Li4Ti3Fe5O16 is Spinel-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(2)O6 octahedra, corners with two equivalent Ti(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra, corners with three equivalent Fe(3)O6 octahedra, and corners with four equivalent Fe(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-68°. In the second Li site, Li(2) is bonded in a rectangular see-saw-like geometry to one O(5), one O(7), and two equivalent O(11) atoms. In the third Li site, Li(3) is bonded in a rectangular see-saw-like geometry to one O(4), one O(8), and two equivalent O(1) atoms. 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(2)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, corners with two equivalent Fe(4)O6 octahedra, corners with three equivalent Fe(1)O6 octahedra, and corners with four equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-67°. There are two inequivalent Ti sites. In the first Ti site, Ti(1) 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 Fe(3)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Fe(1)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, and edges with two equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 54-56°. In the second Ti site, Ti(2) 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 Fe(1)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one Fe(3)O6 octahedra, and edges with four equivalent Fe(4)O6 octahedra. The corner-sharing octahedral tilt angles are 54°. There are four inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to one O(2), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form distorted FeO6 octahedra that share corners with two equivalent Ti(2)O6 octahedra, corners with four equivalent Fe(4)O6 octahedra, corners with three equivalent Li(4)O4 tetrahedra,  an edgeedge with one Fe(2)O6 octahedra, and edges with two equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-54°. In the second Fe site, Fe(2) 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 Fe(3)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Fe(1)O6 octahedra, and edges with four equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles are 48°. In the third Fe site, Fe(3) is bonded to one O(12), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form FeO6 octahedra that share corners with two equivalent Fe(2)O6 octahedra, corners with four equivalent Ti(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra,  an edgeedge with one Ti(2)O6 octahedra, and edges with two equivalent Fe(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 48-56°. In the fourth Fe site, Fe(4) 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 Fe(1)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one Fe(3)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, and edges with two equivalent Fe(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-53°. 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(2), one Fe(1), and one Fe(4) atom. In the second O site, O(2) is bonded to one Li(4), two equivalent Ti(1), and one Fe(1) atom to form distorted OLiTi2Fe tetrahedra that share corners with two equivalent O(4)LiTi2Fe tetrahedra, corners with two equivalent O(6)LiTiFe2 tetrahedra,  a cornercorner with one O(8)LiFe3 trigonal pyramid, and edges with two equivalent O(6)LiTiFe2 tetrahedra. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Li(1), two equivalent Ti(1), and one Fe(2) atom. In the fourth O site, O(4) is bonded to one Li(3), two equivalent Ti(1), and one Fe(2) atom to form OLiTi2Fe tetrahedra that share corners with two equivalent O(2)LiTi2Fe tetrahedra, corners with four equivalent O(6)LiTiFe2 tetrahedra, and  a cornercorner with one O(8)LiFe3 trigonal pyramid. In the fifth O site, O(5) is bonded to one Li(2), one Ti(2), and two equivalent Fe(4) atoms to form OLiTiFe2 tetrahedra that share corners with two equivalent O(12)LiFe3 tetrahedra, corners with four equivalent O(9)LiTiFe2 tetrahedra, and  an edgeedge with one O(8)LiFe3 trigonal pyramid. In the sixth O site, O(6) is bonded to one Li(4), one Ti(1), one Fe(1), and one Fe(2) atom to form distorted OLiTiFe2 tetrahedra that share  a cornercorner with one O(2)LiTi2Fe tetrahedra,  a cornercorner with one O(6)LiTiFe2 tetrahedra, corners with two equivalent O(4)LiTi2Fe tetrahedra,  a cornercorner with one O(8)LiFe3 trigonal pyramid,  an edgeedge with one O(2)LiTi2Fe tetrahedra, and  an edgeedge with one O(6)LiTiFe2 tetrahedra. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), two equivalent Ti(1), and one Fe(3) atom. In the eighth O site, O(8) is bonded to one Li(3), one Fe(1), and two equivalent Fe(4) atoms to form OLiFe3 trigonal pyramids that share  a cornercorner with one O(2)LiTi2Fe tetrahedra,  a cornercorner with one O(4)LiTi2Fe tetrahedra, corners with two equivalent O(12)LiFe3 tetrahedra, corners with two equivalent O(6)LiTiFe2 tetrahedra, corners with two equivalent O(9)LiTiFe2 tetrahedra, and  an edgeedge with one O(5)LiTiFe2 tetrahedra. In the ninth O site, O(9) is bonded to one Li(1), one Ti(2), one Fe(3), and one Fe(4) atom to form distorted OLiTiFe2 tetrahedra that share  a cornercorner with one O(12)LiFe3 tetrahedra,  a cornercorner with one O(9)LiTiFe2 tetrahedra, corners with two equivalent O(5)LiTiFe2 tetrahedra,  a cornercorner with one O(8)LiFe3 trigonal pyramid,  an edgeedge with one O(12)LiFe3 tetrahedra, and  an edgeedge with one O(9)LiTiFe2 tetrahedra. In the tenth O site, O(10) is bonded in a rectangular see-saw-like geometry to one Li(4), one Ti(2), and two equivalent Fe(4) atoms. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one Ti(1), one Fe(2), and one Fe(3) atom. In the twelfth O site, O(12) is bonded to one Li(1), one Fe(3), and two equivalent Fe(4) atoms to form OLiFe3 tetrahedra that share corners with two equivalent O(5)LiTiFe2 tetrahedra, corners with two equivalent O(9)LiTiFe2 tetrahedra, corners with two equivalent O(8)LiFe3 trigonal pyramids, and edges with two equivalent O(9)LiTiFe2 tetrahedra.
Li4Ti3Fe5O16 is Spinel-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(2)O6 octahedra, corners with two equivalent Ti(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra, corners with three equivalent Fe(3)O6 octahedra, and corners with four equivalent Fe(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-68°. The Li(1)-O(12) bond length is 1.99 Å. The Li(1)-O(3) bond length is 1.98 Å. Both Li(1)-O(9) bond lengths are 1.92 Å. In the second Li site, Li(2) is bonded in a rectangular see-saw-like geometry to one O(5), one O(7), and two equivalent O(11) atoms. The Li(2)-O(5) bond length is 1.81 Å. The Li(2)-O(7) bond length is 2.00 Å. Both Li(2)-O(11) bond lengths are 1.93 Å. In the third Li site, Li(3) is bonded in a rectangular see-saw-like geometry to one O(4), one O(8), and two equivalent O(1) atoms. The Li(3)-O(4) bond length is 1.82 Å. The Li(3)-O(8) bond length is 1.91 Å. Both Li(3)-O(1) bond lengths are 1.96 Å. 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(2)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, corners with two equivalent Fe(4)O6 octahedra, corners with three equivalent Fe(1)O6 octahedra, and corners with four equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-67°. The Li(4)-O(10) bond length is 2.00 Å. The Li(4)-O(2) bond length is 1.91 Å. Both Li(4)-O(6) bond lengths are 1.96 Å. There are two inequivalent Ti sites. In the first Ti site, Ti(1) 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 Fe(3)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Fe(1)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, and edges with two equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 54-56°. The Ti(1)-O(11) bond length is 2.13 Å. The Ti(1)-O(2) bond length is 1.94 Å. The Ti(1)-O(3) bond length is 1.96 Å. The Ti(1)-O(4) bond length is 1.96 Å. The Ti(1)-O(6) bond length is 1.93 Å. The Ti(1)-O(7) bond length is 2.01 Å. In the second Ti site, Ti(2) 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 Fe(1)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one Fe(3)O6 octahedra, and edges with four equivalent Fe(4)O6 octahedra. The corner-sharing octahedral tilt angles are 54°. The Ti(2)-O(10) bond length is 1.97 Å. The Ti(2)-O(5) bond length is 1.95 Å. Both Ti(2)-O(1) bond lengths are 2.09 Å. Both Ti(2)-O(9) bond lengths are 1.92 Å. There are four inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to one O(2), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form distorted FeO6 octahedra that share corners with two equivalent Ti(2)O6 octahedra, corners with four equivalent Fe(4)O6 octahedra, corners with three equivalent Li(4)O4 tetrahedra,  an edgeedge with one Fe(2)O6 octahedra, and edges with two equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-54°. The Fe(1)-O(2) bond length is 2.25 Å. The Fe(1)-O(8) bond length is 1.99 Å. Both Fe(1)-O(1) bond lengths are 1.96 Å. Both Fe(1)-O(6) bond lengths are 2.17 Å. In the second Fe site, Fe(2) 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 Fe(3)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Fe(1)O6 octahedra, and edges with four equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles are 48°. The Fe(2)-O(3) bond length is 2.01 Å. The Fe(2)-O(4) bond length is 1.97 Å. Both Fe(2)-O(11) bond lengths are 1.93 Å. Both Fe(2)-O(6) bond lengths are 1.95 Å. In the third Fe site, Fe(3) is bonded to one O(12), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form FeO6 octahedra that share corners with two equivalent Fe(2)O6 octahedra, corners with four equivalent Ti(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra,  an edgeedge with one Ti(2)O6 octahedra, and edges with two equivalent Fe(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 48-56°. The Fe(3)-O(12) bond length is 2.13 Å. The Fe(3)-O(7) bond length is 2.00 Å. Both Fe(3)-O(11) bond lengths are 1.98 Å. Both Fe(3)-O(9) bond lengths are 2.20 Å. In the fourth Fe site, Fe(4) 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 Fe(1)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one Fe(3)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, and edges with two equivalent Fe(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-53°. The Fe(4)-O(1) bond length is 1.94 Å. The Fe(4)-O(10) bond length is 1.92 Å. The Fe(4)-O(12) bond length is 1.92 Å. The Fe(4)-O(5) bond length is 1.94 Å. The Fe(4)-O(8) bond length is 1.96 Å. The Fe(4)-O(9) bond length is 1.93 Å. 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(2), one Fe(1), and one Fe(4) atom. In the second O site, O(2) is bonded to one Li(4), two equivalent Ti(1), and one Fe(1) atom to form distorted OLiTi2Fe tetrahedra that share corners with two equivalent O(4)LiTi2Fe tetrahedra, corners with two equivalent O(6)LiTiFe2 tetrahedra,  a cornercorner with one O(8)LiFe3 trigonal pyramid, and edges with two equivalent O(6)LiTiFe2 tetrahedra. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Li(1), two equivalent Ti(1), and one Fe(2) atom. In the fourth O site, O(4) is bonded to one Li(3), two equivalent Ti(1), and one Fe(2) atom to form OLiTi2Fe tetrahedra that share corners with two equivalent O(2)LiTi2Fe tetrahedra, corners with four equivalent O(6)LiTiFe2 tetrahedra, and  a cornercorner with one O(8)LiFe3 trigonal pyramid. In the fifth O site, O(5) is bonded to one Li(2), one Ti(2), and two equivalent Fe(4) atoms to form OLiTiFe2 tetrahedra that share corners with two equivalent O(12)LiFe3 tetrahedra, corners with four equivalent O(9)LiTiFe2 tetrahedra, and  an edgeedge with one O(8)LiFe3 trigonal pyramid. In the sixth O site, O(6) is bonded to one Li(4), one Ti(1), one Fe(1), and one Fe(2) atom to form distorted OLiTiFe2 tetrahedra that share  a cornercorner with one O(2)LiTi2Fe tetrahedra,  a cornercorner with one O(6)LiTiFe2 tetrahedra, corners with two equivalent O(4)LiTi2Fe tetrahedra,  a cornercorner with one O(8)LiFe3 trigonal pyramid,  an edgeedge with one O(2)LiTi2Fe tetrahedra, and  an edgeedge with one O(6)LiTiFe2 tetrahedra. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), two equivalent Ti(1), and one Fe(3) atom. In the eighth O site, O(8) is bonded to one Li(3), one Fe(1), and two equivalent Fe(4) atoms to form OLiFe3 trigonal pyramids that share  a cornercorner with one O(2)LiTi2Fe tetrahedra,  a cornercorner with one O(4)LiTi2Fe tetrahedra, corners with two equivalent O(12)LiFe3 tetrahedra, corners with two equivalent O(6)LiTiFe2 tetrahedra, corners with two equivalent O(9)LiTiFe2 tetrahedra, and  an edgeedge with one O(5)LiTiFe2 tetrahedra. In the ninth O site, O(9) is bonded to one Li(1), one Ti(2), one Fe(3), and one Fe(4) atom to form distorted OLiTiFe2 tetrahedra that share  a cornercorner with one O(12)LiFe3 tetrahedra,  a cornercorner with one O(9)LiTiFe2 tetrahedra, corners with two equivalent O(5)LiTiFe2 tetrahedra,  a cornercorner with one O(8)LiFe3 trigonal pyramid,  an edgeedge with one O(12)LiFe3 tetrahedra, and  an edgeedge with one O(9)LiTiFe2 tetrahedra. In the tenth O site, O(10) is bonded in a rectangular see-saw-like geometry to one Li(4), one Ti(2), and two equivalent Fe(4) atoms. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one Ti(1), one Fe(2), and one Fe(3) atom. In the twelfth O site, O(12) is bonded to one Li(1), one Fe(3), and two equivalent Fe(4) atoms to form OLiFe3 tetrahedra that share corners with two equivalent O(5)LiTiFe2 tetrahedra, corners with two equivalent O(9)LiTiFe2 tetrahedra, corners with two equivalent O(8)LiFe3 trigonal pyramids, and edges with two equivalent O(9)LiTiFe2 tetrahedra.