Li4Ti15O32 crystallizes in the trigonal R3m space group. There are four inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(8) and three equivalent O(7) atoms to form LiO4 tetrahedra that share corners with three equivalent Li(2)O6 octahedra, corners with three equivalent Ti(5)O6 octahedra, and corners with six equivalent Ti(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-65°. In the second Li site, Li(2) is bonded to three equivalent O(4) and three equivalent O(7) atoms to form LiO6 octahedra that share corners with three equivalent Li(1)O4 tetrahedra, corners with three equivalent Li(4)O4 tetrahedra, edges with three equivalent Ti(4)O6 octahedra, and edges with three equivalent Ti(5)O6 octahedra. In the third Li site, Li(3) is bonded to one O(14) and three equivalent O(10) atoms to form LiO4 tetrahedra that share corners with three equivalent Ti(6)O6 octahedra, corners with three equivalent Ti(7)O6 octahedra, and corners with six equivalent Ti(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-61°. In the fourth Li site, Li(4) is bonded to one O(12) and three equivalent O(4) atoms to form LiO4 tetrahedra that share corners with three equivalent Li(2)O6 octahedra, corners with three equivalent Ti(4)O6 octahedra, and corners with six equivalent Ti(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-61°. There are seven 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(5) atoms to form edge-sharing TiO6 octahedra. In the second Ti site, Ti(2) is bonded to three equivalent O(1) and three equivalent O(13) atoms to form edge-sharing TiO6 octahedra. In the third Ti site, Ti(3) is bonded to three equivalent O(5) and three equivalent O(6) atoms to form edge-sharing TiO6 octahedra. In the fourth Ti site, Ti(4) is bonded to one O(11), one O(12), two equivalent O(10), and two equivalent O(7) atoms to form TiO6 octahedra that share  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra, corners with two equivalent Li(3)O4 tetrahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Ti(7)O6 octahedra, and edges with four equivalent Ti(4)O6 octahedra. In the fifth Ti site, Ti(5) is bonded to one O(8), one O(9), two equivalent O(4), and two equivalent O(6) atoms to form TiO6 octahedra that share  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Ti(3)O6 octahedra, and edges with four equivalent Ti(5)O6 octahedra. In the sixth Ti site, Ti(6) is bonded to one O(14), one O(16), two equivalent O(13), and two equivalent O(15) atoms to form TiO6 octahedra that share  a cornercorner with one Li(3)O4 tetrahedra,  an edgeedge with one Ti(2)O6 octahedra,  an edgeedge with one Ti(7)O6 octahedra, and edges with four equivalent Ti(6)O6 octahedra. In the seventh Ti site, Ti(7) is bonded to three equivalent O(10) and three equivalent O(15) atoms to form TiO6 octahedra that share corners with three equivalent Li(3)O4 tetrahedra, edges with three equivalent Ti(4)O6 octahedra, and edges with three equivalent Ti(6)O6 octahedra. There are sixteen inequivalent O sites. In the first O site, O(1) is bonded in a distorted T-shaped geometry to one Ti(2) and two equivalent Ti(1) atoms. In the second O site, O(2) is bonded in a distorted trigonal non-coplanar geometry to three equivalent Ti(1) atoms. In the third O site, O(3) is bonded in a distorted T-shaped geometry to three equivalent Ti(1) atoms. In the fourth O site, O(4) is bonded in a rectangular see-saw-like geometry to one Li(2), one Li(4), and two equivalent Ti(5) atoms. In the fifth O site, O(5) is bonded in a distorted trigonal non-coplanar geometry to one Ti(3) and two equivalent Ti(1) atoms. In the sixth O site, O(6) is bonded in a 3-coordinate geometry to one Ti(3) and two equivalent Ti(5) atoms. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(1), one Li(2), and two equivalent Ti(4) atoms. In the eighth O site, O(8) is bonded in a distorted tetrahedral geometry to one Li(1) and three equivalent Ti(5) atoms. In the ninth O site, O(9) is bonded in a distorted T-shaped geometry to three equivalent Ti(5) atoms. In the tenth O site, O(10) is bonded to one Li(3), one Ti(7), and two equivalent Ti(4) atoms to form a mixture of distorted edge and corner-sharing OLiTi3 tetrahedra. In the eleventh O site, O(11) is bonded in a distorted T-shaped geometry to three equivalent Ti(4) atoms. In the twelfth O site, O(12) is bonded to one Li(4) and three equivalent Ti(4) atoms to form distorted edge-sharing OLiTi3 tetrahedra. In the thirteenth O site, O(13) is bonded in a distorted trigonal non-coplanar geometry to one Ti(2) and two equivalent Ti(6) atoms. In the fourteenth O site, O(14) is bonded to one Li(3) and three equivalent Ti(6) atoms to form distorted corner-sharing OLiTi3 trigonal pyramids. In the fifteenth O site, O(15) is bonded in a distorted T-shaped geometry to one Ti(7) and two equivalent Ti(6) atoms. In the sixteenth O site, O(16) is bonded in a distorted trigonal non-coplanar geometry to three equivalent Ti(6) atoms.
Li4Ti15O32 crystallizes in the trigonal R3m space group. There are four inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(8) and three equivalent O(7) atoms to form LiO4 tetrahedra that share corners with three equivalent Li(2)O6 octahedra, corners with three equivalent Ti(5)O6 octahedra, and corners with six equivalent Ti(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-65°. The Li(1)-O(8) bond length is 1.98 Å. All Li(1)-O(7) bond lengths are 1.99 Å. In the second Li site, Li(2) is bonded to three equivalent O(4) and three equivalent O(7) atoms to form LiO6 octahedra that share corners with three equivalent Li(1)O4 tetrahedra, corners with three equivalent Li(4)O4 tetrahedra, edges with three equivalent Ti(4)O6 octahedra, and edges with three equivalent Ti(5)O6 octahedra. All Li(2)-O(4) bond lengths are 2.11 Å. All Li(2)-O(7) bond lengths are 2.16 Å. In the third Li site, Li(3) is bonded to one O(14) and three equivalent O(10) atoms to form LiO4 tetrahedra that share corners with three equivalent Ti(6)O6 octahedra, corners with three equivalent Ti(7)O6 octahedra, and corners with six equivalent Ti(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-61°. The Li(3)-O(14) bond length is 1.99 Å. All Li(3)-O(10) bond lengths are 2.04 Å. In the fourth Li site, Li(4) is bonded to one O(12) and three equivalent O(4) atoms to form LiO4 tetrahedra that share corners with three equivalent Li(2)O6 octahedra, corners with three equivalent Ti(4)O6 octahedra, and corners with six equivalent Ti(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-61°. The Li(4)-O(12) bond length is 2.05 Å. All Li(4)-O(4) bond lengths are 1.97 Å. There are seven 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(5) atoms to form edge-sharing TiO6 octahedra. The Ti(1)-O(2) bond length is 1.99 Å. The Ti(1)-O(3) bond length is 1.99 Å. Both Ti(1)-O(1) bond lengths are 2.04 Å. Both Ti(1)-O(5) bond lengths are 1.94 Å. In the second Ti site, Ti(2) is bonded to three equivalent O(1) and three equivalent O(13) atoms to form edge-sharing TiO6 octahedra. All Ti(2)-O(1) bond lengths are 1.90 Å. All Ti(2)-O(13) bond lengths are 2.08 Å. In the third Ti site, Ti(3) is bonded to three equivalent O(5) and three equivalent O(6) atoms to form edge-sharing TiO6 octahedra. All Ti(3)-O(5) bond lengths are 2.09 Å. All Ti(3)-O(6) bond lengths are 1.90 Å. In the fourth Ti site, Ti(4) is bonded to one O(11), one O(12), two equivalent O(10), and two equivalent O(7) atoms to form TiO6 octahedra that share  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra, corners with two equivalent Li(3)O4 tetrahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Ti(7)O6 octahedra, and edges with four equivalent Ti(4)O6 octahedra. The Ti(4)-O(11) bond length is 1.98 Å. The Ti(4)-O(12) bond length is 2.03 Å. Both Ti(4)-O(10) bond lengths are 2.05 Å. Both Ti(4)-O(7) bond lengths are 1.92 Å. In the fifth Ti site, Ti(5) is bonded to one O(8), one O(9), two equivalent O(4), and two equivalent O(6) atoms to form TiO6 octahedra that share  a cornercorner with one Li(1)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Ti(3)O6 octahedra, and edges with four equivalent Ti(5)O6 octahedra. The Ti(5)-O(8) bond length is 2.04 Å. The Ti(5)-O(9) bond length is 1.97 Å. Both Ti(5)-O(4) bond lengths are 1.92 Å. Both Ti(5)-O(6) bond lengths are 2.04 Å. In the sixth Ti site, Ti(6) is bonded to one O(14), one O(16), two equivalent O(13), and two equivalent O(15) atoms to form TiO6 octahedra that share  a cornercorner with one Li(3)O4 tetrahedra,  an edgeedge with one Ti(2)O6 octahedra,  an edgeedge with one Ti(7)O6 octahedra, and edges with four equivalent Ti(6)O6 octahedra. The Ti(6)-O(14) bond length is 2.04 Å. The Ti(6)-O(16) bond length is 1.98 Å. Both Ti(6)-O(13) bond lengths are 1.94 Å. Both Ti(6)-O(15) bond lengths are 2.01 Å. In the seventh Ti site, Ti(7) is bonded to three equivalent O(10) and three equivalent O(15) atoms to form TiO6 octahedra that share corners with three equivalent Li(3)O4 tetrahedra, edges with three equivalent Ti(4)O6 octahedra, and edges with three equivalent Ti(6)O6 octahedra. All Ti(7)-O(10) bond lengths are 2.01 Å. All Ti(7)-O(15) bond lengths are 1.96 Å. There are sixteen inequivalent O sites. In the first O site, O(1) is bonded in a distorted T-shaped geometry to one Ti(2) and two equivalent Ti(1) atoms. In the second O site, O(2) is bonded in a distorted trigonal non-coplanar geometry to three equivalent Ti(1) atoms. In the third O site, O(3) is bonded in a distorted T-shaped geometry to three equivalent Ti(1) atoms. In the fourth O site, O(4) is bonded in a rectangular see-saw-like geometry to one Li(2), one Li(4), and two equivalent Ti(5) atoms. In the fifth O site, O(5) is bonded in a distorted trigonal non-coplanar geometry to one Ti(3) and two equivalent Ti(1) atoms. In the sixth O site, O(6) is bonded in a 3-coordinate geometry to one Ti(3) and two equivalent Ti(5) atoms. In the seventh O site, O(7) is bonded in a rectangular see-saw-like geometry to one Li(1), one Li(2), and two equivalent Ti(4) atoms. In the eighth O site, O(8) is bonded in a distorted tetrahedral geometry to one Li(1) and three equivalent Ti(5) atoms. In the ninth O site, O(9) is bonded in a distorted T-shaped geometry to three equivalent Ti(5) atoms. In the tenth O site, O(10) is bonded to one Li(3), one Ti(7), and two equivalent Ti(4) atoms to form a mixture of distorted edge and corner-sharing OLiTi3 tetrahedra. In the eleventh O site, O(11) is bonded in a distorted T-shaped geometry to three equivalent Ti(4) atoms. In the twelfth O site, O(12) is bonded to one Li(4) and three equivalent Ti(4) atoms to form distorted edge-sharing OLiTi3 tetrahedra. In the thirteenth O site, O(13) is bonded in a distorted trigonal non-coplanar geometry to one Ti(2) and two equivalent Ti(6) atoms. In the fourteenth O site, O(14) is bonded to one Li(3) and three equivalent Ti(6) atoms to form distorted corner-sharing OLiTi3 trigonal pyramids. In the fifteenth O site, O(15) is bonded in a distorted T-shaped geometry to one Ti(7) and two equivalent Ti(6) atoms. In the sixteenth O site, O(16) is bonded in a distorted trigonal non-coplanar geometry to three equivalent Ti(6) atoms.