Mg5Ti13O30 crystallizes in the monoclinic Pm space group. There are five inequivalent Mg sites. In the first Mg site, Mg(1) is bonded in a 6-coordinate geometry to one O(16), one O(5), two equivalent O(1), and two equivalent O(6) atoms. In the second Mg site, Mg(2) is bonded in a 6-coordinate geometry to one O(3), one O(4), two equivalent O(2), and two equivalent O(8) atoms. In the third Mg site, Mg(3) is bonded in a 6-coordinate geometry to one O(14), one O(4), two equivalent O(13), and two equivalent O(9) atoms. In the fourth Mg site, Mg(4) is bonded to one O(15), one O(5), two equivalent O(10), and two equivalent O(7) atoms to form distorted MgO6 octahedra that share corners with two equivalent Ti(2)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, edges with two equivalent Ti(3)O6 octahedra, and edges with two equivalent Ti(4)O6 octahedra. The corner-sharing octahedral tilt angles are 29°. In the fifth Mg site, Mg(5) is bonded in a 6-coordinate geometry to one O(14), one O(3), two equivalent O(12), and two equivalent O(18) atoms. There are seven inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(1), one O(12), one O(18), one O(2), one O(3), and one O(6) atom to form a mixture of distorted corner and edge-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 30-48°. In the second Ti site, Ti(2) is bonded to one O(10), one O(2), one O(5), one O(6), one O(7), and one O(8) atom to form distorted TiO6 octahedra that share  a cornercorner with one Mg(4)O6 octahedra,  a cornercorner with one Ti(2)O6 octahedra,  a cornercorner with one Ti(3)O6 octahedra,  a cornercorner with one Ti(7)O6 octahedra,  an edgeedge with one Mg(4)O6 octahedra,  an edgeedge with one Ti(1)O6 octahedra, and edges with two equivalent Ti(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 29-49°. In the third Ti site, Ti(3) is bonded to one O(11), one O(13), one O(15), one O(17), one O(7), and one O(9) atom to form distorted TiO6 octahedra that share  a cornercorner with one Ti(2)O6 octahedra,  a cornercorner with one Ti(3)O6 octahedra,  a cornercorner with one Ti(7)O6 octahedra,  an edgeedge with one Mg(4)O6 octahedra,  an edgeedge with one Ti(4)O6 octahedra, and edges with two equivalent Ti(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 30-47°. In the fourth Ti site, Ti(4) is bonded to one O(10), one O(13), one O(2), one O(4), one O(7), and one O(8) atom to form distorted TiO6 octahedra that share  a cornercorner with one Ti(1)O6 octahedra,  a cornercorner with one Ti(4)O6 octahedra,  a cornercorner with one Ti(5)O6 octahedra,  an edgeedge with one Mg(4)O6 octahedra,  an edgeedge with one Ti(3)O6 octahedra, and edges with two equivalent Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 31-49°. In the fifth Ti site, Ti(5) is bonded to one O(11), one O(12), one O(13), one O(14), one O(17), and one O(9) atom to form a mixture of distorted corner and edge-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 30-48°. In the sixth Ti site, Ti(6) is bonded in a 6-coordinate geometry to one O(15), one O(16), two equivalent O(11), and two equivalent O(17) atoms. In the seventh Ti site, Ti(7) is bonded to one O(1), one O(12), one O(16), one O(17), one O(18), and one O(6) atom to form a mixture of distorted corner and edge-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 31-51°. There are eighteen inequivalent O sites. In the first O site, O(1) is bonded in a distorted T-shaped geometry to one Mg(1), one Ti(1), and one Ti(7) atom. In the second O site, O(2) is bonded to one Mg(2), one Ti(1), one Ti(2), and one Ti(4) atom to form OMgTi3 trigonal pyramids that share  a cornercorner with one O(5)Mg2Ti2 trigonal pyramid,  a cornercorner with one O(12)MgTi3 trigonal pyramid,  a cornercorner with one O(13)MgTi3 trigonal pyramid,  a cornercorner with one O(2)MgTi3 trigonal pyramid,  an edgeedge with one O(3)Mg2Ti2 trigonal pyramid,  an edgeedge with one O(4)Mg2Ti2 trigonal pyramid,  an edgeedge with one O(6)MgTi3 trigonal pyramid, and  an edgeedge with one O(7)MgTi3 trigonal pyramid. In the third O site, O(3) is bonded to one Mg(2), one Mg(5), and two equivalent Ti(1) atoms to form distorted OMg2Ti2 trigonal pyramids that share  a cornercorner with one O(14)Mg2Ti2 trigonal pyramid,  a cornercorner with one O(4)Mg2Ti2 trigonal pyramid, corners with two equivalent O(6)MgTi3 trigonal pyramids, edges with two equivalent O(12)MgTi3 trigonal pyramids, and edges with two equivalent O(2)MgTi3 trigonal pyramids. In the fourth O site, O(4) is bonded to one Mg(2), one Mg(3), and two equivalent Ti(4) atoms to form distorted OMg2Ti2 trigonal pyramids that share  a cornercorner with one O(14)Mg2Ti2 trigonal pyramid,  a cornercorner with one O(3)Mg2Ti2 trigonal pyramid, corners with two equivalent O(7)MgTi3 trigonal pyramids, edges with two equivalent O(13)MgTi3 trigonal pyramids, and edges with two equivalent O(2)MgTi3 trigonal pyramids. In the fifth O site, O(5) is bonded to one Mg(1), one Mg(4), and two equivalent Ti(2) atoms to form a mixture of distorted corner and edge-sharing OMg2Ti2 trigonal pyramids. In the sixth O site, O(6) is bonded to one Mg(1), one Ti(1), one Ti(2), and one Ti(7) atom to form distorted OMgTi3 trigonal pyramids that share  a cornercorner with one O(3)Mg2Ti2 trigonal pyramid,  a cornercorner with one O(6)MgTi3 trigonal pyramid,  a cornercorner with one O(7)MgTi3 trigonal pyramid,  a cornercorner with one O(17)Ti4 trigonal pyramid,  an edgeedge with one O(5)Mg2Ti2 trigonal pyramid,  an edgeedge with one O(12)MgTi3 trigonal pyramid,  an edgeedge with one O(16)MgTi3 trigonal pyramid, and  an edgeedge with one O(2)MgTi3 trigonal pyramid. In the seventh O site, O(7) is bonded to one Mg(4), one Ti(2), one Ti(3), and one Ti(4) atom to form distorted OMgTi3 trigonal pyramids that share  a cornercorner with one O(4)Mg2Ti2 trigonal pyramid,  a cornercorner with one O(6)MgTi3 trigonal pyramid,  a cornercorner with one O(7)MgTi3 trigonal pyramid,  a cornercorner with one O(17)Ti4 trigonal pyramid,  an edgeedge with one O(5)Mg2Ti2 trigonal pyramid,  an edgeedge with one O(13)MgTi3 trigonal pyramid,  an edgeedge with one O(15)MgTi3 trigonal pyramid, and  an edgeedge with one O(2)MgTi3 trigonal pyramid. In the eighth O site, O(8) is bonded in a distorted trigonal non-coplanar geometry to one Mg(2), one Ti(2), and one Ti(4) atom. In the ninth O site, O(9) is bonded in a distorted trigonal non-coplanar geometry to one Mg(3), one Ti(3), and one Ti(5) atom. In the tenth O site, O(10) is bonded in a distorted trigonal non-coplanar geometry to one Mg(4), one Ti(2), and one Ti(4) atom. In the eleventh O site, O(11) is bonded in a distorted T-shaped geometry to one Ti(3), one Ti(5), and one Ti(6) atom. In the twelfth O site, O(12) is bonded to one Mg(5), one Ti(1), one Ti(5), and one Ti(7) atom to form OMgTi3 trigonal pyramids that share  a cornercorner with one O(12)MgTi3 trigonal pyramid,  a cornercorner with one O(13)MgTi3 trigonal pyramid,  a cornercorner with one O(16)MgTi3 trigonal pyramid,  a cornercorner with one O(2)MgTi3 trigonal pyramid,  an edgeedge with one O(14)Mg2Ti2 trigonal pyramid,  an edgeedge with one O(3)Mg2Ti2 trigonal pyramid,  an edgeedge with one O(6)MgTi3 trigonal pyramid, and  an edgeedge with one O(17)Ti4 trigonal pyramid. In the thirteenth O site, O(13) is bonded to one Mg(3), one Ti(3), one Ti(4), and one Ti(5) atom to form OMgTi3 trigonal pyramids that share  a cornercorner with one O(12)MgTi3 trigonal pyramid,  a cornercorner with one O(13)MgTi3 trigonal pyramid,  a cornercorner with one O(15)MgTi3 trigonal pyramid,  a cornercorner with one O(2)MgTi3 trigonal pyramid,  an edgeedge with one O(14)Mg2Ti2 trigonal pyramid,  an edgeedge with one O(4)Mg2Ti2 trigonal pyramid,  an edgeedge with one O(7)MgTi3 trigonal pyramid, and  an edgeedge with one O(17)Ti4 trigonal pyramid. In the fourteenth O site, O(14) is bonded to one Mg(3), one Mg(5), and two equivalent Ti(5) atoms to form distorted OMg2Ti2 trigonal pyramids that share  a cornercorner with one O(3)Mg2Ti2 trigonal pyramid,  a cornercorner with one O(4)Mg2Ti2 trigonal pyramid, corners with two equivalent O(17)Ti4 trigonal pyramids, edges with two equivalent O(12)MgTi3 trigonal pyramids, and edges with two equivalent O(13)MgTi3 trigonal pyramids. In the fifteenth O site, O(15) is bonded to one Mg(4), one Ti(6), and two equivalent Ti(3) atoms to form distorted OMgTi3 trigonal pyramids that share  a cornercorner with one O(5)Mg2Ti2 trigonal pyramid,  a cornercorner with one O(16)MgTi3 trigonal pyramid, corners with two equivalent O(13)MgTi3 trigonal pyramids, edges with two equivalent O(7)MgTi3 trigonal pyramids, and edges with two equivalent O(17)Ti4 trigonal pyramids. In the sixteenth O site, O(16) is bonded to one Mg(1), one Ti(6), and two equivalent Ti(7) atoms to form distorted OMgTi3 trigonal pyramids that share  a cornercorner with one O(5)Mg2Ti2 trigonal pyramid,  a cornercorner with one O(15)MgTi3 trigonal pyramid, corners with two equivalent O(12)MgTi3 trigonal pyramids, edges with two equivalent O(6)MgTi3 trigonal pyramids, and edges with two equivalent O(17)Ti4 trigonal pyramids. In the seventeenth O site, O(17) is bonded to one Ti(3), one Ti(5), one Ti(6), and one Ti(7) atom to form distorted OTi4 trigonal pyramids that share  a cornercorner with one O(14)Mg2Ti2 trigonal pyramid,  a cornercorner with one O(6)MgTi3 trigonal pyramid,  a cornercorner with one O(7)MgTi3 trigonal pyramid,  a cornercorner with one O(17)Ti4 trigonal pyramid,  an edgeedge with one O(12)MgTi3 trigonal pyramid,  an edgeedge with one O(13)MgTi3 trigonal pyramid,  an edgeedge with one O(15)MgTi3 trigonal pyramid, and  an edgeedge with one O(16)MgTi3 trigonal pyramid. In the eighteenth O site, O(18) is bonded in a distorted trigonal non-coplanar geometry to one Mg(5), one Ti(1), and one Ti(7) atom.
Mg5Ti13O30 crystallizes in the monoclinic Pm space group. There are five inequivalent Mg sites. In the first Mg site, Mg(1) is bonded in a 6-coordinate geometry to one O(16), one O(5), two equivalent O(1), and two equivalent O(6) atoms. The Mg(1)-O(16) bond length is 2.08 Å. The Mg(1)-O(5) bond length is 2.04 Å. Both Mg(1)-O(1) bond lengths are 1.99 Å. Both Mg(1)-O(6) bond lengths are 2.19 Å. In the second Mg site, Mg(2) is bonded in a 6-coordinate geometry to one O(3), one O(4), two equivalent O(2), and two equivalent O(8) atoms. The Mg(2)-O(3) bond length is 2.05 Å. The Mg(2)-O(4) bond length is 2.06 Å. Both Mg(2)-O(2) bond lengths are 2.20 Å. Both Mg(2)-O(8) bond lengths are 2.00 Å. In the third Mg site, Mg(3) is bonded in a 6-coordinate geometry to one O(14), one O(4), two equivalent O(13), and two equivalent O(9) atoms. The Mg(3)-O(14) bond length is 2.05 Å. The Mg(3)-O(4) bond length is 2.04 Å. Both Mg(3)-O(13) bond lengths are 2.21 Å. Both Mg(3)-O(9) bond lengths are 2.01 Å. In the fourth Mg site, Mg(4) is bonded to one O(15), one O(5), two equivalent O(10), and two equivalent O(7) atoms to form distorted MgO6 octahedra that share corners with two equivalent Ti(2)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, edges with two equivalent Ti(3)O6 octahedra, and edges with two equivalent Ti(4)O6 octahedra. The corner-sharing octahedral tilt angles are 29°. The Mg(4)-O(15) bond length is 2.10 Å. The Mg(4)-O(5) bond length is 2.05 Å. Both Mg(4)-O(10) bond lengths are 1.99 Å. Both Mg(4)-O(7) bond lengths are 2.18 Å. In the fifth Mg site, Mg(5) is bonded in a 6-coordinate geometry to one O(14), one O(3), two equivalent O(12), and two equivalent O(18) atoms. The Mg(5)-O(14) bond length is 2.07 Å. The Mg(5)-O(3) bond length is 2.06 Å. Both Mg(5)-O(12) bond lengths are 2.19 Å. Both Mg(5)-O(18) bond lengths are 1.99 Å. There are seven inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(1), one O(12), one O(18), one O(2), one O(3), and one O(6) atom to form a mixture of distorted corner and edge-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 30-48°. The Ti(1)-O(1) bond length is 2.00 Å. The Ti(1)-O(12) bond length is 1.95 Å. The Ti(1)-O(18) bond length is 1.83 Å. The Ti(1)-O(2) bond length is 1.95 Å. The Ti(1)-O(3) bond length is 2.00 Å. The Ti(1)-O(6) bond length is 2.17 Å. In the second Ti site, Ti(2) is bonded to one O(10), one O(2), one O(5), one O(6), one O(7), and one O(8) atom to form distorted TiO6 octahedra that share  a cornercorner with one Mg(4)O6 octahedra,  a cornercorner with one Ti(2)O6 octahedra,  a cornercorner with one Ti(3)O6 octahedra,  a cornercorner with one Ti(7)O6 octahedra,  an edgeedge with one Mg(4)O6 octahedra,  an edgeedge with one Ti(1)O6 octahedra, and edges with two equivalent Ti(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 29-49°. The Ti(2)-O(10) bond length is 1.81 Å. The Ti(2)-O(2) bond length is 2.17 Å. The Ti(2)-O(5) bond length is 2.01 Å. The Ti(2)-O(6) bond length is 1.96 Å. The Ti(2)-O(7) bond length is 1.95 Å. The Ti(2)-O(8) bond length is 2.00 Å. In the third Ti site, Ti(3) is bonded to one O(11), one O(13), one O(15), one O(17), one O(7), and one O(9) atom to form distorted TiO6 octahedra that share  a cornercorner with one Ti(2)O6 octahedra,  a cornercorner with one Ti(3)O6 octahedra,  a cornercorner with one Ti(7)O6 octahedra,  an edgeedge with one Mg(4)O6 octahedra,  an edgeedge with one Ti(4)O6 octahedra, and edges with two equivalent Ti(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 30-47°. The Ti(3)-O(11) bond length is 1.89 Å. The Ti(3)-O(13) bond length is 2.10 Å. The Ti(3)-O(15) bond length is 2.05 Å. The Ti(3)-O(17) bond length is 1.97 Å. The Ti(3)-O(7) bond length is 1.92 Å. The Ti(3)-O(9) bond length is 1.95 Å. In the fourth Ti site, Ti(4) is bonded to one O(10), one O(13), one O(2), one O(4), one O(7), and one O(8) atom to form distorted TiO6 octahedra that share  a cornercorner with one Ti(1)O6 octahedra,  a cornercorner with one Ti(4)O6 octahedra,  a cornercorner with one Ti(5)O6 octahedra,  an edgeedge with one Mg(4)O6 octahedra,  an edgeedge with one Ti(3)O6 octahedra, and edges with two equivalent Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 31-49°. The Ti(4)-O(10) bond length is 1.99 Å. The Ti(4)-O(13) bond length is 1.96 Å. The Ti(4)-O(2) bond length is 1.94 Å. The Ti(4)-O(4) bond length is 2.01 Å. The Ti(4)-O(7) bond length is 2.21 Å. The Ti(4)-O(8) bond length is 1.81 Å. In the fifth Ti site, Ti(5) is bonded to one O(11), one O(12), one O(13), one O(14), one O(17), and one O(9) atom to form a mixture of distorted corner and edge-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 30-48°. The Ti(5)-O(11) bond length is 2.05 Å. The Ti(5)-O(12) bond length is 1.93 Å. The Ti(5)-O(13) bond length is 1.96 Å. The Ti(5)-O(14) bond length is 1.99 Å. The Ti(5)-O(17) bond length is 2.17 Å. The Ti(5)-O(9) bond length is 1.82 Å. In the sixth Ti site, Ti(6) is bonded in a 6-coordinate geometry to one O(15), one O(16), two equivalent O(11), and two equivalent O(17) atoms. The Ti(6)-O(15) bond length is 2.01 Å. The Ti(6)-O(16) bond length is 2.00 Å. Both Ti(6)-O(11) bond lengths are 1.94 Å. Both Ti(6)-O(17) bond lengths are 2.14 Å. In the seventh Ti site, Ti(7) is bonded to one O(1), one O(12), one O(16), one O(17), one O(18), and one O(6) atom to form a mixture of distorted corner and edge-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 31-51°. The Ti(7)-O(1) bond length is 1.81 Å. The Ti(7)-O(12) bond length is 2.17 Å. The Ti(7)-O(16) bond length is 2.07 Å. The Ti(7)-O(17) bond length is 1.97 Å. The Ti(7)-O(18) bond length is 1.95 Å. The Ti(7)-O(6) bond length is 1.92 Å. There are eighteen inequivalent O sites. In the first O site, O(1) is bonded in a distorted T-shaped geometry to one Mg(1), one Ti(1), and one Ti(7) atom. In the second O site, O(2) is bonded to one Mg(2), one Ti(1), one Ti(2), and one Ti(4) atom to form OMgTi3 trigonal pyramids that share  a cornercorner with one O(5)Mg2Ti2 trigonal pyramid,  a cornercorner with one O(12)MgTi3 trigonal pyramid,  a cornercorner with one O(13)MgTi3 trigonal pyramid,  a cornercorner with one O(2)MgTi3 trigonal pyramid,  an edgeedge with one O(3)Mg2Ti2 trigonal pyramid,  an edgeedge with one O(4)Mg2Ti2 trigonal pyramid,  an edgeedge with one O(6)MgTi3 trigonal pyramid, and  an edgeedge with one O(7)MgTi3 trigonal pyramid. In the third O site, O(3) is bonded to one Mg(2), one Mg(5), and two equivalent Ti(1) atoms to form distorted OMg2Ti2 trigonal pyramids that share  a cornercorner with one O(14)Mg2Ti2 trigonal pyramid,  a cornercorner with one O(4)Mg2Ti2 trigonal pyramid, corners with two equivalent O(6)MgTi3 trigonal pyramids, edges with two equivalent O(12)MgTi3 trigonal pyramids, and edges with two equivalent O(2)MgTi3 trigonal pyramids. In the fourth O site, O(4) is bonded to one Mg(2), one Mg(3), and two equivalent Ti(4) atoms to form distorted OMg2Ti2 trigonal pyramids that share  a cornercorner with one O(14)Mg2Ti2 trigonal pyramid,  a cornercorner with one O(3)Mg2Ti2 trigonal pyramid, corners with two equivalent O(7)MgTi3 trigonal pyramids, edges with two equivalent O(13)MgTi3 trigonal pyramids, and edges with two equivalent O(2)MgTi3 trigonal pyramids. In the fifth O site, O(5) is bonded to one Mg(1), one Mg(4), and two equivalent Ti(2) atoms to form a mixture of distorted corner and edge-sharing OMg2Ti2 trigonal pyramids. In the sixth O site, O(6) is bonded to one Mg(1), one Ti(1), one Ti(2), and one Ti(7) atom to form distorted OMgTi3 trigonal pyramids that share  a cornercorner with one O(3)Mg2Ti2 trigonal pyramid,  a cornercorner with one O(6)MgTi3 trigonal pyramid,  a cornercorner with one O(7)MgTi3 trigonal pyramid,  a cornercorner with one O(17)Ti4 trigonal pyramid,  an edgeedge with one O(5)Mg2Ti2 trigonal pyramid,  an edgeedge with one O(12)MgTi3 trigonal pyramid,  an edgeedge with one O(16)MgTi3 trigonal pyramid, and  an edgeedge with one O(2)MgTi3 trigonal pyramid. In the seventh O site, O(7) is bonded to one Mg(4), one Ti(2), one Ti(3), and one Ti(4) atom to form distorted OMgTi3 trigonal pyramids that share  a cornercorner with one O(4)Mg2Ti2 trigonal pyramid,  a cornercorner with one O(6)MgTi3 trigonal pyramid,  a cornercorner with one O(7)MgTi3 trigonal pyramid,  a cornercorner with one O(17)Ti4 trigonal pyramid,  an edgeedge with one O(5)Mg2Ti2 trigonal pyramid,  an edgeedge with one O(13)MgTi3 trigonal pyramid,  an edgeedge with one O(15)MgTi3 trigonal pyramid, and  an edgeedge with one O(2)MgTi3 trigonal pyramid. In the eighth O site, O(8) is bonded in a distorted trigonal non-coplanar geometry to one Mg(2), one Ti(2), and one Ti(4) atom. In the ninth O site, O(9) is bonded in a distorted trigonal non-coplanar geometry to one Mg(3), one Ti(3), and one Ti(5) atom. In the tenth O site, O(10) is bonded in a distorted trigonal non-coplanar geometry to one Mg(4), one Ti(2), and one Ti(4) atom. In the eleventh O site, O(11) is bonded in a distorted T-shaped geometry to one Ti(3), one Ti(5), and one Ti(6) atom. In the twelfth O site, O(12) is bonded to one Mg(5), one Ti(1), one Ti(5), and one Ti(7) atom to form OMgTi3 trigonal pyramids that share  a cornercorner with one O(12)MgTi3 trigonal pyramid,  a cornercorner with one O(13)MgTi3 trigonal pyramid,  a cornercorner with one O(16)MgTi3 trigonal pyramid,  a cornercorner with one O(2)MgTi3 trigonal pyramid,  an edgeedge with one O(14)Mg2Ti2 trigonal pyramid,  an edgeedge with one O(3)Mg2Ti2 trigonal pyramid,  an edgeedge with one O(6)MgTi3 trigonal pyramid, and  an edgeedge with one O(17)Ti4 trigonal pyramid. In the thirteenth O site, O(13) is bonded to one Mg(3), one Ti(3), one Ti(4), and one Ti(5) atom to form OMgTi3 trigonal pyramids that share  a cornercorner with one O(12)MgTi3 trigonal pyramid,  a cornercorner with one O(13)MgTi3 trigonal pyramid,  a cornercorner with one O(15)MgTi3 trigonal pyramid,  a cornercorner with one O(2)MgTi3 trigonal pyramid,  an edgeedge with one O(14)Mg2Ti2 trigonal pyramid,  an edgeedge with one O(4)Mg2Ti2 trigonal pyramid,  an edgeedge with one O(7)MgTi3 trigonal pyramid, and  an edgeedge with one O(17)Ti4 trigonal pyramid. In the fourteenth O site, O(14) is bonded to one Mg(3), one Mg(5), and two equivalent Ti(5) atoms to form distorted OMg2Ti2 trigonal pyramids that share  a cornercorner with one O(3)Mg2Ti2 trigonal pyramid,  a cornercorner with one O(4)Mg2Ti2 trigonal pyramid, corners with two equivalent O(17)Ti4 trigonal pyramids, edges with two equivalent O(12)MgTi3 trigonal pyramids, and edges with two equivalent O(13)MgTi3 trigonal pyramids. In the fifteenth O site, O(15) is bonded to one Mg(4), one Ti(6), and two equivalent Ti(3) atoms to form distorted OMgTi3 trigonal pyramids that share  a cornercorner with one O(5)Mg2Ti2 trigonal pyramid,  a cornercorner with one O(16)MgTi3 trigonal pyramid, corners with two equivalent O(13)MgTi3 trigonal pyramids, edges with two equivalent O(7)MgTi3 trigonal pyramids, and edges with two equivalent O(17)Ti4 trigonal pyramids. In the sixteenth O site, O(16) is bonded to one Mg(1), one Ti(6), and two equivalent Ti(7) atoms to form distorted OMgTi3 trigonal pyramids that share  a cornercorner with one O(5)Mg2Ti2 trigonal pyramid,  a cornercorner with one O(15)MgTi3 trigonal pyramid, corners with two equivalent O(12)MgTi3 trigonal pyramids, edges with two equivalent O(6)MgTi3 trigonal pyramids, and edges with two equivalent O(17)Ti4 trigonal pyramids. In the seventeenth O site, O(17) is bonded to one Ti(3), one Ti(5), one Ti(6), and one Ti(7) atom to form distorted OTi4 trigonal pyramids that share  a cornercorner with one O(14)Mg2Ti2 trigonal pyramid,  a cornercorner with one O(6)MgTi3 trigonal pyramid,  a cornercorner with one O(7)MgTi3 trigonal pyramid,  a cornercorner with one O(17)Ti4 trigonal pyramid,  an edgeedge with one O(12)MgTi3 trigonal pyramid,  an edgeedge with one O(13)MgTi3 trigonal pyramid,  an edgeedge with one O(15)MgTi3 trigonal pyramid, and  an edgeedge with one O(16)MgTi3 trigonal pyramid. In the eighteenth O site, O(18) is bonded in a distorted trigonal non-coplanar geometry to one Mg(5), one Ti(1), and one Ti(7) atom.