Mg2V9O13 crystallizes in the monoclinic C2/m space group. Mg(1) is bonded to two equivalent O(2), two equivalent O(4), and two equivalent O(5) atoms to form distorted MgO6 pentagonal pyramids that share corners with two equivalent V(2)O6 octahedra, corners with two equivalent V(3)O6 octahedra, corners with four equivalent V(4)O6 octahedra, corners with four equivalent V(5)O6 octahedra,  an edgeedge with one V(4)O6 octahedra,  an edgeedge with one V(5)O6 octahedra, and faces with two equivalent Mg(1)O6 pentagonal pyramids. The corner-sharing octahedral tilt angles range from 26-74°. There are five inequivalent V sites. In the first V site, V(1) is bonded to two equivalent O(6) and four equivalent O(7) atoms to form a mixture of corner and edge-sharing VO6 octahedra. The corner-sharing octahedral tilt angles are 4°. In the second V site, V(2) is bonded to one O(4), two equivalent O(1), and three equivalent O(3) atoms to form VO6 octahedra that share corners with two equivalent V(2)O6 octahedra, corners with two equivalent V(4)O6 octahedra, corners with two equivalent Mg(1)O6 pentagonal pyramids, edges with five equivalent V(2)O6 octahedra, and edges with five equivalent V(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-13°. In the third V site, V(3) is bonded to one O(5), two equivalent O(6), and three equivalent O(7) atoms to form VO6 octahedra that share corners with two equivalent V(1)O6 octahedra, corners with three equivalent V(5)O6 octahedra, corners with two equivalent Mg(1)O6 pentagonal pyramids, edges with three equivalent V(1)O6 octahedra, edges with three equivalent V(5)O6 octahedra, and edges with four equivalent V(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 2-13°. In the fourth V site, V(4) is bonded to one O(1), one O(2), two equivalent O(3), and two equivalent O(4) atoms to form distorted VO6 octahedra that share  a cornercorner with one V(4)O6 octahedra,  a cornercorner with one V(5)O6 octahedra, corners with two equivalent V(2)O6 octahedra, corners with four equivalent Mg(1)O6 pentagonal pyramids, edges with two equivalent V(4)O6 octahedra, edges with five equivalent V(2)O6 octahedra, and  an edgeedge with one Mg(1)O6 pentagonal pyramid. The corner-sharing octahedral tilt angles range from 0-65°. In the fifth V site, V(5) is bonded to one O(2), one O(7), two equivalent O(5), and two equivalent O(6) atoms to form distorted VO6 octahedra that share  a cornercorner with one V(4)O6 octahedra, corners with three equivalent V(3)O6 octahedra, corners with four equivalent Mg(1)O6 pentagonal pyramids, edges with two equivalent V(1)O6 octahedra, edges with two equivalent V(5)O6 octahedra, edges with three equivalent V(3)O6 octahedra, and  an edgeedge with one Mg(1)O6 pentagonal pyramid. The corner-sharing octahedral tilt angles range from 2-65°. There are seven inequivalent O sites. In the first O site, O(7) is bonded to one V(5), two equivalent V(1), and three equivalent V(3) atoms to form OV6 octahedra that share corners with two equivalent O(7)V6 octahedra, corners with two equivalent O(6)V5 square pyramids,  a cornercorner with one O(2)Mg2V2 tetrahedra,  a cornercorner with one O(5)Mg2V3 trigonal bipyramid, edges with five equivalent O(7)V6 octahedra, edges with five equivalent O(6)V5 square pyramids, and edges with two equivalent O(5)Mg2V3 trigonal bipyramids. The corner-sharing octahedra are not tilted. In the second O site, O(1) is bonded to two equivalent V(4) and four equivalent V(2) atoms to form OV6 octahedra that share corners with four equivalent O(3)V5 square pyramids, corners with two equivalent O(2)Mg2V2 tetrahedra, edges with two equivalent O(1)V6 octahedra, edges with six equivalent O(3)V5 square pyramids, and edges with four equivalent O(4)Mg2V3 trigonal bipyramids. In the third O site, O(2) is bonded to two equivalent Mg(1), one V(4), and one V(5) atom to form OMg2V2 tetrahedra that share  a cornercorner with one O(1)V6 octahedra,  a cornercorner with one O(7)V6 octahedra, corners with two equivalent O(3)V5 square pyramids, corners with two equivalent O(6)V5 square pyramids, corners with two equivalent O(2)Mg2V2 tetrahedra, corners with four equivalent O(4)Mg2V3 trigonal bipyramids, corners with four equivalent O(5)Mg2V3 trigonal bipyramids,  an edgeedge with one O(4)Mg2V3 trigonal bipyramid, and  an edgeedge with one O(5)Mg2V3 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 6-8°. In the fourth O site, O(3) is bonded to two equivalent V(4) and three equivalent V(2) atoms to form OV5 square pyramids that share corners with two equivalent O(1)V6 octahedra, corners with two equivalent O(2)Mg2V2 tetrahedra, corners with five equivalent O(4)Mg2V3 trigonal bipyramids, edges with three equivalent O(1)V6 octahedra, edges with four equivalent O(3)V5 square pyramids, and  an edgeedge with one O(4)Mg2V3 trigonal bipyramid. The corner-sharing octahedral tilt angles are 7°. In the fifth O site, O(4) is bonded to two equivalent Mg(1), one V(2), and two equivalent V(4) atoms to form distorted OMg2V3 trigonal bipyramids that share corners with five equivalent O(3)V5 square pyramids, corners with four equivalent O(2)Mg2V2 tetrahedra, corners with two equivalent O(5)Mg2V3 trigonal bipyramids, edges with two equivalent O(1)V6 octahedra,  an edgeedge with one O(3)V5 square pyramid,  an edgeedge with one O(2)Mg2V2 tetrahedra,  an edgeedge with one O(5)Mg2V3 trigonal bipyramid, and edges with two equivalent O(4)Mg2V3 trigonal bipyramids. In the sixth O site, O(5) is bonded to two equivalent Mg(1), one V(3), and two equivalent V(5) atoms to form distorted OMg2V3 trigonal bipyramids that share  a cornercorner with one O(7)V6 octahedra, corners with four equivalent O(6)V5 square pyramids, corners with four equivalent O(2)Mg2V2 tetrahedra, corners with two equivalent O(4)Mg2V3 trigonal bipyramids, edges with two equivalent O(7)V6 octahedra,  an edgeedge with one O(6)V5 square pyramid,  an edgeedge with one O(2)Mg2V2 tetrahedra,  an edgeedge with one O(4)Mg2V3 trigonal bipyramid, and edges with two equivalent O(5)Mg2V3 trigonal bipyramids. The corner-sharing octahedral tilt angles are 5°. In the seventh O site, O(6) is bonded to one V(1), two equivalent V(3), and two equivalent V(5) atoms to form OV5 square pyramids that share corners with two equivalent O(7)V6 octahedra,  a cornercorner with one O(6)V5 square pyramid, corners with two equivalent O(2)Mg2V2 tetrahedra, corners with four equivalent O(5)Mg2V3 trigonal bipyramids, edges with five equivalent O(7)V6 octahedra, edges with two equivalent O(6)V5 square pyramids, and  an edgeedge with one O(5)Mg2V3 trigonal bipyramid. The corner-sharing octahedral tilt angles are 8°.
Mg2V9O13 crystallizes in the monoclinic C2/m space group. Mg(1) is bonded to two equivalent O(2), two equivalent O(4), and two equivalent O(5) atoms to form distorted MgO6 pentagonal pyramids that share corners with two equivalent V(2)O6 octahedra, corners with two equivalent V(3)O6 octahedra, corners with four equivalent V(4)O6 octahedra, corners with four equivalent V(5)O6 octahedra,  an edgeedge with one V(4)O6 octahedra,  an edgeedge with one V(5)O6 octahedra, and faces with two equivalent Mg(1)O6 pentagonal pyramids. The corner-sharing octahedral tilt angles range from 26-74°. Both Mg(1)-O(2) bond lengths are 2.05 Å. Both Mg(1)-O(4) bond lengths are 2.33 Å. Both Mg(1)-O(5) bond lengths are 2.29 Å. There are five inequivalent V sites. In the first V site, V(1) is bonded to two equivalent O(6) and four equivalent O(7) atoms to form a mixture of corner and edge-sharing VO6 octahedra. The corner-sharing octahedral tilt angles are 4°. Both V(1)-O(6) bond lengths are 2.14 Å. All V(1)-O(7) bond lengths are 2.14 Å. In the second V site, V(2) is bonded to one O(4), two equivalent O(1), and three equivalent O(3) atoms to form VO6 octahedra that share corners with two equivalent V(2)O6 octahedra, corners with two equivalent V(4)O6 octahedra, corners with two equivalent Mg(1)O6 pentagonal pyramids, edges with five equivalent V(2)O6 octahedra, and edges with five equivalent V(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-13°. The V(2)-O(4) bond length is 2.08 Å. Both V(2)-O(1) bond lengths are 2.14 Å. There are two shorter (2.13 Å) and one longer (2.18 Å) V(2)-O(3) bond length. In the third V site, V(3) is bonded to one O(5), two equivalent O(6), and three equivalent O(7) atoms to form VO6 octahedra that share corners with two equivalent V(1)O6 octahedra, corners with three equivalent V(5)O6 octahedra, corners with two equivalent Mg(1)O6 pentagonal pyramids, edges with three equivalent V(1)O6 octahedra, edges with three equivalent V(5)O6 octahedra, and edges with four equivalent V(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 2-13°. The V(3)-O(5) bond length is 2.08 Å. Both V(3)-O(6) bond lengths are 2.13 Å. There are two shorter (2.15 Å) and one longer (2.29 Å) V(3)-O(7) bond length. In the fourth V site, V(4) is bonded to one O(1), one O(2), two equivalent O(3), and two equivalent O(4) atoms to form distorted VO6 octahedra that share  a cornercorner with one V(4)O6 octahedra,  a cornercorner with one V(5)O6 octahedra, corners with two equivalent V(2)O6 octahedra, corners with four equivalent Mg(1)O6 pentagonal pyramids, edges with two equivalent V(4)O6 octahedra, edges with five equivalent V(2)O6 octahedra, and  an edgeedge with one Mg(1)O6 pentagonal pyramid. The corner-sharing octahedral tilt angles range from 0-65°. The V(4)-O(1) bond length is 2.42 Å. The V(4)-O(2) bond length is 2.05 Å. Both V(4)-O(3) bond lengths are 2.13 Å. Both V(4)-O(4) bond lengths are 2.07 Å. In the fifth V site, V(5) is bonded to one O(2), one O(7), two equivalent O(5), and two equivalent O(6) atoms to form distorted VO6 octahedra that share  a cornercorner with one V(4)O6 octahedra, corners with three equivalent V(3)O6 octahedra, corners with four equivalent Mg(1)O6 pentagonal pyramids, edges with two equivalent V(1)O6 octahedra, edges with two equivalent V(5)O6 octahedra, edges with three equivalent V(3)O6 octahedra, and  an edgeedge with one Mg(1)O6 pentagonal pyramid. The corner-sharing octahedral tilt angles range from 2-65°. The V(5)-O(2) bond length is 2.05 Å. The V(5)-O(7) bond length is 2.48 Å. Both V(5)-O(5) bond lengths are 2.08 Å. Both V(5)-O(6) bond lengths are 2.14 Å. There are seven inequivalent O sites. In the first O site, O(7) is bonded to one V(5), two equivalent V(1), and three equivalent V(3) atoms to form OV6 octahedra that share corners with two equivalent O(7)V6 octahedra, corners with two equivalent O(6)V5 square pyramids,  a cornercorner with one O(2)Mg2V2 tetrahedra,  a cornercorner with one O(5)Mg2V3 trigonal bipyramid, edges with five equivalent O(7)V6 octahedra, edges with five equivalent O(6)V5 square pyramids, and edges with two equivalent O(5)Mg2V3 trigonal bipyramids. The corner-sharing octahedra are not tilted. In the second O site, O(1) is bonded to two equivalent V(4) and four equivalent V(2) atoms to form OV6 octahedra that share corners with four equivalent O(3)V5 square pyramids, corners with two equivalent O(2)Mg2V2 tetrahedra, edges with two equivalent O(1)V6 octahedra, edges with six equivalent O(3)V5 square pyramids, and edges with four equivalent O(4)Mg2V3 trigonal bipyramids. In the third O site, O(2) is bonded to two equivalent Mg(1), one V(4), and one V(5) atom to form OMg2V2 tetrahedra that share  a cornercorner with one O(1)V6 octahedra,  a cornercorner with one O(7)V6 octahedra, corners with two equivalent O(3)V5 square pyramids, corners with two equivalent O(6)V5 square pyramids, corners with two equivalent O(2)Mg2V2 tetrahedra, corners with four equivalent O(4)Mg2V3 trigonal bipyramids, corners with four equivalent O(5)Mg2V3 trigonal bipyramids,  an edgeedge with one O(4)Mg2V3 trigonal bipyramid, and  an edgeedge with one O(5)Mg2V3 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 6-8°. In the fourth O site, O(3) is bonded to two equivalent V(4) and three equivalent V(2) atoms to form OV5 square pyramids that share corners with two equivalent O(1)V6 octahedra, corners with two equivalent O(2)Mg2V2 tetrahedra, corners with five equivalent O(4)Mg2V3 trigonal bipyramids, edges with three equivalent O(1)V6 octahedra, edges with four equivalent O(3)V5 square pyramids, and  an edgeedge with one O(4)Mg2V3 trigonal bipyramid. The corner-sharing octahedral tilt angles are 7°. In the fifth O site, O(4) is bonded to two equivalent Mg(1), one V(2), and two equivalent V(4) atoms to form distorted OMg2V3 trigonal bipyramids that share corners with five equivalent O(3)V5 square pyramids, corners with four equivalent O(2)Mg2V2 tetrahedra, corners with two equivalent O(5)Mg2V3 trigonal bipyramids, edges with two equivalent O(1)V6 octahedra,  an edgeedge with one O(3)V5 square pyramid,  an edgeedge with one O(2)Mg2V2 tetrahedra,  an edgeedge with one O(5)Mg2V3 trigonal bipyramid, and edges with two equivalent O(4)Mg2V3 trigonal bipyramids. In the sixth O site, O(5) is bonded to two equivalent Mg(1), one V(3), and two equivalent V(5) atoms to form distorted OMg2V3 trigonal bipyramids that share  a cornercorner with one O(7)V6 octahedra, corners with four equivalent O(6)V5 square pyramids, corners with four equivalent O(2)Mg2V2 tetrahedra, corners with two equivalent O(4)Mg2V3 trigonal bipyramids, edges with two equivalent O(7)V6 octahedra,  an edgeedge with one O(6)V5 square pyramid,  an edgeedge with one O(2)Mg2V2 tetrahedra,  an edgeedge with one O(4)Mg2V3 trigonal bipyramid, and edges with two equivalent O(5)Mg2V3 trigonal bipyramids. The corner-sharing octahedral tilt angles are 5°. In the seventh O site, O(6) is bonded to one V(1), two equivalent V(3), and two equivalent V(5) atoms to form OV5 square pyramids that share corners with two equivalent O(7)V6 octahedra,  a cornercorner with one O(6)V5 square pyramid, corners with two equivalent O(2)Mg2V2 tetrahedra, corners with four equivalent O(5)Mg2V3 trigonal bipyramids, edges with five equivalent O(7)V6 octahedra, edges with two equivalent O(6)V5 square pyramids, and  an edgeedge with one O(5)Mg2V3 trigonal bipyramid. The corner-sharing octahedral tilt angles are 8°.