Na5Ti12O24 crystallizes in the monoclinic Pm space group. There are four inequivalent Na sites. In the first Na site, Na(1) is bonded in a 4-coordinate geometry to one O(16), one O(4), and two equivalent O(1) atoms. In the second Na site, Na(2) is bonded in a 4-coordinate geometry to one O(14), one O(2), and two equivalent O(15) atoms. In the third Na site, Na(3) is bonded in a 4-coordinate geometry to one O(11), one O(8), and two equivalent O(10) atoms. In the fourth Na site, Na(4) is bonded in a 4-coordinate geometry to one O(10), one O(12), one O(7), and one O(9) atom. There are eight inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(16), one O(6), two equivalent O(1), and two equivalent O(13) atoms to form a mixture of corner and edge-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 47-49°. In the second Ti site, Ti(2) is bonded to one O(1), one O(13), one O(14), one O(15), one O(2), and one O(5) atom to form a mixture of corner and edge-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 43-52°. In the third Ti site, Ti(3) is bonded to one O(10), one O(11), one O(12), one O(3), one O(7), and one O(8) atom to form a mixture of corner and edge-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 45-50°. In the fourth Ti site, Ti(4) is bonded to one O(4), one O(9), two equivalent O(12), and two equivalent O(7) atoms to form a mixture of distorted corner and edge-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 44-47°. In the fifth Ti site, Ti(5) is bonded to one O(10), one O(13), one O(5), one O(6), one O(7), and one O(9) atom to form a mixture of corner and edge-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 45-52°. In the sixth Ti site, Ti(6) is bonded to one O(14), one O(8), two equivalent O(10), and two equivalent O(5) atoms to form a mixture of corner and edge-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 43-48°. In the seventh Ti site, Ti(7) is bonded to one O(11), one O(2), two equivalent O(15), and two equivalent O(3) atoms to form a mixture of corner and edge-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 47-48°. In the eighth Ti site, Ti(8) is bonded to one O(1), one O(12), one O(15), one O(16), one O(3), and one O(4) atom to form a mixture of corner and edge-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 44-50°. There are sixteen inequivalent O sites. In the first O site, O(1) is bonded to one Na(1), one Ti(1), one Ti(2), and one Ti(8) atom to form a mixture of corner and edge-sharing ONaTi3 trigonal pyramids. In the second O site, O(2) is bonded to one Na(2), one Ti(7), and two equivalent Ti(2) atoms to form a mixture of corner and edge-sharing ONaTi3 tetrahedra. In the third O site, O(3) is bonded in a distorted T-shaped geometry to one Ti(3), one Ti(7), and one Ti(8) atom. In the fourth O site, O(4) is bonded to one Na(1), one Ti(4), and two equivalent Ti(8) atoms to form ONaTi3 trigonal pyramids that share  a cornercorner with one O(9)Na2Ti3 square pyramid,  a cornercorner with one O(16)NaTi3 tetrahedra, corners with two equivalent O(7)NaTi3 tetrahedra, corners with two equivalent O(15)NaTi3 trigonal pyramids,  an edgeedge with one O(16)NaTi3 tetrahedra, and edges with two equivalent O(1)NaTi3 trigonal pyramids. In the fifth O site, O(5) is bonded in a distorted trigonal planar geometry to one Ti(2), one Ti(5), and one Ti(6) atom. In the sixth O site, O(6) is bonded in a 3-coordinate geometry to one Ti(1) and two equivalent Ti(5) atoms. In the seventh O site, O(7) is bonded to one Na(4), one Ti(3), one Ti(4), and one Ti(5) atom to form ONaTi3 tetrahedra that share  a cornercorner with one O(10)Na2Ti3 square pyramid,  a cornercorner with one O(9)Na2Ti3 square pyramid,  a cornercorner with one O(7)NaTi3 tetrahedra,  a cornercorner with one O(8)NaTi3 tetrahedra,  a cornercorner with one O(11)NaTi3 trigonal pyramid,  a cornercorner with one O(4)NaTi3 trigonal pyramid,  an edgeedge with one O(10)Na2Ti3 square pyramid, and  an edgeedge with one O(9)Na2Ti3 square pyramid. In the eighth O site, O(8) is bonded to one Na(3), one Ti(6), and two equivalent Ti(3) atoms to form ONaTi3 tetrahedra that share corners with two equivalent O(10)Na2Ti3 square pyramids, corners with two equivalent O(7)NaTi3 tetrahedra,  a cornercorner with one O(11)NaTi3 trigonal pyramid,  a cornercorner with one O(14)NaTi3 trigonal pyramid, edges with two equivalent O(10)Na2Ti3 square pyramids, and  an edgeedge with one O(11)NaTi3 trigonal pyramid. In the ninth O site, O(9) is bonded to two equivalent Na(4), one Ti(4), and two equivalent Ti(5) atoms to form ONa2Ti3 square pyramids that share corners with two equivalent O(7)NaTi3 tetrahedra,  a cornercorner with one O(4)NaTi3 trigonal pyramid, edges with two equivalent O(10)Na2Ti3 square pyramids, and edges with two equivalent O(7)NaTi3 tetrahedra. In the tenth O site, O(10) is bonded to one Na(3), one Na(4), one Ti(3), one Ti(5), and one Ti(6) atom to form ONa2Ti3 square pyramids that share  a cornercorner with one O(7)NaTi3 tetrahedra,  a cornercorner with one O(8)NaTi3 tetrahedra,  a cornercorner with one O(14)NaTi3 trigonal pyramid,  an edgeedge with one O(10)Na2Ti3 square pyramid,  an edgeedge with one O(9)Na2Ti3 square pyramid,  an edgeedge with one O(7)NaTi3 tetrahedra,  an edgeedge with one O(8)NaTi3 tetrahedra, and  an edgeedge with one O(11)NaTi3 trigonal pyramid. In the eleventh O site, O(11) is bonded to one Na(3), one Ti(7), and two equivalent Ti(3) atoms to form distorted ONaTi3 trigonal pyramids that share  a cornercorner with one O(2)NaTi3 tetrahedra,  a cornercorner with one O(8)NaTi3 tetrahedra, corners with two equivalent O(7)NaTi3 tetrahedra, corners with two equivalent O(15)NaTi3 trigonal pyramids, edges with two equivalent O(10)Na2Ti3 square pyramids, and  an edgeedge with one O(8)NaTi3 tetrahedra. In the twelfth O site, O(12) is bonded in a rectangular see-saw-like geometry to one Na(4), one Ti(3), one Ti(4), and one Ti(8) atom. In the thirteenth O site, O(13) is bonded in a 3-coordinate geometry to one Ti(1), one Ti(2), and one Ti(5) atom. In the fourteenth O site, O(14) is bonded to one Na(2), one Ti(6), and two equivalent Ti(2) atoms to form distorted ONaTi3 trigonal pyramids that share corners with two equivalent O(10)Na2Ti3 square pyramids,  a cornercorner with one O(2)NaTi3 tetrahedra,  a cornercorner with one O(8)NaTi3 tetrahedra, corners with two equivalent O(1)NaTi3 trigonal pyramids,  an edgeedge with one O(2)NaTi3 tetrahedra, and edges with two equivalent O(15)NaTi3 trigonal pyramids. In the fifteenth O site, O(15) is bonded to one Na(2), one Ti(2), one Ti(7), and one Ti(8) atom to form a mixture of corner and edge-sharing ONaTi3 trigonal pyramids. In the sixteenth O site, O(16) is bonded to one Na(1), one Ti(1), and two equivalent Ti(8) atoms to form a mixture of corner and edge-sharing ONaTi3 tetrahedra.
Na5Ti12O24 crystallizes in the monoclinic Pm space group. There are four inequivalent Na sites. In the first Na site, Na(1) is bonded in a 4-coordinate geometry to one O(16), one O(4), and two equivalent O(1) atoms. The Na(1)-O(16) bond length is 2.12 Å. The Na(1)-O(4) bond length is 2.43 Å. Both Na(1)-O(1) bond lengths are 2.25 Å. In the second Na site, Na(2) is bonded in a 4-coordinate geometry to one O(14), one O(2), and two equivalent O(15) atoms. The Na(2)-O(14) bond length is 2.40 Å. The Na(2)-O(2) bond length is 2.12 Å. Both Na(2)-O(15) bond lengths are 2.24 Å. In the third Na site, Na(3) is bonded in a 4-coordinate geometry to one O(11), one O(8), and two equivalent O(10) atoms. The Na(3)-O(11) bond length is 2.45 Å. The Na(3)-O(8) bond length is 2.10 Å. Both Na(3)-O(10) bond lengths are 2.23 Å. In the fourth Na site, Na(4) is bonded in a 4-coordinate geometry to one O(10), one O(12), one O(7), and one O(9) atom. The Na(4)-O(10) bond length is 2.22 Å. The Na(4)-O(12) bond length is 2.37 Å. The Na(4)-O(7) bond length is 2.10 Å. The Na(4)-O(9) bond length is 2.22 Å. There are eight inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(16), one O(6), two equivalent O(1), and two equivalent O(13) atoms to form a mixture of corner and edge-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 47-49°. The Ti(1)-O(16) bond length is 1.99 Å. The Ti(1)-O(6) bond length is 2.02 Å. Both Ti(1)-O(1) bond lengths are 2.09 Å. Both Ti(1)-O(13) bond lengths are 2.02 Å. In the second Ti site, Ti(2) is bonded to one O(1), one O(13), one O(14), one O(15), one O(2), and one O(5) atom to form a mixture of corner and edge-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 43-52°. The Ti(2)-O(1) bond length is 1.95 Å. The Ti(2)-O(13) bond length is 2.00 Å. The Ti(2)-O(14) bond length is 2.11 Å. The Ti(2)-O(15) bond length is 2.04 Å. The Ti(2)-O(2) bond length is 2.01 Å. The Ti(2)-O(5) bond length is 2.01 Å. In the third Ti site, Ti(3) is bonded to one O(10), one O(11), one O(12), one O(3), one O(7), and one O(8) atom to form a mixture of corner and edge-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 45-50°. The Ti(3)-O(10) bond length is 2.05 Å. The Ti(3)-O(11) bond length is 2.07 Å. The Ti(3)-O(12) bond length is 2.03 Å. The Ti(3)-O(3) bond length is 2.02 Å. The Ti(3)-O(7) bond length is 1.99 Å. The Ti(3)-O(8) bond length is 2.01 Å. In the fourth Ti site, Ti(4) is bonded to one O(4), one O(9), two equivalent O(12), and two equivalent O(7) atoms to form a mixture of distorted corner and edge-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 44-47°. The Ti(4)-O(4) bond length is 1.97 Å. The Ti(4)-O(9) bond length is 2.08 Å. Both Ti(4)-O(12) bond lengths are 2.06 Å. Both Ti(4)-O(7) bond lengths are 2.02 Å. In the fifth Ti site, Ti(5) is bonded to one O(10), one O(13), one O(5), one O(6), one O(7), and one O(9) atom to form a mixture of corner and edge-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 45-52°. The Ti(5)-O(10) bond length is 2.07 Å. The Ti(5)-O(13) bond length is 2.02 Å. The Ti(5)-O(5) bond length is 2.05 Å. The Ti(5)-O(6) bond length is 2.03 Å. The Ti(5)-O(7) bond length is 1.98 Å. The Ti(5)-O(9) bond length is 2.04 Å. In the sixth Ti site, Ti(6) is bonded to one O(14), one O(8), two equivalent O(10), and two equivalent O(5) atoms to form a mixture of corner and edge-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 43-48°. The Ti(6)-O(14) bond length is 2.01 Å. The Ti(6)-O(8) bond length is 2.00 Å. Both Ti(6)-O(10) bond lengths are 2.03 Å. Both Ti(6)-O(5) bond lengths are 2.03 Å. In the seventh Ti site, Ti(7) is bonded to one O(11), one O(2), two equivalent O(15), and two equivalent O(3) atoms to form a mixture of corner and edge-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 47-48°. The Ti(7)-O(11) bond length is 2.03 Å. The Ti(7)-O(2) bond length is 1.98 Å. Both Ti(7)-O(15) bond lengths are 2.08 Å. Both Ti(7)-O(3) bond lengths are 2.03 Å. In the eighth Ti site, Ti(8) is bonded to one O(1), one O(12), one O(15), one O(16), one O(3), and one O(4) atom to form a mixture of corner and edge-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 44-50°. The Ti(8)-O(1) bond length is 2.00 Å. The Ti(8)-O(12) bond length is 2.05 Å. The Ti(8)-O(15) bond length is 1.92 Å. The Ti(8)-O(16) bond length is 1.99 Å. The Ti(8)-O(3) bond length is 2.02 Å. The Ti(8)-O(4) bond length is 2.15 Å. There are sixteen inequivalent O sites. In the first O site, O(1) is bonded to one Na(1), one Ti(1), one Ti(2), and one Ti(8) atom to form a mixture of corner and edge-sharing ONaTi3 trigonal pyramids. In the second O site, O(2) is bonded to one Na(2), one Ti(7), and two equivalent Ti(2) atoms to form a mixture of corner and edge-sharing ONaTi3 tetrahedra. In the third O site, O(3) is bonded in a distorted T-shaped geometry to one Ti(3), one Ti(7), and one Ti(8) atom. In the fourth O site, O(4) is bonded to one Na(1), one Ti(4), and two equivalent Ti(8) atoms to form ONaTi3 trigonal pyramids that share  a cornercorner with one O(9)Na2Ti3 square pyramid,  a cornercorner with one O(16)NaTi3 tetrahedra, corners with two equivalent O(7)NaTi3 tetrahedra, corners with two equivalent O(15)NaTi3 trigonal pyramids,  an edgeedge with one O(16)NaTi3 tetrahedra, and edges with two equivalent O(1)NaTi3 trigonal pyramids. In the fifth O site, O(5) is bonded in a distorted trigonal planar geometry to one Ti(2), one Ti(5), and one Ti(6) atom. In the sixth O site, O(6) is bonded in a 3-coordinate geometry to one Ti(1) and two equivalent Ti(5) atoms. In the seventh O site, O(7) is bonded to one Na(4), one Ti(3), one Ti(4), and one Ti(5) atom to form ONaTi3 tetrahedra that share  a cornercorner with one O(10)Na2Ti3 square pyramid,  a cornercorner with one O(9)Na2Ti3 square pyramid,  a cornercorner with one O(7)NaTi3 tetrahedra,  a cornercorner with one O(8)NaTi3 tetrahedra,  a cornercorner with one O(11)NaTi3 trigonal pyramid,  a cornercorner with one O(4)NaTi3 trigonal pyramid,  an edgeedge with one O(10)Na2Ti3 square pyramid, and  an edgeedge with one O(9)Na2Ti3 square pyramid. In the eighth O site, O(8) is bonded to one Na(3), one Ti(6), and two equivalent Ti(3) atoms to form ONaTi3 tetrahedra that share corners with two equivalent O(10)Na2Ti3 square pyramids, corners with two equivalent O(7)NaTi3 tetrahedra,  a cornercorner with one O(11)NaTi3 trigonal pyramid,  a cornercorner with one O(14)NaTi3 trigonal pyramid, edges with two equivalent O(10)Na2Ti3 square pyramids, and  an edgeedge with one O(11)NaTi3 trigonal pyramid. In the ninth O site, O(9) is bonded to two equivalent Na(4), one Ti(4), and two equivalent Ti(5) atoms to form ONa2Ti3 square pyramids that share corners with two equivalent O(7)NaTi3 tetrahedra,  a cornercorner with one O(4)NaTi3 trigonal pyramid, edges with two equivalent O(10)Na2Ti3 square pyramids, and edges with two equivalent O(7)NaTi3 tetrahedra. In the tenth O site, O(10) is bonded to one Na(3), one Na(4), one Ti(3), one Ti(5), and one Ti(6) atom to form ONa2Ti3 square pyramids that share  a cornercorner with one O(7)NaTi3 tetrahedra,  a cornercorner with one O(8)NaTi3 tetrahedra,  a cornercorner with one O(14)NaTi3 trigonal pyramid,  an edgeedge with one O(10)Na2Ti3 square pyramid,  an edgeedge with one O(9)Na2Ti3 square pyramid,  an edgeedge with one O(7)NaTi3 tetrahedra,  an edgeedge with one O(8)NaTi3 tetrahedra, and  an edgeedge with one O(11)NaTi3 trigonal pyramid. In the eleventh O site, O(11) is bonded to one Na(3), one Ti(7), and two equivalent Ti(3) atoms to form distorted ONaTi3 trigonal pyramids that share  a cornercorner with one O(2)NaTi3 tetrahedra,  a cornercorner with one O(8)NaTi3 tetrahedra, corners with two equivalent O(7)NaTi3 tetrahedra, corners with two equivalent O(15)NaTi3 trigonal pyramids, edges with two equivalent O(10)Na2Ti3 square pyramids, and  an edgeedge with one O(8)NaTi3 tetrahedra. In the twelfth O site, O(12) is bonded in a rectangular see-saw-like geometry to one Na(4), one Ti(3), one Ti(4), and one Ti(8) atom. In the thirteenth O site, O(13) is bonded in a 3-coordinate geometry to one Ti(1), one Ti(2), and one Ti(5) atom. In the fourteenth O site, O(14) is bonded to one Na(2), one Ti(6), and two equivalent Ti(2) atoms to form distorted ONaTi3 trigonal pyramids that share corners with two equivalent O(10)Na2Ti3 square pyramids,  a cornercorner with one O(2)NaTi3 tetrahedra,  a cornercorner with one O(8)NaTi3 tetrahedra, corners with two equivalent O(1)NaTi3 trigonal pyramids,  an edgeedge with one O(2)NaTi3 tetrahedra, and edges with two equivalent O(15)NaTi3 trigonal pyramids. In the fifteenth O site, O(15) is bonded to one Na(2), one Ti(2), one Ti(7), and one Ti(8) atom to form a mixture of corner and edge-sharing ONaTi3 trigonal pyramids. In the sixteenth O site, O(16) is bonded to one Na(1), one Ti(1), and two equivalent Ti(8) atoms to form a mixture of corner and edge-sharing ONaTi3 tetrahedra.