MgAl2O4 is Spinel-like structured and crystallizes in the trigonal P3m1 space group. There are six inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one O(10) and three equivalent O(1) atoms to form MgO4 tetrahedra that share corners with three equivalent Mg(2)O6 octahedra, corners with three equivalent Al(4)O6 octahedra, and corners with six equivalent Al(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-61°. In the second Mg site, Mg(2) is bonded to three equivalent O(1) and three equivalent O(11) atoms to form MgO6 octahedra that share corners with three equivalent Mg(1)O4 tetrahedra, corners with three equivalent Al(6)O4 tetrahedra, edges with three equivalent Al(1)O6 octahedra, and edges with three equivalent Al(4)O6 octahedra. In the third Mg site, Mg(3) is bonded to one O(2) and three equivalent O(4) atoms to form MgO4 tetrahedra that share corners with three equivalent Mg(4)O6 octahedra, corners with three equivalent Al(1)O6 octahedra, and corners with six equivalent Al(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-63°. In the fourth Mg site, Mg(4) is bonded to three equivalent O(3) and three equivalent O(4) atoms to form MgO6 octahedra that share corners with three equivalent Mg(3)O4 tetrahedra, corners with three equivalent Al(5)O4 tetrahedra, edges with three equivalent Al(1)O6 octahedra, and edges with three equivalent Al(2)O6 octahedra. In the fifth Mg site, Mg(5) is bonded to one O(6) and three equivalent O(7) atoms to form MgO4 tetrahedra that share corners with three equivalent Al(2)O6 octahedra, corners with three equivalent Al(3)O6 octahedra, and corners with six equivalent Al(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-59°. In the sixth Mg site, Mg(6) is bonded to one O(12) and three equivalent O(8) atoms to form MgO4 tetrahedra that share corners with three equivalent Al(3)O6 octahedra, corners with three equivalent Al(4)O6 octahedra, and corners with six equivalent Al(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-61°. There are six inequivalent Al sites. In the first Al site, Al(1) is bonded to one O(2), one O(5), two equivalent O(1), and two equivalent O(3) atoms to form AlO6 octahedra that share  a cornercorner with one Mg(3)O4 tetrahedra,  a cornercorner with one Al(6)O4 tetrahedra, corners with two equivalent Mg(1)O4 tetrahedra, corners with two equivalent Al(5)O4 tetrahedra,  an edgeedge with one Mg(2)O6 octahedra,  an edgeedge with one Mg(4)O6 octahedra, and edges with four equivalent Al(1)O6 octahedra. In the second Al site, Al(2) is bonded to one O(6), one O(9), two equivalent O(4), and two equivalent O(8) atoms to form AlO6 octahedra that share  a cornercorner with one Mg(5)O4 tetrahedra,  a cornercorner with one Al(5)O4 tetrahedra, corners with two equivalent Mg(3)O4 tetrahedra, corners with two equivalent Mg(6)O4 tetrahedra,  an edgeedge with one Mg(4)O6 octahedra,  an edgeedge with one Al(3)O6 octahedra, and edges with four equivalent Al(2)O6 octahedra. In the third Al site, Al(3) is bonded to three equivalent O(7) and three equivalent O(8) atoms to form AlO6 octahedra that share corners with three equivalent Mg(5)O4 tetrahedra, corners with three equivalent Mg(6)O4 tetrahedra, edges with three equivalent Al(2)O6 octahedra, and edges with three equivalent Al(4)O6 octahedra. In the fourth Al site, Al(4) is bonded to one O(10), one O(12), two equivalent O(11), and two equivalent O(7) atoms to form AlO6 octahedra that share  a cornercorner with one Mg(1)O4 tetrahedra,  a cornercorner with one Mg(6)O4 tetrahedra, corners with two equivalent Mg(5)O4 tetrahedra, corners with two equivalent Al(6)O4 tetrahedra,  an edgeedge with one Mg(2)O6 octahedra,  an edgeedge with one Al(3)O6 octahedra, and edges with four equivalent Al(4)O6 octahedra. In the fifth Al site, Al(5) is bonded to one O(9) and three equivalent O(3) atoms to form AlO4 tetrahedra that share corners with three equivalent Mg(4)O6 octahedra, corners with three equivalent Al(2)O6 octahedra, and corners with six equivalent Al(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-60°. In the sixth Al site, Al(6) is bonded to one O(5) and three equivalent O(11) atoms to form AlO4 tetrahedra that share corners with three equivalent Mg(2)O6 octahedra, corners with three equivalent Al(1)O6 octahedra, and corners with six equivalent Al(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-61°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a rectangular see-saw-like geometry to one Mg(1), one Mg(2), and two equivalent Al(1) atoms. In the second O site, O(2) is bonded in a distorted rectangular see-saw-like geometry to one Mg(3) and three equivalent Al(1) atoms. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Mg(4), one Al(5), and two equivalent Al(1) atoms. In the fourth O site, O(4) is bonded in a rectangular see-saw-like geometry to one Mg(3), one Mg(4), and two equivalent Al(2) atoms. In the fifth O site, O(5) is bonded in a distorted rectangular see-saw-like geometry to one Al(6) and three equivalent Al(1) atoms. In the sixth O site, O(6) is bonded to one Mg(5) and three equivalent Al(2) atoms to form distorted corner-sharing OMgAl3 trigonal pyramids. In the seventh O site, O(7) is bonded to one Mg(5), one Al(3), and two equivalent Al(4) atoms to form a mixture of distorted corner and edge-sharing OMgAl3 trigonal pyramids. In the eighth O site, O(8) is bonded to one Mg(6), one Al(3), and two equivalent Al(2) atoms to form a mixture of distorted corner and edge-sharing OMgAl3 tetrahedra. In the ninth O site, O(9) is bonded in a distorted rectangular see-saw-like geometry to one Al(5) and three equivalent Al(2) atoms. In the tenth O site, O(10) is bonded to one Mg(1) and three equivalent Al(4) atoms to form a mixture of distorted corner and edge-sharing OMgAl3 trigonal pyramids. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Mg(2), one Al(6), and two equivalent Al(4) atoms. In the twelfth O site, O(12) is bonded to one Mg(6) and three equivalent Al(4) atoms to form corner-sharing OMgAl3 tetrahedra.
MgAl2O4 is Spinel-like structured and crystallizes in the trigonal P3m1 space group. There are six inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one O(10) and three equivalent O(1) atoms to form MgO4 tetrahedra that share corners with three equivalent Mg(2)O6 octahedra, corners with three equivalent Al(4)O6 octahedra, and corners with six equivalent Al(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-61°. The Mg(1)-O(10) bond length is 2.00 Å. All Mg(1)-O(1) bond lengths are 1.93 Å. In the second Mg site, Mg(2) is bonded to three equivalent O(1) and three equivalent O(11) atoms to form MgO6 octahedra that share corners with three equivalent Mg(1)O4 tetrahedra, corners with three equivalent Al(6)O4 tetrahedra, edges with three equivalent Al(1)O6 octahedra, and edges with three equivalent Al(4)O6 octahedra. All Mg(2)-O(1) bond lengths are 2.01 Å. All Mg(2)-O(11) bond lengths are 2.10 Å. In the third Mg site, Mg(3) is bonded to one O(2) and three equivalent O(4) atoms to form MgO4 tetrahedra that share corners with three equivalent Mg(4)O6 octahedra, corners with three equivalent Al(1)O6 octahedra, and corners with six equivalent Al(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-63°. The Mg(3)-O(2) bond length is 1.97 Å. All Mg(3)-O(4) bond lengths are 1.93 Å. In the fourth Mg site, Mg(4) is bonded to three equivalent O(3) and three equivalent O(4) atoms to form MgO6 octahedra that share corners with three equivalent Mg(3)O4 tetrahedra, corners with three equivalent Al(5)O4 tetrahedra, edges with three equivalent Al(1)O6 octahedra, and edges with three equivalent Al(2)O6 octahedra. All Mg(4)-O(3) bond lengths are 2.08 Å. All Mg(4)-O(4) bond lengths are 2.03 Å. In the fifth Mg site, Mg(5) is bonded to one O(6) and three equivalent O(7) atoms to form MgO4 tetrahedra that share corners with three equivalent Al(2)O6 octahedra, corners with three equivalent Al(3)O6 octahedra, and corners with six equivalent Al(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-59°. The Mg(5)-O(6) bond length is 1.93 Å. All Mg(5)-O(7) bond lengths are 1.96 Å. In the sixth Mg site, Mg(6) is bonded to one O(12) and three equivalent O(8) atoms to form MgO4 tetrahedra that share corners with three equivalent Al(3)O6 octahedra, corners with three equivalent Al(4)O6 octahedra, and corners with six equivalent Al(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-61°. The Mg(6)-O(12) bond length is 2.05 Å. All Mg(6)-O(8) bond lengths are 1.97 Å. There are six inequivalent Al sites. In the first Al site, Al(1) is bonded to one O(2), one O(5), two equivalent O(1), and two equivalent O(3) atoms to form AlO6 octahedra that share  a cornercorner with one Mg(3)O4 tetrahedra,  a cornercorner with one Al(6)O4 tetrahedra, corners with two equivalent Mg(1)O4 tetrahedra, corners with two equivalent Al(5)O4 tetrahedra,  an edgeedge with one Mg(2)O6 octahedra,  an edgeedge with one Mg(4)O6 octahedra, and edges with four equivalent Al(1)O6 octahedra. The Al(1)-O(2) bond length is 1.93 Å. The Al(1)-O(5) bond length is 2.04 Å. Both Al(1)-O(1) bond lengths are 1.88 Å. Both Al(1)-O(3) bond lengths are 1.98 Å. In the second Al site, Al(2) is bonded to one O(6), one O(9), two equivalent O(4), and two equivalent O(8) atoms to form AlO6 octahedra that share  a cornercorner with one Mg(5)O4 tetrahedra,  a cornercorner with one Al(5)O4 tetrahedra, corners with two equivalent Mg(3)O4 tetrahedra, corners with two equivalent Mg(6)O4 tetrahedra,  an edgeedge with one Mg(4)O6 octahedra,  an edgeedge with one Al(3)O6 octahedra, and edges with four equivalent Al(2)O6 octahedra. The Al(2)-O(6) bond length is 1.94 Å. The Al(2)-O(9) bond length is 2.07 Å. Both Al(2)-O(4) bond lengths are 1.88 Å. Both Al(2)-O(8) bond lengths are 1.93 Å. In the third Al site, Al(3) is bonded to three equivalent O(7) and three equivalent O(8) atoms to form AlO6 octahedra that share corners with three equivalent Mg(5)O4 tetrahedra, corners with three equivalent Mg(6)O4 tetrahedra, edges with three equivalent Al(2)O6 octahedra, and edges with three equivalent Al(4)O6 octahedra. All Al(3)-O(7) bond lengths are 1.94 Å. All Al(3)-O(8) bond lengths are 1.91 Å. In the fourth Al site, Al(4) is bonded to one O(10), one O(12), two equivalent O(11), and two equivalent O(7) atoms to form AlO6 octahedra that share  a cornercorner with one Mg(1)O4 tetrahedra,  a cornercorner with one Mg(6)O4 tetrahedra, corners with two equivalent Mg(5)O4 tetrahedra, corners with two equivalent Al(6)O4 tetrahedra,  an edgeedge with one Mg(2)O6 octahedra,  an edgeedge with one Al(3)O6 octahedra, and edges with four equivalent Al(4)O6 octahedra. The Al(4)-O(10) bond length is 1.93 Å. The Al(4)-O(12) bond length is 1.92 Å. Both Al(4)-O(11) bond lengths are 1.99 Å. Both Al(4)-O(7) bond lengths are 1.92 Å. In the fifth Al site, Al(5) is bonded to one O(9) and three equivalent O(3) atoms to form AlO4 tetrahedra that share corners with three equivalent Mg(4)O6 octahedra, corners with three equivalent Al(2)O6 octahedra, and corners with six equivalent Al(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-60°. The Al(5)-O(9) bond length is 1.86 Å. All Al(5)-O(3) bond lengths are 1.84 Å. In the sixth Al site, Al(6) is bonded to one O(5) and three equivalent O(11) atoms to form AlO4 tetrahedra that share corners with three equivalent Mg(2)O6 octahedra, corners with three equivalent Al(1)O6 octahedra, and corners with six equivalent Al(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-61°. The Al(6)-O(5) bond length is 1.87 Å. All Al(6)-O(11) bond lengths are 1.82 Å. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a rectangular see-saw-like geometry to one Mg(1), one Mg(2), and two equivalent Al(1) atoms. In the second O site, O(2) is bonded in a distorted rectangular see-saw-like geometry to one Mg(3) and three equivalent Al(1) atoms. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Mg(4), one Al(5), and two equivalent Al(1) atoms. In the fourth O site, O(4) is bonded in a rectangular see-saw-like geometry to one Mg(3), one Mg(4), and two equivalent Al(2) atoms. In the fifth O site, O(5) is bonded in a distorted rectangular see-saw-like geometry to one Al(6) and three equivalent Al(1) atoms. In the sixth O site, O(6) is bonded to one Mg(5) and three equivalent Al(2) atoms to form distorted corner-sharing OMgAl3 trigonal pyramids. In the seventh O site, O(7) is bonded to one Mg(5), one Al(3), and two equivalent Al(4) atoms to form a mixture of distorted corner and edge-sharing OMgAl3 trigonal pyramids. In the eighth O site, O(8) is bonded to one Mg(6), one Al(3), and two equivalent Al(2) atoms to form a mixture of distorted corner and edge-sharing OMgAl3 tetrahedra. In the ninth O site, O(9) is bonded in a distorted rectangular see-saw-like geometry to one Al(5) and three equivalent Al(2) atoms. In the tenth O site, O(10) is bonded to one Mg(1) and three equivalent Al(4) atoms to form a mixture of distorted corner and edge-sharing OMgAl3 trigonal pyramids. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Mg(2), one Al(6), and two equivalent Al(4) atoms. In the twelfth O site, O(12) is bonded to one Mg(6) and three equivalent Al(4) atoms to form corner-sharing OMgAl3 tetrahedra.