The structure described by Li2TiFe3O8 is Spinel-derived structured and crystallizes in the hexagonal P6_3mc space group. There are two inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(3) and three equivalent O(2) atoms to form LiO4 tetrahedra that share corners with three equivalent Ti(1)O6 octahedra and corners with nine equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-61°. In the second Li site, Li(2) is bonded to one O(4) and three equivalent O(1) atoms to form distorted LiO4 tetrahedra that share corners with three equivalent Ti(1)O6 octahedra, corners with three equivalent Fe(1)O6 octahedra, and edges with three equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 59-64°. Ti(1) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form TiO6 octahedra that share corners with six equivalent Fe(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra, corners with three equivalent Li(2)O4 tetrahedra, and edges with three equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles are 51°. Fe(1) is bonded to one O(3), one O(4), two equivalent O(1), and two equivalent O(2) atoms to form FeO6 octahedra that share corners with two equivalent Ti(1)O6 octahedra,  a cornercorner with one Li(2)O4 tetrahedra, corners with three equivalent Li(1)O4 tetrahedra,  an edgeedge with one Ti(1)O6 octahedra, edges with four equivalent Fe(1)O6 octahedra, and  an edgeedge with one Li(2)O4 tetrahedra. The corner-sharing octahedral tilt angles are 51°. There are four inequivalent O sites. In the first O site, O(1) is bonded in a rectangular see-saw-like geometry to one Li(2), one Ti(1), and two equivalent Fe(1) atoms. In the second O site, O(2) is bonded to one Li(1), one Ti(1), and two equivalent Fe(1) atoms to form distorted OLiTiFe2 tetrahedra that share corners with two equivalent O(4)LiFe3 tetrahedra, corners with two equivalent O(2)LiTiFe2 tetrahedra,  a cornercorner with one O(3)LiFe3 trigonal pyramid, edges with two equivalent O(2)LiTiFe2 tetrahedra, and  an edgeedge with one O(3)LiFe3 trigonal pyramid. In the third O site, O(3) is bonded to one Li(1) and three equivalent Fe(1) atoms to form distorted OLiFe3 trigonal pyramids that share corners with three equivalent O(4)LiFe3 tetrahedra, corners with three equivalent O(2)LiTiFe2 tetrahedra, and edges with three equivalent O(2)LiTiFe2 tetrahedra. In the fourth O site, O(4) is bonded to one Li(2) and three equivalent Fe(1) atoms to form OLiFe3 tetrahedra that share corners with six equivalent O(2)LiTiFe2 tetrahedra and corners with three equivalent O(3)LiFe3 trigonal pyramids. is represented by the CIF file [CIF]
data_Li2TiFe3O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.935
_cell_length_b   5.935
_cell_length_c   9.586
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   292.424
_cell_formula_units_Z   2
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  0.333  0.667  0.896  1.0
  Li  Li1  1  0.000  0.000  0.995  1.0
  Li  Li2  1  0.000  0.000  0.495  1.0
  Li  Li3  1  0.667  0.333  0.396  1.0
  Ti  Ti4  1  0.333  0.667  0.495  1.0
  Ti  Ti5  1  0.667  0.333  0.995  1.0
  Fe  Fe6  1  0.171  0.829  0.215  1.0
  Fe  Fe7  1  0.171  0.342  0.215  1.0
  Fe  Fe8  1  0.658  0.829  0.215  1.0
  Fe  Fe9  1  0.342  0.171  0.715  1.0
  Fe  Fe10  1  0.829  0.658  0.715  1.0
  Fe  Fe11  1  0.829  0.171  0.715  1.0
  O  O12  1  0.168  0.832  0.595  1.0
  O  O13  1  0.039  0.519  0.343  1.0
  O  O14  1  0.333  0.667  0.104  1.0
  O  O15  1  0.000  0.000  0.306  1.0
  O  O16  1  0.000  0.000  0.806  1.0
  O  O17  1  0.168  0.337  0.595  1.0
  O  O18  1  0.481  0.961  0.343  1.0
  O  O19  1  0.481  0.519  0.343  1.0
  O  O20  1  0.337  0.168  0.095  1.0
  O  O21  1  0.663  0.832  0.595  1.0
  O  O22  1  0.519  0.481  0.843  1.0
  O  O23  1  0.519  0.039  0.843  1.0
  O  O24  1  0.667  0.333  0.604  1.0
  O  O25  1  0.832  0.663  0.095  1.0
  O  O26  1  0.961  0.481  0.843  1.0
  O  O27  1  0.832  0.168  0.095  1.0
[/CIF]
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The structure described by Li2TiFe3O8 is Spinel-derived structured and crystallizes in the hexagonal P6_3mc space group. There are two inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(3) and three equivalent O(2) atoms to form LiO4 tetrahedra that share corners with three equivalent Ti(1)O6 octahedra and corners with nine equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-61°. In the second Li site, Li(2) is bonded to one O(4) and three equivalent O(1) atoms to form distorted LiO4 tetrahedra that share corners with three equivalent Ti(1)O6 octahedra, corners with three equivalent Fe(1)O6 octahedra, and edges with three equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 59-64°. Ti(1) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form TiO6 octahedra that share corners with six equivalent Fe(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra, corners with three equivalent Li(2)O4 tetrahedra, and edges with three equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles are 51°. Fe(1) is bonded to one O(3), one O(4), two equivalent O(1), and two equivalent O(2) atoms to form FeO6 octahedra that share corners with two equivalent Ti(1)O6 octahedra,  a cornercorner with one Li(2)O4 tetrahedra, corners with three equivalent Li(1)O4 tetrahedra,  an edgeedge with one Ti(1)O6 octahedra, edges with four equivalent Fe(1)O6 octahedra, and  an edgeedge with one Li(2)O4 tetrahedra. The corner-sharing octahedral tilt angles are 51°. There are four inequivalent O sites. In the first O site, O(1) is bonded in a rectangular see-saw-like geometry to one Li(2), one Ti(1), and two equivalent Fe(1) atoms. In the second O site, O(2) is bonded to one Li(1), one Ti(1), and two equivalent Fe(1) atoms to form distorted OLiTiFe2 tetrahedra that share corners with two equivalent O(4)LiFe3 tetrahedra, corners with two equivalent O(2)LiTiFe2 tetrahedra,  a cornercorner with one O(3)LiFe3 trigonal pyramid, edges with two equivalent O(2)LiTiFe2 tetrahedra, and  an edgeedge with one O(3)LiFe3 trigonal pyramid. In the third O site, O(3) is bonded to one Li(1) and three equivalent Fe(1) atoms to form distorted OLiFe3 trigonal pyramids that share corners with three equivalent O(4)LiFe3 tetrahedra, corners with three equivalent O(2)LiTiFe2 tetrahedra, and edges with three equivalent O(2)LiTiFe2 tetrahedra. In the fourth O site, O(4) is bonded to one Li(2) and three equivalent Fe(1) atoms to form OLiFe3 tetrahedra that share corners with six equivalent O(2)LiTiFe2 tetrahedra and corners with three equivalent O(3)LiFe3 trigonal pyramids. is represented by the CIF file [CIF]
data_Li2TiFe3O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.935
_cell_length_b   5.935
_cell_length_c   9.586
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   292.424
_cell_formula_units_Z   2
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  0.333  0.667  0.896  1.0
  Li  Li1  1  0.000  0.000  0.995  1.0
  Li  Li2  1  0.000  0.000  0.495  1.0
  Li  Li3  1  0.667  0.333  0.396  1.0
  Ti  Ti4  1  0.333  0.667  0.495  1.0
  Ti  Ti5  1  0.667  0.333  0.995  1.0
  Fe  Fe6  1  0.171  0.829  0.215  1.0
  Fe  Fe7  1  0.171  0.342  0.215  1.0
  Fe  Fe8  1  0.658  0.829  0.215  1.0
  Fe  Fe9  1  0.342  0.171  0.715  1.0
  Fe  Fe10  1  0.829  0.658  0.715  1.0
  Fe  Fe11  1  0.829  0.171  0.715  1.0
  O  O12  1  0.168  0.832  0.595  1.0
  O  O13  1  0.039  0.519  0.343  1.0
  O  O14  1  0.333  0.667  0.104  1.0
  O  O15  1  0.000  0.000  0.306  1.0
  O  O16  1  0.000  0.000  0.806  1.0
  O  O17  1  0.168  0.337  0.595  1.0
  O  O18  1  0.481  0.961  0.343  1.0
  O  O19  1  0.481  0.519  0.343  1.0
  O  O20  1  0.337  0.168  0.095  1.0
  O  O21  1  0.663  0.832  0.595  1.0
  O  O22  1  0.519  0.481  0.843  1.0
  O  O23  1  0.519  0.039  0.843  1.0
  O  O24  1  0.667  0.333  0.604  1.0
  O  O25  1  0.832  0.663  0.095  1.0
  O  O26  1  0.961  0.481  0.843  1.0
  O  O27  1  0.832  0.168  0.095  1.0
[/CIF]
.