Li3MgTi8O16 is Spinel-derived structured and crystallizes in the trigonal R3m space group. There are three inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(6) and three equivalent O(1) atoms to form LiO4 tetrahedra that share corners with three equivalent Ti(2)O6 octahedra, corners with three equivalent Ti(4)O6 octahedra, and corners with six equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 59-62°. In the second Li site, Li(2) is bonded to one O(7) and three equivalent O(4) atoms to form LiO4 tetrahedra that share corners with three equivalent Mg(1)O6 octahedra, corners with three equivalent Ti(4)O6 octahedra, and corners with six equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-60°. In the third Li site, Li(3) is bonded to one O(3) and three equivalent O(8) atoms to form LiO4 tetrahedra that share corners with three equivalent Ti(1)O6 octahedra, corners with three equivalent Ti(2)O6 octahedra, and corners with six equivalent Ti(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-60°. Mg(1) is bonded to three equivalent O(4) and three equivalent O(5) atoms to form MgO6 octahedra that share corners with three equivalent Li(2)O4 tetrahedra, corners with three equivalent Ti(3)O4 tetrahedra, edges with three equivalent Ti(1)O6 octahedra, and edges with three equivalent Ti(4)O6 octahedra. There are four inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(2), one O(3), two equivalent O(1), and two equivalent O(4) atoms to form TiO6 octahedra that share  a cornercorner with one Li(3)O4 tetrahedra,  a cornercorner with one Ti(3)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra, corners with two equivalent Li(2)O4 tetrahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra, and edges with four equivalent Ti(1)O6 octahedra. In the second Ti site, Ti(2) is bonded to three equivalent O(1) and three equivalent O(8) atoms to form TiO6 octahedra that share corners with three equivalent Li(1)O4 tetrahedra, corners with three equivalent Li(3)O4 tetrahedra, edges with three equivalent Ti(1)O6 octahedra, and edges with three equivalent Ti(4)O6 octahedra. In the third Ti site, Ti(3) is bonded to one O(2) and three equivalent O(5) atoms to form TiO4 tetrahedra that share corners with three equivalent Mg(1)O6 octahedra, corners with three equivalent Ti(1)O6 octahedra, and corners with six equivalent Ti(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-58°. In the fourth Ti site, Ti(4) is bonded to one O(6), one O(7), two equivalent O(5), and two equivalent O(8) atoms to form TiO6 octahedra that share  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 tetrahedra, corners with two equivalent Li(3)O4 tetrahedra, corners with two equivalent Ti(3)O4 tetrahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra, and edges with four equivalent Ti(4)O6 octahedra. There are eight inequivalent O sites. In the first O site, O(1) is bonded to one Li(1), one Ti(2), and two equivalent Ti(1) atoms to form a mixture of distorted corner and edge-sharing OLiTi3 tetrahedra. In the second O site, O(2) is bonded in a distorted rectangular see-saw-like geometry to one Ti(3) and three equivalent Ti(1) atoms. In the third O site, O(3) is bonded to one Li(3) and three equivalent Ti(1) atoms to form distorted corner-sharing OLiTi3 trigonal pyramids. In the fourth O site, O(4) is bonded in a rectangular see-saw-like geometry to one Li(2), one Mg(1), and two equivalent Ti(1) atoms. In the fifth O site, O(5) is bonded in a distorted rectangular see-saw-like geometry to one Mg(1), one Ti(3), and two equivalent Ti(4) atoms. In the sixth O site, O(6) is bonded to one Li(1) and three equivalent Ti(4) atoms to form corner-sharing OLiTi3 tetrahedra. In the seventh O site, O(7) is bonded in a distorted rectangular see-saw-like geometry to one Li(2) and three equivalent Ti(4) atoms. In the eighth O site, O(8) is bonded to one Li(3), one Ti(2), and two equivalent Ti(4) atoms to form a mixture of distorted corner and edge-sharing OLiTi3 trigonal pyramids.
Li3MgTi8O16 is Spinel-derived structured and crystallizes in the trigonal R3m space group. There are three inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(6) and three equivalent O(1) atoms to form LiO4 tetrahedra that share corners with three equivalent Ti(2)O6 octahedra, corners with three equivalent Ti(4)O6 octahedra, and corners with six equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 59-62°. The Li(1)-O(6) bond length is 2.09 Å. All Li(1)-O(1) bond lengths are 2.03 Å. In the second Li site, Li(2) is bonded to one O(7) and three equivalent O(4) atoms to form LiO4 tetrahedra that share corners with three equivalent Mg(1)O6 octahedra, corners with three equivalent Ti(4)O6 octahedra, and corners with six equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-60°. The Li(2)-O(7) bond length is 2.10 Å. All Li(2)-O(4) bond lengths are 2.00 Å. In the third Li site, Li(3) is bonded to one O(3) and three equivalent O(8) atoms to form LiO4 tetrahedra that share corners with three equivalent Ti(1)O6 octahedra, corners with three equivalent Ti(2)O6 octahedra, and corners with six equivalent Ti(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-60°. The Li(3)-O(3) bond length is 1.97 Å. All Li(3)-O(8) bond lengths are 2.01 Å. Mg(1) is bonded to three equivalent O(4) and three equivalent O(5) atoms to form MgO6 octahedra that share corners with three equivalent Li(2)O4 tetrahedra, corners with three equivalent Ti(3)O4 tetrahedra, edges with three equivalent Ti(1)O6 octahedra, and edges with three equivalent Ti(4)O6 octahedra. All Mg(1)-O(4) bond lengths are 2.06 Å. All Mg(1)-O(5) bond lengths are 2.13 Å. There are four inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(2), one O(3), two equivalent O(1), and two equivalent O(4) atoms to form TiO6 octahedra that share  a cornercorner with one Li(3)O4 tetrahedra,  a cornercorner with one Ti(3)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra, corners with two equivalent Li(2)O4 tetrahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra, and edges with four equivalent Ti(1)O6 octahedra. The Ti(1)-O(2) bond length is 2.13 Å. The Ti(1)-O(3) bond length is 2.00 Å. Both Ti(1)-O(1) bond lengths are 2.03 Å. Both Ti(1)-O(4) bond lengths are 1.98 Å. In the second Ti site, Ti(2) is bonded to three equivalent O(1) and three equivalent O(8) atoms to form TiO6 octahedra that share corners with three equivalent Li(1)O4 tetrahedra, corners with three equivalent Li(3)O4 tetrahedra, edges with three equivalent Ti(1)O6 octahedra, and edges with three equivalent Ti(4)O6 octahedra. All Ti(2)-O(1) bond lengths are 2.00 Å. All Ti(2)-O(8) bond lengths are 2.05 Å. In the third Ti site, Ti(3) is bonded to one O(2) and three equivalent O(5) atoms to form TiO4 tetrahedra that share corners with three equivalent Mg(1)O6 octahedra, corners with three equivalent Ti(1)O6 octahedra, and corners with six equivalent Ti(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-58°. The Ti(3)-O(2) bond length is 1.93 Å. All Ti(3)-O(5) bond lengths are 1.90 Å. In the fourth Ti site, Ti(4) is bonded to one O(6), one O(7), two equivalent O(5), and two equivalent O(8) atoms to form TiO6 octahedra that share  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 tetrahedra, corners with two equivalent Li(3)O4 tetrahedra, corners with two equivalent Ti(3)O4 tetrahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra, and edges with four equivalent Ti(4)O6 octahedra. The Ti(4)-O(6) bond length is 2.01 Å. The Ti(4)-O(7) bond length is 2.02 Å. Both Ti(4)-O(5) bond lengths are 2.13 Å. Both Ti(4)-O(8) bond lengths are 1.98 Å. There are eight inequivalent O sites. In the first O site, O(1) is bonded to one Li(1), one Ti(2), and two equivalent Ti(1) atoms to form a mixture of distorted corner and edge-sharing OLiTi3 tetrahedra. In the second O site, O(2) is bonded in a distorted rectangular see-saw-like geometry to one Ti(3) and three equivalent Ti(1) atoms. In the third O site, O(3) is bonded to one Li(3) and three equivalent Ti(1) atoms to form distorted corner-sharing OLiTi3 trigonal pyramids. In the fourth O site, O(4) is bonded in a rectangular see-saw-like geometry to one Li(2), one Mg(1), and two equivalent Ti(1) atoms. In the fifth O site, O(5) is bonded in a distorted rectangular see-saw-like geometry to one Mg(1), one Ti(3), and two equivalent Ti(4) atoms. In the sixth O site, O(6) is bonded to one Li(1) and three equivalent Ti(4) atoms to form corner-sharing OLiTi3 tetrahedra. In the seventh O site, O(7) is bonded in a distorted rectangular see-saw-like geometry to one Li(2) and three equivalent Ti(4) atoms. In the eighth O site, O(8) is bonded to one Li(3), one Ti(2), and two equivalent Ti(4) atoms to form a mixture of distorted corner and edge-sharing OLiTi3 trigonal pyramids.