The material described by Li3TiFe3O8 crystallizes in the hexagonal P6_3mc space group. Li(1) is bonded to one O(3), one O(4), two equivalent O(1), and two equivalent O(2) atoms to form distorted LiO6 octahedra that share corners with seven equivalent Fe(1)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, edges with four equivalent Li(1)O6 octahedra, and  a faceface with one Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 2-47°. Ti(1) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form distorted TiO6 octahedra that share corners with six equivalent Fe(1)O6 octahedra, edges with three equivalent Fe(1)O6 octahedra, and edges with six equivalent Li(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, corners with seven equivalent Li(1)O6 octahedra,  an edgeedge with one Ti(1)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with four equivalent Fe(1)O6 octahedra, and  a faceface with one Li(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 2-51°. There are four inequivalent O sites. In the first O site, O(1) is bonded to two equivalent Li(1), one Ti(1), and two equivalent Fe(1) atoms to form distorted OLi2TiFe2 trigonal bipyramids that share corners with seven equivalent O(2)Li2TiFe2 square pyramids, corners with two equivalent O(1)Li2TiFe2 trigonal bipyramids, edges with two equivalent O(3)Li3Fe3 octahedra, edges with two equivalent O(4)Li3Fe3 pentagonal pyramids, edges with two equivalent O(2)Li2TiFe2 square pyramids, and edges with two equivalent O(1)Li2TiFe2 trigonal bipyramids. In the second O site, O(2) is bonded to two equivalent Li(1), one Ti(1), and two equivalent Fe(1) atoms to form OLi2TiFe2 square pyramids that share corners with two equivalent O(2)Li2TiFe2 square pyramids, corners with seven equivalent O(1)Li2TiFe2 trigonal bipyramids, edges with two equivalent O(3)Li3Fe3 octahedra, edges with two equivalent O(4)Li3Fe3 pentagonal pyramids, edges with two equivalent O(2)Li2TiFe2 square pyramids, and edges with two equivalent O(1)Li2TiFe2 trigonal bipyramids. In the third O site, O(3) is bonded to three equivalent Li(1) and three equivalent Fe(1) atoms to form OLi3Fe3 octahedra that share corners with six equivalent O(4)Li3Fe3 pentagonal pyramids, edges with six equivalent O(2)Li2TiFe2 square pyramids, and edges with six equivalent O(1)Li2TiFe2 trigonal bipyramids. In the fourth O site, O(4) is bonded to three equivalent Li(1) and three equivalent Fe(1) atoms to form distorted OLi3Fe3 pentagonal pyramids that share corners with six equivalent O(3)Li3Fe3 octahedra, edges with six equivalent O(2)Li2TiFe2 square pyramids, and edges with six equivalent O(1)Li2TiFe2 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 4-10°. is represented by the CIF card [CIF]
data_Li3TiFe3O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.918
_cell_length_b   5.918
_cell_length_c   9.617
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   291.720
_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  0.824  0.176  0.558  1.0
  Li  Li1  1  0.824  0.648  0.558  1.0
  Li  Li2  1  0.352  0.176  0.558  1.0
  Li  Li3  1  0.648  0.824  0.058  1.0
  Li  Li4  1  0.176  0.352  0.058  1.0
  Li  Li5  1  0.176  0.824  0.058  1.0
  Ti  Ti6  1  0.667  0.333  0.003  1.0
  Ti  Ti7  1  0.333  0.667  0.503  1.0
  Fe  Fe8  1  0.831  0.169  0.285  1.0
  Fe  Fe9  1  0.831  0.661  0.285  1.0
  Fe  Fe10  1  0.339  0.169  0.285  1.0
  Fe  Fe11  1  0.661  0.831  0.785  1.0
  Fe  Fe12  1  0.169  0.339  0.785  1.0
  Fe  Fe13  1  0.169  0.831  0.785  1.0
  O  O14  1  0.833  0.167  0.909  1.0
  O  O15  1  0.964  0.482  0.154  1.0
  O  O16  1  0.833  0.665  0.909  1.0
  O  O17  1  0.000  0.000  0.677  1.0
  O  O18  1  0.667  0.333  0.405  1.0
  O  O19  1  0.000  0.000  0.177  1.0
  O  O20  1  0.518  0.036  0.154  1.0
  O  O21  1  0.518  0.482  0.154  1.0
  O  O22  1  0.335  0.167  0.909  1.0
  O  O23  1  0.665  0.833  0.409  1.0
  O  O24  1  0.482  0.518  0.654  1.0
  O  O25  1  0.333  0.667  0.905  1.0
  O  O26  1  0.167  0.335  0.409  1.0
  O  O27  1  0.482  0.964  0.654  1.0
  O  O28  1  0.036  0.518  0.654  1.0
  O  O29  1  0.167  0.833  0.409  1.0
[/CIF]
.
The material described by Li3TiFe3O8 crystallizes in the hexagonal P6_3mc space group. Li(1) is bonded to one O(3), one O(4), two equivalent O(1), and two equivalent O(2) atoms to form distorted LiO6 octahedra that share corners with seven equivalent Fe(1)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, edges with four equivalent Li(1)O6 octahedra, and  a faceface with one Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 2-47°. Ti(1) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form distorted TiO6 octahedra that share corners with six equivalent Fe(1)O6 octahedra, edges with three equivalent Fe(1)O6 octahedra, and edges with six equivalent Li(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, corners with seven equivalent Li(1)O6 octahedra,  an edgeedge with one Ti(1)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with four equivalent Fe(1)O6 octahedra, and  a faceface with one Li(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 2-51°. There are four inequivalent O sites. In the first O site, O(1) is bonded to two equivalent Li(1), one Ti(1), and two equivalent Fe(1) atoms to form distorted OLi2TiFe2 trigonal bipyramids that share corners with seven equivalent O(2)Li2TiFe2 square pyramids, corners with two equivalent O(1)Li2TiFe2 trigonal bipyramids, edges with two equivalent O(3)Li3Fe3 octahedra, edges with two equivalent O(4)Li3Fe3 pentagonal pyramids, edges with two equivalent O(2)Li2TiFe2 square pyramids, and edges with two equivalent O(1)Li2TiFe2 trigonal bipyramids. In the second O site, O(2) is bonded to two equivalent Li(1), one Ti(1), and two equivalent Fe(1) atoms to form OLi2TiFe2 square pyramids that share corners with two equivalent O(2)Li2TiFe2 square pyramids, corners with seven equivalent O(1)Li2TiFe2 trigonal bipyramids, edges with two equivalent O(3)Li3Fe3 octahedra, edges with two equivalent O(4)Li3Fe3 pentagonal pyramids, edges with two equivalent O(2)Li2TiFe2 square pyramids, and edges with two equivalent O(1)Li2TiFe2 trigonal bipyramids. In the third O site, O(3) is bonded to three equivalent Li(1) and three equivalent Fe(1) atoms to form OLi3Fe3 octahedra that share corners with six equivalent O(4)Li3Fe3 pentagonal pyramids, edges with six equivalent O(2)Li2TiFe2 square pyramids, and edges with six equivalent O(1)Li2TiFe2 trigonal bipyramids. In the fourth O site, O(4) is bonded to three equivalent Li(1) and three equivalent Fe(1) atoms to form distorted OLi3Fe3 pentagonal pyramids that share corners with six equivalent O(3)Li3Fe3 octahedra, edges with six equivalent O(2)Li2TiFe2 square pyramids, and edges with six equivalent O(1)Li2TiFe2 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 4-10°. is represented by the CIF card [CIF]
data_Li3TiFe3O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.918
_cell_length_b   5.918
_cell_length_c   9.617
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   291.720
_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  0.824  0.176  0.558  1.0
  Li  Li1  1  0.824  0.648  0.558  1.0
  Li  Li2  1  0.352  0.176  0.558  1.0
  Li  Li3  1  0.648  0.824  0.058  1.0
  Li  Li4  1  0.176  0.352  0.058  1.0
  Li  Li5  1  0.176  0.824  0.058  1.0
  Ti  Ti6  1  0.667  0.333  0.003  1.0
  Ti  Ti7  1  0.333  0.667  0.503  1.0
  Fe  Fe8  1  0.831  0.169  0.285  1.0
  Fe  Fe9  1  0.831  0.661  0.285  1.0
  Fe  Fe10  1  0.339  0.169  0.285  1.0
  Fe  Fe11  1  0.661  0.831  0.785  1.0
  Fe  Fe12  1  0.169  0.339  0.785  1.0
  Fe  Fe13  1  0.169  0.831  0.785  1.0
  O  O14  1  0.833  0.167  0.909  1.0
  O  O15  1  0.964  0.482  0.154  1.0
  O  O16  1  0.833  0.665  0.909  1.0
  O  O17  1  0.000  0.000  0.677  1.0
  O  O18  1  0.667  0.333  0.405  1.0
  O  O19  1  0.000  0.000  0.177  1.0
  O  O20  1  0.518  0.036  0.154  1.0
  O  O21  1  0.518  0.482  0.154  1.0
  O  O22  1  0.335  0.167  0.909  1.0
  O  O23  1  0.665  0.833  0.409  1.0
  O  O24  1  0.482  0.518  0.654  1.0
  O  O25  1  0.333  0.667  0.905  1.0
  O  O26  1  0.167  0.335  0.409  1.0
  O  O27  1  0.482  0.964  0.654  1.0
  O  O28  1  0.036  0.518  0.654  1.0
  O  O29  1  0.167  0.833  0.409  1.0
[/CIF]
.