Li4Ti2Cr3Fe3O16 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 Cr(1)O6 octahedra, corners with two equivalent Cr(2)O6 octahedra, corners with three equivalent Ti(2)O6 octahedra, and corners with four equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-63°. 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 Cr(2)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, corners with three equivalent Ti(2)O6 octahedra,  an edgeedge with one Fe(1)O6 octahedra, and edges with two equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-64°. 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 trigonal pyramids that share  a cornercorner with one Fe(1)O6 octahedra, corners with two equivalent Cr(1)O6 octahedra, corners with three equivalent Ti(1)O6 octahedra,  an edgeedge with one Cr(2)O6 octahedra, and edges with two equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 63-64°. 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 Cr(2)O6 octahedra, corners with two equivalent Fe(1)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, corners with three equivalent Ti(1)O6 octahedra, and corners with four equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 53-63°. There are two inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(2), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form TiO6 octahedra that share corners with two equivalent Cr(2)O6 octahedra, corners with four equivalent Fe(2)O6 octahedra, corners with three equivalent Li(4)O4 tetrahedra, corners with three equivalent Li(3)O4 trigonal pyramids,  an edgeedge with one Fe(1)O6 octahedra, and edges with two equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-52°. In the second Ti site, Ti(2) 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 Cr(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra, corners with three equivalent Li(2)O4 tetrahedra,  an edgeedge with one Cr(2)O6 octahedra, and edges with two equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-53°. There are two inequivalent Cr sites. In the first Cr site, Cr(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 CrO6 octahedra that share corners with two equivalent Ti(2)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  a cornercorner with one Li(3)O4 trigonal pyramid,  an edgeedge with one Ti(1)O6 octahedra, edges with two equivalent Cr(1)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 50-52°. In the second Cr site, Cr(2) is bonded to one O(10), one O(5), two equivalent O(1), and two equivalent O(9) atoms to form CrO6 octahedra that share corners with two equivalent Ti(1)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(2)O6 octahedra, edges with four equivalent Fe(2)O6 octahedra, and  an edgeedge with one Li(3)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 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 Ti(2)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  a cornercorner with one Li(3)O4 trigonal pyramid,  an edgeedge with one Ti(1)O6 octahedra, edges with four equivalent Cr(1)O6 octahedra, and  an edgeedge with one Li(2)O4 tetrahedra. The corner-sharing octahedral tilt angles are 53°. 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(1)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(2)O6 octahedra, edges with two equivalent Cr(2)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, and  an edgeedge with one Li(3)O4 trigonal pyramid. 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 Cr(2), and one Fe(2) atom. In the second O site, O(2) is bonded in a distorted rectangular see-saw-like geometry to one Li(4), one Ti(1), and two equivalent Cr(1) atoms. In the third O site, O(3) is bonded to one Li(1), two equivalent Cr(1), and one Fe(1) atom to form distorted OLiCr2Fe trigonal pyramids that share  a cornercorner with one O(12)LiTiFe2 tetrahedra, corners with two equivalent O(9)LiTiCrFe tetrahedra, and corners with three equivalent O(4)LiCr2Fe tetrahedra. In the fourth O site, O(4) is bonded to one Li(3), two equivalent Cr(1), and one Fe(1) atom to form corner-sharing OLiCr2Fe tetrahedra. In the fifth O site, O(5) is bonded to one Li(2), one Cr(2), and two equivalent Fe(2) atoms to form OLiCrFe2 tetrahedra that share corners with two equivalent O(12)LiTiFe2 tetrahedra, corners with four equivalent O(9)LiTiCrFe tetrahedra, and corners with three equivalent O(10)LiCrFe2 trigonal pyramids. In the sixth O site, O(6) is bonded in a distorted rectangular see-saw-like geometry to one Li(4), one Ti(1), one Cr(1), and one Fe(1) atom. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), one Ti(2), and two equivalent Cr(1) atoms. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Li(3), one Ti(1), and two equivalent Fe(2) atoms. In the ninth O site, O(9) is bonded to one Li(1), one Ti(2), one Cr(2), and one Fe(2) atom to form distorted OLiTiCrFe tetrahedra that share  a cornercorner with one O(9)LiTiCrFe tetrahedra,  a cornercorner with one O(12)LiTiFe2 tetrahedra, corners with two equivalent O(5)LiCrFe2 tetrahedra,  a cornercorner with one O(3)LiCr2Fe trigonal pyramid,  an edgeedge with one O(9)LiTiCrFe tetrahedra,  an edgeedge with one O(12)LiTiFe2 tetrahedra, and  an edgeedge with one O(10)LiCrFe2 trigonal pyramid. In the tenth O site, O(10) is bonded to one Li(4), one Cr(2), and two equivalent Fe(2) atoms to form distorted OLiCrFe2 trigonal pyramids that share corners with three equivalent O(5)LiCrFe2 tetrahedra,  an edgeedge with one O(12)LiTiFe2 tetrahedra, and edges with two equivalent O(9)LiTiCrFe tetrahedra. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one Ti(2), one Cr(1), and one Fe(1) atom. In the twelfth O site, O(12) is bonded to one Li(1), one Ti(2), and two equivalent Fe(2) atoms to form distorted OLiTiFe2 tetrahedra that share corners with two equivalent O(5)LiCrFe2 tetrahedra, corners with two equivalent O(9)LiTiCrFe tetrahedra,  a cornercorner with one O(3)LiCr2Fe trigonal pyramid, edges with two equivalent O(9)LiTiCrFe tetrahedra, and  an edgeedge with one O(10)LiCrFe2 trigonal pyramid.
Li4Ti2Cr3Fe3O16 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 Cr(1)O6 octahedra, corners with two equivalent Cr(2)O6 octahedra, corners with three equivalent Ti(2)O6 octahedra, and corners with four equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-63°. The Li(1)-O(12) bond length is 2.02 Å. The Li(1)-O(3) bond length is 1.97 Å. Both Li(1)-O(9) bond lengths are 1.98 Å. 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 Cr(2)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, corners with three equivalent Ti(2)O6 octahedra,  an edgeedge with one Fe(1)O6 octahedra, and edges with two equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-64°. The Li(2)-O(5) bond length is 1.78 Å. The Li(2)-O(7) bond length is 1.97 Å. Both Li(2)-O(11) bond lengths are 1.94 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 trigonal pyramids that share  a cornercorner with one Fe(1)O6 octahedra, corners with two equivalent Cr(1)O6 octahedra, corners with three equivalent Ti(1)O6 octahedra,  an edgeedge with one Cr(2)O6 octahedra, and edges with two equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 63-64°. The Li(3)-O(4) bond length is 1.76 Å. The Li(3)-O(8) bond length is 1.94 Å. Both Li(3)-O(1) bond lengths are 1.95 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 Cr(2)O6 octahedra, corners with two equivalent Fe(1)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, corners with three equivalent Ti(1)O6 octahedra, and corners with four equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 53-63°. The Li(4)-O(10) bond length is 2.01 Å. The Li(4)-O(2) bond length is 1.95 Å. Both Li(4)-O(6) bond lengths are 1.95 Å. There are two inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(2), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form TiO6 octahedra that share corners with two equivalent Cr(2)O6 octahedra, corners with four equivalent Fe(2)O6 octahedra, corners with three equivalent Li(4)O4 tetrahedra, corners with three equivalent Li(3)O4 trigonal pyramids,  an edgeedge with one Fe(1)O6 octahedra, and edges with two equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-52°. The Ti(1)-O(2) bond length is 1.97 Å. The Ti(1)-O(8) bond length is 2.09 Å. Both Ti(1)-O(1) bond lengths are 2.01 Å. Both Ti(1)-O(6) bond lengths are 1.99 Å. In the second Ti site, Ti(2) 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 Cr(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra, corners with three equivalent Li(2)O4 tetrahedra,  an edgeedge with one Cr(2)O6 octahedra, and edges with two equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-53°. The Ti(2)-O(12) bond length is 2.16 Å. The Ti(2)-O(7) bond length is 1.90 Å. Both Ti(2)-O(11) bond lengths are 1.89 Å. Both Ti(2)-O(9) bond lengths are 2.13 Å. There are two inequivalent Cr sites. In the first Cr site, Cr(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 CrO6 octahedra that share corners with two equivalent Ti(2)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  a cornercorner with one Li(3)O4 trigonal pyramid,  an edgeedge with one Ti(1)O6 octahedra, edges with two equivalent Cr(1)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 50-52°. The Cr(1)-O(11) bond length is 2.06 Å. The Cr(1)-O(2) bond length is 2.01 Å. The Cr(1)-O(3) bond length is 1.97 Å. The Cr(1)-O(4) bond length is 1.95 Å. The Cr(1)-O(6) bond length is 2.02 Å. The Cr(1)-O(7) bond length is 2.07 Å. In the second Cr site, Cr(2) is bonded to one O(10), one O(5), two equivalent O(1), and two equivalent O(9) atoms to form CrO6 octahedra that share corners with two equivalent Ti(1)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(2)O6 octahedra, edges with four equivalent Fe(2)O6 octahedra, and  an edgeedge with one Li(3)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 52°. The Cr(2)-O(10) bond length is 1.97 Å. The Cr(2)-O(5) bond length is 1.97 Å. Both Cr(2)-O(1) bond lengths are 2.05 Å. Both Cr(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 Ti(2)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  a cornercorner with one Li(3)O4 trigonal pyramid,  an edgeedge with one Ti(1)O6 octahedra, edges with four equivalent Cr(1)O6 octahedra, and  an edgeedge with one Li(2)O4 tetrahedra. The corner-sharing octahedral tilt angles are 53°. The Fe(1)-O(3) bond length is 1.95 Å. The Fe(1)-O(4) bond length is 1.93 Å. Both Fe(1)-O(11) bond lengths are 2.11 Å. Both Fe(1)-O(6) bond lengths are 2.04 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 Ti(1)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(2)O6 octahedra, edges with two equivalent Cr(2)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, and  an edgeedge with one Li(3)O4 trigonal pyramid. The corner-sharing octahedral tilt angles range from 50-52°. The Fe(2)-O(1) bond length is 1.99 Å. The Fe(2)-O(10) bond length is 1.92 Å. The Fe(2)-O(12) bond length is 1.95 Å. The Fe(2)-O(5) bond length is 1.92 Å. The Fe(2)-O(8) bond length is 2.01 Å. The Fe(2)-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(1), one Cr(2), and one Fe(2) atom. In the second O site, O(2) is bonded in a distorted rectangular see-saw-like geometry to one Li(4), one Ti(1), and two equivalent Cr(1) atoms. In the third O site, O(3) is bonded to one Li(1), two equivalent Cr(1), and one Fe(1) atom to form distorted OLiCr2Fe trigonal pyramids that share  a cornercorner with one O(12)LiTiFe2 tetrahedra, corners with two equivalent O(9)LiTiCrFe tetrahedra, and corners with three equivalent O(4)LiCr2Fe tetrahedra. In the fourth O site, O(4) is bonded to one Li(3), two equivalent Cr(1), and one Fe(1) atom to form corner-sharing OLiCr2Fe tetrahedra. In the fifth O site, O(5) is bonded to one Li(2), one Cr(2), and two equivalent Fe(2) atoms to form OLiCrFe2 tetrahedra that share corners with two equivalent O(12)LiTiFe2 tetrahedra, corners with four equivalent O(9)LiTiCrFe tetrahedra, and corners with three equivalent O(10)LiCrFe2 trigonal pyramids. In the sixth O site, O(6) is bonded in a distorted rectangular see-saw-like geometry to one Li(4), one Ti(1), one Cr(1), and one Fe(1) atom. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), one Ti(2), and two equivalent Cr(1) atoms. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Li(3), one Ti(1), and two equivalent Fe(2) atoms. In the ninth O site, O(9) is bonded to one Li(1), one Ti(2), one Cr(2), and one Fe(2) atom to form distorted OLiTiCrFe tetrahedra that share  a cornercorner with one O(9)LiTiCrFe tetrahedra,  a cornercorner with one O(12)LiTiFe2 tetrahedra, corners with two equivalent O(5)LiCrFe2 tetrahedra,  a cornercorner with one O(3)LiCr2Fe trigonal pyramid,  an edgeedge with one O(9)LiTiCrFe tetrahedra,  an edgeedge with one O(12)LiTiFe2 tetrahedra, and  an edgeedge with one O(10)LiCrFe2 trigonal pyramid. In the tenth O site, O(10) is bonded to one Li(4), one Cr(2), and two equivalent Fe(2) atoms to form distorted OLiCrFe2 trigonal pyramids that share corners with three equivalent O(5)LiCrFe2 tetrahedra,  an edgeedge with one O(12)LiTiFe2 tetrahedra, and edges with two equivalent O(9)LiTiCrFe tetrahedra. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one Ti(2), one Cr(1), and one Fe(1) atom. In the twelfth O site, O(12) is bonded to one Li(1), one Ti(2), and two equivalent Fe(2) atoms to form distorted OLiTiFe2 tetrahedra that share corners with two equivalent O(5)LiCrFe2 tetrahedra, corners with two equivalent O(9)LiTiCrFe tetrahedra,  a cornercorner with one O(3)LiCr2Fe trigonal pyramid, edges with two equivalent O(9)LiTiCrFe tetrahedra, and  an edgeedge with one O(10)LiCrFe2 trigonal pyramid.