MgAl2O4 crystallizes in the hexagonal P-6 space group. There are three inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to six equivalent O(2) atoms to form distorted MgO6 pentagonal pyramids that share corners with six equivalent Al(1)O6 octahedra, corners with six equivalent Al(2)O6 octahedra, edges with three equivalent Al(1)O6 octahedra, and faces with two equivalent Mg(1)O6 pentagonal pyramids. The corner-sharing octahedral tilt angles range from 27-74°. In the second Mg site, Mg(2) is bonded to six equivalent O(1) atoms to form distorted MgO6 pentagonal pyramids that share corners with six equivalent Al(1)O6 octahedra, corners with six equivalent Al(2)O6 octahedra, edges with three equivalent Al(2)O6 octahedra, and faces with two equivalent Mg(2)O6 pentagonal pyramids. The corner-sharing octahedral tilt angles range from 27-73°. In the third Mg site, Mg(3) is bonded in a distorted trigonal planar geometry to three equivalent O(3) atoms. There are two inequivalent Al sites. In the first Al site, Al(1) is bonded to one O(1), one O(3), two equivalent O(2), and two equivalent O(4) atoms to form AlO6 octahedra that share corners with four equivalent Al(2)O6 octahedra, corners with two equivalent Mg(1)O6 pentagonal pyramids, corners with two equivalent Mg(2)O6 pentagonal pyramids, edges with two equivalent Al(1)O6 octahedra, edges with two equivalent Al(2)O6 octahedra, and  an edgeedge with one Mg(1)O6 pentagonal pyramid. The corner-sharing octahedral tilt angles are 55°. In the second Al site, Al(2) is bonded to one O(2), one O(4), two equivalent O(1), and two equivalent O(3) atoms to form AlO6 octahedra that share corners with four equivalent Al(1)O6 octahedra, corners with two equivalent Mg(1)O6 pentagonal pyramids, corners with two equivalent Mg(2)O6 pentagonal pyramids, edges with two equivalent Al(1)O6 octahedra, edges with two equivalent Al(2)O6 octahedra, and  an edgeedge with one Mg(2)O6 pentagonal pyramid. The corner-sharing octahedral tilt angles are 55°. There are four inequivalent O sites. In the first O site, O(1) is bonded to two equivalent Mg(2), one Al(1), and two equivalent Al(2) atoms to form distorted OMg2Al3 trigonal bipyramids that share corners with three equivalent O(3)MgAl3 tetrahedra, corners with four equivalent O(1)Mg2Al3 trigonal bipyramids,  an edgeedge with one O(3)MgAl3 tetrahedra, edges with two equivalent O(2)Mg2Al3 trigonal bipyramids, and edges with four equivalent O(1)Mg2Al3 trigonal bipyramids. In the second O site, O(2) is bonded to two equivalent Mg(1), one Al(2), and two equivalent Al(1) atoms to form distorted OMg2Al3 trigonal bipyramids that share corners with four equivalent O(3)MgAl3 tetrahedra, corners with four equivalent O(2)Mg2Al3 trigonal bipyramids, edges with two equivalent O(1)Mg2Al3 trigonal bipyramids, and edges with four equivalent O(2)Mg2Al3 trigonal bipyramids. In the third O site, O(3) is bonded to one Mg(3), one Al(1), and two equivalent Al(2) atoms to form distorted OMgAl3 tetrahedra that share corners with four equivalent O(3)MgAl3 tetrahedra, corners with three equivalent O(1)Mg2Al3 trigonal bipyramids, corners with four equivalent O(2)Mg2Al3 trigonal bipyramids, and  an edgeedge with one O(1)Mg2Al3 trigonal bipyramid. In the fourth O site, O(4) is bonded in a 3-coordinate geometry to one Al(2) and two equivalent Al(1) atoms.
MgAl2O4 crystallizes in the hexagonal P-6 space group. There are three inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to six equivalent O(2) atoms to form distorted MgO6 pentagonal pyramids that share corners with six equivalent Al(1)O6 octahedra, corners with six equivalent Al(2)O6 octahedra, edges with three equivalent Al(1)O6 octahedra, and faces with two equivalent Mg(1)O6 pentagonal pyramids. The corner-sharing octahedral tilt angles range from 27-74°. All Mg(1)-O(2) bond lengths are 2.11 Å. In the second Mg site, Mg(2) is bonded to six equivalent O(1) atoms to form distorted MgO6 pentagonal pyramids that share corners with six equivalent Al(1)O6 octahedra, corners with six equivalent Al(2)O6 octahedra, edges with three equivalent Al(2)O6 octahedra, and faces with two equivalent Mg(2)O6 pentagonal pyramids. The corner-sharing octahedral tilt angles range from 27-73°. All Mg(2)-O(1) bond lengths are 2.11 Å. In the third Mg site, Mg(3) is bonded in a distorted trigonal planar geometry to three equivalent O(3) atoms. All Mg(3)-O(3) bond lengths are 2.27 Å. There are two inequivalent Al sites. In the first Al site, Al(1) is bonded to one O(1), one O(3), two equivalent O(2), and two equivalent O(4) atoms to form AlO6 octahedra that share corners with four equivalent Al(2)O6 octahedra, corners with two equivalent Mg(1)O6 pentagonal pyramids, corners with two equivalent Mg(2)O6 pentagonal pyramids, edges with two equivalent Al(1)O6 octahedra, edges with two equivalent Al(2)O6 octahedra, and  an edgeedge with one Mg(1)O6 pentagonal pyramid. The corner-sharing octahedral tilt angles are 55°. The Al(1)-O(1) bond length is 1.94 Å. The Al(1)-O(3) bond length is 1.90 Å. Both Al(1)-O(2) bond lengths are 1.98 Å. Both Al(1)-O(4) bond lengths are 1.90 Å. In the second Al site, Al(2) is bonded to one O(2), one O(4), two equivalent O(1), and two equivalent O(3) atoms to form AlO6 octahedra that share corners with four equivalent Al(1)O6 octahedra, corners with two equivalent Mg(1)O6 pentagonal pyramids, corners with two equivalent Mg(2)O6 pentagonal pyramids, edges with two equivalent Al(1)O6 octahedra, edges with two equivalent Al(2)O6 octahedra, and  an edgeedge with one Mg(2)O6 pentagonal pyramid. The corner-sharing octahedral tilt angles are 55°. The Al(2)-O(2) bond length is 1.95 Å. The Al(2)-O(4) bond length is 1.89 Å. Both Al(2)-O(1) bond lengths are 1.98 Å. Both Al(2)-O(3) bond lengths are 1.89 Å. There are four inequivalent O sites. In the first O site, O(1) is bonded to two equivalent Mg(2), one Al(1), and two equivalent Al(2) atoms to form distorted OMg2Al3 trigonal bipyramids that share corners with three equivalent O(3)MgAl3 tetrahedra, corners with four equivalent O(1)Mg2Al3 trigonal bipyramids,  an edgeedge with one O(3)MgAl3 tetrahedra, edges with two equivalent O(2)Mg2Al3 trigonal bipyramids, and edges with four equivalent O(1)Mg2Al3 trigonal bipyramids. In the second O site, O(2) is bonded to two equivalent Mg(1), one Al(2), and two equivalent Al(1) atoms to form distorted OMg2Al3 trigonal bipyramids that share corners with four equivalent O(3)MgAl3 tetrahedra, corners with four equivalent O(2)Mg2Al3 trigonal bipyramids, edges with two equivalent O(1)Mg2Al3 trigonal bipyramids, and edges with four equivalent O(2)Mg2Al3 trigonal bipyramids. In the third O site, O(3) is bonded to one Mg(3), one Al(1), and two equivalent Al(2) atoms to form distorted OMgAl3 tetrahedra that share corners with four equivalent O(3)MgAl3 tetrahedra, corners with three equivalent O(1)Mg2Al3 trigonal bipyramids, corners with four equivalent O(2)Mg2Al3 trigonal bipyramids, and  an edgeedge with one O(1)Mg2Al3 trigonal bipyramid. In the fourth O site, O(4) is bonded in a 3-coordinate geometry to one Al(2) and two equivalent Al(1) atoms.