The crystal structure described by Li2TiFe3O8 is Spinel-derived structured and crystallizes in the triclinic P-1 space group. There are two inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(1), one O(4), one O(6), and one O(8) atom to form LiO4 tetrahedra that share  a cornercorner with one Fe(2)O6 octahedra,  a cornercorner with one Fe(4)O6 octahedra,  a cornercorner with one Fe(6)O6 octahedra, corners with two equivalent Fe(1)O6 octahedra, corners with two equivalent Fe(3)O6 octahedra, corners with two equivalent Fe(5)O6 octahedra, and corners with three equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-63°. In the second Li site, Li(2) is bonded to one O(2), one O(3), one O(5), and one O(7) atom to form LiO4 tetrahedra that share  a cornercorner with one Fe(1)O6 octahedra,  a cornercorner with one Fe(3)O6 octahedra,  a cornercorner with one Fe(5)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, corners with two equivalent Fe(4)O6 octahedra, corners with two equivalent Fe(6)O6 octahedra, and corners with three equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-63°. Ti(1) is bonded to one O(3), one O(4), one O(5), one O(6), one O(7), and one O(8) atom to form TiO6 octahedra that share corners with three equivalent Li(1)O4 tetrahedra, corners with three equivalent Li(2)O4 tetrahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra,  an edgeedge with one Fe(3)O6 octahedra,  an edgeedge with one Fe(4)O6 octahedra,  an edgeedge with one Fe(5)O6 octahedra, and  an edgeedge with one Fe(6)O6 octahedra. There are six inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to two equivalent O(2), two equivalent O(4), and two equivalent O(8) atoms to form FeO6 octahedra that share corners with two equivalent Li(2)O4 tetrahedra, corners with four equivalent Li(1)O4 tetrahedra, edges with two equivalent Ti(1)O6 octahedra, edges with two equivalent Fe(3)O6 octahedra, and edges with two equivalent Fe(5)O6 octahedra. In the second Fe site, Fe(2) is bonded to two equivalent O(1), two equivalent O(5), and two equivalent O(7) atoms to form FeO6 octahedra that share corners with two equivalent Li(1)O4 tetrahedra, corners with four equivalent Li(2)O4 tetrahedra, edges with two equivalent Ti(1)O6 octahedra, edges with two equivalent Fe(4)O6 octahedra, and edges with two equivalent Fe(6)O6 octahedra. In the third Fe site, Fe(3) is bonded to two equivalent O(2), two equivalent O(6), and two equivalent O(8) atoms to form FeO6 octahedra that share corners with two equivalent Li(2)O4 tetrahedra, corners with four equivalent Li(1)O4 tetrahedra, edges with two equivalent Ti(1)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, and edges with two equivalent Fe(5)O6 octahedra. In the fourth Fe site, Fe(4) is bonded to two equivalent O(1), two equivalent O(3), and two equivalent O(5) atoms to form FeO6 octahedra that share corners with two equivalent Li(1)O4 tetrahedra, corners with four equivalent Li(2)O4 tetrahedra, edges with two equivalent Ti(1)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, and edges with two equivalent Fe(6)O6 octahedra. In the fifth Fe site, Fe(5) is bonded to two equivalent O(2), two equivalent O(4), and two equivalent O(6) atoms to form FeO6 octahedra that share corners with two equivalent Li(2)O4 tetrahedra, corners with four equivalent Li(1)O4 tetrahedra, edges with two equivalent Ti(1)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, and edges with two equivalent Fe(3)O6 octahedra. In the sixth Fe site, Fe(6) is bonded to two equivalent O(1), two equivalent O(3), and two equivalent O(7) atoms to form FeO6 octahedra that share corners with two equivalent Li(1)O4 tetrahedra, corners with four equivalent Li(2)O4 tetrahedra, edges with two equivalent Ti(1)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, and edges with two equivalent Fe(4)O6 octahedra. There are eight inequivalent O sites. In the first O site, O(1) is bonded in a distorted rectangular see-saw-like geometry to one Li(1), one Fe(2), one Fe(4), and one Fe(6) atom. In the second O site, O(2) is bonded to one Li(2), one Fe(1), one Fe(3), and one Fe(5) atom to form distorted OLiFe3 trigonal pyramids that share  a cornercorner with one O(3)LiTiFe2 trigonal pyramid,  a cornercorner with one O(5)LiTiFe2 trigonal pyramid, corners with two equivalent O(4)LiTiFe2 trigonal pyramids, corners with two equivalent O(6)LiTiFe2 trigonal pyramids, corners with three equivalent O(2)LiFe3 trigonal pyramids,  an edgeedge with one O(4)LiTiFe2 trigonal pyramid, and  an edgeedge with one O(6)LiTiFe2 trigonal pyramid. In the third O site, O(3) is bonded to one Li(2), one Ti(1), one Fe(4), and one Fe(6) atom to form distorted OLiTiFe2 trigonal pyramids that share  a cornercorner with one O(2)LiFe3 trigonal pyramid,  a cornercorner with one O(4)LiTiFe2 trigonal pyramid,  a cornercorner with one O(6)LiTiFe2 trigonal pyramid, corners with two equivalent O(3)LiTiFe2 trigonal pyramids, corners with two equivalent O(5)LiTiFe2 trigonal pyramids, and  an edgeedge with one O(5)LiTiFe2 trigonal pyramid. In the fourth O site, O(4) is bonded to one Li(1), one Ti(1), one Fe(1), and one Fe(5) atom to form distorted OLiTiFe2 trigonal pyramids that share  a cornercorner with one O(3)LiTiFe2 trigonal pyramid,  a cornercorner with one O(5)LiTiFe2 trigonal pyramid, corners with two equivalent O(2)LiFe3 trigonal pyramids, corners with two equivalent O(4)LiTiFe2 trigonal pyramids, corners with two equivalent O(6)LiTiFe2 trigonal pyramids,  an edgeedge with one O(2)LiFe3 trigonal pyramid, and  an edgeedge with one O(6)LiTiFe2 trigonal pyramid. In the fifth O site, O(5) is bonded to one Li(2), one Ti(1), one Fe(2), and one Fe(4) atom to form distorted OLiTiFe2 trigonal pyramids that share  a cornercorner with one O(2)LiFe3 trigonal pyramid,  a cornercorner with one O(4)LiTiFe2 trigonal pyramid,  a cornercorner with one O(6)LiTiFe2 trigonal pyramid, corners with two equivalent O(3)LiTiFe2 trigonal pyramids, corners with two equivalent O(5)LiTiFe2 trigonal pyramids, and  an edgeedge with one O(3)LiTiFe2 trigonal pyramid. In the sixth O site, O(6) is bonded to one Li(1), one Ti(1), one Fe(3), and one Fe(5) atom to form distorted OLiTiFe2 trigonal pyramids that share  a cornercorner with one O(3)LiTiFe2 trigonal pyramid,  a cornercorner with one O(5)LiTiFe2 trigonal pyramid, corners with two equivalent O(2)LiFe3 trigonal pyramids, corners with two equivalent O(4)LiTiFe2 trigonal pyramids, corners with two equivalent O(6)LiTiFe2 trigonal pyramids,  an edgeedge with one O(2)LiFe3 trigonal pyramid, and  an edgeedge with one O(4)LiTiFe2 trigonal pyramid. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), one Ti(1), one Fe(2), and one Fe(6) atom. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Li(1), one Ti(1), one Fe(1), and one Fe(3) atom. is represented by the CIF file [CIF]
data_Li2TiFe3O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.987
_cell_length_b   6.012
_cell_length_c   10.331
_cell_angle_alpha   89.690
_cell_angle_beta   106.476
_cell_angle_gamma   120.213
_symmetry_Int_Tables_number   1
_cell_volume   303.873
_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  0.116  0.069  0.189  1.0
  Li  Li1  1  0.124  0.560  0.689  1.0
  Li  Li2  1  0.876  0.440  0.311  1.0
  Li  Li3  1  0.884  0.931  0.811  1.0
  Ti  Ti4  1  0.507  0.228  0.750  1.0
  Ti  Ti5  1  0.494  0.772  0.250  1.0
  Fe  Fe6  1  0.500  1.000  1.000  1.0
  Fe  Fe7  1  0.000  0.000  0.500  1.0
  Fe  Fe8  1  0.000  0.500  0.000  1.0
  Fe  Fe9  1  0.500  0.000  0.500  1.0
  Fe  Fe10  1  0.500  0.500  0.000  1.0
  Fe  Fe11  1  0.500  0.500  0.500  1.0
  O  O12  1  0.271  0.146  0.397  1.0
  O  O13  1  0.253  0.629  0.897  1.0
  O  O14  1  0.747  0.371  0.103  1.0
  O  O15  1  0.729  0.854  0.603  1.0
  O  O16  1  0.719  0.352  0.624  1.0
  O  O17  1  0.709  0.850  0.125  1.0
  O  O18  1  0.262  0.906  0.624  1.0
  O  O19  1  0.244  0.410  0.116  1.0
  O  O20  1  0.280  0.367  0.619  1.0
  O  O21  1  0.268  0.869  0.126  1.0
  O  O22  1  0.732  0.130  0.874  1.0
  O  O23  1  0.720  0.633  0.381  1.0
  O  O24  1  0.756  0.590  0.884  1.0
  O  O25  1  0.738  0.094  0.376  1.0
  O  O26  1  0.291  0.150  0.875  1.0
  O  O27  1  0.281  0.648  0.376  1.0
[/CIF]
.
The crystal structure described by Li2TiFe3O8 is Spinel-derived structured and crystallizes in the triclinic P-1 space group. There are two inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(1), one O(4), one O(6), and one O(8) atom to form LiO4 tetrahedra that share  a cornercorner with one Fe(2)O6 octahedra,  a cornercorner with one Fe(4)O6 octahedra,  a cornercorner with one Fe(6)O6 octahedra, corners with two equivalent Fe(1)O6 octahedra, corners with two equivalent Fe(3)O6 octahedra, corners with two equivalent Fe(5)O6 octahedra, and corners with three equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-63°. In the second Li site, Li(2) is bonded to one O(2), one O(3), one O(5), and one O(7) atom to form LiO4 tetrahedra that share  a cornercorner with one Fe(1)O6 octahedra,  a cornercorner with one Fe(3)O6 octahedra,  a cornercorner with one Fe(5)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, corners with two equivalent Fe(4)O6 octahedra, corners with two equivalent Fe(6)O6 octahedra, and corners with three equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-63°. Ti(1) is bonded to one O(3), one O(4), one O(5), one O(6), one O(7), and one O(8) atom to form TiO6 octahedra that share corners with three equivalent Li(1)O4 tetrahedra, corners with three equivalent Li(2)O4 tetrahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra,  an edgeedge with one Fe(3)O6 octahedra,  an edgeedge with one Fe(4)O6 octahedra,  an edgeedge with one Fe(5)O6 octahedra, and  an edgeedge with one Fe(6)O6 octahedra. There are six inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to two equivalent O(2), two equivalent O(4), and two equivalent O(8) atoms to form FeO6 octahedra that share corners with two equivalent Li(2)O4 tetrahedra, corners with four equivalent Li(1)O4 tetrahedra, edges with two equivalent Ti(1)O6 octahedra, edges with two equivalent Fe(3)O6 octahedra, and edges with two equivalent Fe(5)O6 octahedra. In the second Fe site, Fe(2) is bonded to two equivalent O(1), two equivalent O(5), and two equivalent O(7) atoms to form FeO6 octahedra that share corners with two equivalent Li(1)O4 tetrahedra, corners with four equivalent Li(2)O4 tetrahedra, edges with two equivalent Ti(1)O6 octahedra, edges with two equivalent Fe(4)O6 octahedra, and edges with two equivalent Fe(6)O6 octahedra. In the third Fe site, Fe(3) is bonded to two equivalent O(2), two equivalent O(6), and two equivalent O(8) atoms to form FeO6 octahedra that share corners with two equivalent Li(2)O4 tetrahedra, corners with four equivalent Li(1)O4 tetrahedra, edges with two equivalent Ti(1)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, and edges with two equivalent Fe(5)O6 octahedra. In the fourth Fe site, Fe(4) is bonded to two equivalent O(1), two equivalent O(3), and two equivalent O(5) atoms to form FeO6 octahedra that share corners with two equivalent Li(1)O4 tetrahedra, corners with four equivalent Li(2)O4 tetrahedra, edges with two equivalent Ti(1)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, and edges with two equivalent Fe(6)O6 octahedra. In the fifth Fe site, Fe(5) is bonded to two equivalent O(2), two equivalent O(4), and two equivalent O(6) atoms to form FeO6 octahedra that share corners with two equivalent Li(2)O4 tetrahedra, corners with four equivalent Li(1)O4 tetrahedra, edges with two equivalent Ti(1)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, and edges with two equivalent Fe(3)O6 octahedra. In the sixth Fe site, Fe(6) is bonded to two equivalent O(1), two equivalent O(3), and two equivalent O(7) atoms to form FeO6 octahedra that share corners with two equivalent Li(1)O4 tetrahedra, corners with four equivalent Li(2)O4 tetrahedra, edges with two equivalent Ti(1)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, and edges with two equivalent Fe(4)O6 octahedra. There are eight inequivalent O sites. In the first O site, O(1) is bonded in a distorted rectangular see-saw-like geometry to one Li(1), one Fe(2), one Fe(4), and one Fe(6) atom. In the second O site, O(2) is bonded to one Li(2), one Fe(1), one Fe(3), and one Fe(5) atom to form distorted OLiFe3 trigonal pyramids that share  a cornercorner with one O(3)LiTiFe2 trigonal pyramid,  a cornercorner with one O(5)LiTiFe2 trigonal pyramid, corners with two equivalent O(4)LiTiFe2 trigonal pyramids, corners with two equivalent O(6)LiTiFe2 trigonal pyramids, corners with three equivalent O(2)LiFe3 trigonal pyramids,  an edgeedge with one O(4)LiTiFe2 trigonal pyramid, and  an edgeedge with one O(6)LiTiFe2 trigonal pyramid. In the third O site, O(3) is bonded to one Li(2), one Ti(1), one Fe(4), and one Fe(6) atom to form distorted OLiTiFe2 trigonal pyramids that share  a cornercorner with one O(2)LiFe3 trigonal pyramid,  a cornercorner with one O(4)LiTiFe2 trigonal pyramid,  a cornercorner with one O(6)LiTiFe2 trigonal pyramid, corners with two equivalent O(3)LiTiFe2 trigonal pyramids, corners with two equivalent O(5)LiTiFe2 trigonal pyramids, and  an edgeedge with one O(5)LiTiFe2 trigonal pyramid. In the fourth O site, O(4) is bonded to one Li(1), one Ti(1), one Fe(1), and one Fe(5) atom to form distorted OLiTiFe2 trigonal pyramids that share  a cornercorner with one O(3)LiTiFe2 trigonal pyramid,  a cornercorner with one O(5)LiTiFe2 trigonal pyramid, corners with two equivalent O(2)LiFe3 trigonal pyramids, corners with two equivalent O(4)LiTiFe2 trigonal pyramids, corners with two equivalent O(6)LiTiFe2 trigonal pyramids,  an edgeedge with one O(2)LiFe3 trigonal pyramid, and  an edgeedge with one O(6)LiTiFe2 trigonal pyramid. In the fifth O site, O(5) is bonded to one Li(2), one Ti(1), one Fe(2), and one Fe(4) atom to form distorted OLiTiFe2 trigonal pyramids that share  a cornercorner with one O(2)LiFe3 trigonal pyramid,  a cornercorner with one O(4)LiTiFe2 trigonal pyramid,  a cornercorner with one O(6)LiTiFe2 trigonal pyramid, corners with two equivalent O(3)LiTiFe2 trigonal pyramids, corners with two equivalent O(5)LiTiFe2 trigonal pyramids, and  an edgeedge with one O(3)LiTiFe2 trigonal pyramid. In the sixth O site, O(6) is bonded to one Li(1), one Ti(1), one Fe(3), and one Fe(5) atom to form distorted OLiTiFe2 trigonal pyramids that share  a cornercorner with one O(3)LiTiFe2 trigonal pyramid,  a cornercorner with one O(5)LiTiFe2 trigonal pyramid, corners with two equivalent O(2)LiFe3 trigonal pyramids, corners with two equivalent O(4)LiTiFe2 trigonal pyramids, corners with two equivalent O(6)LiTiFe2 trigonal pyramids,  an edgeedge with one O(2)LiFe3 trigonal pyramid, and  an edgeedge with one O(4)LiTiFe2 trigonal pyramid. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), one Ti(1), one Fe(2), and one Fe(6) atom. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Li(1), one Ti(1), one Fe(1), and one Fe(3) atom. is represented by the CIF file [CIF]
data_Li2TiFe3O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.987
_cell_length_b   6.012
_cell_length_c   10.331
_cell_angle_alpha   89.690
_cell_angle_beta   106.476
_cell_angle_gamma   120.213
_symmetry_Int_Tables_number   1
_cell_volume   303.873
_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  0.116  0.069  0.189  1.0
  Li  Li1  1  0.124  0.560  0.689  1.0
  Li  Li2  1  0.876  0.440  0.311  1.0
  Li  Li3  1  0.884  0.931  0.811  1.0
  Ti  Ti4  1  0.507  0.228  0.750  1.0
  Ti  Ti5  1  0.494  0.772  0.250  1.0
  Fe  Fe6  1  0.500  1.000  1.000  1.0
  Fe  Fe7  1  0.000  0.000  0.500  1.0
  Fe  Fe8  1  0.000  0.500  0.000  1.0
  Fe  Fe9  1  0.500  0.000  0.500  1.0
  Fe  Fe10  1  0.500  0.500  0.000  1.0
  Fe  Fe11  1  0.500  0.500  0.500  1.0
  O  O12  1  0.271  0.146  0.397  1.0
  O  O13  1  0.253  0.629  0.897  1.0
  O  O14  1  0.747  0.371  0.103  1.0
  O  O15  1  0.729  0.854  0.603  1.0
  O  O16  1  0.719  0.352  0.624  1.0
  O  O17  1  0.709  0.850  0.125  1.0
  O  O18  1  0.262  0.906  0.624  1.0
  O  O19  1  0.244  0.410  0.116  1.0
  O  O20  1  0.280  0.367  0.619  1.0
  O  O21  1  0.268  0.869  0.126  1.0
  O  O22  1  0.732  0.130  0.874  1.0
  O  O23  1  0.720  0.633  0.381  1.0
  O  O24  1  0.756  0.590  0.884  1.0
  O  O25  1  0.738  0.094  0.376  1.0
  O  O26  1  0.291  0.150  0.875  1.0
  O  O27  1  0.281  0.648  0.376  1.0
[/CIF]
.