The crystal structure described by Li4Ti3O8 crystallizes in the monoclinic C2/m space group. There are three inequivalent Li sites. In the first Li site, Li(1) is bonded to two equivalent O(2) and four equivalent O(3) atoms to form LiO6 octahedra that share corners with six equivalent Li(3)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, edges with four equivalent Li(2)O6 octahedra, and edges with four equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 10-11°. In the second Li site, Li(2) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(3) atoms to form LiO6 octahedra that share corners with six equivalent Ti(1)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Li(3)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, and edges with two equivalent Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 5-9°. In the third Li site, Li(3) is bonded to two equivalent O(2) and four equivalent O(3) atoms to form LiO6 octahedra that share corners with six equivalent Li(1)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, edges with four equivalent Li(2)O6 octahedra, and edges with four equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 10-11°. There are two inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(3) atoms to form TiO6 octahedra that share corners with six equivalent Li(2)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Li(3)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, and edges with two equivalent Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 5-9°. In the second Ti site, Ti(2) is bonded to two equivalent O(1) and four equivalent O(3) atoms to form TiO6 octahedra that share edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(3)O6 octahedra, edges with four equivalent Li(2)O6 octahedra, and edges with four equivalent Ti(1)O6 octahedra. There are three inequivalent O sites. In the first O site, O(1) is bonded to two equivalent Li(2), one Ti(2), and two equivalent Ti(1) atoms to form OLi2Ti3 square pyramids that share corners with four equivalent O(3)Li3Ti2 square pyramids, corners with five equivalent O(1)Li2Ti3 square pyramids, edges with four equivalent O(2)Li4Ti2 octahedra, and edges with four equivalent O(3)Li3Ti2 square pyramids. In the second O site, O(2) is bonded to one Li(1), one Li(3), two equivalent Li(2), and two equivalent Ti(1) atoms to form OLi4Ti2 octahedra that share corners with six equivalent O(2)Li4Ti2 octahedra, edges with four equivalent O(1)Li2Ti3 square pyramids, and edges with eight equivalent O(3)Li3Ti2 square pyramids. The corner-sharing octahedra are not tilted. In the third O site, O(3) is bonded to one Li(1), one Li(2), one Li(3), one Ti(1), and one Ti(2) atom to form OLi3Ti2 square pyramids that share corners with two equivalent O(1)Li2Ti3 square pyramids, corners with seven equivalent O(3)Li3Ti2 square pyramids, edges with four equivalent O(2)Li4Ti2 octahedra, edges with two equivalent O(1)Li2Ti3 square pyramids, and edges with two equivalent O(3)Li3Ti2 square pyramids. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li4Ti3O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.905
_cell_length_b   5.905
_cell_length_c   6.008
_cell_angle_alpha   59.602
_cell_angle_beta   59.602
_cell_angle_gamma   60.606
_symmetry_Int_Tables_number   1
_cell_volume   147.882
_cell_formula_units_Z   1
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  0.500  0.500  0.500  1.0
  Li  Li1  1  0.000  0.500  0.000  1.0
  Li  Li2  1  0.500  0.000  0.000  1.0
  Li  Li3  1  0.000  0.000  0.000  1.0
  Ti  Ti4  1  0.000  0.500  0.500  1.0
  Ti  Ti5  1  0.500  0.000  0.500  1.0
  Ti  Ti6  1  0.000  0.000  0.500  1.0
  O  O7  1  0.243  0.243  0.274  1.0
  O  O8  1  0.250  0.250  0.719  1.0
  O  O9  1  0.245  0.784  0.715  1.0
  O  O10  1  0.216  0.755  0.285  1.0
  O  O11  1  0.755  0.216  0.285  1.0
  O  O12  1  0.784  0.245  0.715  1.0
  O  O13  1  0.750  0.750  0.281  1.0
  O  O14  1  0.757  0.757  0.726  1.0
[/CIF]
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The crystal structure described by Li4Ti3O8 crystallizes in the monoclinic C2/m space group. There are three inequivalent Li sites. In the first Li site, Li(1) is bonded to two equivalent O(2) and four equivalent O(3) atoms to form LiO6 octahedra that share corners with six equivalent Li(3)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, edges with four equivalent Li(2)O6 octahedra, and edges with four equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 10-11°. In the second Li site, Li(2) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(3) atoms to form LiO6 octahedra that share corners with six equivalent Ti(1)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Li(3)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, and edges with two equivalent Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 5-9°. In the third Li site, Li(3) is bonded to two equivalent O(2) and four equivalent O(3) atoms to form LiO6 octahedra that share corners with six equivalent Li(1)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, edges with four equivalent Li(2)O6 octahedra, and edges with four equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 10-11°. There are two inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(3) atoms to form TiO6 octahedra that share corners with six equivalent Li(2)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(2)O6 octahedra, edges with two equivalent Li(3)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, and edges with two equivalent Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 5-9°. In the second Ti site, Ti(2) is bonded to two equivalent O(1) and four equivalent O(3) atoms to form TiO6 octahedra that share edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Li(3)O6 octahedra, edges with four equivalent Li(2)O6 octahedra, and edges with four equivalent Ti(1)O6 octahedra. There are three inequivalent O sites. In the first O site, O(1) is bonded to two equivalent Li(2), one Ti(2), and two equivalent Ti(1) atoms to form OLi2Ti3 square pyramids that share corners with four equivalent O(3)Li3Ti2 square pyramids, corners with five equivalent O(1)Li2Ti3 square pyramids, edges with four equivalent O(2)Li4Ti2 octahedra, and edges with four equivalent O(3)Li3Ti2 square pyramids. In the second O site, O(2) is bonded to one Li(1), one Li(3), two equivalent Li(2), and two equivalent Ti(1) atoms to form OLi4Ti2 octahedra that share corners with six equivalent O(2)Li4Ti2 octahedra, edges with four equivalent O(1)Li2Ti3 square pyramids, and edges with eight equivalent O(3)Li3Ti2 square pyramids. The corner-sharing octahedra are not tilted. In the third O site, O(3) is bonded to one Li(1), one Li(2), one Li(3), one Ti(1), and one Ti(2) atom to form OLi3Ti2 square pyramids that share corners with two equivalent O(1)Li2Ti3 square pyramids, corners with seven equivalent O(3)Li3Ti2 square pyramids, edges with four equivalent O(2)Li4Ti2 octahedra, edges with two equivalent O(1)Li2Ti3 square pyramids, and edges with two equivalent O(3)Li3Ti2 square pyramids. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li4Ti3O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.905
_cell_length_b   5.905
_cell_length_c   6.008
_cell_angle_alpha   59.602
_cell_angle_beta   59.602
_cell_angle_gamma   60.606
_symmetry_Int_Tables_number   1
_cell_volume   147.882
_cell_formula_units_Z   1
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  0.500  0.500  0.500  1.0
  Li  Li1  1  0.000  0.500  0.000  1.0
  Li  Li2  1  0.500  0.000  0.000  1.0
  Li  Li3  1  0.000  0.000  0.000  1.0
  Ti  Ti4  1  0.000  0.500  0.500  1.0
  Ti  Ti5  1  0.500  0.000  0.500  1.0
  Ti  Ti6  1  0.000  0.000  0.500  1.0
  O  O7  1  0.243  0.243  0.274  1.0
  O  O8  1  0.250  0.250  0.719  1.0
  O  O9  1  0.245  0.784  0.715  1.0
  O  O10  1  0.216  0.755  0.285  1.0
  O  O11  1  0.755  0.216  0.285  1.0
  O  O12  1  0.784  0.245  0.715  1.0
  O  O13  1  0.750  0.750  0.281  1.0
  O  O14  1  0.757  0.757  0.726  1.0
[/CIF]
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