Li4Cr3Mn2Fe3O16 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 Mn(2)O6 octahedra, and corners with four equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 54-64°. 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 Mn(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 61-64°. 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 tetrahedra that share  a cornercorner with one Fe(1)O6 octahedra, corners with two equivalent Cr(1)O6 octahedra, corners with three equivalent Mn(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 62-65°. 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 Cr(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 Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-63°. 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 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 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 are 51°. 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 Mn(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 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 51°. 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 Cr(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 Cr(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 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 50-51°. 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, edges with four equivalent Cr(1)O6 octahedra, and  an edgeedge with one Li(2)O4 tetrahedra. 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(2)O4 tetrahedra,  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 Cr(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 are 50°. 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 Cr(2), one Mn(1), and one Fe(2) atom. In the second O site, O(2) is bonded to one Li(4), two equivalent Cr(1), and one Mn(1) atom to form distorted OLiMnCr2 trigonal pyramids that share corners with two equivalent O(4)LiCr2Fe tetrahedra,  a cornercorner with one O(10)LiCrFe2 trigonal pyramid, and  an edgeedge with one O(3)LiCr2Fe trigonal pyramid. 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)LiMnFe2 tetrahedra, corners with three equivalent O(4)LiCr2Fe tetrahedra, and  an edgeedge with one O(2)LiMnCr2 trigonal pyramid. In the fourth O site, O(4) is bonded to one Li(3), two equivalent Cr(1), and one Fe(1) atom to form OLiCr2Fe tetrahedra that share corners with two equivalent O(2)LiMnCr2 trigonal pyramids and corners with three equivalent O(3)LiCr2Fe trigonal pyramids. 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)LiMnFe2 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 Cr(1), one Mn(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), two equivalent Cr(1), and one Mn(2) atom. In the eighth O site, O(8) is bonded in a 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 Cr(2), one Mn(2), and one Fe(2) atom. 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,  a cornercorner with one O(2)LiMnCr2 trigonal pyramid, and  an edgeedge with one O(12)LiMnFe2 tetrahedra. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one Cr(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 OLiMnFe2 tetrahedra that share corners with two equivalent O(5)LiCrFe2 tetrahedra,  a cornercorner with one O(3)LiCr2Fe trigonal pyramid, and  an edgeedge with one O(10)LiCrFe2 trigonal pyramid.
Li4Cr3Mn2Fe3O16 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 Mn(2)O6 octahedra, and corners with four equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 54-64°. The Li(1)-O(12) bond length is 1.99 Å. The Li(1)-O(3) bond length is 1.95 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 Mn(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 61-64°. The Li(2)-O(5) bond length is 1.77 Å. The Li(2)-O(7) bond length is 1.97 Å. Both Li(2)-O(11) bond lengths are 1.97 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 Cr(1)O6 octahedra, corners with three equivalent Mn(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 62-65°. The Li(3)-O(4) bond length is 1.77 Å. The Li(3)-O(8) bond length is 2.00 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 Cr(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 Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-63°. The Li(4)-O(10) bond length is 1.95 Å. The Li(4)-O(2) bond length is 2.00 Å. Both Li(4)-O(6) bond lengths are 1.98 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 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 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 are 51°. The Cr(1)-O(11) bond length is 2.04 Å. The Cr(1)-O(2) bond length is 1.99 Å. The Cr(1)-O(3) bond length is 1.94 Å. The Cr(1)-O(4) bond length is 1.96 Å. The Cr(1)-O(6) bond length is 2.00 Å. The Cr(1)-O(7) bond length is 2.02 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 Mn(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 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 51°. The Cr(2)-O(10) bond length is 1.95 Å. The Cr(2)-O(5) bond length is 1.96 Å. Both Cr(2)-O(1) bond lengths are 2.05 Å. Both Cr(2)-O(9) bond lengths are 2.00 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 Cr(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 Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-51°. The Mn(1)-O(2) bond length is 2.00 Å. The Mn(1)-O(8) bond length is 1.98 Å. Both Mn(1)-O(1) bond lengths are 2.00 Å. Both Mn(1)-O(6) bond lengths are 1.98 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 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 50-51°. The Mn(2)-O(12) bond length is 1.97 Å. The Mn(2)-O(7) bond length is 2.06 Å. Both Mn(2)-O(11) bond lengths are 1.99 Å. Both Mn(2)-O(9) bond lengths are 1.96 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, edges with four equivalent Cr(1)O6 octahedra, and  an edgeedge with one Li(2)O4 tetrahedra. The corner-sharing octahedral tilt angles are 50°. The Fe(1)-O(3) bond length is 1.98 Å. The Fe(1)-O(4) bond length is 1.96 Å. Both Fe(1)-O(11) bond lengths are 2.04 Å. Both Fe(1)-O(6) bond lengths are 2.03 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(2)O4 tetrahedra,  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 Cr(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 are 50°. The Fe(2)-O(1) bond length is 2.05 Å. The Fe(2)-O(10) bond length is 1.96 Å. The Fe(2)-O(12) bond length is 2.03 Å. The Fe(2)-O(5) bond length is 1.95 Å. The Fe(2)-O(8) bond length is 2.04 Å. The Fe(2)-O(9) bond length is 2.07 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 Cr(2), one Mn(1), and one Fe(2) atom. In the second O site, O(2) is bonded to one Li(4), two equivalent Cr(1), and one Mn(1) atom to form distorted OLiMnCr2 trigonal pyramids that share corners with two equivalent O(4)LiCr2Fe tetrahedra,  a cornercorner with one O(10)LiCrFe2 trigonal pyramid, and  an edgeedge with one O(3)LiCr2Fe trigonal pyramid. 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)LiMnFe2 tetrahedra, corners with three equivalent O(4)LiCr2Fe tetrahedra, and  an edgeedge with one O(2)LiMnCr2 trigonal pyramid. In the fourth O site, O(4) is bonded to one Li(3), two equivalent Cr(1), and one Fe(1) atom to form OLiCr2Fe tetrahedra that share corners with two equivalent O(2)LiMnCr2 trigonal pyramids and corners with three equivalent O(3)LiCr2Fe trigonal pyramids. 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)LiMnFe2 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 Cr(1), one Mn(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), two equivalent Cr(1), and one Mn(2) atom. In the eighth O site, O(8) is bonded in a 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 Cr(2), one Mn(2), and one Fe(2) atom. 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,  a cornercorner with one O(2)LiMnCr2 trigonal pyramid, and  an edgeedge with one O(12)LiMnFe2 tetrahedra. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one Cr(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 OLiMnFe2 tetrahedra that share corners with two equivalent O(5)LiCrFe2 tetrahedra,  a cornercorner with one O(3)LiCr2Fe trigonal pyramid, and  an edgeedge with one O(10)LiCrFe2 trigonal pyramid.