Li4Cr2Mn3Fe3O16 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 Mn(1)O6 octahedra, corners with two equivalent Fe(1)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, corners with three equivalent Cr(2)O6 octahedra, and corners with four equivalent Mn(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-63°. 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 Fe(2)O6 octahedra, corners with two equivalent Mn(2)O6 octahedra, corners with three equivalent Cr(2)O6 octahedra,  an edgeedge with one Mn(1)O6 octahedra, and edges with two equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 60-64°. 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 Fe(2)O6 octahedra, corners with two equivalent Mn(1)O6 octahedra, corners with two equivalent Mn(2)O6 octahedra, corners with three equivalent Cr(1)O6 octahedra, and corners with four equivalent Fe(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(2), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form CrO6 octahedra that share corners with two equivalent Fe(2)O6 octahedra, corners with four equivalent Mn(2)O6 octahedra, corners with three equivalent Li(4)O4 tetrahedra,  an edgeedge with one Mn(1)O6 octahedra, and edges with two equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-53°. In the second Cr site, Cr(2) is bonded to one O(12), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form CrO6 octahedra that share corners with two equivalent Mn(1)O6 octahedra, corners with four equivalent Fe(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra, corners with three equivalent Li(2)O4 tetrahedra,  an edgeedge with one Fe(2)O6 octahedra, and edges with two equivalent Mn(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-52°. There are two inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to one O(3), one O(4), two equivalent O(11), and two equivalent O(6) atoms to form MnO6 octahedra that share corners with two equivalent Cr(2)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Cr(1)O6 octahedra, edges with four 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 Mn site, Mn(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 MnO6 octahedra that share corners with two equivalent Cr(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 Cr(2)O6 octahedra, edges with two equivalent Mn(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(11), one O(2), one O(3), one O(4), one O(6), and one O(7) atom to form FeO6 octahedra that share corners with two equivalent Cr(2)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Cr(1)O6 octahedra, edges with two equivalent Mn(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 51-52°. In the second Fe site, Fe(2) is bonded to one O(10), one O(5), two equivalent O(1), and two equivalent O(9) atoms to form FeO6 octahedra that share corners with two equivalent Cr(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 Cr(2)O6 octahedra, and edges with four equivalent Mn(2)O6 octahedra. The corner-sharing octahedral tilt angles are 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 Cr(1), one Mn(2), and one Fe(2) atom. In the second O site, O(2) is bonded to one Li(4), one Cr(1), and two equivalent Fe(1) atoms to form distorted corner-sharing OLiCrFe2 tetrahedra. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Li(1), one Mn(1), and two equivalent Fe(1) atoms. In the fourth O site, O(4) is bonded to one Li(3), one Mn(1), and two equivalent Fe(1) atoms to form distorted corner-sharing OLiMnFe2 tetrahedra. In the fifth O site, O(5) is bonded to one Li(2), two equivalent Mn(2), and one Fe(2) atom to form distorted OLiMn2Fe tetrahedra that share corners with two equivalent O(12)LiMn2Cr tetrahedra and corners with four equivalent O(9)LiMnCrFe tetrahedra. 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), one Cr(2), and two equivalent Fe(1) atoms. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Li(3), one Cr(1), and two equivalent Mn(2) atoms. In the ninth O site, O(9) is bonded to one Li(1), one Cr(2), one Mn(2), and one Fe(2) atom to form distorted OLiMnCrFe tetrahedra that share  a cornercorner with one O(12)LiMn2Cr tetrahedra,  a cornercorner with one O(9)LiMnCrFe tetrahedra, corners with two equivalent O(5)LiMn2Fe tetrahedra,  an edgeedge with one O(12)LiMn2Cr tetrahedra, and  an edgeedge with one O(9)LiMnCrFe tetrahedra. In the tenth O site, O(10) is bonded in a rectangular see-saw-like geometry to one Li(4), two equivalent Mn(2), and one Fe(2) atom. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one Cr(2), one Mn(1), and one Fe(1) atom. In the twelfth O site, O(12) is bonded to one Li(1), one Cr(2), and two equivalent Mn(2) atoms to form distorted OLiMn2Cr tetrahedra that share corners with two equivalent O(5)LiMn2Fe tetrahedra, corners with two equivalent O(9)LiMnCrFe tetrahedra, and edges with two equivalent O(9)LiMnCrFe tetrahedra.
Li4Cr2Mn3Fe3O16 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 Mn(1)O6 octahedra, corners with two equivalent Fe(1)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, corners with three equivalent Cr(2)O6 octahedra, and corners with four equivalent Mn(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-63°. The Li(1)-O(12) bond length is 2.00 Å. The Li(1)-O(3) bond length is 1.99 Å. Both Li(1)-O(9) bond lengths are 1.94 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 Fe(2)O6 octahedra, corners with two equivalent Mn(2)O6 octahedra, corners with three equivalent Cr(2)O6 octahedra,  an edgeedge with one Mn(1)O6 octahedra, and edges with two equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 60-64°. The Li(2)-O(5) bond length is 1.78 Å. The Li(2)-O(7) bond length is 1.95 Å. Both Li(2)-O(11) bond lengths are 1.92 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 1.77 Å. The Li(3)-O(8) bond length is 1.93 Å. Both Li(3)-O(1) bond lengths are 1.93 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 Fe(2)O6 octahedra, corners with two equivalent Mn(1)O6 octahedra, corners with two equivalent Mn(2)O6 octahedra, corners with three equivalent Cr(1)O6 octahedra, and corners with four equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-63°. The Li(4)-O(10) bond length is 2.04 Å. The Li(4)-O(2) bond length is 1.94 Å. Both Li(4)-O(6) bond lengths are 1.95 Å. There are two inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(2), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form CrO6 octahedra that share corners with two equivalent Fe(2)O6 octahedra, corners with four equivalent Mn(2)O6 octahedra, corners with three equivalent Li(4)O4 tetrahedra,  an edgeedge with one Mn(1)O6 octahedra, and edges with two equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-53°. The Cr(1)-O(2) bond length is 2.01 Å. The Cr(1)-O(8) bond length is 2.12 Å. Both Cr(1)-O(1) bond lengths are 2.04 Å. Both Cr(1)-O(6) bond lengths are 2.05 Å. In the second Cr site, Cr(2) is bonded to one O(12), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form CrO6 octahedra that share corners with two equivalent Mn(1)O6 octahedra, corners with four equivalent Fe(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra, corners with three equivalent Li(2)O4 tetrahedra,  an edgeedge with one Fe(2)O6 octahedra, and edges with two equivalent Mn(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-52°. The Cr(2)-O(12) bond length is 2.10 Å. The Cr(2)-O(7) bond length is 2.00 Å. Both Cr(2)-O(11) bond lengths are 2.04 Å. Both Cr(2)-O(9) bond lengths are 2.04 Å. There are two inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to one O(3), one O(4), two equivalent O(11), and two equivalent O(6) atoms to form MnO6 octahedra that share corners with two equivalent Cr(2)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Cr(1)O6 octahedra, edges with four equivalent Fe(1)O6 octahedra, and  an edgeedge with one Li(2)O4 tetrahedra. The corner-sharing octahedral tilt angles are 51°. The Mn(1)-O(3) bond length is 1.93 Å. The Mn(1)-O(4) bond length is 1.91 Å. Both Mn(1)-O(11) bond lengths are 1.99 Å. Both Mn(1)-O(6) bond lengths are 1.95 Å. In the second Mn site, Mn(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 MnO6 octahedra that share corners with two equivalent Cr(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 Cr(2)O6 octahedra, edges with two equivalent Mn(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(1) bond length is 1.97 Å. The Mn(2)-O(10) bond length is 1.93 Å. The Mn(2)-O(12) bond length is 1.96 Å. The Mn(2)-O(5) bond length is 1.92 Å. The Mn(2)-O(8) bond length is 1.97 Å. The Mn(2)-O(9) bond length is 1.94 Å. There are two inequivalent Fe sites. In the first Fe site, Fe(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 FeO6 octahedra that share corners with two equivalent Cr(2)O6 octahedra,  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Cr(1)O6 octahedra, edges with two equivalent Mn(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 51-52°. The Fe(1)-O(11) bond length is 2.05 Å. The Fe(1)-O(2) bond length is 2.01 Å. The Fe(1)-O(3) bond length is 1.99 Å. The Fe(1)-O(4) bond length is 1.96 Å. The Fe(1)-O(6) bond length is 2.06 Å. The Fe(1)-O(7) bond length is 2.02 Å. In the second Fe site, Fe(2) is bonded to one O(10), one O(5), two equivalent O(1), and two equivalent O(9) atoms to form FeO6 octahedra that share corners with two equivalent Cr(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 Cr(2)O6 octahedra, and edges with four equivalent Mn(2)O6 octahedra. The corner-sharing octahedral tilt angles are 53°. The Fe(2)-O(10) bond length is 2.01 Å. The Fe(2)-O(5) bond length is 1.99 Å. Both Fe(2)-O(1) bond lengths are 2.03 Å. Both Fe(2)-O(9) bond lengths are 2.05 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(1), one Mn(2), and one Fe(2) atom. In the second O site, O(2) is bonded to one Li(4), one Cr(1), and two equivalent Fe(1) atoms to form distorted corner-sharing OLiCrFe2 tetrahedra. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Li(1), one Mn(1), and two equivalent Fe(1) atoms. In the fourth O site, O(4) is bonded to one Li(3), one Mn(1), and two equivalent Fe(1) atoms to form distorted corner-sharing OLiMnFe2 tetrahedra. In the fifth O site, O(5) is bonded to one Li(2), two equivalent Mn(2), and one Fe(2) atom to form distorted OLiMn2Fe tetrahedra that share corners with two equivalent O(12)LiMn2Cr tetrahedra and corners with four equivalent O(9)LiMnCrFe tetrahedra. 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), one Cr(2), and two equivalent Fe(1) atoms. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Li(3), one Cr(1), and two equivalent Mn(2) atoms. In the ninth O site, O(9) is bonded to one Li(1), one Cr(2), one Mn(2), and one Fe(2) atom to form distorted OLiMnCrFe tetrahedra that share  a cornercorner with one O(12)LiMn2Cr tetrahedra,  a cornercorner with one O(9)LiMnCrFe tetrahedra, corners with two equivalent O(5)LiMn2Fe tetrahedra,  an edgeedge with one O(12)LiMn2Cr tetrahedra, and  an edgeedge with one O(9)LiMnCrFe tetrahedra. In the tenth O site, O(10) is bonded in a rectangular see-saw-like geometry to one Li(4), two equivalent Mn(2), and one Fe(2) atom. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one Cr(2), one Mn(1), and one Fe(1) atom. In the twelfth O site, O(12) is bonded to one Li(1), one Cr(2), and two equivalent Mn(2) atoms to form distorted OLiMn2Cr tetrahedra that share corners with two equivalent O(5)LiMn2Fe tetrahedra, corners with two equivalent O(9)LiMnCrFe tetrahedra, and edges with two equivalent O(9)LiMnCrFe tetrahedra.