Li4Ti3Mn2Fe3O16 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(1)O6 octahedra, corners with two equivalent Ti(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra, corners with three equivalent Mn(2)O6 octahedra, and corners with four equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-65°. 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 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(1)O6 octahedra, corners with three equivalent Mn(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra, and edges with two equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 60-65°. 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(1)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, corners with three equivalent Mn(1)O6 octahedra, and corners with four equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-64°. 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 Mn(2)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 Mn(1)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, and edges with two equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-52°. 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 Mn(1)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one Mn(2)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 50°. There are two inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to one O(2), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form MnO6 octahedra that share corners with two equivalent Ti(2)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(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-51°. In the second Mn site, Mn(2) is bonded to one O(12), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form MnO6 octahedra that share corners with two equivalent Fe(1)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(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-52°. 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 Mn(2)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 Mn(1)O6 octahedra, and edges with four equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles are 50°. 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 Mn(1)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one Mn(2)O6 octahedra, edges with two equivalent Ti(2)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 50-51°. 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 Mn(1), and one Fe(2) atom. In the second O site, O(2) is bonded to one Li(4), two equivalent Ti(1), and one Mn(1) atom to form distorted OLiTi2Mn tetrahedra that share corners with two equivalent O(4)LiTi2Fe tetrahedra, corners with two equivalent O(6)LiTiMnFe tetrahedra, and edges with two equivalent O(6)LiTiMnFe 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(1) atom. In the fourth O site, O(4) is bonded to one Li(3), two equivalent Ti(1), and one Fe(1) atom to form distorted OLiTi2Fe tetrahedra that share corners with two equivalent O(2)LiTi2Mn tetrahedra and corners with four equivalent O(6)LiTiMnFe tetrahedra. In the fifth O site, O(5) is bonded to one Li(2), one Ti(2), and two equivalent Fe(2) atoms to form corner-sharing OLiTiFe2 tetrahedra. In the sixth O site, O(6) is bonded to one Li(4), one Ti(1), one Mn(1), and one Fe(1) atom to form distorted OLiTiMnFe tetrahedra that share  a cornercorner with one O(2)LiTi2Mn tetrahedra,  a cornercorner with one O(6)LiTiMnFe tetrahedra, corners with two equivalent O(4)LiTi2Fe tetrahedra,  an edgeedge with one O(2)LiTi2Mn tetrahedra, and  an edgeedge with one O(6)LiTiMnFe tetrahedra. In the seventh O site, O(7) is bonded in a distorted rectangular see-saw-like geometry to one Li(2), two equivalent Ti(1), and one Mn(2) atom. In the eighth O site, O(8) is bonded in a distorted rectangular see-saw-like geometry to one Li(3), one Mn(1), and two equivalent Fe(2) atoms. In the ninth O site, O(9) is bonded in a distorted rectangular see-saw-like geometry to one Li(1), one Ti(2), one Mn(2), and one Fe(2) atom. 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(2) 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 Mn(2), and one Fe(1) atom. In the twelfth O site, O(12) is bonded to one Li(1), one Mn(2), and two equivalent Fe(2) atoms to form distorted corner-sharing OLiMnFe2 trigonal pyramids.
Li4Ti3Mn2Fe3O16 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(1)O6 octahedra, corners with two equivalent Ti(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra, corners with three equivalent Mn(2)O6 octahedra, and corners with four equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-65°. The Li(1)-O(12) bond length is 1.91 Å. The Li(1)-O(3) bond length is 2.06 Å. Both Li(1)-O(9) bond lengths are 2.00 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 2.05 Å. Both Li(2)-O(11) bond lengths are 2.00 Å. 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(1)O6 octahedra, corners with three equivalent Mn(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra, and edges with two equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 60-65°. The Li(3)-O(4) bond length is 1.78 Å. The Li(3)-O(8) bond length is 1.97 Å. Both Li(3)-O(1) bond lengths are 1.99 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(1)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, corners with three equivalent Mn(1)O6 octahedra, and corners with four equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-64°. The Li(4)-O(10) bond length is 1.94 Å. The Li(4)-O(2) bond length is 2.04 Å. Both Li(4)-O(6) bond lengths are 2.01 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 Mn(2)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 Mn(1)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, and edges with two equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-52°. The Ti(1)-O(11) bond length is 1.98 Å. The Ti(1)-O(2) bond length is 2.03 Å. The Ti(1)-O(3) bond length is 1.97 Å. The Ti(1)-O(4) bond length is 1.96 Å. The Ti(1)-O(6) bond length is 1.99 Å. The Ti(1)-O(7) bond length is 1.94 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 Mn(1)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one Mn(2)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 50°. The Ti(2)-O(10) bond length is 1.93 Å. The Ti(2)-O(5) bond length is 1.95 Å. Both Ti(2)-O(1) bond lengths are 2.07 Å. Both Ti(2)-O(9) bond lengths are 1.96 Å. There are two inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to one O(2), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form MnO6 octahedra that share corners with two equivalent Ti(2)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(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-51°. The Mn(1)-O(2) bond length is 2.03 Å. The Mn(1)-O(8) bond length is 1.96 Å. Both Mn(1)-O(1) bond lengths are 2.00 Å. Both Mn(1)-O(6) bond lengths are 2.02 Å. In the second Mn site, Mn(2) is bonded to one O(12), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form MnO6 octahedra that share corners with two equivalent Fe(1)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(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-52°. The Mn(2)-O(12) bond length is 2.17 Å. The Mn(2)-O(7) bond length is 2.31 Å. Both Mn(2)-O(11) bond lengths are 2.03 Å. Both Mn(2)-O(9) bond lengths are 1.99 Å. 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 Mn(2)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 Mn(1)O6 octahedra, and edges with four equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles are 50°. The Fe(1)-O(3) bond length is 2.03 Å. The Fe(1)-O(4) bond length is 1.99 Å. Both Fe(1)-O(11) bond lengths are 2.06 Å. Both Fe(1)-O(6) bond lengths are 2.06 Å. 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 Mn(1)O6 octahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra,  an edgeedge with one Mn(2)O6 octahedra, edges with two equivalent Ti(2)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 50-51°. The Fe(2)-O(1) bond length is 2.09 Å. The Fe(2)-O(10) bond length is 2.00 Å. The Fe(2)-O(12) bond length is 1.97 Å. The Fe(2)-O(5) bond length is 1.97 Å. The Fe(2)-O(8) bond length is 2.08 Å. The Fe(2)-O(9) bond length is 2.14 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 Mn(1), and one Fe(2) atom. In the second O site, O(2) is bonded to one Li(4), two equivalent Ti(1), and one Mn(1) atom to form distorted OLiTi2Mn tetrahedra that share corners with two equivalent O(4)LiTi2Fe tetrahedra, corners with two equivalent O(6)LiTiMnFe tetrahedra, and edges with two equivalent O(6)LiTiMnFe 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(1) atom. In the fourth O site, O(4) is bonded to one Li(3), two equivalent Ti(1), and one Fe(1) atom to form distorted OLiTi2Fe tetrahedra that share corners with two equivalent O(2)LiTi2Mn tetrahedra and corners with four equivalent O(6)LiTiMnFe tetrahedra. In the fifth O site, O(5) is bonded to one Li(2), one Ti(2), and two equivalent Fe(2) atoms to form corner-sharing OLiTiFe2 tetrahedra. In the sixth O site, O(6) is bonded to one Li(4), one Ti(1), one Mn(1), and one Fe(1) atom to form distorted OLiTiMnFe tetrahedra that share  a cornercorner with one O(2)LiTi2Mn tetrahedra,  a cornercorner with one O(6)LiTiMnFe tetrahedra, corners with two equivalent O(4)LiTi2Fe tetrahedra,  an edgeedge with one O(2)LiTi2Mn tetrahedra, and  an edgeedge with one O(6)LiTiMnFe tetrahedra. In the seventh O site, O(7) is bonded in a distorted rectangular see-saw-like geometry to one Li(2), two equivalent Ti(1), and one Mn(2) atom. In the eighth O site, O(8) is bonded in a distorted rectangular see-saw-like geometry to one Li(3), one Mn(1), and two equivalent Fe(2) atoms. In the ninth O site, O(9) is bonded in a distorted rectangular see-saw-like geometry to one Li(1), one Ti(2), one Mn(2), and one Fe(2) atom. 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(2) 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 Mn(2), and one Fe(1) atom. In the twelfth O site, O(12) is bonded to one Li(1), one Mn(2), and two equivalent Fe(2) atoms to form distorted corner-sharing OLiMnFe2 trigonal pyramids.