Al2O3 crystallizes in the triclinic P1 space group. There are eighteen inequivalent Al sites. In the first Al site, Al(1) is bonded to one O(1), one O(2), and two equivalent O(7) atoms to form AlO4 tetrahedra that share  a cornercorner with one Al(2)O6 octahedra, corners with two equivalent Al(4)O6 octahedra, corners with four equivalent Al(5)O6 octahedra, and corners with two equivalent Al(1)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 59-61°. In the second Al site, Al(2) is bonded to one O(2), one O(25), two equivalent O(10), and two equivalent O(9) atoms to form AlO6 octahedra that share  a cornercorner with one Al(1)O4 tetrahedra, corners with two equivalent Al(11)O4 tetrahedra, corners with four equivalent Al(7)O4 tetrahedra, edges with two equivalent Al(2)O6 octahedra, and edges with two equivalent Al(5)O6 octahedra. In the third Al site, Al(3) is bonded to one O(4), one O(5), and two equivalent O(12) atoms to form AlO4 tetrahedra that share  a cornercorner with one Al(4)O6 octahedra, corners with two equivalent Al(6)O6 octahedra, corners with four equivalent Al(8)O6 octahedra, and corners with two equivalent Al(3)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 58-63°. In the fourth Al site, Al(4) is bonded to one O(5), one O(7), two equivalent O(14), and two equivalent O(15) atoms to form AlO6 octahedra that share  a cornercorner with one Al(3)O4 tetrahedra, corners with two equivalent Al(1)O4 tetrahedra, corners with four equivalent Al(10)O4 tetrahedra, edges with two equivalent Al(4)O6 octahedra, and edges with two equivalent Al(8)O6 octahedra. In the fifth Al site, Al(5) is bonded to one O(6), one O(9), two equivalent O(1), and two equivalent O(2) atoms to form AlO6 octahedra that share  a cornercorner with one Al(7)O4 tetrahedra, corners with two equivalent Al(10)O4 tetrahedra, corners with four equivalent Al(1)O4 tetrahedra, edges with two equivalent Al(2)O6 octahedra, and edges with two equivalent Al(5)O6 octahedra. In the sixth Al site, Al(6) is bonded to one O(12), one O(8), two equivalent O(20), and two equivalent O(21) atoms to form AlO6 octahedra that share corners with two equivalent Al(3)O4 tetrahedra, corners with four equivalent Al(14)O4 tetrahedra, corners with two equivalent Al(12)O4 trigonal pyramids, and edges with two equivalent Al(6)O6 octahedra. In the seventh Al site, Al(7) is bonded to one O(10), one O(9), and two equivalent O(3) atoms to form AlO4 tetrahedra that share  a cornercorner with one Al(5)O6 octahedra, corners with two equivalent Al(17)O6 octahedra, corners with four equivalent Al(2)O6 octahedra, and corners with two equivalent Al(7)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 54-65°. In the eighth Al site, Al(8) is bonded to one O(11), one O(14), two equivalent O(4), and two equivalent O(5) atoms to form AlO6 octahedra that share  a cornercorner with one Al(10)O4 tetrahedra, corners with two equivalent Al(14)O4 tetrahedra, corners with four equivalent Al(3)O4 tetrahedra, edges with two equivalent Al(4)O6 octahedra, and edges with two equivalent Al(8)O6 octahedra. In the ninth Al site, Al(9) is bonded in a 5-coordinate geometry to one O(17), two equivalent O(23), and two equivalent O(24) atoms. In the tenth Al site, Al(10) is bonded to one O(14), one O(15), and two equivalent O(6) atoms to form AlO4 tetrahedra that share  a cornercorner with one Al(8)O6 octahedra, corners with two equivalent Al(5)O6 octahedra, corners with four equivalent Al(4)O6 octahedra, and corners with two equivalent Al(10)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 54-67°. In the eleventh Al site, Al(11) is bonded to one O(18), one O(19), and two equivalent O(25) atoms to form AlO4 tetrahedra that share corners with two equivalent Al(2)O6 octahedra, corners with four equivalent Al(17)O6 octahedra,  a cornercorner with one Al(13)O5 square pyramid, and corners with two equivalent Al(11)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 59-60°. In the twelfth Al site, Al(12) is bonded to one O(16), one O(17), and two equivalent O(8) atoms to form AlO4 trigonal pyramids that share corners with two equivalent Al(6)O6 octahedra, corners with two equivalent Al(16)O4 tetrahedra, and corners with two equivalent Al(12)O4 trigonal pyramids. The corner-sharing octahedral tilt angles are 63°. In the thirteenth Al site, Al(13) is bonded to one O(19), two equivalent O(26), and two equivalent O(27) atoms to form AlO5 square pyramids that share  a cornercorner with one Al(11)O4 tetrahedra, corners with four equivalent Al(18)O4 tetrahedra, edges with two equivalent Al(17)O6 octahedra, and edges with two equivalent Al(13)O5 square pyramids. In the fourteenth Al site, Al(14) is bonded to one O(20), one O(21), and two equivalent O(11) atoms to form AlO4 tetrahedra that share corners with two equivalent Al(8)O6 octahedra, corners with four equivalent Al(6)O6 octahedra, and corners with two equivalent Al(14)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 55-56°. In the fifteenth Al site, Al(15) is bonded to one O(22), one O(23), and two equivalent O(13) atoms to form corner-sharing AlO4 tetrahedra. In the sixteenth Al site, Al(16) is bonded to one O(23), one O(24), and two equivalent O(16) atoms to form corner-sharing AlO4 tetrahedra. In the seventeenth Al site, Al(17) is bonded to one O(26), one O(3), two equivalent O(18), and two equivalent O(19) atoms to form AlO6 octahedra that share  a cornercorner with one Al(18)O4 tetrahedra, corners with two equivalent Al(7)O4 tetrahedra, corners with four equivalent Al(11)O4 tetrahedra, edges with two equivalent Al(17)O6 octahedra, and edges with two equivalent Al(13)O5 square pyramids. In the eighteenth Al site, Al(18) is bonded to one O(26), one O(27), and two equivalent O(22) atoms to form AlO4 tetrahedra that share  a cornercorner with one Al(17)O6 octahedra, corners with four equivalent Al(13)O5 square pyramids, corners with two equivalent Al(15)O4 tetrahedra, and corners with two equivalent Al(18)O4 tetrahedra. The corner-sharing octahedral tilt angles are 60°. There are twenty-seven inequivalent O sites. In the first O site, O(1) is bonded in a trigonal planar geometry to one Al(1) and two equivalent Al(5) atoms. In the second O site, O(2) is bonded to one Al(1), one Al(2), and two equivalent Al(5) atoms to form distorted corner-sharing OAl4 tetrahedra. In the third O site, O(3) is bonded in a trigonal planar geometry to one Al(17) and two equivalent Al(7) atoms. In the fourth O site, O(4) is bonded in a trigonal non-coplanar geometry to one Al(3) and two equivalent Al(8) atoms. In the fifth O site, O(5) is bonded to one Al(3), one Al(4), and two equivalent Al(8) atoms to form a mixture of distorted corner and edge-sharing OAl4 tetrahedra. In the sixth O site, O(6) is bonded in a trigonal planar geometry to one Al(5) and two equivalent Al(10) atoms. In the seventh O site, O(7) is bonded in a trigonal planar geometry to one Al(4) and two equivalent Al(1) atoms. In the eighth O site, O(8) is bonded in a trigonal planar geometry to one Al(6) and two equivalent Al(12) atoms. In the ninth O site, O(9) is bonded in a distorted rectangular see-saw-like geometry to one Al(5), one Al(7), and two equivalent Al(2) atoms. In the tenth O site, O(10) is bonded in a trigonal planar geometry to one Al(7) and two equivalent Al(2) atoms. In the eleventh O site, O(11) is bonded in a trigonal planar geometry to one Al(8) and two equivalent Al(14) atoms. In the twelfth O site, O(12) is bonded in a trigonal planar geometry to one Al(6) and two equivalent Al(3) atoms. In the thirteenth O site, O(13) is bonded in a bent 120 degrees geometry to two equivalent Al(15) atoms. In the fourteenth O site, O(14) is bonded to one Al(10), one Al(8), and two equivalent Al(4) atoms to form a mixture of distorted corner and edge-sharing OAl4 tetrahedra. In the fifteenth O site, O(15) is bonded in a trigonal planar geometry to one Al(10) and two equivalent Al(4) atoms. In the sixteenth O site, O(16) is bonded in a trigonal non-coplanar geometry to one Al(12) and two equivalent Al(16) atoms. In the seventeenth O site, O(17) is bonded in a bent 150 degrees geometry to one Al(12) and one Al(9) atom. In the eighteenth O site, O(18) is bonded in a trigonal planar geometry to one Al(11) and two equivalent Al(17) atoms. In the nineteenth O site, O(19) is bonded to one Al(11), one Al(13), and two equivalent Al(17) atoms to form a mixture of distorted corner and edge-sharing OAl4 trigonal pyramids. In the twentieth O site, O(20) is bonded in a trigonal planar geometry to one Al(14) and two equivalent Al(6) atoms. In the twenty-first O site, O(21) is bonded in a trigonal planar geometry to one Al(14) and two equivalent Al(6) atoms. In the twenty-second O site, O(22) is bonded in a trigonal non-coplanar geometry to one Al(15) and two equivalent Al(18) atoms. In the twenty-third O site, O(23) is bonded in a 4-coordinate geometry to one Al(15), one Al(16), and two equivalent Al(9) atoms. In the twenty-fourth O site, O(24) is bonded in a trigonal non-coplanar geometry to one Al(16) and two equivalent Al(9) atoms. In the twenty-fifth O site, O(25) is bonded in a trigonal planar geometry to one Al(2) and two equivalent Al(11) atoms. In the twenty-sixth O site, O(26) is bonded to one Al(17), one Al(18), and two equivalent Al(13) atoms to form a mixture of distorted corner and edge-sharing OAl4 trigonal pyramids. In the twenty-seventh O site, O(27) is bonded in a trigonal planar geometry to one Al(18) and two equivalent Al(13) atoms.
Al2O3 crystallizes in the triclinic P1 space group. There are eighteen inequivalent Al sites. In the first Al site, Al(1) is bonded to one O(1), one O(2), and two equivalent O(7) atoms to form AlO4 tetrahedra that share  a cornercorner with one Al(2)O6 octahedra, corners with two equivalent Al(4)O6 octahedra, corners with four equivalent Al(5)O6 octahedra, and corners with two equivalent Al(1)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 59-61°. The Al(1)-O(1) bond length is 1.79 Å. The Al(1)-O(2) bond length is 1.84 Å. Both Al(1)-O(7) bond lengths are 1.74 Å. In the second Al site, Al(2) is bonded to one O(2), one O(25), two equivalent O(10), and two equivalent O(9) atoms to form AlO6 octahedra that share  a cornercorner with one Al(1)O4 tetrahedra, corners with two equivalent Al(11)O4 tetrahedra, corners with four equivalent Al(7)O4 tetrahedra, edges with two equivalent Al(2)O6 octahedra, and edges with two equivalent Al(5)O6 octahedra. The Al(2)-O(2) bond length is 1.88 Å. The Al(2)-O(25) bond length is 1.96 Å. Both Al(2)-O(10) bond lengths are 1.89 Å. There is one shorter (2.00 Å) and one longer (2.01 Å) Al(2)-O(9) bond length. In the third Al site, Al(3) is bonded to one O(4), one O(5), and two equivalent O(12) atoms to form AlO4 tetrahedra that share  a cornercorner with one Al(4)O6 octahedra, corners with two equivalent Al(6)O6 octahedra, corners with four equivalent Al(8)O6 octahedra, and corners with two equivalent Al(3)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 58-63°. The Al(3)-O(4) bond length is 1.80 Å. The Al(3)-O(5) bond length is 1.83 Å. There is one shorter (1.74 Å) and one longer (1.75 Å) Al(3)-O(12) bond length. In the fourth Al site, Al(4) is bonded to one O(5), one O(7), two equivalent O(14), and two equivalent O(15) atoms to form AlO6 octahedra that share  a cornercorner with one Al(3)O4 tetrahedra, corners with two equivalent Al(1)O4 tetrahedra, corners with four equivalent Al(10)O4 tetrahedra, edges with two equivalent Al(4)O6 octahedra, and edges with two equivalent Al(8)O6 octahedra. The Al(4)-O(5) bond length is 1.89 Å. The Al(4)-O(7) bond length is 1.95 Å. There is one shorter (1.99 Å) and one longer (2.00 Å) Al(4)-O(14) bond length. There is one shorter (1.88 Å) and one longer (1.89 Å) Al(4)-O(15) bond length. In the fifth Al site, Al(5) is bonded to one O(6), one O(9), two equivalent O(1), and two equivalent O(2) atoms to form AlO6 octahedra that share  a cornercorner with one Al(7)O4 tetrahedra, corners with two equivalent Al(10)O4 tetrahedra, corners with four equivalent Al(1)O4 tetrahedra, edges with two equivalent Al(2)O6 octahedra, and edges with two equivalent Al(5)O6 octahedra. The Al(5)-O(6) bond length is 1.83 Å. The Al(5)-O(9) bond length is 2.04 Å. There is one shorter (1.89 Å) and one longer (1.90 Å) Al(5)-O(1) bond length. There is one shorter (2.04 Å) and one longer (2.05 Å) Al(5)-O(2) bond length. In the sixth Al site, Al(6) is bonded to one O(12), one O(8), two equivalent O(20), and two equivalent O(21) atoms to form AlO6 octahedra that share corners with two equivalent Al(3)O4 tetrahedra, corners with four equivalent Al(14)O4 tetrahedra, corners with two equivalent Al(12)O4 trigonal pyramids, and edges with two equivalent Al(6)O6 octahedra. The Al(6)-O(12) bond length is 1.95 Å. The Al(6)-O(8) bond length is 1.95 Å. Both Al(6)-O(20) bond lengths are 1.92 Å. There is one shorter (1.96 Å) and one longer (1.97 Å) Al(6)-O(21) bond length. In the seventh Al site, Al(7) is bonded to one O(10), one O(9), and two equivalent O(3) atoms to form AlO4 tetrahedra that share  a cornercorner with one Al(5)O6 octahedra, corners with two equivalent Al(17)O6 octahedra, corners with four equivalent Al(2)O6 octahedra, and corners with two equivalent Al(7)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 54-65°. The Al(7)-O(10) bond length is 1.75 Å. The Al(7)-O(9) bond length is 1.78 Å. Both Al(7)-O(3) bond lengths are 1.80 Å. In the eighth Al site, Al(8) is bonded to one O(11), one O(14), two equivalent O(4), and two equivalent O(5) atoms to form AlO6 octahedra that share  a cornercorner with one Al(10)O4 tetrahedra, corners with two equivalent Al(14)O4 tetrahedra, corners with four equivalent Al(3)O4 tetrahedra, edges with two equivalent Al(4)O6 octahedra, and edges with two equivalent Al(8)O6 octahedra. The Al(8)-O(11) bond length is 1.83 Å. The Al(8)-O(14) bond length is 2.02 Å. Both Al(8)-O(4) bond lengths are 1.90 Å. There is one shorter (2.04 Å) and one longer (2.05 Å) Al(8)-O(5) bond length. In the ninth Al site, Al(9) is bonded in a 5-coordinate geometry to one O(17), two equivalent O(23), and two equivalent O(24) atoms. The Al(9)-O(17) bond length is 1.66 Å. There is one shorter (2.22 Å) and one longer (2.35 Å) Al(9)-O(23) bond length. There is one shorter (1.85 Å) and one longer (1.87 Å) Al(9)-O(24) bond length. In the tenth Al site, Al(10) is bonded to one O(14), one O(15), and two equivalent O(6) atoms to form AlO4 tetrahedra that share  a cornercorner with one Al(8)O6 octahedra, corners with two equivalent Al(5)O6 octahedra, corners with four equivalent Al(4)O6 octahedra, and corners with two equivalent Al(10)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 54-67°. The Al(10)-O(14) bond length is 1.78 Å. The Al(10)-O(15) bond length is 1.75 Å. Both Al(10)-O(6) bond lengths are 1.80 Å. In the eleventh Al site, Al(11) is bonded to one O(18), one O(19), and two equivalent O(25) atoms to form AlO4 tetrahedra that share corners with two equivalent Al(2)O6 octahedra, corners with four equivalent Al(17)O6 octahedra,  a cornercorner with one Al(13)O5 square pyramid, and corners with two equivalent Al(11)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 59-60°. The Al(11)-O(18) bond length is 1.79 Å. The Al(11)-O(19) bond length is 1.84 Å. Both Al(11)-O(25) bond lengths are 1.74 Å. In the twelfth Al site, Al(12) is bonded to one O(16), one O(17), and two equivalent O(8) atoms to form AlO4 trigonal pyramids that share corners with two equivalent Al(6)O6 octahedra, corners with two equivalent Al(16)O4 tetrahedra, and corners with two equivalent Al(12)O4 trigonal pyramids. The corner-sharing octahedral tilt angles are 63°. The Al(12)-O(16) bond length is 1.97 Å. The Al(12)-O(17) bond length is 1.73 Å. There is one shorter (1.72 Å) and one longer (1.73 Å) Al(12)-O(8) bond length. In the thirteenth Al site, Al(13) is bonded to one O(19), two equivalent O(26), and two equivalent O(27) atoms to form AlO5 square pyramids that share  a cornercorner with one Al(11)O4 tetrahedra, corners with four equivalent Al(18)O4 tetrahedra, edges with two equivalent Al(17)O6 octahedra, and edges with two equivalent Al(13)O5 square pyramids. The Al(13)-O(19) bond length is 1.85 Å. There is one shorter (2.01 Å) and one longer (2.02 Å) Al(13)-O(26) bond length. Both Al(13)-O(27) bond lengths are 1.88 Å. In the fourteenth Al site, Al(14) is bonded to one O(20), one O(21), and two equivalent O(11) atoms to form AlO4 tetrahedra that share corners with two equivalent Al(8)O6 octahedra, corners with four equivalent Al(6)O6 octahedra, and corners with two equivalent Al(14)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 55-56°. The Al(14)-O(20) bond length is 1.76 Å. The Al(14)-O(21) bond length is 1.77 Å. Both Al(14)-O(11) bond lengths are 1.81 Å. In the fifteenth Al site, Al(15) is bonded to one O(22), one O(23), and two equivalent O(13) atoms to form corner-sharing AlO4 tetrahedra. The Al(15)-O(22) bond length is 1.88 Å. The Al(15)-O(23) bond length is 1.79 Å. Both Al(15)-O(13) bond lengths are 1.72 Å. In the sixteenth Al site, Al(16) is bonded to one O(23), one O(24), and two equivalent O(16) atoms to form corner-sharing AlO4 tetrahedra. The Al(16)-O(23) bond length is 1.84 Å. The Al(16)-O(24) bond length is 1.81 Å. Both Al(16)-O(16) bond lengths are 1.74 Å. In the seventeenth Al site, Al(17) is bonded to one O(26), one O(3), two equivalent O(18), and two equivalent O(19) atoms to form AlO6 octahedra that share  a cornercorner with one Al(18)O4 tetrahedra, corners with two equivalent Al(7)O4 tetrahedra, corners with four equivalent Al(11)O4 tetrahedra, edges with two equivalent Al(17)O6 octahedra, and edges with two equivalent Al(13)O5 square pyramids. The Al(17)-O(26) bond length is 2.06 Å. The Al(17)-O(3) bond length is 1.85 Å. Both Al(17)-O(18) bond lengths are 1.88 Å. There is one shorter (2.07 Å) and one longer (2.09 Å) Al(17)-O(19) bond length. In the eighteenth Al site, Al(18) is bonded to one O(26), one O(27), and two equivalent O(22) atoms to form AlO4 tetrahedra that share  a cornercorner with one Al(17)O6 octahedra, corners with four equivalent Al(13)O5 square pyramids, corners with two equivalent Al(15)O4 tetrahedra, and corners with two equivalent Al(18)O4 tetrahedra. The corner-sharing octahedral tilt angles are 60°. The Al(18)-O(26) bond length is 1.87 Å. The Al(18)-O(27) bond length is 1.81 Å. Both Al(18)-O(22) bond lengths are 1.76 Å. There are twenty-seven inequivalent O sites. In the first O site, O(1) is bonded in a trigonal planar geometry to one Al(1) and two equivalent Al(5) atoms. In the second O site, O(2) is bonded to one Al(1), one Al(2), and two equivalent Al(5) atoms to form distorted corner-sharing OAl4 tetrahedra. In the third O site, O(3) is bonded in a trigonal planar geometry to one Al(17) and two equivalent Al(7) atoms. In the fourth O site, O(4) is bonded in a trigonal non-coplanar geometry to one Al(3) and two equivalent Al(8) atoms. In the fifth O site, O(5) is bonded to one Al(3), one Al(4), and two equivalent Al(8) atoms to form a mixture of distorted corner and edge-sharing OAl4 tetrahedra. In the sixth O site, O(6) is bonded in a trigonal planar geometry to one Al(5) and two equivalent Al(10) atoms. In the seventh O site, O(7) is bonded in a trigonal planar geometry to one Al(4) and two equivalent Al(1) atoms. In the eighth O site, O(8) is bonded in a trigonal planar geometry to one Al(6) and two equivalent Al(12) atoms. In the ninth O site, O(9) is bonded in a distorted rectangular see-saw-like geometry to one Al(5), one Al(7), and two equivalent Al(2) atoms. In the tenth O site, O(10) is bonded in a trigonal planar geometry to one Al(7) and two equivalent Al(2) atoms. In the eleventh O site, O(11) is bonded in a trigonal planar geometry to one Al(8) and two equivalent Al(14) atoms. In the twelfth O site, O(12) is bonded in a trigonal planar geometry to one Al(6) and two equivalent Al(3) atoms. In the thirteenth O site, O(13) is bonded in a bent 120 degrees geometry to two equivalent Al(15) atoms. In the fourteenth O site, O(14) is bonded to one Al(10), one Al(8), and two equivalent Al(4) atoms to form a mixture of distorted corner and edge-sharing OAl4 tetrahedra. In the fifteenth O site, O(15) is bonded in a trigonal planar geometry to one Al(10) and two equivalent Al(4) atoms. In the sixteenth O site, O(16) is bonded in a trigonal non-coplanar geometry to one Al(12) and two equivalent Al(16) atoms. In the seventeenth O site, O(17) is bonded in a bent 150 degrees geometry to one Al(12) and one Al(9) atom. In the eighteenth O site, O(18) is bonded in a trigonal planar geometry to one Al(11) and two equivalent Al(17) atoms. In the nineteenth O site, O(19) is bonded to one Al(11), one Al(13), and two equivalent Al(17) atoms to form a mixture of distorted corner and edge-sharing OAl4 trigonal pyramids. In the twentieth O site, O(20) is bonded in a trigonal planar geometry to one Al(14) and two equivalent Al(6) atoms. In the twenty-first O site, O(21) is bonded in a trigonal planar geometry to one Al(14) and two equivalent Al(6) atoms. In the twenty-second O site, O(22) is bonded in a trigonal non-coplanar geometry to one Al(15) and two equivalent Al(18) atoms. In the twenty-third O site, O(23) is bonded in a 4-coordinate geometry to one Al(15), one Al(16), and two equivalent Al(9) atoms. In the twenty-fourth O site, O(24) is bonded in a trigonal non-coplanar geometry to one Al(16) and two equivalent Al(9) atoms. In the twenty-fifth O site, O(25) is bonded in a trigonal planar geometry to one Al(2) and two equivalent Al(11) atoms. In the twenty-sixth O site, O(26) is bonded to one Al(17), one Al(18), and two equivalent Al(13) atoms to form a mixture of distorted corner and edge-sharing OAl4 trigonal pyramids. In the twenty-seventh O site, O(27) is bonded in a trigonal planar geometry to one Al(18) and two equivalent Al(13) atoms.