Al2O3 crystallizes in the monoclinic Pm space group. There are twelve inequivalent Al sites. In the first Al site, Al(1) is bonded to one O(1), one O(18), two equivalent O(7), and two equivalent O(9) atoms to form AlO6 octahedra that share corners with two equivalent Al(6)O5 trigonal bipyramids, edges with two equivalent Al(1)O6 octahedra, edges with two equivalent Al(9)O5 trigonal bipyramids, and edges with two equivalent Al(3)O4 trigonal pyramids. In the second Al site, Al(2) is bonded to one O(15), one O(3), two equivalent O(13), and two equivalent O(6) atoms to form AlO6 octahedra that share corners with two equivalent Al(5)O4 tetrahedra, corners with two equivalent Al(8)O5 trigonal bipyramids, edges with two equivalent Al(2)O6 octahedra, and edges with two equivalent Al(4)O5 trigonal bipyramids. In the third Al site, Al(3) is bonded to one O(8), one O(9), and two equivalent O(1) atoms to form AlO4 trigonal pyramids that share corners with two equivalent Al(11)O6 octahedra, corners with two equivalent Al(3)O4 trigonal pyramids, and edges with two equivalent Al(1)O6 octahedra. The corner-sharing octahedral tilt angles are 52°. In the fourth Al site, Al(4) is bonded to one O(10), one O(13), one O(5), and two equivalent O(3) atoms to form AlO5 trigonal bipyramids that share corners with two equivalent Al(12)O6 octahedra,  a cornercorner with one Al(9)O5 trigonal bipyramid, corners with two equivalent Al(4)O5 trigonal bipyramids, edges with two equivalent Al(2)O6 octahedra,  an edgeedge with one Al(6)O5 trigonal bipyramid, and  an edgeedge with one Al(8)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles are 53°. In the fifth Al site, Al(5) is bonded to one O(4), one O(6), and two equivalent O(14) atoms to form AlO4 tetrahedra that share corners with two equivalent Al(11)O6 octahedra, corners with two equivalent Al(2)O6 octahedra, and corners with two equivalent Al(5)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 54-64°. In the sixth Al site, Al(6) is bonded to one O(10), one O(5), one O(7), and two equivalent O(16) atoms to form AlO5 trigonal bipyramids that share corners with two equivalent Al(1)O6 octahedra,  a cornercorner with one Al(8)O5 trigonal bipyramid, corners with two equivalent Al(6)O5 trigonal bipyramids, edges with two equivalent Al(12)O6 octahedra,  an edgeedge with one Al(4)O5 trigonal bipyramid, and  an edgeedge with one Al(9)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles are 55°. In the seventh Al site, Al(7) is bonded in a 5-coordinate geometry to one O(11), one O(4), one O(9), and two equivalent O(2) atoms. In the eighth Al site, Al(8) is bonded to one O(12), one O(13), one O(5), and two equivalent O(17) atoms to form AlO5 trigonal bipyramids that share corners with two equivalent Al(2)O6 octahedra,  a cornercorner with one Al(6)O5 trigonal bipyramid, corners with two equivalent Al(8)O5 trigonal bipyramids, edges with two equivalent Al(12)O6 octahedra,  an edgeedge with one Al(4)O5 trigonal bipyramid, and  an edgeedge with one Al(9)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles are 50°. In the ninth Al site, Al(9) is bonded to one O(12), one O(5), one O(7), and two equivalent O(18) atoms to form AlO5 trigonal bipyramids that share corners with two equivalent Al(12)O6 octahedra,  a cornercorner with one Al(4)O5 trigonal bipyramid, corners with two equivalent Al(9)O5 trigonal bipyramids, edges with two equivalent Al(1)O6 octahedra,  an edgeedge with one Al(6)O5 trigonal bipyramid, and  an edgeedge with one Al(8)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles are 52°. In the tenth Al site, Al(10) is bonded in a 5-coordinate geometry to one O(11), one O(4), one O(6), and two equivalent O(15) atoms. In the eleventh Al site, Al(11) is bonded to one O(14), one O(2), two equivalent O(11), and two equivalent O(8) atoms to form AlO6 octahedra that share corners with two equivalent Al(5)O4 tetrahedra, corners with two equivalent Al(3)O4 trigonal pyramids, and edges with two equivalent Al(11)O6 octahedra. In the twelfth Al site, Al(12) is bonded to one O(16), one O(17), two equivalent O(10), and two equivalent O(12) atoms to form AlO6 octahedra that share corners with two equivalent Al(4)O5 trigonal bipyramids, corners with two equivalent Al(9)O5 trigonal bipyramids, edges with two equivalent Al(12)O6 octahedra, edges with two equivalent Al(6)O5 trigonal bipyramids, and edges with two equivalent Al(8)O5 trigonal bipyramids. There are eighteen inequivalent O sites. In the first O site, O(1) is bonded in a distorted trigonal non-coplanar geometry to one Al(1) and two equivalent Al(3) atoms. In the second O site, O(2) is bonded in a trigonal non-coplanar geometry to one Al(11) and two equivalent Al(7) atoms. In the third O site, O(3) is bonded in a trigonal non-coplanar geometry to one Al(2) and two equivalent Al(4) atoms. In the fourth O site, O(4) is bonded in a distorted T-shaped geometry to one Al(10), one Al(5), and one Al(7) atom. In the fifth O site, O(5) is bonded in a rectangular see-saw-like geometry to one Al(4), one Al(6), one Al(8), and one Al(9) atom. In the sixth O site, O(6) is bonded to one Al(10), one Al(5), and two equivalent Al(2) atoms to form a mixture of distorted corner and edge-sharing OAl4 trigonal pyramids. In the seventh O site, O(7) is bonded to one Al(6), one Al(9), and two equivalent Al(1) atoms to form corner-sharing OAl4 trigonal pyramids. In the eighth O site, O(8) is bonded in a distorted trigonal planar geometry to one Al(3) and two equivalent Al(11) atoms. In the ninth O site, O(9) is bonded in a rectangular see-saw-like geometry to one Al(3), one Al(7), and two equivalent Al(1) atoms. In the tenth O site, O(10) is bonded to one Al(4), one Al(6), and two equivalent Al(12) atoms to form a mixture of corner and edge-sharing OAl4 trigonal pyramids. In the eleventh O site, O(11) is bonded to one Al(10), one Al(7), and two equivalent Al(11) atoms to form distorted corner-sharing OAl4 trigonal pyramids. In the twelfth O site, O(12) is bonded to one Al(8), one Al(9), and two equivalent Al(12) atoms to form a mixture of corner and edge-sharing OAl4 trigonal pyramids. In the thirteenth O site, O(13) is bonded to one Al(4), one Al(8), and two equivalent Al(2) atoms to form a mixture of corner and edge-sharing OAl4 trigonal pyramids. In the fourteenth O site, O(14) is bonded in a trigonal planar geometry to one Al(11) and two equivalent Al(5) atoms. In the fifteenth O site, O(15) is bonded in a trigonal non-coplanar geometry to one Al(2) and two equivalent Al(10) atoms. In the sixteenth O site, O(16) is bonded in a trigonal non-coplanar geometry to one Al(12) and two equivalent Al(6) atoms. In the seventeenth O site, O(17) is bonded in a trigonal non-coplanar geometry to one Al(12) and two equivalent Al(8) atoms. In the eighteenth O site, O(18) is bonded in a trigonal non-coplanar geometry to one Al(1) and two equivalent Al(9) atoms.
Al2O3 crystallizes in the monoclinic Pm space group. There are twelve inequivalent Al sites. In the first Al site, Al(1) is bonded to one O(1), one O(18), two equivalent O(7), and two equivalent O(9) atoms to form AlO6 octahedra that share corners with two equivalent Al(6)O5 trigonal bipyramids, edges with two equivalent Al(1)O6 octahedra, edges with two equivalent Al(9)O5 trigonal bipyramids, and edges with two equivalent Al(3)O4 trigonal pyramids. The Al(1)-O(1) bond length is 1.88 Å. The Al(1)-O(18) bond length is 1.88 Å. Both Al(1)-O(7) bond lengths are 1.94 Å. Both Al(1)-O(9) bond lengths are 2.07 Å. In the second Al site, Al(2) is bonded to one O(15), one O(3), two equivalent O(13), and two equivalent O(6) atoms to form AlO6 octahedra that share corners with two equivalent Al(5)O4 tetrahedra, corners with two equivalent Al(8)O5 trigonal bipyramids, edges with two equivalent Al(2)O6 octahedra, and edges with two equivalent Al(4)O5 trigonal bipyramids. The Al(2)-O(15) bond length is 1.90 Å. The Al(2)-O(3) bond length is 1.89 Å. Both Al(2)-O(13) bond lengths are 2.04 Å. Both Al(2)-O(6) bond lengths are 1.93 Å. In the third Al site, Al(3) is bonded to one O(8), one O(9), and two equivalent O(1) atoms to form AlO4 trigonal pyramids that share corners with two equivalent Al(11)O6 octahedra, corners with two equivalent Al(3)O4 trigonal pyramids, and edges with two equivalent Al(1)O6 octahedra. The corner-sharing octahedral tilt angles are 52°. The Al(3)-O(8) bond length is 1.72 Å. The Al(3)-O(9) bond length is 1.93 Å. Both Al(3)-O(1) bond lengths are 1.75 Å. In the fourth Al site, Al(4) is bonded to one O(10), one O(13), one O(5), and two equivalent O(3) atoms to form AlO5 trigonal bipyramids that share corners with two equivalent Al(12)O6 octahedra,  a cornercorner with one Al(9)O5 trigonal bipyramid, corners with two equivalent Al(4)O5 trigonal bipyramids, edges with two equivalent Al(2)O6 octahedra,  an edgeedge with one Al(6)O5 trigonal bipyramid, and  an edgeedge with one Al(8)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles are 53°. The Al(4)-O(10) bond length is 1.81 Å. The Al(4)-O(13) bond length is 1.93 Å. The Al(4)-O(5) bond length is 2.11 Å. Both Al(4)-O(3) bond lengths are 1.76 Å. In the fifth Al site, Al(5) is bonded to one O(4), one O(6), and two equivalent O(14) atoms to form AlO4 tetrahedra that share corners with two equivalent Al(11)O6 octahedra, corners with two equivalent Al(2)O6 octahedra, and corners with two equivalent Al(5)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 54-64°. The Al(5)-O(4) bond length is 1.82 Å. The Al(5)-O(6) bond length is 1.78 Å. Both Al(5)-O(14) bond lengths are 1.77 Å. In the sixth Al site, Al(6) is bonded to one O(10), one O(5), one O(7), and two equivalent O(16) atoms to form AlO5 trigonal bipyramids that share corners with two equivalent Al(1)O6 octahedra,  a cornercorner with one Al(8)O5 trigonal bipyramid, corners with two equivalent Al(6)O5 trigonal bipyramids, edges with two equivalent Al(12)O6 octahedra,  an edgeedge with one Al(4)O5 trigonal bipyramid, and  an edgeedge with one Al(9)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles are 55°. The Al(6)-O(10) bond length is 1.94 Å. The Al(6)-O(5) bond length is 1.95 Å. The Al(6)-O(7) bond length is 1.82 Å. Both Al(6)-O(16) bond lengths are 1.78 Å. In the seventh Al site, Al(7) is bonded in a 5-coordinate geometry to one O(11), one O(4), one O(9), and two equivalent O(2) atoms. The Al(7)-O(11) bond length is 2.36 Å. The Al(7)-O(4) bond length is 1.81 Å. The Al(7)-O(9) bond length is 1.88 Å. Both Al(7)-O(2) bond lengths are 1.78 Å. In the eighth Al site, Al(8) is bonded to one O(12), one O(13), one O(5), and two equivalent O(17) atoms to form AlO5 trigonal bipyramids that share corners with two equivalent Al(2)O6 octahedra,  a cornercorner with one Al(6)O5 trigonal bipyramid, corners with two equivalent Al(8)O5 trigonal bipyramids, edges with two equivalent Al(12)O6 octahedra,  an edgeedge with one Al(4)O5 trigonal bipyramid, and  an edgeedge with one Al(9)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles are 50°. The Al(8)-O(12) bond length is 2.01 Å. The Al(8)-O(13) bond length is 1.79 Å. The Al(8)-O(5) bond length is 2.03 Å. Both Al(8)-O(17) bond lengths are 1.79 Å. In the ninth Al site, Al(9) is bonded to one O(12), one O(5), one O(7), and two equivalent O(18) atoms to form AlO5 trigonal bipyramids that share corners with two equivalent Al(12)O6 octahedra,  a cornercorner with one Al(4)O5 trigonal bipyramid, corners with two equivalent Al(9)O5 trigonal bipyramids, edges with two equivalent Al(1)O6 octahedra,  an edgeedge with one Al(6)O5 trigonal bipyramid, and  an edgeedge with one Al(8)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles are 52°. The Al(9)-O(12) bond length is 1.79 Å. The Al(9)-O(5) bond length is 2.06 Å. The Al(9)-O(7) bond length is 1.93 Å. Both Al(9)-O(18) bond lengths are 1.81 Å. In the tenth Al site, Al(10) is bonded in a 5-coordinate geometry to one O(11), one O(4), one O(6), and two equivalent O(15) atoms. The Al(10)-O(11) bond length is 1.78 Å. The Al(10)-O(4) bond length is 1.88 Å. The Al(10)-O(6) bond length is 2.37 Å. Both Al(10)-O(15) bond lengths are 1.78 Å. In the eleventh Al site, Al(11) is bonded to one O(14), one O(2), two equivalent O(11), and two equivalent O(8) atoms to form AlO6 octahedra that share corners with two equivalent Al(5)O4 tetrahedra, corners with two equivalent Al(3)O4 trigonal pyramids, and edges with two equivalent Al(11)O6 octahedra. The Al(11)-O(14) bond length is 1.87 Å. The Al(11)-O(2) bond length is 1.95 Å. Both Al(11)-O(11) bond lengths are 1.95 Å. Both Al(11)-O(8) bond lengths are 1.99 Å. In the twelfth Al site, Al(12) is bonded to one O(16), one O(17), two equivalent O(10), and two equivalent O(12) atoms to form AlO6 octahedra that share corners with two equivalent Al(4)O5 trigonal bipyramids, corners with two equivalent Al(9)O5 trigonal bipyramids, edges with two equivalent Al(12)O6 octahedra, edges with two equivalent Al(6)O5 trigonal bipyramids, and edges with two equivalent Al(8)O5 trigonal bipyramids. The Al(12)-O(16) bond length is 1.87 Å. The Al(12)-O(17) bond length is 1.85 Å. Both Al(12)-O(10) bond lengths are 1.97 Å. Both Al(12)-O(12) bond lengths are 1.99 Å. There are eighteen inequivalent O sites. In the first O site, O(1) is bonded in a distorted trigonal non-coplanar geometry to one Al(1) and two equivalent Al(3) atoms. In the second O site, O(2) is bonded in a trigonal non-coplanar geometry to one Al(11) and two equivalent Al(7) atoms. In the third O site, O(3) is bonded in a trigonal non-coplanar geometry to one Al(2) and two equivalent Al(4) atoms. In the fourth O site, O(4) is bonded in a distorted T-shaped geometry to one Al(10), one Al(5), and one Al(7) atom. In the fifth O site, O(5) is bonded in a rectangular see-saw-like geometry to one Al(4), one Al(6), one Al(8), and one Al(9) atom. In the sixth O site, O(6) is bonded to one Al(10), one Al(5), and two equivalent Al(2) atoms to form a mixture of distorted corner and edge-sharing OAl4 trigonal pyramids. In the seventh O site, O(7) is bonded to one Al(6), one Al(9), and two equivalent Al(1) atoms to form corner-sharing OAl4 trigonal pyramids. In the eighth O site, O(8) is bonded in a distorted trigonal planar geometry to one Al(3) and two equivalent Al(11) atoms. In the ninth O site, O(9) is bonded in a rectangular see-saw-like geometry to one Al(3), one Al(7), and two equivalent Al(1) atoms. In the tenth O site, O(10) is bonded to one Al(4), one Al(6), and two equivalent Al(12) atoms to form a mixture of corner and edge-sharing OAl4 trigonal pyramids. In the eleventh O site, O(11) is bonded to one Al(10), one Al(7), and two equivalent Al(11) atoms to form distorted corner-sharing OAl4 trigonal pyramids. In the twelfth O site, O(12) is bonded to one Al(8), one Al(9), and two equivalent Al(12) atoms to form a mixture of corner and edge-sharing OAl4 trigonal pyramids. In the thirteenth O site, O(13) is bonded to one Al(4), one Al(8), and two equivalent Al(2) atoms to form a mixture of corner and edge-sharing OAl4 trigonal pyramids. In the fourteenth O site, O(14) is bonded in a trigonal planar geometry to one Al(11) and two equivalent Al(5) atoms. In the fifteenth O site, O(15) is bonded in a trigonal non-coplanar geometry to one Al(2) and two equivalent Al(10) atoms. In the sixteenth O site, O(16) is bonded in a trigonal non-coplanar geometry to one Al(12) and two equivalent Al(6) atoms. In the seventeenth O site, O(17) is bonded in a trigonal non-coplanar geometry to one Al(12) and two equivalent Al(8) atoms. In the eighteenth O site, O(18) is bonded in a trigonal non-coplanar geometry to one Al(1) and two equivalent Al(9) atoms.