Mg5Al7O16 is Spinel-like structured and crystallizes in the monoclinic P2/m space group. There are three inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent O(4) and four equivalent O(6) atoms to form MgO6 octahedra that share corners with two equivalent Mg(2)O4 tetrahedra, corners with four equivalent Mg(3)O4 tetrahedra, edges with two equivalent Al(2)O6 octahedra, and edges with four equivalent Al(4)O6 octahedra. In the second Mg site, Mg(2) is bonded to one O(2), one O(4), and two equivalent O(5) atoms to form MgO4 tetrahedra that share  a cornercorner with one Mg(1)O6 octahedra,  a cornercorner with one Al(2)O6 octahedra, corners with two equivalent Al(1)O6 octahedra, corners with two equivalent Al(3)O6 octahedra, and corners with six equivalent Al(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-65°. In the third Mg site, Mg(3) is bonded to one O(1), one O(3), and two equivalent O(6) atoms to form MgO4 tetrahedra that share  a cornercorner with one Al(1)O6 octahedra,  a cornercorner with one Al(3)O6 octahedra, corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent Al(2)O6 octahedra, and corners with six equivalent Al(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-65°. There are four inequivalent Al sites. In the first Al site, Al(1) is bonded to two equivalent O(3) and four equivalent O(5) atoms to form AlO6 octahedra that share corners with two equivalent Mg(3)O4 tetrahedra, corners with four equivalent Mg(2)O4 tetrahedra, edges with two equivalent Al(3)O6 octahedra, and edges with four equivalent Al(4)O6 octahedra. In the second Al site, Al(2) is bonded to two equivalent O(2) and four equivalent O(6) atoms to form AlO6 octahedra that share corners with two equivalent Mg(2)O4 tetrahedra, corners with four equivalent Mg(3)O4 tetrahedra, edges with two equivalent Mg(1)O6 octahedra, and edges with four equivalent Al(4)O6 octahedra. In the third Al site, Al(3) is bonded to two equivalent O(1) and four equivalent O(5) atoms to form AlO6 octahedra that share corners with two equivalent Mg(3)O4 tetrahedra, corners with four equivalent Mg(2)O4 tetrahedra, edges with two equivalent Al(1)O6 octahedra, and edges with four equivalent Al(4)O6 octahedra. In the fourth Al site, Al(4) is bonded to one O(1), one O(2), one O(3), one O(4), one O(5), and one O(6) atom to form AlO6 octahedra that share corners with three equivalent Mg(2)O4 tetrahedra, corners with three equivalent Mg(3)O4 tetrahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Al(1)O6 octahedra,  an edgeedge with one Al(2)O6 octahedra,  an edgeedge with one Al(3)O6 octahedra, and edges with two equivalent Al(4)O6 octahedra. There are six inequivalent O sites. In the first O site, O(1) is bonded to one Mg(3), one Al(3), and two equivalent Al(4) atoms to form distorted OMgAl3 trigonal pyramids that share  a cornercorner with one O(3)MgAl3 tetrahedra,  a cornercorner with one O(1)MgAl3 trigonal pyramid, corners with two equivalent O(4)Mg2Al2 trigonal pyramids, corners with two equivalent O(2)MgAl3 trigonal pyramids, corners with two equivalent O(5)MgAl3 trigonal pyramids,  an edgeedge with one O(3)MgAl3 tetrahedra, and edges with two equivalent O(5)MgAl3 trigonal pyramids. In the second O site, O(2) is bonded to one Mg(2), one Al(2), and two equivalent Al(4) atoms to form distorted OMgAl3 trigonal pyramids that share corners with two equivalent O(3)MgAl3 tetrahedra,  a cornercorner with one O(4)Mg2Al2 trigonal pyramid,  a cornercorner with one O(2)MgAl3 trigonal pyramid, corners with two equivalent O(1)MgAl3 trigonal pyramids, corners with four equivalent O(5)MgAl3 trigonal pyramids, and  an edgeedge with one O(4)Mg2Al2 trigonal pyramid. In the third O site, O(3) is bonded to one Mg(3), one Al(1), and two equivalent Al(4) atoms to form distorted OMgAl3 tetrahedra that share  a cornercorner with one O(3)MgAl3 tetrahedra,  a cornercorner with one O(1)MgAl3 trigonal pyramid, corners with two equivalent O(4)Mg2Al2 trigonal pyramids, corners with two equivalent O(2)MgAl3 trigonal pyramids, corners with two equivalent O(5)MgAl3 trigonal pyramids,  an edgeedge with one O(1)MgAl3 trigonal pyramid, and edges with two equivalent O(5)MgAl3 trigonal pyramids. In the fourth O site, O(4) is bonded to one Mg(1), one Mg(2), and two equivalent Al(4) atoms to form distorted OMg2Al2 trigonal pyramids that share corners with two equivalent O(3)MgAl3 tetrahedra,  a cornercorner with one O(4)Mg2Al2 trigonal pyramid,  a cornercorner with one O(2)MgAl3 trigonal pyramid, corners with two equivalent O(1)MgAl3 trigonal pyramids, corners with four equivalent O(5)MgAl3 trigonal pyramids, and  an edgeedge with one O(2)MgAl3 trigonal pyramid. In the fifth O site, O(5) is bonded to one Mg(2), one Al(1), one Al(3), and one Al(4) atom to form distorted OMgAl3 trigonal pyramids that share  a cornercorner with one O(3)MgAl3 tetrahedra,  a cornercorner with one O(1)MgAl3 trigonal pyramid, corners with two equivalent O(4)Mg2Al2 trigonal pyramids, corners with two equivalent O(2)MgAl3 trigonal pyramids, corners with five equivalent O(5)MgAl3 trigonal pyramids,  an edgeedge with one O(3)MgAl3 tetrahedra,  an edgeedge with one O(1)MgAl3 trigonal pyramid, and  an edgeedge with one O(5)MgAl3 trigonal pyramid. In the sixth O site, O(6) is bonded in a rectangular see-saw-like geometry to one Mg(1), one Mg(3), one Al(2), and one Al(4) atom.
Mg5Al7O16 is Spinel-like structured and crystallizes in the monoclinic P2/m space group. There are three inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent O(4) and four equivalent O(6) atoms to form MgO6 octahedra that share corners with two equivalent Mg(2)O4 tetrahedra, corners with four equivalent Mg(3)O4 tetrahedra, edges with two equivalent Al(2)O6 octahedra, and edges with four equivalent Al(4)O6 octahedra. Both Mg(1)-O(4) bond lengths are 2.08 Å. All Mg(1)-O(6) bond lengths are 2.07 Å. In the second Mg site, Mg(2) is bonded to one O(2), one O(4), and two equivalent O(5) atoms to form MgO4 tetrahedra that share  a cornercorner with one Mg(1)O6 octahedra,  a cornercorner with one Al(2)O6 octahedra, corners with two equivalent Al(1)O6 octahedra, corners with two equivalent Al(3)O6 octahedra, and corners with six equivalent Al(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-65°. The Mg(2)-O(2) bond length is 1.97 Å. The Mg(2)-O(4) bond length is 1.97 Å. Both Mg(2)-O(5) bond lengths are 1.96 Å. In the third Mg site, Mg(3) is bonded to one O(1), one O(3), and two equivalent O(6) atoms to form MgO4 tetrahedra that share  a cornercorner with one Al(1)O6 octahedra,  a cornercorner with one Al(3)O6 octahedra, corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent Al(2)O6 octahedra, and corners with six equivalent Al(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-65°. The Mg(3)-O(1) bond length is 2.00 Å. The Mg(3)-O(3) bond length is 1.96 Å. Both Mg(3)-O(6) bond lengths are 1.97 Å. There are four inequivalent Al sites. In the first Al site, Al(1) is bonded to two equivalent O(3) and four equivalent O(5) atoms to form AlO6 octahedra that share corners with two equivalent Mg(3)O4 tetrahedra, corners with four equivalent Mg(2)O4 tetrahedra, edges with two equivalent Al(3)O6 octahedra, and edges with four equivalent Al(4)O6 octahedra. Both Al(1)-O(3) bond lengths are 1.91 Å. All Al(1)-O(5) bond lengths are 1.94 Å. In the second Al site, Al(2) is bonded to two equivalent O(2) and four equivalent O(6) atoms to form AlO6 octahedra that share corners with two equivalent Mg(2)O4 tetrahedra, corners with four equivalent Mg(3)O4 tetrahedra, edges with two equivalent Mg(1)O6 octahedra, and edges with four equivalent Al(4)O6 octahedra. Both Al(2)-O(2) bond lengths are 1.96 Å. All Al(2)-O(6) bond lengths are 1.92 Å. In the third Al site, Al(3) is bonded to two equivalent O(1) and four equivalent O(5) atoms to form AlO6 octahedra that share corners with two equivalent Mg(3)O4 tetrahedra, corners with four equivalent Mg(2)O4 tetrahedra, edges with two equivalent Al(1)O6 octahedra, and edges with four equivalent Al(4)O6 octahedra. Both Al(3)-O(1) bond lengths are 1.95 Å. All Al(3)-O(5) bond lengths are 1.94 Å. In the fourth Al site, Al(4) is bonded to one O(1), one O(2), one O(3), one O(4), one O(5), and one O(6) atom to form AlO6 octahedra that share corners with three equivalent Mg(2)O4 tetrahedra, corners with three equivalent Mg(3)O4 tetrahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Al(1)O6 octahedra,  an edgeedge with one Al(2)O6 octahedra,  an edgeedge with one Al(3)O6 octahedra, and edges with two equivalent Al(4)O6 octahedra. The Al(4)-O(1) bond length is 1.96 Å. The Al(4)-O(2) bond length is 1.95 Å. The Al(4)-O(3) bond length is 1.94 Å. The Al(4)-O(4) bond length is 1.91 Å. The Al(4)-O(5) bond length is 1.95 Å. The Al(4)-O(6) bond length is 1.91 Å. There are six inequivalent O sites. In the first O site, O(1) is bonded to one Mg(3), one Al(3), and two equivalent Al(4) atoms to form distorted OMgAl3 trigonal pyramids that share  a cornercorner with one O(3)MgAl3 tetrahedra,  a cornercorner with one O(1)MgAl3 trigonal pyramid, corners with two equivalent O(4)Mg2Al2 trigonal pyramids, corners with two equivalent O(2)MgAl3 trigonal pyramids, corners with two equivalent O(5)MgAl3 trigonal pyramids,  an edgeedge with one O(3)MgAl3 tetrahedra, and edges with two equivalent O(5)MgAl3 trigonal pyramids. In the second O site, O(2) is bonded to one Mg(2), one Al(2), and two equivalent Al(4) atoms to form distorted OMgAl3 trigonal pyramids that share corners with two equivalent O(3)MgAl3 tetrahedra,  a cornercorner with one O(4)Mg2Al2 trigonal pyramid,  a cornercorner with one O(2)MgAl3 trigonal pyramid, corners with two equivalent O(1)MgAl3 trigonal pyramids, corners with four equivalent O(5)MgAl3 trigonal pyramids, and  an edgeedge with one O(4)Mg2Al2 trigonal pyramid. In the third O site, O(3) is bonded to one Mg(3), one Al(1), and two equivalent Al(4) atoms to form distorted OMgAl3 tetrahedra that share  a cornercorner with one O(3)MgAl3 tetrahedra,  a cornercorner with one O(1)MgAl3 trigonal pyramid, corners with two equivalent O(4)Mg2Al2 trigonal pyramids, corners with two equivalent O(2)MgAl3 trigonal pyramids, corners with two equivalent O(5)MgAl3 trigonal pyramids,  an edgeedge with one O(1)MgAl3 trigonal pyramid, and edges with two equivalent O(5)MgAl3 trigonal pyramids. In the fourth O site, O(4) is bonded to one Mg(1), one Mg(2), and two equivalent Al(4) atoms to form distorted OMg2Al2 trigonal pyramids that share corners with two equivalent O(3)MgAl3 tetrahedra,  a cornercorner with one O(4)Mg2Al2 trigonal pyramid,  a cornercorner with one O(2)MgAl3 trigonal pyramid, corners with two equivalent O(1)MgAl3 trigonal pyramids, corners with four equivalent O(5)MgAl3 trigonal pyramids, and  an edgeedge with one O(2)MgAl3 trigonal pyramid. In the fifth O site, O(5) is bonded to one Mg(2), one Al(1), one Al(3), and one Al(4) atom to form distorted OMgAl3 trigonal pyramids that share  a cornercorner with one O(3)MgAl3 tetrahedra,  a cornercorner with one O(1)MgAl3 trigonal pyramid, corners with two equivalent O(4)Mg2Al2 trigonal pyramids, corners with two equivalent O(2)MgAl3 trigonal pyramids, corners with five equivalent O(5)MgAl3 trigonal pyramids,  an edgeedge with one O(3)MgAl3 tetrahedra,  an edgeedge with one O(1)MgAl3 trigonal pyramid, and  an edgeedge with one O(5)MgAl3 trigonal pyramid. In the sixth O site, O(6) is bonded in a rectangular see-saw-like geometry to one Mg(1), one Mg(3), one Al(2), and one Al(4) atom.