Li4Co5Ni3O16 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 Ni(1)O6 octahedra, corners with two equivalent Co(1)O6 octahedra, corners with two equivalent Co(3)O6 octahedra, corners with three equivalent Co(4)O6 octahedra, and corners with four equivalent Ni(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-62°. 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 Co(3)O6 octahedra, corners with two equivalent Ni(2)O6 octahedra, corners with three equivalent Co(4)O6 octahedra,  an edgeedge with one Ni(1)O6 octahedra, and edges with two equivalent Co(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 62-65°. 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 Ni(1)O6 octahedra, corners with two equivalent Co(1)O6 octahedra, corners with three equivalent Co(2)O6 octahedra,  an edgeedge with one Co(3)O6 octahedra, and edges with two equivalent Ni(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 61-64°. 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 Co(3)O6 octahedra, corners with two equivalent Ni(1)O6 octahedra, corners with two equivalent Ni(2)O6 octahedra, corners with three equivalent Co(2)O6 octahedra, and corners with four equivalent Co(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-62°. There are four inequivalent Co sites. In the first Co site, Co(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 CoO6 octahedra that share corners with two equivalent Co(4)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 Co(2)O6 octahedra, edges with two equivalent Co(1)O6 octahedra, edges with two equivalent Ni(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 Co site, Co(2) is bonded to one O(2), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form CoO6 octahedra that share corners with two equivalent Co(3)O6 octahedra, corners with four equivalent Ni(2)O6 octahedra, corners with three equivalent Li(4)O4 tetrahedra, corners with three equivalent Li(3)O4 trigonal pyramids,  an edgeedge with one Ni(1)O6 octahedra, and edges with two equivalent Co(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-52°. In the third Co site, Co(3) is bonded to one O(10), one O(5), two equivalent O(1), and two equivalent O(9) atoms to form CoO6 octahedra that share corners with two equivalent Co(2)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 Co(4)O6 octahedra, edges with four equivalent Ni(2)O6 octahedra, and  an edgeedge with one Li(3)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 51°. In the fourth Co site, Co(4) is bonded to one O(12), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form CoO6 octahedra that share corners with two equivalent Ni(1)O6 octahedra, corners with four equivalent Co(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra, corners with three equivalent Li(2)O4 tetrahedra,  an edgeedge with one Co(3)O6 octahedra, and edges with two equivalent Ni(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-52°. There are two inequivalent Ni sites. In the first Ni site, Ni(1) is bonded to one O(3), one O(4), two equivalent O(11), and two equivalent O(6) atoms to form NiO6 octahedra that share corners with two equivalent Co(4)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 Co(2)O6 octahedra, edges with four equivalent Co(1)O6 octahedra, and  an edgeedge with one Li(2)O4 tetrahedra. The corner-sharing octahedral tilt angles are 51°. In the second Ni site, Ni(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 NiO6 octahedra that share corners with two equivalent Co(2)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 Co(4)O6 octahedra, edges with two equivalent Co(3)O6 octahedra, edges with two equivalent Ni(2)O6 octahedra, and  an edgeedge with one Li(3)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 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 Co(2), one Co(3), and one Ni(2) atom. In the second O site, O(2) is bonded to one Li(4), one Co(2), and two equivalent Co(1) atoms to form distorted OLiCo3 tetrahedra that share  a cornercorner with one O(10)LiCoNi2 tetrahedra, corners with two equivalent O(4)LiCo2Ni tetrahedra, and  an edgeedge with one O(3)LiCo2Ni trigonal pyramid. In the third O site, O(3) is bonded to one Li(1), two equivalent Co(1), and one Ni(1) atom to form distorted OLiCo2Ni trigonal pyramids that share  a cornercorner with one O(12)LiCoNi2 tetrahedra, corners with two equivalent O(9)LiCo2Ni tetrahedra, corners with three equivalent O(4)LiCo2Ni tetrahedra, and  an edgeedge with one O(2)LiCo3 tetrahedra. In the fourth O site, O(4) is bonded to one Li(3), two equivalent Co(1), and one Ni(1) atom to form OLiCo2Ni tetrahedra that share corners with two equivalent O(2)LiCo3 tetrahedra and corners with three equivalent O(3)LiCo2Ni trigonal pyramids. In the fifth O site, O(5) is bonded to one Li(2), one Co(3), and two equivalent Ni(2) atoms to form OLiCoNi2 tetrahedra that share corners with two equivalent O(12)LiCoNi2 tetrahedra, corners with three equivalent O(10)LiCoNi2 tetrahedra, and corners with four equivalent O(9)LiCo2Ni tetrahedra. In the sixth O site, O(6) is bonded in a distorted rectangular see-saw-like geometry to one Li(4), one Co(1), one Co(2), and one Ni(1) atom. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), one Co(4), and two equivalent Co(1) atoms. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Li(3), one Co(2), and two equivalent Ni(2) atoms. In the ninth O site, O(9) is bonded to one Li(1), one Co(3), one Co(4), and one Ni(2) atom to form distorted OLiCo2Ni tetrahedra that share  a cornercorner with one O(9)LiCo2Ni tetrahedra,  a cornercorner with one O(12)LiCoNi2 tetrahedra, corners with two equivalent O(5)LiCoNi2 tetrahedra,  a cornercorner with one O(3)LiCo2Ni trigonal pyramid,  an edgeedge with one O(9)LiCo2Ni tetrahedra,  an edgeedge with one O(10)LiCoNi2 tetrahedra, and  an edgeedge with one O(12)LiCoNi2 tetrahedra. In the tenth O site, O(10) is bonded to one Li(4), one Co(3), and two equivalent Ni(2) atoms to form distorted OLiCoNi2 tetrahedra that share  a cornercorner with one O(2)LiCo3 tetrahedra, corners with three equivalent O(5)LiCoNi2 tetrahedra,  an edgeedge with one O(12)LiCoNi2 tetrahedra, and edges with two equivalent O(9)LiCo2Ni tetrahedra. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one Co(1), one Co(4), and one Ni(1) atom. In the twelfth O site, O(12) is bonded to one Li(1), one Co(4), and two equivalent Ni(2) atoms to form distorted OLiCoNi2 tetrahedra that share corners with two equivalent O(9)LiCo2Ni tetrahedra, corners with two equivalent O(5)LiCoNi2 tetrahedra,  a cornercorner with one O(3)LiCo2Ni trigonal pyramid,  an edgeedge with one O(10)LiCoNi2 tetrahedra, and edges with two equivalent O(9)LiCo2Ni tetrahedra.
Li4Co5Ni3O16 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 Ni(1)O6 octahedra, corners with two equivalent Co(1)O6 octahedra, corners with two equivalent Co(3)O6 octahedra, corners with three equivalent Co(4)O6 octahedra, and corners with four equivalent Ni(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-62°. The Li(1)-O(12) bond length is 1.91 Å. The Li(1)-O(3) bond length is 1.95 Å. Both Li(1)-O(9) bond lengths are 1.88 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 Co(3)O6 octahedra, corners with two equivalent Ni(2)O6 octahedra, corners with three equivalent Co(4)O6 octahedra,  an edgeedge with one Ni(1)O6 octahedra, and edges with two equivalent Co(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 62-65°. The Li(2)-O(5) bond length is 1.74 Å. The Li(2)-O(7) bond length is 1.87 Å. Both Li(2)-O(11) bond lengths are 1.83 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 Ni(1)O6 octahedra, corners with two equivalent Co(1)O6 octahedra, corners with three equivalent Co(2)O6 octahedra,  an edgeedge with one Co(3)O6 octahedra, and edges with two equivalent Ni(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 61-64°. The Li(3)-O(4) bond length is 1.73 Å. The Li(3)-O(8) bond length is 1.85 Å. Both Li(3)-O(1) bond lengths are 1.83 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 Co(3)O6 octahedra, corners with two equivalent Ni(1)O6 octahedra, corners with two equivalent Ni(2)O6 octahedra, corners with three equivalent Co(2)O6 octahedra, and corners with four equivalent Co(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-62°. The Li(4)-O(10) bond length is 1.97 Å. The Li(4)-O(2) bond length is 1.88 Å. Both Li(4)-O(6) bond lengths are 1.90 Å. There are four inequivalent Co sites. In the first Co site, Co(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 CoO6 octahedra that share corners with two equivalent Co(4)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 Co(2)O6 octahedra, edges with two equivalent Co(1)O6 octahedra, edges with two equivalent Ni(1)O6 octahedra, and  an edgeedge with one Li(2)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 51-52°. The Co(1)-O(11) bond length is 1.95 Å. The Co(1)-O(2) bond length is 1.88 Å. The Co(1)-O(3) bond length is 1.86 Å. The Co(1)-O(4) bond length is 1.86 Å. The Co(1)-O(6) bond length is 1.91 Å. The Co(1)-O(7) bond length is 1.92 Å. In the second Co site, Co(2) is bonded to one O(2), one O(8), two equivalent O(1), and two equivalent O(6) atoms to form CoO6 octahedra that share corners with two equivalent Co(3)O6 octahedra, corners with four equivalent Ni(2)O6 octahedra, corners with three equivalent Li(4)O4 tetrahedra, corners with three equivalent Li(3)O4 trigonal pyramids,  an edgeedge with one Ni(1)O6 octahedra, and edges with two equivalent Co(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-52°. The Co(2)-O(2) bond length is 1.93 Å. The Co(2)-O(8) bond length is 1.98 Å. Both Co(2)-O(1) bond lengths are 1.95 Å. Both Co(2)-O(6) bond lengths are 1.95 Å. In the third Co site, Co(3) is bonded to one O(10), one O(5), two equivalent O(1), and two equivalent O(9) atoms to form CoO6 octahedra that share corners with two equivalent Co(2)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 Co(4)O6 octahedra, edges with four equivalent Ni(2)O6 octahedra, and  an edgeedge with one Li(3)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 51°. The Co(3)-O(10) bond length is 1.86 Å. The Co(3)-O(5) bond length is 1.87 Å. Both Co(3)-O(1) bond lengths are 1.94 Å. Both Co(3)-O(9) bond lengths are 1.91 Å. In the fourth Co site, Co(4) is bonded to one O(12), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form CoO6 octahedra that share corners with two equivalent Ni(1)O6 octahedra, corners with four equivalent Co(1)O6 octahedra, corners with three equivalent Li(1)O4 tetrahedra, corners with three equivalent Li(2)O4 tetrahedra,  an edgeedge with one Co(3)O6 octahedra, and edges with two equivalent Ni(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-52°. The Co(4)-O(12) bond length is 1.93 Å. The Co(4)-O(7) bond length is 1.95 Å. Both Co(4)-O(11) bond lengths are 1.97 Å. Both Co(4)-O(9) bond lengths are 1.93 Å. There are two inequivalent Ni sites. In the first Ni site, Ni(1) is bonded to one O(3), one O(4), two equivalent O(11), and two equivalent O(6) atoms to form NiO6 octahedra that share corners with two equivalent Co(4)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 Co(2)O6 octahedra, edges with four equivalent Co(1)O6 octahedra, and  an edgeedge with one Li(2)O4 tetrahedra. The corner-sharing octahedral tilt angles are 51°. The Ni(1)-O(3) bond length is 1.83 Å. The Ni(1)-O(4) bond length is 1.84 Å. Both Ni(1)-O(11) bond lengths are 1.93 Å. Both Ni(1)-O(6) bond lengths are 1.90 Å. In the second Ni site, Ni(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 NiO6 octahedra that share corners with two equivalent Co(2)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 Co(4)O6 octahedra, edges with two equivalent Co(3)O6 octahedra, edges with two equivalent Ni(2)O6 octahedra, and  an edgeedge with one Li(3)O4 trigonal pyramid. The corner-sharing octahedral tilt angles are 52°. The Ni(2)-O(1) bond length is 1.92 Å. The Ni(2)-O(10) bond length is 1.84 Å. The Ni(2)-O(12) bond length is 1.90 Å. The Ni(2)-O(5) bond length is 1.84 Å. The Ni(2)-O(8) bond length is 1.93 Å. The Ni(2)-O(9) bond length is 1.89 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 Co(2), one Co(3), and one Ni(2) atom. In the second O site, O(2) is bonded to one Li(4), one Co(2), and two equivalent Co(1) atoms to form distorted OLiCo3 tetrahedra that share  a cornercorner with one O(10)LiCoNi2 tetrahedra, corners with two equivalent O(4)LiCo2Ni tetrahedra, and  an edgeedge with one O(3)LiCo2Ni trigonal pyramid. In the third O site, O(3) is bonded to one Li(1), two equivalent Co(1), and one Ni(1) atom to form distorted OLiCo2Ni trigonal pyramids that share  a cornercorner with one O(12)LiCoNi2 tetrahedra, corners with two equivalent O(9)LiCo2Ni tetrahedra, corners with three equivalent O(4)LiCo2Ni tetrahedra, and  an edgeedge with one O(2)LiCo3 tetrahedra. In the fourth O site, O(4) is bonded to one Li(3), two equivalent Co(1), and one Ni(1) atom to form OLiCo2Ni tetrahedra that share corners with two equivalent O(2)LiCo3 tetrahedra and corners with three equivalent O(3)LiCo2Ni trigonal pyramids. In the fifth O site, O(5) is bonded to one Li(2), one Co(3), and two equivalent Ni(2) atoms to form OLiCoNi2 tetrahedra that share corners with two equivalent O(12)LiCoNi2 tetrahedra, corners with three equivalent O(10)LiCoNi2 tetrahedra, and corners with four equivalent O(9)LiCo2Ni tetrahedra. In the sixth O site, O(6) is bonded in a distorted rectangular see-saw-like geometry to one Li(4), one Co(1), one Co(2), and one Ni(1) atom. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(2), one Co(4), and two equivalent Co(1) atoms. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Li(3), one Co(2), and two equivalent Ni(2) atoms. In the ninth O site, O(9) is bonded to one Li(1), one Co(3), one Co(4), and one Ni(2) atom to form distorted OLiCo2Ni tetrahedra that share  a cornercorner with one O(9)LiCo2Ni tetrahedra,  a cornercorner with one O(12)LiCoNi2 tetrahedra, corners with two equivalent O(5)LiCoNi2 tetrahedra,  a cornercorner with one O(3)LiCo2Ni trigonal pyramid,  an edgeedge with one O(9)LiCo2Ni tetrahedra,  an edgeedge with one O(10)LiCoNi2 tetrahedra, and  an edgeedge with one O(12)LiCoNi2 tetrahedra. In the tenth O site, O(10) is bonded to one Li(4), one Co(3), and two equivalent Ni(2) atoms to form distorted OLiCoNi2 tetrahedra that share  a cornercorner with one O(2)LiCo3 tetrahedra, corners with three equivalent O(5)LiCoNi2 tetrahedra,  an edgeedge with one O(12)LiCoNi2 tetrahedra, and edges with two equivalent O(9)LiCo2Ni tetrahedra. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(2), one Co(1), one Co(4), and one Ni(1) atom. In the twelfth O site, O(12) is bonded to one Li(1), one Co(4), and two equivalent Ni(2) atoms to form distorted OLiCoNi2 tetrahedra that share corners with two equivalent O(9)LiCo2Ni tetrahedra, corners with two equivalent O(5)LiCoNi2 tetrahedra,  a cornercorner with one O(3)LiCo2Ni trigonal pyramid,  an edgeedge with one O(10)LiCoNi2 tetrahedra, and edges with two equivalent O(9)LiCo2Ni tetrahedra.