The structure described by LiTi2O4 crystallizes in the monoclinic P2_1/m space group. There are two inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(1), one O(2), and three equivalent O(4) atoms to form distorted LiO5 trigonal bipyramids that share corners with three equivalent Ti(3)O6 octahedra, corners with two equivalent Li(1)O5 trigonal bipyramids, edges with three equivalent Ti(1)O6 octahedra, edges with three equivalent Ti(2)O6 octahedra, and edges with two equivalent Li(1)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 4-78°. In the second Li site, Li(2) is bonded to one O(6), one O(7), one O(8), and two equivalent O(5) atoms to form LiO5 trigonal bipyramids that share  a cornercorner with one Ti(2)O6 octahedra, corners with two equivalent Ti(1)O6 octahedra, corners with two equivalent Li(2)O5 trigonal bipyramids, edges with three equivalent Ti(3)O6 octahedra, and edges with three equivalent Ti(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 4-73°. There are four inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(1), one O(3), one O(4), one O(5), and two equivalent O(2) atoms to form distorted TiO6 octahedra that share corners with two equivalent Ti(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra, corners with two equivalent Li(2)O5 trigonal bipyramids,  an edgeedge with one Ti(3)O6 octahedra,  an edgeedge with one Ti(4)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, and edges with three equivalent Li(1)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 3-23°. In the second Ti site, Ti(2) is bonded to one O(2), one O(3), one O(4), one O(6), and two equivalent O(1) atoms to form TiO6 octahedra that share corners with two equivalent Ti(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra,  a cornercorner with one Li(2)O5 trigonal bipyramid,  an edgeedge with one Ti(3)O6 octahedra,  an edgeedge with one Ti(4)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, and edges with three equivalent Li(1)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 3-24°. In the third Ti site, Ti(3) is bonded to one O(4), one O(5), one O(6), and three equivalent O(7) atoms to form TiO6 octahedra that share corners with two equivalent Ti(3)O6 octahedra, corners with two equivalent Ti(4)O6 octahedra, corners with three equivalent Li(1)O5 trigonal bipyramids,  an edgeedge with one Ti(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra, edges with two equivalent Ti(3)O6 octahedra, and edges with three equivalent Li(2)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 2-23°. In the fourth Ti site, Ti(4) is bonded to one O(3), one O(5), one O(6), and three equivalent O(8) atoms to form TiO6 octahedra that share corners with two equivalent Ti(3)O6 octahedra, corners with two equivalent Ti(4)O6 octahedra,  an edgeedge with one Ti(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra, edges with two equivalent Ti(4)O6 octahedra, and edges with three equivalent Li(2)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 2-22°. There are eight inequivalent O sites. In the first O site, O(1) is bonded to one Li(1), one Ti(1), and two equivalent Ti(2) atoms to form OLiTi3 trigonal pyramids that share  a cornercorner with one O(5)Li2Ti3 trigonal bipyramid,  a cornercorner with one O(2)LiTi3 trigonal pyramid, corners with two equivalent O(1)LiTi3 trigonal pyramids, edges with three equivalent O(4)Li3Ti3 octahedra, and edges with two equivalent O(2)LiTi3 trigonal pyramids. In the second O site, O(2) is bonded to one Li(1), one Ti(2), and two equivalent Ti(1) atoms to form distorted OLiTi3 trigonal pyramids that share corners with two equivalent O(5)Li2Ti3 trigonal bipyramids,  a cornercorner with one O(1)LiTi3 trigonal pyramid, corners with two equivalent O(2)LiTi3 trigonal pyramids, edges with three equivalent O(4)Li3Ti3 octahedra, and edges with two equivalent O(1)LiTi3 trigonal pyramids. In the third O site, O(3) is bonded in a T-shaped geometry to one Ti(1), one Ti(2), and one Ti(4) atom. In the fourth O site, O(4) is bonded to three equivalent Li(1), one Ti(1), one Ti(2), and one Ti(3) atom to form OLi3Ti3 octahedra that share corners with two equivalent O(4)Li3Ti3 octahedra, corners with three equivalent O(7)LiTi3 trigonal pyramids, edges with two equivalent O(4)Li3Ti3 octahedra,  an edgeedge with one O(5)Li2Ti3 trigonal bipyramid, edges with three equivalent O(1)LiTi3 trigonal pyramids, and edges with three equivalent O(2)LiTi3 trigonal pyramids. The corner-sharing octahedral tilt angles are 25°. In the fifth O site, O(5) is bonded to two equivalent Li(2), one Ti(1), one Ti(3), and one Ti(4) atom to form OLi2Ti3 trigonal bipyramids that share corners with two equivalent O(5)Li2Ti3 trigonal bipyramids,  a cornercorner with one O(1)LiTi3 trigonal pyramid,  a cornercorner with one O(7)LiTi3 trigonal pyramid, corners with two equivalent O(2)LiTi3 trigonal pyramids,  an edgeedge with one O(4)Li3Ti3 octahedra, and edges with two equivalent O(7)LiTi3 trigonal pyramids. In the sixth O site, O(6) is bonded in a rectangular see-saw-like geometry to one Li(2), one Ti(2), one Ti(3), and one Ti(4) atom. In the seventh O site, O(7) is bonded to one Li(2) and three equivalent Ti(3) atoms to form distorted OLiTi3 trigonal pyramids that share corners with three equivalent O(4)Li3Ti3 octahedra,  a cornercorner with one O(5)Li2Ti3 trigonal bipyramid, corners with two equivalent O(7)LiTi3 trigonal pyramids, edges with two equivalent O(5)Li2Ti3 trigonal bipyramids, and edges with two equivalent O(7)LiTi3 trigonal pyramids. The corner-sharing octahedral tilt angles range from 5-80°. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Li(2) and three equivalent Ti(4) atoms. is represented by the CIF card [CIF]
data_LiTi2O4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   3.851
_cell_length_b   8.246
_cell_length_c   9.053
_cell_angle_alpha   89.963
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   287.495
_cell_formula_units_Z   4
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  0.250  0.497  0.902  1.0
  Li  Li1  1  0.750  0.503  0.098  1.0
  Li  Li2  1  0.750  0.751  0.408  1.0
  Li  Li3  1  0.250  0.249  0.592  1.0
  Ti  Ti4  1  0.250  0.776  0.130  1.0
  Ti  Ti5  1  0.250  0.238  0.142  1.0
  Ti  Ti6  1  0.250  0.487  0.360  1.0
  Ti  Ti7  1  0.250  0.010  0.363  1.0
  Ti  Ti8  1  0.750  0.990  0.637  1.0
  Ti  Ti9  1  0.750  0.513  0.640  1.0
  Ti  Ti10  1  0.750  0.762  0.858  1.0
  Ti  Ti11  1  0.750  0.224  0.870  1.0
  O  O12  1  0.250  0.741  0.900  1.0
  O  O13  1  0.250  0.253  0.904  1.0
  O  O14  1  0.750  0.747  0.096  1.0
  O  O15  1  0.750  0.259  0.100  1.0
  O  O16  1  0.250  0.002  0.141  1.0
  O  O17  1  0.250  0.501  0.145  1.0
  O  O18  1  0.250  0.749  0.342  1.0
  O  O19  1  0.250  0.252  0.364  1.0
  O  O20  1  0.750  0.508  0.400  1.0
  O  O21  1  0.750  0.992  0.402  1.0
  O  O22  1  0.250  0.008  0.598  1.0
  O  O23  1  0.250  0.492  0.600  1.0
  O  O24  1  0.750  0.748  0.636  1.0
  O  O25  1  0.750  0.251  0.658  1.0
  O  O26  1  0.750  0.499  0.855  1.0
  O  O27  1  0.750  0.998  0.859  1.0
[/CIF]
.
The structure described by LiTi2O4 crystallizes in the monoclinic P2_1/m space group. There are two inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(1), one O(2), and three equivalent O(4) atoms to form distorted LiO5 trigonal bipyramids that share corners with three equivalent Ti(3)O6 octahedra, corners with two equivalent Li(1)O5 trigonal bipyramids, edges with three equivalent Ti(1)O6 octahedra, edges with three equivalent Ti(2)O6 octahedra, and edges with two equivalent Li(1)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 4-78°. In the second Li site, Li(2) is bonded to one O(6), one O(7), one O(8), and two equivalent O(5) atoms to form LiO5 trigonal bipyramids that share  a cornercorner with one Ti(2)O6 octahedra, corners with two equivalent Ti(1)O6 octahedra, corners with two equivalent Li(2)O5 trigonal bipyramids, edges with three equivalent Ti(3)O6 octahedra, and edges with three equivalent Ti(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 4-73°. There are four inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(1), one O(3), one O(4), one O(5), and two equivalent O(2) atoms to form distorted TiO6 octahedra that share corners with two equivalent Ti(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra, corners with two equivalent Li(2)O5 trigonal bipyramids,  an edgeedge with one Ti(3)O6 octahedra,  an edgeedge with one Ti(4)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, and edges with three equivalent Li(1)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 3-23°. In the second Ti site, Ti(2) is bonded to one O(2), one O(3), one O(4), one O(6), and two equivalent O(1) atoms to form TiO6 octahedra that share corners with two equivalent Ti(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra,  a cornercorner with one Li(2)O5 trigonal bipyramid,  an edgeedge with one Ti(3)O6 octahedra,  an edgeedge with one Ti(4)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, and edges with three equivalent Li(1)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 3-24°. In the third Ti site, Ti(3) is bonded to one O(4), one O(5), one O(6), and three equivalent O(7) atoms to form TiO6 octahedra that share corners with two equivalent Ti(3)O6 octahedra, corners with two equivalent Ti(4)O6 octahedra, corners with three equivalent Li(1)O5 trigonal bipyramids,  an edgeedge with one Ti(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra, edges with two equivalent Ti(3)O6 octahedra, and edges with three equivalent Li(2)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 2-23°. In the fourth Ti site, Ti(4) is bonded to one O(3), one O(5), one O(6), and three equivalent O(8) atoms to form TiO6 octahedra that share corners with two equivalent Ti(3)O6 octahedra, corners with two equivalent Ti(4)O6 octahedra,  an edgeedge with one Ti(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra, edges with two equivalent Ti(4)O6 octahedra, and edges with three equivalent Li(2)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 2-22°. There are eight inequivalent O sites. In the first O site, O(1) is bonded to one Li(1), one Ti(1), and two equivalent Ti(2) atoms to form OLiTi3 trigonal pyramids that share  a cornercorner with one O(5)Li2Ti3 trigonal bipyramid,  a cornercorner with one O(2)LiTi3 trigonal pyramid, corners with two equivalent O(1)LiTi3 trigonal pyramids, edges with three equivalent O(4)Li3Ti3 octahedra, and edges with two equivalent O(2)LiTi3 trigonal pyramids. In the second O site, O(2) is bonded to one Li(1), one Ti(2), and two equivalent Ti(1) atoms to form distorted OLiTi3 trigonal pyramids that share corners with two equivalent O(5)Li2Ti3 trigonal bipyramids,  a cornercorner with one O(1)LiTi3 trigonal pyramid, corners with two equivalent O(2)LiTi3 trigonal pyramids, edges with three equivalent O(4)Li3Ti3 octahedra, and edges with two equivalent O(1)LiTi3 trigonal pyramids. In the third O site, O(3) is bonded in a T-shaped geometry to one Ti(1), one Ti(2), and one Ti(4) atom. In the fourth O site, O(4) is bonded to three equivalent Li(1), one Ti(1), one Ti(2), and one Ti(3) atom to form OLi3Ti3 octahedra that share corners with two equivalent O(4)Li3Ti3 octahedra, corners with three equivalent O(7)LiTi3 trigonal pyramids, edges with two equivalent O(4)Li3Ti3 octahedra,  an edgeedge with one O(5)Li2Ti3 trigonal bipyramid, edges with three equivalent O(1)LiTi3 trigonal pyramids, and edges with three equivalent O(2)LiTi3 trigonal pyramids. The corner-sharing octahedral tilt angles are 25°. In the fifth O site, O(5) is bonded to two equivalent Li(2), one Ti(1), one Ti(3), and one Ti(4) atom to form OLi2Ti3 trigonal bipyramids that share corners with two equivalent O(5)Li2Ti3 trigonal bipyramids,  a cornercorner with one O(1)LiTi3 trigonal pyramid,  a cornercorner with one O(7)LiTi3 trigonal pyramid, corners with two equivalent O(2)LiTi3 trigonal pyramids,  an edgeedge with one O(4)Li3Ti3 octahedra, and edges with two equivalent O(7)LiTi3 trigonal pyramids. In the sixth O site, O(6) is bonded in a rectangular see-saw-like geometry to one Li(2), one Ti(2), one Ti(3), and one Ti(4) atom. In the seventh O site, O(7) is bonded to one Li(2) and three equivalent Ti(3) atoms to form distorted OLiTi3 trigonal pyramids that share corners with three equivalent O(4)Li3Ti3 octahedra,  a cornercorner with one O(5)Li2Ti3 trigonal bipyramid, corners with two equivalent O(7)LiTi3 trigonal pyramids, edges with two equivalent O(5)Li2Ti3 trigonal bipyramids, and edges with two equivalent O(7)LiTi3 trigonal pyramids. The corner-sharing octahedral tilt angles range from 5-80°. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Li(2) and three equivalent Ti(4) atoms. is represented by the CIF card [CIF]
data_LiTi2O4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   3.851
_cell_length_b   8.246
_cell_length_c   9.053
_cell_angle_alpha   89.963
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   287.495
_cell_formula_units_Z   4
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  0.250  0.497  0.902  1.0
  Li  Li1  1  0.750  0.503  0.098  1.0
  Li  Li2  1  0.750  0.751  0.408  1.0
  Li  Li3  1  0.250  0.249  0.592  1.0
  Ti  Ti4  1  0.250  0.776  0.130  1.0
  Ti  Ti5  1  0.250  0.238  0.142  1.0
  Ti  Ti6  1  0.250  0.487  0.360  1.0
  Ti  Ti7  1  0.250  0.010  0.363  1.0
  Ti  Ti8  1  0.750  0.990  0.637  1.0
  Ti  Ti9  1  0.750  0.513  0.640  1.0
  Ti  Ti10  1  0.750  0.762  0.858  1.0
  Ti  Ti11  1  0.750  0.224  0.870  1.0
  O  O12  1  0.250  0.741  0.900  1.0
  O  O13  1  0.250  0.253  0.904  1.0
  O  O14  1  0.750  0.747  0.096  1.0
  O  O15  1  0.750  0.259  0.100  1.0
  O  O16  1  0.250  0.002  0.141  1.0
  O  O17  1  0.250  0.501  0.145  1.0
  O  O18  1  0.250  0.749  0.342  1.0
  O  O19  1  0.250  0.252  0.364  1.0
  O  O20  1  0.750  0.508  0.400  1.0
  O  O21  1  0.750  0.992  0.402  1.0
  O  O22  1  0.250  0.008  0.598  1.0
  O  O23  1  0.250  0.492  0.600  1.0
  O  O24  1  0.750  0.748  0.636  1.0
  O  O25  1  0.750  0.251  0.658  1.0
  O  O26  1  0.750  0.499  0.855  1.0
  O  O27  1  0.750  0.998  0.859  1.0
[/CIF]
.