Li2MgCo13O28 crystallizes in the triclinic P-1 space group. Li(1) is bonded to one O(10), one O(11), one O(12), one O(13), one O(3), and one O(6) atom to form LiO6 octahedra that share  a cornercorner with one Co(3)O6 octahedra,  a cornercorner with one Co(6)O6 octahedra,  a cornercorner with one Co(7)O6 octahedra, corners with three equivalent Co(5)O6 octahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Co(3)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra,  an edgeedge with one Co(6)O6 octahedra, and edges with two equivalent Co(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 11-16°. Mg(1) is bonded to two equivalent O(11), two equivalent O(13), and two equivalent O(7) atoms to form MgO6 octahedra that share edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Co(3)O6 octahedra, edges with two equivalent Co(4)O6 octahedra, and edges with two equivalent Co(5)O6 octahedra. There are seven inequivalent Co sites. In the first Co site, Co(1) is bonded to one O(1), one O(2), one O(4), one O(5), one O(8), and one O(9) atom to form edge-sharing CoO6 octahedra. In the second Co site, Co(2) is bonded to one O(1), one O(10), one O(12), one O(4), and two equivalent O(6) atoms to form CoO6 octahedra that share  an edgeedge with one Co(1)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra,  an edgeedge with one Co(5)O6 octahedra,  an edgeedge with one Co(7)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, and edges with two equivalent Co(6)O6 octahedra. In the third Co site, Co(3) is bonded to one O(11), one O(2), one O(5), one O(7), and two equivalent O(3) atoms to form CoO6 octahedra that share  a cornercorner with one Li(1)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra,  an edgeedge with one Co(3)O6 octahedra,  an edgeedge with one Co(5)O6 octahedra, and edges with two equivalent Co(4)O6 octahedra. The corner-sharing octahedral tilt angles are 15°. In the fourth Co site, Co(4) is bonded to one O(13), one O(14), one O(2), one O(3), one O(7), and one O(9) atom to form CoO6 octahedra that share  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra,  an edgeedge with one Co(5)O6 octahedra,  an edgeedge with one Co(6)O6 octahedra, and edges with two equivalent Co(3)O6 octahedra. In the fifth Co site, Co(5) is bonded to one O(10), one O(11), one O(13), one O(14), one O(4), and one O(5) atom to form CoO6 octahedra that share corners with three equivalent Li(1)O6 octahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra,  an edgeedge with one Co(3)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra, and  an edgeedge with one Co(6)O6 octahedra. The corner-sharing octahedral tilt angles range from 11-16°. In the sixth Co site, Co(6) is bonded to one O(10), one O(12), one O(14), one O(6), one O(8), and one O(9) atom to form CoO6 octahedra that share  a cornercorner with one Li(1)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra,  an edgeedge with one Co(5)O6 octahedra,  an edgeedge with one Co(7)O6 octahedra, and edges with two equivalent Co(2)O6 octahedra. The corner-sharing octahedral tilt angles are 14°. In the seventh Co site, Co(7) is bonded to two equivalent O(1), two equivalent O(12), and two equivalent O(8) atoms to form CoO6 octahedra that share corners with two equivalent Li(1)O6 octahedra, edges with two equivalent Co(1)O6 octahedra, edges with two equivalent Co(2)O6 octahedra, and edges with two equivalent Co(6)O6 octahedra. The corner-sharing octahedral tilt angles are 13°. There are fourteen inequivalent O sites. In the first O site, O(1) is bonded in a distorted T-shaped geometry to one Co(1), one Co(2), and one Co(7) atom. In the second O site, O(2) is bonded in a distorted trigonal non-coplanar geometry to one Co(1), one Co(3), and one Co(4) atom. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Li(1), one Co(4), and two equivalent Co(3) atoms. In the fourth O site, O(4) is bonded in a distorted T-shaped geometry to one Co(1), one Co(2), and one Co(5) atom. In the fifth O site, O(5) is bonded in a distorted T-shaped geometry to one Co(1), one Co(3), and one Co(5) atom. In the sixth O site, O(6) is bonded in a rectangular see-saw-like geometry to one Li(1), one Co(6), and two equivalent Co(2) atoms. In the seventh O site, O(7) is bonded in a distorted T-shaped geometry to one Mg(1), one Co(3), and one Co(4) atom. In the eighth O site, O(8) is bonded in a distorted T-shaped geometry to one Co(1), one Co(6), and one Co(7) atom. In the ninth O site, O(9) is bonded in a distorted T-shaped geometry to one Co(1), one Co(4), and one Co(6) atom. In the tenth O site, O(10) is bonded in a rectangular see-saw-like geometry to one Li(1), one Co(2), one Co(5), and one Co(6) atom. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(1), one Mg(1), one Co(3), and one Co(5) atom. In the twelfth O site, O(12) is bonded in a rectangular see-saw-like geometry to one Li(1), one Co(2), one Co(6), and one Co(7) atom. In the thirteenth O site, O(13) is bonded in a rectangular see-saw-like geometry to one Li(1), one Mg(1), one Co(4), and one Co(5) atom. In the fourteenth O site, O(14) is bonded in a distorted T-shaped geometry to one Co(4), one Co(5), and one Co(6) atom.
Li2MgCo13O28 crystallizes in the triclinic P-1 space group. Li(1) is bonded to one O(10), one O(11), one O(12), one O(13), one O(3), and one O(6) atom to form LiO6 octahedra that share  a cornercorner with one Co(3)O6 octahedra,  a cornercorner with one Co(6)O6 octahedra,  a cornercorner with one Co(7)O6 octahedra, corners with three equivalent Co(5)O6 octahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Co(3)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra,  an edgeedge with one Co(6)O6 octahedra, and edges with two equivalent Co(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 11-16°. The Li(1)-O(10) bond length is 2.18 Å. The Li(1)-O(11) bond length is 2.26 Å. The Li(1)-O(12) bond length is 2.25 Å. The Li(1)-O(13) bond length is 2.20 Å. The Li(1)-O(3) bond length is 2.09 Å. The Li(1)-O(6) bond length is 2.18 Å. Mg(1) is bonded to two equivalent O(11), two equivalent O(13), and two equivalent O(7) atoms to form MgO6 octahedra that share edges with two equivalent Li(1)O6 octahedra, edges with two equivalent Co(3)O6 octahedra, edges with two equivalent Co(4)O6 octahedra, and edges with two equivalent Co(5)O6 octahedra. Both Mg(1)-O(11) bond lengths are 2.02 Å. Both Mg(1)-O(13) bond lengths are 2.02 Å. Both Mg(1)-O(7) bond lengths are 2.07 Å. There are seven inequivalent Co sites. In the first Co site, Co(1) is bonded to one O(1), one O(2), one O(4), one O(5), one O(8), and one O(9) atom to form edge-sharing CoO6 octahedra. The Co(1)-O(1) bond length is 1.90 Å. The Co(1)-O(2) bond length is 1.87 Å. The Co(1)-O(4) bond length is 1.89 Å. The Co(1)-O(5) bond length is 1.88 Å. The Co(1)-O(8) bond length is 1.91 Å. The Co(1)-O(9) bond length is 1.89 Å. In the second Co site, Co(2) is bonded to one O(1), one O(10), one O(12), one O(4), and two equivalent O(6) atoms to form CoO6 octahedra that share  an edgeedge with one Co(1)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra,  an edgeedge with one Co(5)O6 octahedra,  an edgeedge with one Co(7)O6 octahedra, edges with two equivalent Li(1)O6 octahedra, and edges with two equivalent Co(6)O6 octahedra. The Co(2)-O(1) bond length is 1.89 Å. The Co(2)-O(10) bond length is 1.89 Å. The Co(2)-O(12) bond length is 1.89 Å. The Co(2)-O(4) bond length is 1.87 Å. Both Co(2)-O(6) bond lengths are 1.90 Å. In the third Co site, Co(3) is bonded to one O(11), one O(2), one O(5), one O(7), and two equivalent O(3) atoms to form CoO6 octahedra that share  a cornercorner with one Li(1)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra,  an edgeedge with one Co(3)O6 octahedra,  an edgeedge with one Co(5)O6 octahedra, and edges with two equivalent Co(4)O6 octahedra. The corner-sharing octahedral tilt angles are 15°. The Co(3)-O(11) bond length is 1.86 Å. The Co(3)-O(2) bond length is 1.90 Å. The Co(3)-O(5) bond length is 1.91 Å. The Co(3)-O(7) bond length is 1.84 Å. Both Co(3)-O(3) bond lengths are 1.91 Å. In the fourth Co site, Co(4) is bonded to one O(13), one O(14), one O(2), one O(3), one O(7), and one O(9) atom to form CoO6 octahedra that share  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra,  an edgeedge with one Co(5)O6 octahedra,  an edgeedge with one Co(6)O6 octahedra, and edges with two equivalent Co(3)O6 octahedra. The Co(4)-O(13) bond length is 1.86 Å. The Co(4)-O(14) bond length is 1.91 Å. The Co(4)-O(2) bond length is 1.88 Å. The Co(4)-O(3) bond length is 1.91 Å. The Co(4)-O(7) bond length is 1.84 Å. The Co(4)-O(9) bond length is 1.91 Å. In the fifth Co site, Co(5) is bonded to one O(10), one O(11), one O(13), one O(14), one O(4), and one O(5) atom to form CoO6 octahedra that share corners with three equivalent Li(1)O6 octahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra,  an edgeedge with one Co(3)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra, and  an edgeedge with one Co(6)O6 octahedra. The corner-sharing octahedral tilt angles range from 11-16°. The Co(5)-O(10) bond length is 1.92 Å. The Co(5)-O(11) bond length is 1.88 Å. The Co(5)-O(13) bond length is 1.89 Å. The Co(5)-O(14) bond length is 1.92 Å. The Co(5)-O(4) bond length is 1.89 Å. The Co(5)-O(5) bond length is 1.91 Å. In the sixth Co site, Co(6) is bonded to one O(10), one O(12), one O(14), one O(6), one O(8), and one O(9) atom to form CoO6 octahedra that share  a cornercorner with one Li(1)O6 octahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra,  an edgeedge with one Co(5)O6 octahedra,  an edgeedge with one Co(7)O6 octahedra, and edges with two equivalent Co(2)O6 octahedra. The corner-sharing octahedral tilt angles are 14°. The Co(6)-O(10) bond length is 1.91 Å. The Co(6)-O(12) bond length is 1.92 Å. The Co(6)-O(14) bond length is 1.86 Å. The Co(6)-O(6) bond length is 1.93 Å. The Co(6)-O(8) bond length is 1.88 Å. The Co(6)-O(9) bond length is 1.87 Å. In the seventh Co site, Co(7) is bonded to two equivalent O(1), two equivalent O(12), and two equivalent O(8) atoms to form CoO6 octahedra that share corners with two equivalent Li(1)O6 octahedra, edges with two equivalent Co(1)O6 octahedra, edges with two equivalent Co(2)O6 octahedra, and edges with two equivalent Co(6)O6 octahedra. The corner-sharing octahedral tilt angles are 13°. Both Co(7)-O(1) bond lengths are 1.89 Å. Both Co(7)-O(12) bond lengths are 1.92 Å. Both Co(7)-O(8) bond lengths are 1.88 Å. There are fourteen inequivalent O sites. In the first O site, O(1) is bonded in a distorted T-shaped geometry to one Co(1), one Co(2), and one Co(7) atom. In the second O site, O(2) is bonded in a distorted trigonal non-coplanar geometry to one Co(1), one Co(3), and one Co(4) atom. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Li(1), one Co(4), and two equivalent Co(3) atoms. In the fourth O site, O(4) is bonded in a distorted T-shaped geometry to one Co(1), one Co(2), and one Co(5) atom. In the fifth O site, O(5) is bonded in a distorted T-shaped geometry to one Co(1), one Co(3), and one Co(5) atom. In the sixth O site, O(6) is bonded in a rectangular see-saw-like geometry to one Li(1), one Co(6), and two equivalent Co(2) atoms. In the seventh O site, O(7) is bonded in a distorted T-shaped geometry to one Mg(1), one Co(3), and one Co(4) atom. In the eighth O site, O(8) is bonded in a distorted T-shaped geometry to one Co(1), one Co(6), and one Co(7) atom. In the ninth O site, O(9) is bonded in a distorted T-shaped geometry to one Co(1), one Co(4), and one Co(6) atom. In the tenth O site, O(10) is bonded in a rectangular see-saw-like geometry to one Li(1), one Co(2), one Co(5), and one Co(6) atom. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Li(1), one Mg(1), one Co(3), and one Co(5) atom. In the twelfth O site, O(12) is bonded in a rectangular see-saw-like geometry to one Li(1), one Co(2), one Co(6), and one Co(7) atom. In the thirteenth O site, O(13) is bonded in a rectangular see-saw-like geometry to one Li(1), one Mg(1), one Co(4), and one Co(5) atom. In the fourteenth O site, O(14) is bonded in a distorted T-shaped geometry to one Co(4), one Co(5), and one Co(6) atom.