra, corners with two equivalent Fe(1)O6 octahedra, corners with two equivalent Fe(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 56-64°. 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,  a cornercorner with one Li(3)O4 trigonal pyramid,  an edgeedge with one Cr(1)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, and edges with two equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 49-51°. 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, edges with four equivalent Fe(2)O6 octahedra, and  an edgeedge with one Li(3)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 49°. 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 Fe(2)O6 octahedra, corners with three equivalent Li(4)O4 tetrahedra, corners with three equivalent Li(3)O4 trigonal pyramids,  an edgeedge with one Fe(1)O6 octahedra, and edges with two equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 49-53°. 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 Fe(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 Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 49-53°. There are two inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to one O(3), one O(4), two equivalent O(11), and two equivalent O(6) atoms to form FeO6 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,  a cornercorner with one Li(3)O4 trigonal pyramid,  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 Fe site, Fe(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 FeO6 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, edges with two equivalent Fe(2)O6 octahedra, and  an edgeedge with one Li(3)O4 trigonal pyramid. The corner-sharing octahedral tilt angles range from 51-53°. 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 Cr(1), and one Fe(2) 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)LiTi2Fe tetrahedra, corners with two equivalent O(6)LiTiCrFe tetrahedra,  a cornercorner with one O(10)LiTiFe2 trigonal pyramid, and edges with two equivalent O(6)LiTiCrFe 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 Fe(1) atom. In the fourth O site, O(4) is bonded to one Li(3), two equivalent Ti(1), and one Fe(1) atom to form distorted OLiTi2Fe tetrahedra that share corners with two equivalent O(2)LiTi2Cr tetrahedra and corners with four equivalent O(6)LiTiCrFe tetrahedra. In the fifth O site, O(5) is bonded to one Li(2), one Ti(2), and two equivalent Fe(2) atoms to form distorted OLiTiFe2 tetrahedra that share corners with three equivalent O(10)LiTiFe2 trigonal pyramids and corners with four equivalent O(9)LiTiCrFe trigonal pyramids. In the sixth O site, O(6) is bonded to one Li(4), one Ti(1), one Cr(1), and one Fe(1) atom to form distorted OLiTiCrFe tetrahedra that share  a cornercorner with one O(2)LiTi2Cr tetrahedra,  a cornercorner with one O(6)LiTiCrFe tetrahedra, corners with two equivalent O(4)LiTi2Fe tetrahedra,  a cornercorner with one O(10)LiTiFe2 trigonal pyramid,  an edgeedge with one O(2)LiTi2Cr tetrahedra, and  an edgeedge with one O(6)LiTiCrFe 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 rectangular see-saw-like geometry to one Li(3), one Cr(1), and two equivalent Fe(2) atoms. In the ninth O site, O(9) is bonded to one Li(1), one Ti(2), one Cr(2), and one Fe(2) atom to form distorted OLiTiCrFe trigonal pyramids that share corners with two equivalent O(5)LiTiFe2 tetrahedra,  a cornercorner with one O(9)LiTiCrFe trigonal pyramid,  an edgeedge with one O(9)LiTiCrFe trigonal pyramid, and  an edgeedge with one O(10)LiTiFe2 trigonal pyramid. In the tenth O site, O(10) is bonded to one Li(4), one Ti(2), and two equivalent Fe(2) atoms to form distorted OLiTiFe2 trigonal pyramids that share  a cornercorner with one O(2)LiTi2Cr tetrahedra, corners with two equivalent O(6)LiTiCrFe tetrahedra, corners with three equivalent O(5)LiTiFe2 tetrahedra, and edges with two equivalent O(9)LiTiCrFe trigonal pyramids. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one Ti(1), one Cr(2), and one Fe(1) atom. In the twelfth O site, O(12) is bonded in a distorted rectangular see-saw-like geometry to one Li(1), one Cr(2), and two equivalent Fe(2) atoms. is represented by the CIF file [CIF]
data_Li4Ti3Cr2Fe3O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.936
_cell_length_b   5.936
_cell_length_c   9.605
_cell_angle_alpha   89.622
_cell_angle_beta   89.622
_cell_angle_gamma   59.892
_symmetry_Int_Tables_number   1
_cell_volume   292.755
_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  0.669  0.669  0.108  1.0
  Li  Li1  1  0.996  0.996  0.005  1.0
  Li  Li2  1  0.997  0.997  0.503  1.0
  Li  Li3  1  0.333  0.333  0.604  1.0
  Ti  Ti4  1  0.337  0.832  0.786  1.0
  Ti  Ti5  1  0.832  0.337  0.786  1.0
  Ti  Ti6  1  0.169  0.169  0.286  1.0
  Cr  Cr7  1  0.666  0.666  0.514  1.0
  Cr  Cr8  1  0.336  0.336  0.017  1.0
  Fe  Fe9  1  0.831  0.831  0.786  1.0
  Fe  Fe10  1  0.170  0.661  0.287  1.0
  Fe  Fe11  1  0.661  0.170  0.287  1.0
  O  O12  1  0.330  0.841  0.399  1.0
  O  O13  1  0.519  0.519  0.663  1.0
  O  O14  1  0.663  0.663  0.896  1.0
  O  O15  1  0.002  0.002  0.689  1.0
  O  O16  1  0.001  0.001  0.191  1.0
  O  O17  1  0.841  0.330  0.399  1.0
  O  O18  1  0.513  0.957  0.658  1.0
  O  O19  1  0.957  0.513  0.658  1.0
  O  O20  1  0.165  0.165  0.894  1.0
  O  O21  1  0.834  0.834  0.400  1.0
  O  O22  1  0.041  0.473  0.159  1.0
  O  O23  1  0.473  0.041  0.159  1.0
  O  O24  1  0.330  0.330  0.397  1.0
  O  O25  1  0.173  0.672  0.898  1.0
  O  O26  1  0.481  0.481  0.159  1.0
  O  O27  1  0.672  0.173  0.898  1.0
[/CIF]
.