Mg2Ti9O13 crystallizes in the monoclinic C2/m space group. Mg(1) is bonded in a 8-coordinate geometry to one O(3), one O(6), two equivalent O(2), two equivalent O(4), and two equivalent O(5) atoms. There are five inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to two equivalent O(6) and four equivalent O(7) atoms to form a mixture of corner and edge-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles are 11°. In the second Ti site, Ti(2) is bonded to one O(4), two equivalent O(1), and three equivalent O(3) atoms to form a mixture of corner and edge-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 0-12°. In the third Ti site, Ti(3) is bonded to one O(5), two equivalent O(6), and three equivalent O(7) atoms to form a mixture of corner and edge-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 4-11°. In the fourth Ti site, Ti(4) is bonded to one O(1), one O(2), two equivalent O(3), and two equivalent O(4) atoms to form a mixture of corner and edge-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 0-54°. In the fifth Ti site, Ti(5) is bonded to one O(2), one O(7), two equivalent O(5), and two equivalent O(6) atoms to form a mixture of corner and edge-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 4-54°. There are seven inequivalent O sites. In the first O site, O(7) is bonded to one Ti(5), two equivalent Ti(1), and three equivalent Ti(3) atoms to form OTi6 octahedra that share corners with two equivalent O(7)Ti6 octahedra, corners with two equivalent O(6)MgTi5 square pyramids,  a cornercorner with one O(2)Mg2Ti2 tetrahedra,  a cornercorner with one O(5)Mg2Ti3 trigonal bipyramid, edges with five equivalent O(7)Ti6 octahedra, edges with five equivalent O(6)MgTi5 square pyramids, and edges with two equivalent O(5)Mg2Ti3 trigonal bipyramids. The corner-sharing octahedra are not tilted. In the second O site, O(1) is bonded to two equivalent Ti(4) and four equivalent Ti(2) atoms to form OTi6 octahedra that share corners with four equivalent O(3)MgTi5 octahedra, corners with two equivalent O(2)Mg2Ti2 tetrahedra, edges with two equivalent O(1)Ti6 octahedra, edges with six equivalent O(3)MgTi5 octahedra, and edges with four equivalent O(4)Mg2Ti3 trigonal bipyramids. The corner-sharing octahedral tilt angles are 10°. In the third O site, O(2) is bonded to two equivalent Mg(1), one Ti(4), and one Ti(5) atom to form OMg2Ti2 tetrahedra that share  a cornercorner with one O(1)Ti6 octahedra,  a cornercorner with one O(7)Ti6 octahedra, corners with two equivalent O(2)Mg2Ti2 tetrahedra, corners with four equivalent O(4)Mg2Ti3 trigonal bipyramids, corners with four equivalent O(5)Mg2Ti3 trigonal bipyramids, edges with two equivalent O(3)MgTi5 octahedra, edges with two equivalent O(6)MgTi5 square pyramids,  an edgeedge with one O(4)Mg2Ti3 trigonal bipyramid, and  an edgeedge with one O(5)Mg2Ti3 trigonal bipyramid. The corner-sharing octahedra are not tilted. In the fourth O site, O(3) is bonded to one Mg(1), two equivalent Ti(4), and three equivalent Ti(2) atoms to form distorted OMgTi5 octahedra that share corners with two equivalent O(1)Ti6 octahedra,  a cornercorner with one O(6)MgTi5 square pyramid, corners with two equivalent O(5)Mg2Ti3 trigonal bipyramids, corners with three equivalent O(4)Mg2Ti3 trigonal bipyramids, edges with three equivalent O(1)Ti6 octahedra, edges with four equivalent O(3)MgTi5 octahedra, edges with two equivalent O(2)Mg2Ti2 tetrahedra, and edges with three equivalent O(4)Mg2Ti3 trigonal bipyramids. The corner-sharing octahedral tilt angles are 10°. In the fifth O site, O(4) is bonded to two equivalent Mg(1), one Ti(2), and two equivalent Ti(4) atoms to form OMg2Ti3 trigonal bipyramids that share corners with three equivalent O(3)MgTi5 octahedra, corners with two equivalent O(6)MgTi5 square pyramids, corners with four equivalent O(2)Mg2Ti2 tetrahedra, corners with two equivalent O(5)Mg2Ti3 trigonal bipyramids, edges with two equivalent O(1)Ti6 octahedra, edges with three equivalent O(3)MgTi5 octahedra,  an edgeedge with one O(2)Mg2Ti2 tetrahedra,  an edgeedge with one O(5)Mg2Ti3 trigonal bipyramid, and edges with two equivalent O(4)Mg2Ti3 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 1-5°. In the sixth O site, O(5) is bonded to two equivalent Mg(1), one Ti(3), and two equivalent Ti(5) atoms to form distorted OMg2Ti3 trigonal bipyramids that share  a cornercorner with one O(7)Ti6 octahedra, corners with two equivalent O(3)MgTi5 octahedra, corners with two equivalent O(6)MgTi5 square pyramids, corners with four equivalent O(2)Mg2Ti2 tetrahedra, corners with two equivalent O(4)Mg2Ti3 trigonal bipyramids, edges with two equivalent O(7)Ti6 octahedra, edges with three equivalent O(6)MgTi5 square pyramids,  an edgeedge with one O(2)Mg2Ti2 tetrahedra,  an edgeedge with one O(4)Mg2Ti3 trigonal bipyramid, and edges with two equivalent O(5)Mg2Ti3 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 8-42°. In the seventh O site, O(6) is bonded to one Mg(1), one Ti(1), two equivalent Ti(3), and two equivalent Ti(5) atoms to form distorted OMgTi5 square pyramids that share  a cornercorner with one O(3)MgTi5 octahedra, corners with two equivalent O(7)Ti6 octahedra,  a cornercorner with one O(6)MgTi5 square pyramid, corners with two equivalent O(4)Mg2Ti3 trigonal bipyramids, corners with two equivalent O(5)Mg2Ti3 trigonal bipyramids, edges with five equivalent O(7)Ti6 octahedra, edges with two equivalent O(6)MgTi5 square pyramids, edges with two equivalent O(2)Mg2Ti2 tetrahedra, and edges with three equivalent O(5)Mg2Ti3 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 12-50°.
Mg2Ti9O13 crystallizes in the monoclinic C2/m space group. Mg(1) is bonded in a 8-coordinate geometry to one O(3), one O(6), two equivalent O(2), two equivalent O(4), and two equivalent O(5) atoms. The Mg(1)-O(3) bond length is 2.50 Å. The Mg(1)-O(6) bond length is 2.70 Å. Both Mg(1)-O(2) bond lengths are 2.12 Å. Both Mg(1)-O(4) bond lengths are 2.25 Å. Both Mg(1)-O(5) bond lengths are 2.30 Å. There are five inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to two equivalent O(6) and four equivalent O(7) atoms to form a mixture of corner and edge-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles are 11°. Both Ti(1)-O(6) bond lengths are 2.22 Å. All Ti(1)-O(7) bond lengths are 2.15 Å. In the second Ti site, Ti(2) is bonded to one O(4), two equivalent O(1), and three equivalent O(3) atoms to form a mixture of corner and edge-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 0-12°. The Ti(2)-O(4) bond length is 2.09 Å. Both Ti(2)-O(1) bond lengths are 2.14 Å. There are two shorter (2.06 Å) and one longer (2.23 Å) Ti(2)-O(3) bond length. In the third Ti site, Ti(3) is bonded to one O(5), two equivalent O(6), and three equivalent O(7) atoms to form a mixture of corner and edge-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 4-11°. The Ti(3)-O(5) bond length is 2.12 Å. Both Ti(3)-O(6) bond lengths are 2.06 Å. There are two shorter (2.12 Å) and one longer (2.18 Å) Ti(3)-O(7) bond length. In the fourth Ti site, Ti(4) is bonded to one O(1), one O(2), two equivalent O(3), and two equivalent O(4) atoms to form a mixture of corner and edge-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 0-54°. The Ti(4)-O(1) bond length is 2.15 Å. The Ti(4)-O(2) bond length is 2.05 Å. Both Ti(4)-O(3) bond lengths are 2.07 Å. Both Ti(4)-O(4) bond lengths are 2.09 Å. In the fifth Ti site, Ti(5) is bonded to one O(2), one O(7), two equivalent O(5), and two equivalent O(6) atoms to form a mixture of corner and edge-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 4-54°. The Ti(5)-O(2) bond length is 1.95 Å. The Ti(5)-O(7) bond length is 2.13 Å. Both Ti(5)-O(5) bond lengths are 2.09 Å. Both Ti(5)-O(6) bond lengths are 2.06 Å. There are seven inequivalent O sites. In the first O site, O(7) is bonded to one Ti(5), two equivalent Ti(1), and three equivalent Ti(3) atoms to form OTi6 octahedra that share corners with two equivalent O(7)Ti6 octahedra, corners with two equivalent O(6)MgTi5 square pyramids,  a cornercorner with one O(2)Mg2Ti2 tetrahedra,  a cornercorner with one O(5)Mg2Ti3 trigonal bipyramid, edges with five equivalent O(7)Ti6 octahedra, edges with five equivalent O(6)MgTi5 square pyramids, and edges with two equivalent O(5)Mg2Ti3 trigonal bipyramids. The corner-sharing octahedra are not tilted. In the second O site, O(1) is bonded to two equivalent Ti(4) and four equivalent Ti(2) atoms to form OTi6 octahedra that share corners with four equivalent O(3)MgTi5 octahedra, corners with two equivalent O(2)Mg2Ti2 tetrahedra, edges with two equivalent O(1)Ti6 octahedra, edges with six equivalent O(3)MgTi5 octahedra, and edges with four equivalent O(4)Mg2Ti3 trigonal bipyramids. The corner-sharing octahedral tilt angles are 10°. In the third O site, O(2) is bonded to two equivalent Mg(1), one Ti(4), and one Ti(5) atom to form OMg2Ti2 tetrahedra that share  a cornercorner with one O(1)Ti6 octahedra,  a cornercorner with one O(7)Ti6 octahedra, corners with two equivalent O(2)Mg2Ti2 tetrahedra, corners with four equivalent O(4)Mg2Ti3 trigonal bipyramids, corners with four equivalent O(5)Mg2Ti3 trigonal bipyramids, edges with two equivalent O(3)MgTi5 octahedra, edges with two equivalent O(6)MgTi5 square pyramids,  an edgeedge with one O(4)Mg2Ti3 trigonal bipyramid, and  an edgeedge with one O(5)Mg2Ti3 trigonal bipyramid. The corner-sharing octahedra are not tilted. In the fourth O site, O(3) is bonded to one Mg(1), two equivalent Ti(4), and three equivalent Ti(2) atoms to form distorted OMgTi5 octahedra that share corners with two equivalent O(1)Ti6 octahedra,  a cornercorner with one O(6)MgTi5 square pyramid, corners with two equivalent O(5)Mg2Ti3 trigonal bipyramids, corners with three equivalent O(4)Mg2Ti3 trigonal bipyramids, edges with three equivalent O(1)Ti6 octahedra, edges with four equivalent O(3)MgTi5 octahedra, edges with two equivalent O(2)Mg2Ti2 tetrahedra, and edges with three equivalent O(4)Mg2Ti3 trigonal bipyramids. The corner-sharing octahedral tilt angles are 10°. In the fifth O site, O(4) is bonded to two equivalent Mg(1), one Ti(2), and two equivalent Ti(4) atoms to form OMg2Ti3 trigonal bipyramids that share corners with three equivalent O(3)MgTi5 octahedra, corners with two equivalent O(6)MgTi5 square pyramids, corners with four equivalent O(2)Mg2Ti2 tetrahedra, corners with two equivalent O(5)Mg2Ti3 trigonal bipyramids, edges with two equivalent O(1)Ti6 octahedra, edges with three equivalent O(3)MgTi5 octahedra,  an edgeedge with one O(2)Mg2Ti2 tetrahedra,  an edgeedge with one O(5)Mg2Ti3 trigonal bipyramid, and edges with two equivalent O(4)Mg2Ti3 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 1-5°. In the sixth O site, O(5) is bonded to two equivalent Mg(1), one Ti(3), and two equivalent Ti(5) atoms to form distorted OMg2Ti3 trigonal bipyramids that share  a cornercorner with one O(7)Ti6 octahedra, corners with two equivalent O(3)MgTi5 octahedra, corners with two equivalent O(6)MgTi5 square pyramids, corners with four equivalent O(2)Mg2Ti2 tetrahedra, corners with two equivalent O(4)Mg2Ti3 trigonal bipyramids, edges with two equivalent O(7)Ti6 octahedra, edges with three equivalent O(6)MgTi5 square pyramids,  an edgeedge with one O(2)Mg2Ti2 tetrahedra,  an edgeedge with one O(4)Mg2Ti3 trigonal bipyramid, and edges with two equivalent O(5)Mg2Ti3 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 8-42°. In the seventh O site, O(6) is bonded to one Mg(1), one Ti(1), two equivalent Ti(3), and two equivalent Ti(5) atoms to form distorted OMgTi5 square pyramids that share  a cornercorner with one O(3)MgTi5 octahedra, corners with two equivalent O(7)Ti6 octahedra,  a cornercorner with one O(6)MgTi5 square pyramid, corners with two equivalent O(4)Mg2Ti3 trigonal bipyramids, corners with two equivalent O(5)Mg2Ti3 trigonal bipyramids, edges with five equivalent O(7)Ti6 octahedra, edges with two equivalent O(6)MgTi5 square pyramids, edges with two equivalent O(2)Mg2Ti2 tetrahedra, and edges with three equivalent O(5)Mg2Ti3 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 12-50°.