MgTi3V5O16 crystallizes in the triclinic P1 space group. Mg(1) is bonded to one O(11), one O(12), one O(14), one O(16), one O(3), and one O(5) atom to form MgO6 octahedra that share corners with two equivalent Ti(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra, corners with three equivalent Ti(3)O6 octahedra,  an edgeedge with one V(4)O6 octahedra,  an edgeedge with one V(5)O6 octahedra, and edges with two equivalent V(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 11-57°. There are three inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(14), one O(2), one O(3), one O(4), one O(7), and one O(9) atom to form distorted TiO6 octahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent V(3)O6 octahedra,  an edgeedge with one V(1)O6 octahedra, and edges with two equivalent Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 39-60°. In the second Ti site, Ti(2) is bonded to one O(16), one O(2), one O(3), one O(4), one O(8), and one O(9) atom to form distorted TiO6 octahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent V(3)O6 octahedra,  an edgeedge with one V(1)O6 octahedra, and edges with two equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 47-57°. In the third Ti site, Ti(3) is bonded to one O(1), one O(11), one O(12), one O(13), one O(5), and one O(6) atom to form TiO6 octahedra that share corners with two equivalent V(1)O6 octahedra, corners with three equivalent Mg(1)O6 octahedra,  an edgeedge with one V(3)O6 octahedra, edges with two equivalent V(4)O6 octahedra, and edges with two equivalent V(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 11-53°. There are five inequivalent V sites. In the first V site, V(1) is bonded to one O(1), one O(10), one O(2), one O(6), one O(7), and one O(8) atom to form VO6 octahedra that share corners with two equivalent Ti(3)O6 octahedra, corners with two equivalent V(4)O6 octahedra, corners with two equivalent V(5)O6 octahedra,  an edgeedge with one Ti(1)O6 octahedra, and  an edgeedge with one Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-53°. In the second V site, V(2) is bonded in a 6-coordinate geometry to one O(14), one O(16), one O(3), one O(4), one O(7), and one O(8) atom. In the third V site, V(3) is bonded to one O(11), one O(12), one O(14), one O(15), one O(16), and one O(9) atom to form VO6 octahedra that share corners with two equivalent Ti(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra,  an edgeedge with one Ti(3)O6 octahedra,  an edgeedge with one V(4)O6 octahedra,  an edgeedge with one V(5)O6 octahedra, and edges with two equivalent Mg(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 48-60°. In the fourth V site, V(4) is bonded to one O(10), one O(12), one O(13), one O(15), one O(5), and one O(6) atom to form distorted VO6 octahedra that share corners with two equivalent V(1)O6 octahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one V(3)O6 octahedra, edges with two equivalent Ti(3)O6 octahedra, and edges with two equivalent V(5)O6 octahedra. The corner-sharing octahedral tilt angles are 51°. In the fifth V site, V(5) is bonded to one O(1), one O(10), one O(11), one O(13), one O(15), and one O(5) atom to form distorted VO6 octahedra that share corners with two equivalent V(1)O6 octahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one V(3)O6 octahedra, edges with two equivalent Ti(3)O6 octahedra, and edges with two equivalent V(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-51°. There are sixteen inequivalent O sites. In the first O site, O(1) is bonded in a distorted trigonal planar geometry to one Ti(3), one V(1), and one V(5) atom. In the second O site, O(2) is bonded in a distorted trigonal non-coplanar geometry to one Ti(1), one Ti(2), and one V(1) atom. In the third O site, O(3) is bonded to one Mg(1), one Ti(1), one Ti(2), and one V(2) atom to form a mixture of edge and corner-sharing OMgTi2V trigonal pyramids. In the fourth O site, O(4) is bonded in a trigonal non-coplanar geometry to one Ti(1), one Ti(2), and one V(2) atom. In the fifth O site, O(5) is bonded in a see-saw-like geometry to one Mg(1), one Ti(3), one V(4), and one V(5) atom. In the sixth O site, O(6) is bonded in a distorted trigonal planar geometry to one Ti(3), one V(1), and one V(4) atom. In the seventh O site, O(7) is bonded in a 3-coordinate geometry to one Ti(1), one V(1), and one V(2) atom. In the eighth O site, O(8) is bonded in a distorted trigonal non-coplanar geometry to one Ti(2), one V(1), and one V(2) atom. In the ninth O site, O(9) is bonded in a distorted trigonal planar geometry to one Ti(1), one Ti(2), and one V(3) atom. In the tenth O site, O(10) is bonded in a trigonal planar geometry to one V(1), one V(4), and one V(5) atom. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Mg(1), one Ti(3), one V(3), and one V(5) atom. In the twelfth O site, O(12) is bonded in a rectangular see-saw-like geometry to one Mg(1), one Ti(3), one V(3), and one V(4) atom. In the thirteenth O site, O(13) is bonded in a distorted trigonal non-coplanar geometry to one Ti(3), one V(4), and one V(5) atom. In the fourteenth O site, O(14) is bonded in a 4-coordinate geometry to one Mg(1), one Ti(1), one V(2), and one V(3) atom. In the fifteenth O site, O(15) is bonded in a trigonal non-coplanar geometry to one V(3), one V(4), and one V(5) atom. In the sixteenth O site, O(16) is bonded to one Mg(1), one Ti(2), one V(2), and one V(3) atom to form a mixture of distorted edge and corner-sharing OMgTiV2 trigonal pyramids.
MgTi3V5O16 crystallizes in the triclinic P1 space group. Mg(1) is bonded to one O(11), one O(12), one O(14), one O(16), one O(3), and one O(5) atom to form MgO6 octahedra that share corners with two equivalent Ti(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra, corners with three equivalent Ti(3)O6 octahedra,  an edgeedge with one V(4)O6 octahedra,  an edgeedge with one V(5)O6 octahedra, and edges with two equivalent V(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 11-57°. The Mg(1)-O(11) bond length is 2.04 Å. The Mg(1)-O(12) bond length is 2.03 Å. The Mg(1)-O(14) bond length is 2.14 Å. The Mg(1)-O(16) bond length is 2.28 Å. The Mg(1)-O(3) bond length is 2.06 Å. The Mg(1)-O(5) bond length is 2.12 Å. There are three inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(14), one O(2), one O(3), one O(4), one O(7), and one O(9) atom to form distorted TiO6 octahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent V(3)O6 octahedra,  an edgeedge with one V(1)O6 octahedra, and edges with two equivalent Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 39-60°. The Ti(1)-O(14) bond length is 1.84 Å. The Ti(1)-O(2) bond length is 1.86 Å. The Ti(1)-O(3) bond length is 2.03 Å. The Ti(1)-O(4) bond length is 1.95 Å. The Ti(1)-O(7) bond length is 2.27 Å. The Ti(1)-O(9) bond length is 2.12 Å. In the second Ti site, Ti(2) is bonded to one O(16), one O(2), one O(3), one O(4), one O(8), and one O(9) atom to form distorted TiO6 octahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent V(3)O6 octahedra,  an edgeedge with one V(1)O6 octahedra, and edges with two equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 47-57°. The Ti(2)-O(16) bond length is 2.14 Å. The Ti(2)-O(2) bond length is 2.14 Å. The Ti(2)-O(3) bond length is 2.08 Å. The Ti(2)-O(4) bond length is 1.94 Å. The Ti(2)-O(8) bond length is 1.88 Å. The Ti(2)-O(9) bond length is 1.87 Å. In the third Ti site, Ti(3) is bonded to one O(1), one O(11), one O(12), one O(13), one O(5), and one O(6) atom to form TiO6 octahedra that share corners with two equivalent V(1)O6 octahedra, corners with three equivalent Mg(1)O6 octahedra,  an edgeedge with one V(3)O6 octahedra, edges with two equivalent V(4)O6 octahedra, and edges with two equivalent V(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 11-53°. The Ti(3)-O(1) bond length is 2.11 Å. The Ti(3)-O(11) bond length is 1.91 Å. The Ti(3)-O(12) bond length is 1.91 Å. The Ti(3)-O(13) bond length is 1.93 Å. The Ti(3)-O(5) bond length is 2.01 Å. The Ti(3)-O(6) bond length is 2.13 Å. There are five inequivalent V sites. In the first V site, V(1) is bonded to one O(1), one O(10), one O(2), one O(6), one O(7), and one O(8) atom to form VO6 octahedra that share corners with two equivalent Ti(3)O6 octahedra, corners with two equivalent V(4)O6 octahedra, corners with two equivalent V(5)O6 octahedra,  an edgeedge with one Ti(1)O6 octahedra, and  an edgeedge with one Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-53°. The V(1)-O(1) bond length is 2.09 Å. The V(1)-O(10) bond length is 1.96 Å. The V(1)-O(2) bond length is 2.03 Å. The V(1)-O(6) bond length is 2.07 Å. The V(1)-O(7) bond length is 2.10 Å. The V(1)-O(8) bond length is 2.08 Å. In the second V site, V(2) is bonded in a 6-coordinate geometry to one O(14), one O(16), one O(3), one O(4), one O(7), and one O(8) atom. The V(2)-O(14) bond length is 2.40 Å. The V(2)-O(16) bond length is 1.99 Å. The V(2)-O(3) bond length is 2.02 Å. The V(2)-O(4) bond length is 1.95 Å. The V(2)-O(7) bond length is 1.73 Å. The V(2)-O(8) bond length is 2.00 Å. In the third V site, V(3) is bonded to one O(11), one O(12), one O(14), one O(15), one O(16), and one O(9) atom to form VO6 octahedra that share corners with two equivalent Ti(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra,  an edgeedge with one Ti(3)O6 octahedra,  an edgeedge with one V(4)O6 octahedra,  an edgeedge with one V(5)O6 octahedra, and edges with two equivalent Mg(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 48-60°. The V(3)-O(11) bond length is 2.12 Å. The V(3)-O(12) bond length is 2.10 Å. The V(3)-O(14) bond length is 2.06 Å. The V(3)-O(15) bond length is 2.00 Å. The V(3)-O(16) bond length is 2.02 Å. The V(3)-O(9) bond length is 2.04 Å. In the fourth V site, V(4) is bonded to one O(10), one O(12), one O(13), one O(15), one O(5), and one O(6) atom to form distorted VO6 octahedra that share corners with two equivalent V(1)O6 octahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one V(3)O6 octahedra, edges with two equivalent Ti(3)O6 octahedra, and edges with two equivalent V(5)O6 octahedra. The corner-sharing octahedral tilt angles are 51°. The V(4)-O(10) bond length is 1.98 Å. The V(4)-O(12) bond length is 2.17 Å. The V(4)-O(13) bond length is 1.97 Å. The V(4)-O(15) bond length is 1.97 Å. The V(4)-O(5) bond length is 2.02 Å. The V(4)-O(6) bond length is 1.79 Å. In the fifth V site, V(5) is bonded to one O(1), one O(10), one O(11), one O(13), one O(15), and one O(5) atom to form distorted VO6 octahedra that share corners with two equivalent V(1)O6 octahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one V(3)O6 octahedra, edges with two equivalent Ti(3)O6 octahedra, and edges with two equivalent V(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 50-51°. The V(5)-O(1) bond length is 1.79 Å. The V(5)-O(10) bond length is 1.98 Å. The V(5)-O(11) bond length is 2.17 Å. The V(5)-O(13) bond length is 1.96 Å. The V(5)-O(15) bond length is 1.98 Å. The V(5)-O(5) bond length is 2.02 Å. There are sixteen inequivalent O sites. In the first O site, O(1) is bonded in a distorted trigonal planar geometry to one Ti(3), one V(1), and one V(5) atom. In the second O site, O(2) is bonded in a distorted trigonal non-coplanar geometry to one Ti(1), one Ti(2), and one V(1) atom. In the third O site, O(3) is bonded to one Mg(1), one Ti(1), one Ti(2), and one V(2) atom to form a mixture of edge and corner-sharing OMgTi2V trigonal pyramids. In the fourth O site, O(4) is bonded in a trigonal non-coplanar geometry to one Ti(1), one Ti(2), and one V(2) atom. In the fifth O site, O(5) is bonded in a see-saw-like geometry to one Mg(1), one Ti(3), one V(4), and one V(5) atom. In the sixth O site, O(6) is bonded in a distorted trigonal planar geometry to one Ti(3), one V(1), and one V(4) atom. In the seventh O site, O(7) is bonded in a 3-coordinate geometry to one Ti(1), one V(1), and one V(2) atom. In the eighth O site, O(8) is bonded in a distorted trigonal non-coplanar geometry to one Ti(2), one V(1), and one V(2) atom. In the ninth O site, O(9) is bonded in a distorted trigonal planar geometry to one Ti(1), one Ti(2), and one V(3) atom. In the tenth O site, O(10) is bonded in a trigonal planar geometry to one V(1), one V(4), and one V(5) atom. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Mg(1), one Ti(3), one V(3), and one V(5) atom. In the twelfth O site, O(12) is bonded in a rectangular see-saw-like geometry to one Mg(1), one Ti(3), one V(3), and one V(4) atom. In the thirteenth O site, O(13) is bonded in a distorted trigonal non-coplanar geometry to one Ti(3), one V(4), and one V(5) atom. In the fourteenth O site, O(14) is bonded in a 4-coordinate geometry to one Mg(1), one Ti(1), one V(2), and one V(3) atom. In the fifteenth O site, O(15) is bonded in a trigonal non-coplanar geometry to one V(3), one V(4), and one V(5) atom. In the sixteenth O site, O(16) is bonded to one Mg(1), one Ti(2), one V(2), and one V(3) atom to form a mixture of distorted edge and corner-sharing OMgTiV2 trigonal pyramids.