The compound described by Li4Ti5Fe3O16 is Hausmannite-derived structured and crystallizes in the monoclinic Cm space group. There are four inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(12), one O(3), and two equivalent O(9) atoms to form LiO4 tetrahedra that share  a cornercorner with one Fe(1)O6 octahedra, corners with two equivalent Ti(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra, corners with three equivalent Ti(4)O6 octahedra, and corners with four equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 54-63°. In the second Li site, Li(2) is bonded to one O(5), one O(7), and two equivalent O(11) atoms to form distorted LiO4 tetrahedra that share  a cornercorner with one Ti(1)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, corners with three equivalent Ti(4)O6 octahedra,  an edgeedge with one Fe(1)O6 octahedra, and edges with two equivalent Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-67°. In the third Li site, Li(3) is bonded to one O(4), one O(8), and two equivalent O(1) atoms to form distorted LiO4 tetrahedra that share  a cornercorner with one Fe(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra, corners with three equivalent Ti(3)O6 octahedra,  an edgeedge with one Ti(1)O6 octahedra, and edges with two equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-66°. In the fourth Li site, Li(4) is bonded to one O(10), one O(2), and two equivalent O(6) atoms to form LiO4 tetrahedra that share  a cornercorner with one Ti(1)O6 octahedra, corners with two equivalent Fe(1)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, corners with three equivalent Ti(3)O6 octahedra, and corners with four equivalent Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-65°. There are four inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(10), one O(5), two equivalent O(1), and two equivalent O(9) atoms to form TiO6 octahedra that share corners with two equivalent Ti(3)O6 octahedra,  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one Ti(4)O6 octahedra, edges with four equivalent Fe(2)O6 octahedra, and  an edgeedge with one Li(3)O4 tetrahedra. The corner-sharing octahedral tilt angles are 53°. In the second Ti site, Ti(2) is bonded to one O(11), one O(2), one O(3), one O(4), one O(6), and one O(7) atom to form TiO6 octahedra that share corners with two equivalent Ti(4)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(3)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Ti(3)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, and  an edgeedge with one Li(2)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 51-53°. In the third Ti site, Ti(3) is bonded to one O(2), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form distorted TiO6 octahedra that share corners with two equivalent Ti(1)O6 octahedra, corners with four equivalent Fe(2)O6 octahedra, corners with three equivalent Li(3)O4 tetrahedra, corners with three equivalent Li(4)O4 tetrahedra,  an edgeedge with one Fe(1)O6 octahedra, and edges with two equivalent Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-53°. In the fourth Ti site, Ti(4) is bonded to one O(12), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form distorted TiO6 octahedra that share corners with two equivalent Fe(1)O6 octahedra, corners with four equivalent Ti(2)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra, corners with three equivalent Li(2)O4 tetrahedra,  an edgeedge with one Ti(1)O6 octahedra, and edges with two equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-53°. There are two inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to one O(3), one O(4), two equivalent O(11), and two equivalent O(6) atoms to form FeO6 octahedra that share corners with two equivalent Ti(4)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(3)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Ti(3)O6 octahedra, edges with four equivalent Ti(2)O6 octahedra, and  an edgeedge with one Li(2)O4 tetrahedra. The corner-sharing octahedral tilt angles are 51°. In the second Fe site, Fe(2) is bonded to one O(1), one O(10), one O(12), one O(5), one O(8), and one O(9) atom to form FeO6 octahedra that share corners with two equivalent Ti(3)O6 octahedra,  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one Ti(4)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, and  an edgeedge with one Li(3)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 50-52°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a rectangular see-saw-like geometry to one Li(3), one Ti(1), one Ti(3), and one Fe(2) atom. In the second O site, O(2) is bonded to one Li(4), one Ti(3), and two equivalent Ti(2) atoms to form a mixture of distorted corner and edge-sharing OLiTi3 trigonal pyramids. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Li(1), two equivalent Ti(2), and one Fe(1) atom. In the fourth O site, O(4) is bonded to one Li(3), two equivalent Ti(2), and one Fe(1) atom to form OLiTi2Fe tetrahedra that share corners with four equivalent O(6)LiTi2Fe tetrahedra and corners with two equivalent O(2)LiTi3 trigonal pyramids. In the fifth O site, O(5) is bonded to one Li(2), one Ti(1), and two equivalent Fe(2) atoms to form OLiTiFe2 tetrahedra that share corners with two equivalent O(12)LiTiFe2 tetrahedra and corners with four equivalent O(9)LiTi2Fe trigonal pyramids. In the sixth O site, O(6) is bonded to one Li(4), one Ti(2), one Ti(3), and one Fe(1) atom to form distorted OLiTi2Fe tetrahedra that share  a cornercorner with one O(6)LiTi2Fe tetrahedra, corners with two equivalent O(4)LiTi2Fe tetrahedra,  a cornercorner with one O(2)LiTi3 trigonal pyramid,  an edgeedge with one O(6)LiTi2Fe tetrahedra, and  an edgeedge with one O(2)LiTi3 trigonal pyramid. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), one Ti(4), and two equivalent Ti(2) atoms. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Li(3), one Ti(3), and two equivalent Fe(2) atoms. In the ninth O site, O(9) is bonded to one Li(1), one Ti(1), one Ti(4), and one Fe(2) atom to form distorted OLiTi2Fe trigonal pyramids that share  a cornercorner with one O(12)LiTiFe2 tetrahedra, corners with two equivalent O(5)LiTiFe2 tetrahedra,  a cornercorner with one O(9)LiTi2Fe trigonal pyramid,  an edgeedge with one O(12)LiTiFe2 tetrahedra, and  an edgeedge with one O(9)LiTi2Fe trigonal pyramid. In the tenth O site, O(10) is bonded in a rectangular see-saw-like geometry to one Li(4), one Ti(1), and two equivalent Fe(2) atoms. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one Ti(2), one Ti(4), and one Fe(1) atom. In the twelfth O site, O(12) is bonded to one Li(1), one Ti(4), and two equivalent Fe(2) atoms to form OLiTiFe2 tetrahedra that share corners with two equivalent O(5)LiTiFe2 tetrahedra, corners with two equivalent O(9)LiTi2Fe trigonal pyramids, and edges with two equivalent O(9)LiTi2Fe trigonal pyramids. is represented by the CIF file [CIF]
data_Li4Ti5Fe3O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.985
_cell_length_b   5.985
_cell_length_c   9.629
_cell_angle_alpha   89.927
_cell_angle_beta   89.927
_cell_angle_gamma   59.498
_symmetry_Int_Tables_number   1
_cell_volume   297.164
_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  0.662  0.662  0.103  1.0
  Li  Li1  1  0.999  0.999  0.007  1.0
  Li  Li2  1  0.003  0.003  0.507  1.0
  Li  Li3  1  0.332  0.332  0.601  1.0
  Ti  Ti4  1  0.176  0.176  0.271  1.0
  Ti  Ti5  1  0.349  0.840  0.779  1.0
  Ti  Ti6  1  0.667  0.667  0.500  1.0
  Ti  Ti7  1  0.840  0.349  0.779  1.0
  Ti  Ti8  1  0.347  0.347  0.002  1.0
  Fe  Fe9  1  0.829  0.829  0.789  1.0
  Fe  Fe10  1  0.172  0.660  0.290  1.0
  Fe  Fe11  1  0.660  0.172  0.290  1.0
  O  O12  1  0.340  0.827  0.405  1.0
  O  O13  1  0.519  0.519  0.664  1.0
  O  O14  1  0.654  0.654  0.897  1.0
  O  O15  1  0.008  0.008  0.695  1.0
  O  O16  1  0.003  0.003  0.196  1.0
  O  O17  1  0.827  0.340  0.405  1.0
  O  O18  1  0.504  0.958  0.654  1.0
  O  O19  1  0.958  0.504  0.654  1.0
  O  O20  1  0.169  0.169  0.901  1.0
  O  O21  1  0.831  0.831  0.409  1.0
  O  O22  1  0.033  0.476  0.161  1.0
  O  O23  1  0.476  0.033  0.161  1.0
  O  O24  1  0.325  0.325  0.396  1.0
  O  O25  1  0.180  0.662  0.909  1.0
  O  O26  1  0.476  0.476  0.157  1.0
  O  O27  1  0.662  0.180  0.909  1.0
[/CIF]
.
The compound described by Li4Ti5Fe3O16 is Hausmannite-derived structured and crystallizes in the monoclinic Cm space group. There are four inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(12), one O(3), and two equivalent O(9) atoms to form LiO4 tetrahedra that share  a cornercorner with one Fe(1)O6 octahedra, corners with two equivalent Ti(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra, corners with three equivalent Ti(4)O6 octahedra, and corners with four equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 54-63°. In the second Li site, Li(2) is bonded to one O(5), one O(7), and two equivalent O(11) atoms to form distorted LiO4 tetrahedra that share  a cornercorner with one Ti(1)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, corners with three equivalent Ti(4)O6 octahedra,  an edgeedge with one Fe(1)O6 octahedra, and edges with two equivalent Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-67°. In the third Li site, Li(3) is bonded to one O(4), one O(8), and two equivalent O(1) atoms to form distorted LiO4 tetrahedra that share  a cornercorner with one Fe(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra, corners with three equivalent Ti(3)O6 octahedra,  an edgeedge with one Ti(1)O6 octahedra, and edges with two equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-66°. In the fourth Li site, Li(4) is bonded to one O(10), one O(2), and two equivalent O(6) atoms to form LiO4 tetrahedra that share  a cornercorner with one Ti(1)O6 octahedra, corners with two equivalent Fe(1)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, corners with three equivalent Ti(3)O6 octahedra, and corners with four equivalent Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-65°. There are four inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(10), one O(5), two equivalent O(1), and two equivalent O(9) atoms to form TiO6 octahedra that share corners with two equivalent Ti(3)O6 octahedra,  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one Ti(4)O6 octahedra, edges with four equivalent Fe(2)O6 octahedra, and  an edgeedge with one Li(3)O4 tetrahedra. The corner-sharing octahedral tilt angles are 53°. In the second Ti site, Ti(2) is bonded to one O(11), one O(2), one O(3), one O(4), one O(6), and one O(7) atom to form TiO6 octahedra that share corners with two equivalent Ti(4)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(3)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Ti(3)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, and  an edgeedge with one Li(2)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 51-53°. In the third Ti site, Ti(3) is bonded to one O(2), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form distorted TiO6 octahedra that share corners with two equivalent Ti(1)O6 octahedra, corners with four equivalent Fe(2)O6 octahedra, corners with three equivalent Li(3)O4 tetrahedra, corners with three equivalent Li(4)O4 tetrahedra,  an edgeedge with one Fe(1)O6 octahedra, and edges with two equivalent Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-53°. In the fourth Ti site, Ti(4) is bonded to one O(12), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form distorted TiO6 octahedra that share corners with two equivalent Fe(1)O6 octahedra, corners with four equivalent Ti(2)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra, corners with three equivalent Li(2)O4 tetrahedra,  an edgeedge with one Ti(1)O6 octahedra, and edges with two equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-53°. There are two inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to one O(3), one O(4), two equivalent O(11), and two equivalent O(6) atoms to form FeO6 octahedra that share corners with two equivalent Ti(4)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(3)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Ti(3)O6 octahedra, edges with four equivalent Ti(2)O6 octahedra, and  an edgeedge with one Li(2)O4 tetrahedra. The corner-sharing octahedral tilt angles are 51°. In the second Fe site, Fe(2) is bonded to one O(1), one O(10), one O(12), one O(5), one O(8), and one O(9) atom to form FeO6 octahedra that share corners with two equivalent Ti(3)O6 octahedra,  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one Ti(4)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, and  an edgeedge with one Li(3)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 50-52°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a rectangular see-saw-like geometry to one Li(3), one Ti(1), one Ti(3), and one Fe(2) atom. In the second O site, O(2) is bonded to one Li(4), one Ti(3), and two equivalent Ti(2) atoms to form a mixture of distorted corner and edge-sharing OLiTi3 trigonal pyramids. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Li(1), two equivalent Ti(2), and one Fe(1) atom. In the fourth O site, O(4) is bonded to one Li(3), two equivalent Ti(2), and one Fe(1) atom to form OLiTi2Fe tetrahedra that share corners with four equivalent O(6)LiTi2Fe tetrahedra and corners with two equivalent O(2)LiTi3 trigonal pyramids. In the fifth O site, O(5) is bonded to one Li(2), one Ti(1), and two equivalent Fe(2) atoms to form OLiTiFe2 tetrahedra that share corners with two equivalent O(12)LiTiFe2 tetrahedra and corners with four equivalent O(9)LiTi2Fe trigonal pyramids. In the sixth O site, O(6) is bonded to one Li(4), one Ti(2), one Ti(3), and one Fe(1) atom to form distorted OLiTi2Fe tetrahedra that share  a cornercorner with one O(6)LiTi2Fe tetrahedra, corners with two equivalent O(4)LiTi2Fe tetrahedra,  a cornercorner with one O(2)LiTi3 trigonal pyramid,  an edgeedge with one O(6)LiTi2Fe tetrahedra, and  an edgeedge with one O(2)LiTi3 trigonal pyramid. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), one Ti(4), and two equivalent Ti(2) atoms. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Li(3), one Ti(3), and two equivalent Fe(2) atoms. In the ninth O site, O(9) is bonded to one Li(1), one Ti(1), one Ti(4), and one Fe(2) atom to form distorted OLiTi2Fe trigonal pyramids that share  a cornercorner with one O(12)LiTiFe2 tetrahedra, corners with two equivalent O(5)LiTiFe2 tetrahedra,  a cornercorner with one O(9)LiTi2Fe trigonal pyramid,  an edgeedge with one O(12)LiTiFe2 tetrahedra, and  an edgeedge with one O(9)LiTi2Fe trigonal pyramid. In the tenth O site, O(10) is bonded in a rectangular see-saw-like geometry to one Li(4), one Ti(1), and two equivalent Fe(2) atoms. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one Ti(2), one Ti(4), and one Fe(1) atom. In the twelfth O site, O(12) is bonded to one Li(1), one Ti(4), and two equivalent Fe(2) atoms to form OLiTiFe2 tetrahedra that share corners with two equivalent O(5)LiTiFe2 tetrahedra, corners with two equivalent O(9)LiTi2Fe trigonal pyramids, and edges with two equivalent O(9)LiTi2Fe trigonal pyramids. is represented by the CIF file [CIF]
data_Li4Ti5Fe3O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.985
_cell_length_b   5.985
_cell_length_c   9.629
_cell_angle_alpha   89.927
_cell_angle_beta   89.927
_cell_angle_gamma   59.498
_symmetry_Int_Tables_number   1
_cell_volume   297.164
_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  0.662  0.662  0.103  1.0
  Li  Li1  1  0.999  0.999  0.007  1.0
  Li  Li2  1  0.003  0.003  0.507  1.0
  Li  Li3  1  0.332  0.332  0.601  1.0
  Ti  Ti4  1  0.176  0.176  0.271  1.0
  Ti  Ti5  1  0.349  0.840  0.779  1.0
  Ti  Ti6  1  0.667  0.667  0.500  1.0
  Ti  Ti7  1  0.840  0.349  0.779  1.0
  Ti  Ti8  1  0.347  0.347  0.002  1.0
  Fe  Fe9  1  0.829  0.829  0.789  1.0
  Fe  Fe10  1  0.172  0.660  0.290  1.0
  Fe  Fe11  1  0.660  0.172  0.290  1.0
  O  O12  1  0.340  0.827  0.405  1.0
  O  O13  1  0.519  0.519  0.664  1.0
  O  O14  1  0.654  0.654  0.897  1.0
  O  O15  1  0.008  0.008  0.695  1.0
  O  O16  1  0.003  0.003  0.196  1.0
  O  O17  1  0.827  0.340  0.405  1.0
  O  O18  1  0.504  0.958  0.654  1.0
  O  O19  1  0.958  0.504  0.654  1.0
  O  O20  1  0.169  0.169  0.901  1.0
  O  O21  1  0.831  0.831  0.409  1.0
  O  O22  1  0.033  0.476  0.161  1.0
  O  O23  1  0.476  0.033  0.161  1.0
  O  O24  1  0.325  0.325  0.396  1.0
  O  O25  1  0.180  0.662  0.909  1.0
  O  O26  1  0.476  0.476  0.157  1.0
  O  O27  1  0.662  0.180  0.909  1.0
[/CIF]
.