The material described by Li3TiFe3O8 crystallizes in the triclinic P1 space group. There are six inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(13), one O(15), one O(4), and one O(5) atom to form LiO4 tetrahedra that share  a cornercorner with one Li(6)O4 tetrahedra,  a cornercorner with one Ti(1)O4 tetrahedra,  a cornercorner with one Ti(2)O4 tetrahedra,  a cornercorner with one Fe(3)O4 tetrahedra,  a cornercorner with one Fe(4)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra, corners with two equivalent Fe(1)O4 tetrahedra, and corners with two equivalent Fe(5)O4 tetrahedra. In the second Li site, Li(2) is bonded to one O(14), one O(16), one O(3), and one O(6) atom to form LiO4 tetrahedra that share  a cornercorner with one Li(6)O4 tetrahedra,  a cornercorner with one Ti(1)O4 tetrahedra,  a cornercorner with one Ti(2)O4 tetrahedra,  a cornercorner with one Fe(3)O4 tetrahedra,  a cornercorner with one Fe(4)O4 tetrahedra, corners with two equivalent Li(5)O4 tetrahedra, corners with two equivalent Fe(2)O4 tetrahedra, and corners with two equivalent Fe(6)O4 tetrahedra. In the third Li site, Li(3) is bonded to one O(1), one O(11), one O(7), and one O(9) atom to form LiO4 tetrahedra that share  a cornercorner with one Li(4)O4 tetrahedra,  a cornercorner with one Li(5)O4 tetrahedra,  a cornercorner with one Fe(1)O4 tetrahedra,  a cornercorner with one Fe(2)O4 tetrahedra,  a cornercorner with one Fe(5)O4 tetrahedra,  a cornercorner with one Fe(6)O4 tetrahedra, corners with two equivalent Ti(1)O4 tetrahedra, and corners with two equivalent Fe(3)O4 tetrahedra. In the fourth Li site, Li(4) is bonded to one O(12), one O(15), one O(5), and one O(7) atom to form LiO4 tetrahedra that share  a cornercorner with one Li(3)O4 tetrahedra,  a cornercorner with one Ti(1)O4 tetrahedra,  a cornercorner with one Ti(2)O4 tetrahedra,  a cornercorner with one Fe(3)O4 tetrahedra,  a cornercorner with one Fe(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra, corners with two equivalent Fe(1)O4 tetrahedra, and corners with two equivalent Fe(5)O4 tetrahedra. In the fifth Li site, Li(5) is bonded to one O(11), one O(16), one O(6), and one O(8) atom to form LiO4 tetrahedra that share  a cornercorner with one Li(3)O4 tetrahedra,  a cornercorner with one Ti(1)O4 tetrahedra,  a cornercorner with one Ti(2)O4 tetrahedra,  a cornercorner with one Fe(3)O4 tetrahedra,  a cornercorner with one Fe(4)O4 tetrahedra, corners with two equivalent Li(2)O4 tetrahedra, corners with two equivalent Fe(2)O4 tetrahedra, and corners with two equivalent Fe(6)O4 tetrahedra. In the sixth Li site, Li(6) is bonded to one O(10), one O(14), one O(2), and one O(4) atom to form LiO4 tetrahedra that share  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Fe(1)O4 tetrahedra,  a cornercorner with one Fe(2)O4 tetrahedra,  a cornercorner with one Fe(5)O4 tetrahedra,  a cornercorner with one Fe(6)O4 tetrahedra, corners with two equivalent Ti(2)O4 tetrahedra, and corners with two equivalent Fe(4)O4 tetrahedra. There are two inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(1), one O(11), one O(15), and one O(3) atom to form TiO4 tetrahedra that share  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Li(4)O4 tetrahedra,  a cornercorner with one Li(5)O4 tetrahedra,  a cornercorner with one Fe(1)O4 tetrahedra,  a cornercorner with one Fe(2)O4 tetrahedra, corners with two equivalent Li(3)O4 tetrahedra, and corners with two equivalent Fe(3)O4 tetrahedra. In the second Ti site, Ti(2) is bonded to one O(12), one O(16), one O(2), and one O(4) atom to form TiO4 tetrahedra that share  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Li(4)O4 tetrahedra,  a cornercorner with one Li(5)O4 tetrahedra,  a cornercorner with one Fe(1)O4 tetrahedra,  a cornercorner with one Fe(2)O4 tetrahedra, corners with two equivalent Li(6)O4 tetrahedra, and corners with two equivalent Fe(4)O4 tetrahedra. There are six inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to one O(13), one O(15), one O(2), and one O(7) atom to form FeO4 tetrahedra that share  a cornercorner with one Li(3)O4 tetrahedra,  a cornercorner with one Li(6)O4 tetrahedra,  a cornercorner with one Ti(1)O4 tetrahedra,  a cornercorner with one Ti(2)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra, and corners with two equivalent Fe(5)O4 tetrahedra. In the second Fe site, Fe(2) is bonded to one O(1), one O(14), one O(16), and one O(8) atom to form FeO4 tetrahedra that share  a cornercorner with one Li(3)O4 tetrahedra,  a cornercorner with one Li(6)O4 tetrahedra,  a cornercorner with one Ti(1)O4 tetrahedra,  a cornercorner with one Ti(2)O4 tetrahedra, corners with two equivalent Li(2)O4 tetrahedra, corners with two equivalent Li(5)O4 tetrahedra, and corners with two equivalent Fe(6)O4 tetrahedra. In the third Fe site, Fe(3) is bonded to one O(11), one O(3), one O(5), and one O(9) atom to form FeO4 tetrahedra that share  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Li(4)O4 tetrahedra,  a cornercorner with one Li(5)O4 tetrahedra,  a cornercorner with one Fe(5)O4 tetrahedra,  a cornercorner with one Fe(6)O4 tetrahedra, corners with two equivalent Li(3)O4 tetrahedra, and corners with two equivalent Ti(1)O4 tetrahedra. In the fourth Fe site, Fe(4) is bonded to one O(10), one O(12), one O(4), and one O(6) atom to form FeO4 tetrahedra that share  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Li(4)O4 tetrahedra,  a cornercorner with one Li(5)O4 tetrahedra,  a cornercorner with one Fe(5)O4 tetrahedra,  a cornercorner with one Fe(6)O4 tetrahedra, corners with two equivalent Li(6)O4 tetrahedra, and corners with two equivalent Ti(2)O4 tetrahedra. In the fifth Fe site, Fe(5) is bonded to one O(10), one O(13), one O(5), and one O(7) atom to form FeO4 tetrahedra that share  a cornercorner with one Li(3)O4 tetrahedra,  a cornercorner with one Li(6)O4 tetrahedra,  a cornercorner with one Fe(3)O4 tetrahedra,  a cornercorner with one Fe(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra, and corners with two equivalent Fe(1)O4 tetrahedra. In the sixth Fe site, Fe(6) is bonded to one O(14), one O(6), one O(8), and one O(9) atom to form FeO4 tetrahedra that share  a cornercorner with one Li(3)O4 tetrahedra,  a cornercorner with one Li(6)O4 tetrahedra,  a cornercorner with one Fe(3)O4 tetrahedra,  a cornercorner with one Fe(4)O4 tetrahedra, corners with two equivalent Li(2)O4 tetrahedra, corners with two equivalent Li(5)O4 tetrahedra, and corners with two equivalent Fe(2)O4 tetrahedra. There are sixteen inequivalent O sites. In the first O site, O(1) is bonded in a trigonal non-coplanar geometry to one Li(3), one Ti(1), and one Fe(2) atom. In the second O site, O(2) is bonded in a trigonal non-coplanar geometry to one Li(6), one Ti(2), and one Fe(1) atom. In the third O site, O(3) is bonded in a trigonal non-coplanar geometry to one Li(2), one Ti(1), and one Fe(3) atom. In the fourth O site, O(4) is bonded to one Li(1), one Li(6), one Ti(2), and one Fe(4) atom to form OLi2TiFe tetrahedra that share  a cornercorner with one O(14)Li2Fe2 tetrahedra,  a cornercorner with one O(5)Li2Fe2 tetrahedra,  a cornercorner with one O(6)Li2Fe2 tetrahedra,  a cornercorner with one O(15)Li2TiFe tetrahedra, and  a cornercorner with one O(16)Li2TiFe tetrahedra. In the fifth O site, O(5) is bonded to one Li(1), one Li(4), one Fe(3), and one Fe(5) atom to form OLi2Fe2 tetrahedra that share  a cornercorner with one O(11)Li2TiFe tetrahedra,  a cornercorner with one O(4)Li2TiFe tetrahedra, corners with two equivalent O(7)Li2Fe2 tetrahedra, and corners with two equivalent O(15)Li2TiFe tetrahedra. In the sixth O site, O(6) is bonded to one Li(2), one Li(5), one Fe(4), and one Fe(6) atom to form OLi2Fe2 tetrahedra that share  a cornercorner with one O(11)Li2TiFe tetrahedra,  a cornercorner with one O(4)Li2TiFe tetrahedra, corners with two equivalent O(14)Li2Fe2 tetrahedra, and corners with two equivalent O(16)Li2TiFe tetrahedra. In the seventh O site, O(7) is bonded to one Li(3), one Li(4), one Fe(1), and one Fe(5) atom to form OLi2Fe2 tetrahedra that share  a cornercorner with one O(11)Li2TiFe tetrahedra, corners with two equivalent O(5)Li2Fe2 tetrahedra, and corners with two equivalent O(15)Li2TiFe tetrahedra. In the eighth O site, O(8) is bonded in a trigonal planar geometry to one Li(5), one Fe(2), and one Fe(6) atom. In the ninth O site, O(9) is bonded in a trigonal non-coplanar geometry to one Li(3), one Fe(3), and one Fe(6) atom. In the tenth O site, O(10) is bonded in a trigonal non-coplanar geometry to one Li(6), one Fe(4), and one Fe(5) atom. In the eleventh O site, O(11) is bonded to one Li(3), one Li(5), one Ti(1), and one Fe(3) atom to form OLi2TiFe tetrahedra that share  a cornercorner with one O(5)Li2Fe2 tetrahedra,  a cornercorner with one O(6)Li2Fe2 tetrahedra,  a cornercorner with one O(7)Li2Fe2 tetrahedra,  a cornercorner with one O(15)Li2TiFe tetrahedra, and  a cornercorner with one O(16)Li2TiFe tetrahedra. In the twelfth O site, O(12) is bonded in a trigonal non-coplanar geometry to one Li(4), one Ti(2), and one Fe(4) atom. In the thirteenth O site, O(13) is bonded in a trigonal planar geometry to one Li(1), one Fe(1), and one Fe(5) atom. In the fourteenth O site, O(14) is bonded to one Li(2), one Li(6), one Fe(2), and one Fe(6) atom to form OLi2Fe2 tetrahedra that share  a cornercorner with one O(4)Li2TiFe tetrahedra, corners with two equivalent O(6)Li2Fe2 tetrahedra, and corners with two equivalent O(16)Li2TiFe tetrahedra. In the fifteenth O site, O(15) is bonded to one Li(1), one Li(4), one Ti(1), and one Fe(1) atom to form OLi2TiFe tetrahedra that share  a cornercorner with one O(11)Li2TiFe tetrahedra,  a cornercorner with one O(4)Li2TiFe tetrahedra, corners with two equivalent O(5)Li2Fe2 tetrahedra, and corners with two equivalent O(7)Li2Fe2 tetrahedra. In the sixteenth O site, O(16) is bonded to one Li(2), one Li(5), one Ti(2), and one Fe(2) atom to form OLi2TiFe tetrahedra that share  a cornercorner with one O(11)Li2TiFe tetrahedra,  a cornercorner with one O(4)Li2TiFe tetrahedra, corners with two equivalent O(14)Li2Fe2 tetrahedra, and corners with two equivalent O(6)Li2Fe2 tetrahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li3TiFe3O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.619
_cell_length_b   6.608
_cell_length_c   10.260
_cell_angle_alpha   89.929
_cell_angle_beta   89.993
_cell_angle_gamma   89.930
_symmetry_Int_Tables_number   1
_cell_volume   381.003
_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  0.915  0.618  0.506  1.0
  Li  Li1  1  0.915  0.617  0.001  1.0
  Li  Li2  1  0.581  0.130  0.754  1.0
  Li  Li3  1  0.426  0.878  0.501  1.0
  Li  Li4  1  0.427  0.876  0.005  1.0
  Li  Li5  1  0.090  0.373  0.255  1.0
  Ti  Ti6  1  0.081  0.874  0.751  1.0
  Ti  Ti7  1  0.084  0.875  0.250  1.0
  Fe  Fe8  1  0.912  0.132  0.502  1.0
  Fe  Fe9  1  0.913  0.132  0.001  1.0
  Fe  Fe10  1  0.583  0.622  0.750  1.0
  Fe  Fe11  1  0.581  0.623  0.250  1.0
  Fe  Fe12  1  0.415  0.373  0.501  1.0
  Fe  Fe13  1  0.415  0.372  0.002  1.0
  O  O14  1  0.927  0.093  0.816  1.0
  O  O15  1  0.959  0.106  0.317  1.0
  O  O16  1  0.904  0.662  0.808  1.0
  O  O17  1  0.910  0.649  0.303  1.0
  O  O18  1  0.573  0.615  0.564  1.0
  O  O19  1  0.572  0.614  0.064  1.0
  O  O20  1  0.588  0.134  0.556  1.0
  O  O21  1  0.588  0.131  0.039  1.0
  O  O22  1  0.455  0.385  0.817  1.0
  O  O23  1  0.421  0.399  0.316  1.0
  O  O24  1  0.397  0.859  0.803  1.0
  O  O25  1  0.388  0.845  0.307  1.0
  O  O26  1  0.084  0.367  0.539  1.0
  O  O27  1  0.086  0.365  0.057  1.0
  O  O28  1  0.068  0.888  0.570  1.0
  O  O29  1  0.073  0.889  0.069  1.0
[/CIF]
.
The material described by Li3TiFe3O8 crystallizes in the triclinic P1 space group. There are six inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(13), one O(15), one O(4), and one O(5) atom to form LiO4 tetrahedra that share  a cornercorner with one Li(6)O4 tetrahedra,  a cornercorner with one Ti(1)O4 tetrahedra,  a cornercorner with one Ti(2)O4 tetrahedra,  a cornercorner with one Fe(3)O4 tetrahedra,  a cornercorner with one Fe(4)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra, corners with two equivalent Fe(1)O4 tetrahedra, and corners with two equivalent Fe(5)O4 tetrahedra. In the second Li site, Li(2) is bonded to one O(14), one O(16), one O(3), and one O(6) atom to form LiO4 tetrahedra that share  a cornercorner with one Li(6)O4 tetrahedra,  a cornercorner with one Ti(1)O4 tetrahedra,  a cornercorner with one Ti(2)O4 tetrahedra,  a cornercorner with one Fe(3)O4 tetrahedra,  a cornercorner with one Fe(4)O4 tetrahedra, corners with two equivalent Li(5)O4 tetrahedra, corners with two equivalent Fe(2)O4 tetrahedra, and corners with two equivalent Fe(6)O4 tetrahedra. In the third Li site, Li(3) is bonded to one O(1), one O(11), one O(7), and one O(9) atom to form LiO4 tetrahedra that share  a cornercorner with one Li(4)O4 tetrahedra,  a cornercorner with one Li(5)O4 tetrahedra,  a cornercorner with one Fe(1)O4 tetrahedra,  a cornercorner with one Fe(2)O4 tetrahedra,  a cornercorner with one Fe(5)O4 tetrahedra,  a cornercorner with one Fe(6)O4 tetrahedra, corners with two equivalent Ti(1)O4 tetrahedra, and corners with two equivalent Fe(3)O4 tetrahedra. In the fourth Li site, Li(4) is bonded to one O(12), one O(15), one O(5), and one O(7) atom to form LiO4 tetrahedra that share  a cornercorner with one Li(3)O4 tetrahedra,  a cornercorner with one Ti(1)O4 tetrahedra,  a cornercorner with one Ti(2)O4 tetrahedra,  a cornercorner with one Fe(3)O4 tetrahedra,  a cornercorner with one Fe(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra, corners with two equivalent Fe(1)O4 tetrahedra, and corners with two equivalent Fe(5)O4 tetrahedra. In the fifth Li site, Li(5) is bonded to one O(11), one O(16), one O(6), and one O(8) atom to form LiO4 tetrahedra that share  a cornercorner with one Li(3)O4 tetrahedra,  a cornercorner with one Ti(1)O4 tetrahedra,  a cornercorner with one Ti(2)O4 tetrahedra,  a cornercorner with one Fe(3)O4 tetrahedra,  a cornercorner with one Fe(4)O4 tetrahedra, corners with two equivalent Li(2)O4 tetrahedra, corners with two equivalent Fe(2)O4 tetrahedra, and corners with two equivalent Fe(6)O4 tetrahedra. In the sixth Li site, Li(6) is bonded to one O(10), one O(14), one O(2), and one O(4) atom to form LiO4 tetrahedra that share  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Fe(1)O4 tetrahedra,  a cornercorner with one Fe(2)O4 tetrahedra,  a cornercorner with one Fe(5)O4 tetrahedra,  a cornercorner with one Fe(6)O4 tetrahedra, corners with two equivalent Ti(2)O4 tetrahedra, and corners with two equivalent Fe(4)O4 tetrahedra. There are two inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(1), one O(11), one O(15), and one O(3) atom to form TiO4 tetrahedra that share  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Li(4)O4 tetrahedra,  a cornercorner with one Li(5)O4 tetrahedra,  a cornercorner with one Fe(1)O4 tetrahedra,  a cornercorner with one Fe(2)O4 tetrahedra, corners with two equivalent Li(3)O4 tetrahedra, and corners with two equivalent Fe(3)O4 tetrahedra. In the second Ti site, Ti(2) is bonded to one O(12), one O(16), one O(2), and one O(4) atom to form TiO4 tetrahedra that share  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Li(4)O4 tetrahedra,  a cornercorner with one Li(5)O4 tetrahedra,  a cornercorner with one Fe(1)O4 tetrahedra,  a cornercorner with one Fe(2)O4 tetrahedra, corners with two equivalent Li(6)O4 tetrahedra, and corners with two equivalent Fe(4)O4 tetrahedra. There are six inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to one O(13), one O(15), one O(2), and one O(7) atom to form FeO4 tetrahedra that share  a cornercorner with one Li(3)O4 tetrahedra,  a cornercorner with one Li(6)O4 tetrahedra,  a cornercorner with one Ti(1)O4 tetrahedra,  a cornercorner with one Ti(2)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra, and corners with two equivalent Fe(5)O4 tetrahedra. In the second Fe site, Fe(2) is bonded to one O(1), one O(14), one O(16), and one O(8) atom to form FeO4 tetrahedra that share  a cornercorner with one Li(3)O4 tetrahedra,  a cornercorner with one Li(6)O4 tetrahedra,  a cornercorner with one Ti(1)O4 tetrahedra,  a cornercorner with one Ti(2)O4 tetrahedra, corners with two equivalent Li(2)O4 tetrahedra, corners with two equivalent Li(5)O4 tetrahedra, and corners with two equivalent Fe(6)O4 tetrahedra. In the third Fe site, Fe(3) is bonded to one O(11), one O(3), one O(5), and one O(9) atom to form FeO4 tetrahedra that share  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Li(4)O4 tetrahedra,  a cornercorner with one Li(5)O4 tetrahedra,  a cornercorner with one Fe(5)O4 tetrahedra,  a cornercorner with one Fe(6)O4 tetrahedra, corners with two equivalent Li(3)O4 tetrahedra, and corners with two equivalent Ti(1)O4 tetrahedra. In the fourth Fe site, Fe(4) is bonded to one O(10), one O(12), one O(4), and one O(6) atom to form FeO4 tetrahedra that share  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Li(4)O4 tetrahedra,  a cornercorner with one Li(5)O4 tetrahedra,  a cornercorner with one Fe(5)O4 tetrahedra,  a cornercorner with one Fe(6)O4 tetrahedra, corners with two equivalent Li(6)O4 tetrahedra, and corners with two equivalent Ti(2)O4 tetrahedra. In the fifth Fe site, Fe(5) is bonded to one O(10), one O(13), one O(5), and one O(7) atom to form FeO4 tetrahedra that share  a cornercorner with one Li(3)O4 tetrahedra,  a cornercorner with one Li(6)O4 tetrahedra,  a cornercorner with one Fe(3)O4 tetrahedra,  a cornercorner with one Fe(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra, and corners with two equivalent Fe(1)O4 tetrahedra. In the sixth Fe site, Fe(6) is bonded to one O(14), one O(6), one O(8), and one O(9) atom to form FeO4 tetrahedra that share  a cornercorner with one Li(3)O4 tetrahedra,  a cornercorner with one Li(6)O4 tetrahedra,  a cornercorner with one Fe(3)O4 tetrahedra,  a cornercorner with one Fe(4)O4 tetrahedra, corners with two equivalent Li(2)O4 tetrahedra, corners with two equivalent Li(5)O4 tetrahedra, and corners with two equivalent Fe(2)O4 tetrahedra. There are sixteen inequivalent O sites. In the first O site, O(1) is bonded in a trigonal non-coplanar geometry to one Li(3), one Ti(1), and one Fe(2) atom. In the second O site, O(2) is bonded in a trigonal non-coplanar geometry to one Li(6), one Ti(2), and one Fe(1) atom. In the third O site, O(3) is bonded in a trigonal non-coplanar geometry to one Li(2), one Ti(1), and one Fe(3) atom. In the fourth O site, O(4) is bonded to one Li(1), one Li(6), one Ti(2), and one Fe(4) atom to form OLi2TiFe tetrahedra that share  a cornercorner with one O(14)Li2Fe2 tetrahedra,  a cornercorner with one O(5)Li2Fe2 tetrahedra,  a cornercorner with one O(6)Li2Fe2 tetrahedra,  a cornercorner with one O(15)Li2TiFe tetrahedra, and  a cornercorner with one O(16)Li2TiFe tetrahedra. In the fifth O site, O(5) is bonded to one Li(1), one Li(4), one Fe(3), and one Fe(5) atom to form OLi2Fe2 tetrahedra that share  a cornercorner with one O(11)Li2TiFe tetrahedra,  a cornercorner with one O(4)Li2TiFe tetrahedra, corners with two equivalent O(7)Li2Fe2 tetrahedra, and corners with two equivalent O(15)Li2TiFe tetrahedra. In the sixth O site, O(6) is bonded to one Li(2), one Li(5), one Fe(4), and one Fe(6) atom to form OLi2Fe2 tetrahedra that share  a cornercorner with one O(11)Li2TiFe tetrahedra,  a cornercorner with one O(4)Li2TiFe tetrahedra, corners with two equivalent O(14)Li2Fe2 tetrahedra, and corners with two equivalent O(16)Li2TiFe tetrahedra. In the seventh O site, O(7) is bonded to one Li(3), one Li(4), one Fe(1), and one Fe(5) atom to form OLi2Fe2 tetrahedra that share  a cornercorner with one O(11)Li2TiFe tetrahedra, corners with two equivalent O(5)Li2Fe2 tetrahedra, and corners with two equivalent O(15)Li2TiFe tetrahedra. In the eighth O site, O(8) is bonded in a trigonal planar geometry to one Li(5), one Fe(2), and one Fe(6) atom. In the ninth O site, O(9) is bonded in a trigonal non-coplanar geometry to one Li(3), one Fe(3), and one Fe(6) atom. In the tenth O site, O(10) is bonded in a trigonal non-coplanar geometry to one Li(6), one Fe(4), and one Fe(5) atom. In the eleventh O site, O(11) is bonded to one Li(3), one Li(5), one Ti(1), and one Fe(3) atom to form OLi2TiFe tetrahedra that share  a cornercorner with one O(5)Li2Fe2 tetrahedra,  a cornercorner with one O(6)Li2Fe2 tetrahedra,  a cornercorner with one O(7)Li2Fe2 tetrahedra,  a cornercorner with one O(15)Li2TiFe tetrahedra, and  a cornercorner with one O(16)Li2TiFe tetrahedra. In the twelfth O site, O(12) is bonded in a trigonal non-coplanar geometry to one Li(4), one Ti(2), and one Fe(4) atom. In the thirteenth O site, O(13) is bonded in a trigonal planar geometry to one Li(1), one Fe(1), and one Fe(5) atom. In the fourteenth O site, O(14) is bonded to one Li(2), one Li(6), one Fe(2), and one Fe(6) atom to form OLi2Fe2 tetrahedra that share  a cornercorner with one O(4)Li2TiFe tetrahedra, corners with two equivalent O(6)Li2Fe2 tetrahedra, and corners with two equivalent O(16)Li2TiFe tetrahedra. In the fifteenth O site, O(15) is bonded to one Li(1), one Li(4), one Ti(1), and one Fe(1) atom to form OLi2TiFe tetrahedra that share  a cornercorner with one O(11)Li2TiFe tetrahedra,  a cornercorner with one O(4)Li2TiFe tetrahedra, corners with two equivalent O(5)Li2Fe2 tetrahedra, and corners with two equivalent O(7)Li2Fe2 tetrahedra. In the sixteenth O site, O(16) is bonded to one Li(2), one Li(5), one Ti(2), and one Fe(2) atom to form OLi2TiFe tetrahedra that share  a cornercorner with one O(11)Li2TiFe tetrahedra,  a cornercorner with one O(4)Li2TiFe tetrahedra, corners with two equivalent O(14)Li2Fe2 tetrahedra, and corners with two equivalent O(6)Li2Fe2 tetrahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li3TiFe3O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.619
_cell_length_b   6.608
_cell_length_c   10.260
_cell_angle_alpha   89.929
_cell_angle_beta   89.993
_cell_angle_gamma   89.930
_symmetry_Int_Tables_number   1
_cell_volume   381.003
_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  0.915  0.618  0.506  1.0
  Li  Li1  1  0.915  0.617  0.001  1.0
  Li  Li2  1  0.581  0.130  0.754  1.0
  Li  Li3  1  0.426  0.878  0.501  1.0
  Li  Li4  1  0.427  0.876  0.005  1.0
  Li  Li5  1  0.090  0.373  0.255  1.0
  Ti  Ti6  1  0.081  0.874  0.751  1.0
  Ti  Ti7  1  0.084  0.875  0.250  1.0
  Fe  Fe8  1  0.912  0.132  0.502  1.0
  Fe  Fe9  1  0.913  0.132  0.001  1.0
  Fe  Fe10  1  0.583  0.622  0.750  1.0
  Fe  Fe11  1  0.581  0.623  0.250  1.0
  Fe  Fe12  1  0.415  0.373  0.501  1.0
  Fe  Fe13  1  0.415  0.372  0.002  1.0
  O  O14  1  0.927  0.093  0.816  1.0
  O  O15  1  0.959  0.106  0.317  1.0
  O  O16  1  0.904  0.662  0.808  1.0
  O  O17  1  0.910  0.649  0.303  1.0
  O  O18  1  0.573  0.615  0.564  1.0
  O  O19  1  0.572  0.614  0.064  1.0
  O  O20  1  0.588  0.134  0.556  1.0
  O  O21  1  0.588  0.131  0.039  1.0
  O  O22  1  0.455  0.385  0.817  1.0
  O  O23  1  0.421  0.399  0.316  1.0
  O  O24  1  0.397  0.859  0.803  1.0
  O  O25  1  0.388  0.845  0.307  1.0
  O  O26  1  0.084  0.367  0.539  1.0
  O  O27  1  0.086  0.365  0.057  1.0
  O  O28  1  0.068  0.888  0.570  1.0
  O  O29  1  0.073  0.889  0.069  1.0
[/CIF]
.