Ba6Lu2Al4O15 crystallizes in the monoclinic P2/c space group. There are four inequivalent Ba sites. In the first Ba site, Ba(1) is bonded in a 10-coordinate geometry to one O(5), one O(6), one O(7), two equivalent O(2), two equivalent O(4), and three equivalent O(8) atoms. In the second Ba site, Ba(2) is bonded in a 9-coordinate geometry to one O(1), one O(5), one O(6), two equivalent O(2), two equivalent O(3), and two equivalent O(4) atoms. In the third Ba site, Ba(3) is bonded in a 8-coordinate geometry to two equivalent O(1), two equivalent O(3), two equivalent O(6), and two equivalent O(7) atoms. In the fourth Ba site, Ba(4) is bonded in a 8-coordinate geometry to two equivalent O(5), two equivalent O(6), two equivalent O(7), and two equivalent O(8) atoms. Lu(1) is bonded to one O(2), one O(3), one O(4), one O(6), one O(7), and one O(8) atom to form LuO6 octahedra that share corners with two equivalent Al(2)O4 tetrahedra and corners with four equivalent Al(1)O4 tetrahedra. There are two inequivalent Al sites. In the first Al site, Al(1) is bonded to one O(2), one O(3), one O(4), and one O(8) atom to form AlO4 tetrahedra that share corners with four equivalent Lu(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 10-36°. In the second Al site, Al(2) is bonded to one O(1), one O(5), one O(6), and one O(7) atom to form AlO4 tetrahedra that share corners with two equivalent Lu(1)O6 octahedra and  a cornercorner with one Al(2)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 7-30°. There are eight inequivalent O sites. In the first O site, O(4) is bonded in a 6-coordinate geometry to two equivalent Ba(1), two equivalent Ba(2), one Lu(1), and one Al(1) atom. In the second O site, O(5) is bonded in a 4-coordinate geometry to one Ba(1), one Ba(2), one Ba(4), and one Al(2) atom. In the third O site, O(6) is bonded in a 6-coordinate geometry to one Ba(1), one Ba(2), one Ba(3), one Ba(4), one Lu(1), and one Al(2) atom. In the fourth O site, O(7) is bonded in a 2-coordinate geometry to one Ba(1), one Ba(3), one Ba(4), one Lu(1), and one Al(2) atom. In the fifth O site, O(8) is bonded in a 2-coordinate geometry to one Ba(4), three equivalent Ba(1), one Lu(1), and one Al(1) atom. In the sixth O site, O(1) is bonded in a distorted linear geometry to two equivalent Ba(2), two equivalent Ba(3), and two equivalent Al(2) atoms. In the seventh O site, O(2) is bonded in a 6-coordinate geometry to two equivalent Ba(1), two equivalent Ba(2), one Lu(1), and one Al(1) atom. In the eighth O site, O(3) is bonded in a 5-coordinate geometry to one Ba(3), two equivalent Ba(2), one Lu(1), and one Al(1) atom.
Ba6Lu2Al4O15 crystallizes in the monoclinic P2/c space group. There are four inequivalent Ba sites. In the first Ba site, Ba(1) is bonded in a 10-coordinate geometry to one O(5), one O(6), one O(7), two equivalent O(2), two equivalent O(4), and three equivalent O(8) atoms. The Ba(1)-O(5) bond length is 2.53 Å. The Ba(1)-O(6) bond length is 2.81 Å. The Ba(1)-O(7) bond length is 3.11 Å. There is one shorter (2.96 Å) and one longer (2.97 Å) Ba(1)-O(2) bond length. There is one shorter (2.91 Å) and one longer (2.93 Å) Ba(1)-O(4) bond length. There are a spread of Ba(1)-O(8) bond distances ranging from 2.92-3.18 Å. In the second Ba site, Ba(2) is bonded in a 9-coordinate geometry to one O(1), one O(5), one O(6), two equivalent O(2), two equivalent O(3), and two equivalent O(4) atoms. The Ba(2)-O(1) bond length is 2.98 Å. The Ba(2)-O(5) bond length is 2.83 Å. The Ba(2)-O(6) bond length is 2.89 Å. There is one shorter (2.82 Å) and one longer (2.96 Å) Ba(2)-O(2) bond length. There is one shorter (2.94 Å) and one longer (3.00 Å) Ba(2)-O(3) bond length. There is one shorter (2.84 Å) and one longer (2.98 Å) Ba(2)-O(4) bond length. In the third Ba site, Ba(3) is bonded in a 8-coordinate geometry to two equivalent O(1), two equivalent O(3), two equivalent O(6), and two equivalent O(7) atoms. There is one shorter (2.89 Å) and one longer (3.02 Å) Ba(3)-O(1) bond length. Both Ba(3)-O(3) bond lengths are 2.74 Å. Both Ba(3)-O(6) bond lengths are 2.92 Å. Both Ba(3)-O(7) bond lengths are 2.79 Å. In the fourth Ba site, Ba(4) is bonded in a 8-coordinate geometry to two equivalent O(5), two equivalent O(6), two equivalent O(7), and two equivalent O(8) atoms. Both Ba(4)-O(5) bond lengths are 2.84 Å. Both Ba(4)-O(6) bond lengths are 2.87 Å. Both Ba(4)-O(7) bond lengths are 2.81 Å. Both Ba(4)-O(8) bond lengths are 2.96 Å. Lu(1) is bonded to one O(2), one O(3), one O(4), one O(6), one O(7), and one O(8) atom to form LuO6 octahedra that share corners with two equivalent Al(2)O4 tetrahedra and corners with four equivalent Al(1)O4 tetrahedra. The Lu(1)-O(2) bond length is 2.19 Å. The Lu(1)-O(3) bond length is 2.38 Å. The Lu(1)-O(4) bond length is 2.19 Å. The Lu(1)-O(6) bond length is 2.22 Å. The Lu(1)-O(7) bond length is 2.22 Å. The Lu(1)-O(8) bond length is 2.28 Å. There are two inequivalent Al sites. In the first Al site, Al(1) is bonded to one O(2), one O(3), one O(4), and one O(8) atom to form AlO4 tetrahedra that share corners with four equivalent Lu(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 10-36°. The Al(1)-O(2) bond length is 1.80 Å. The Al(1)-O(3) bond length is 1.80 Å. The Al(1)-O(4) bond length is 1.81 Å. The Al(1)-O(8) bond length is 1.80 Å. In the second Al site, Al(2) is bonded to one O(1), one O(5), one O(6), and one O(7) atom to form AlO4 tetrahedra that share corners with two equivalent Lu(1)O6 octahedra and  a cornercorner with one Al(2)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 7-30°. The Al(2)-O(1) bond length is 1.77 Å. The Al(2)-O(5) bond length is 1.74 Å. The Al(2)-O(6) bond length is 1.80 Å. The Al(2)-O(7) bond length is 1.78 Å. There are eight inequivalent O sites. In the first O site, O(4) is bonded in a 6-coordinate geometry to two equivalent Ba(1), two equivalent Ba(2), one Lu(1), and one Al(1) atom. In the second O site, O(5) is bonded in a 4-coordinate geometry to one Ba(1), one Ba(2), one Ba(4), and one Al(2) atom. In the third O site, O(6) is bonded in a 6-coordinate geometry to one Ba(1), one Ba(2), one Ba(3), one Ba(4), one Lu(1), and one Al(2) atom. In the fourth O site, O(7) is bonded in a 2-coordinate geometry to one Ba(1), one Ba(3), one Ba(4), one Lu(1), and one Al(2) atom. In the fifth O site, O(8) is bonded in a 2-coordinate geometry to one Ba(4), three equivalent Ba(1), one Lu(1), and one Al(1) atom. In the sixth O site, O(1) is bonded in a distorted linear geometry to two equivalent Ba(2), two equivalent Ba(3), and two equivalent Al(2) atoms. In the seventh O site, O(2) is bonded in a 6-coordinate geometry to two equivalent Ba(1), two equivalent Ba(2), one Lu(1), and one Al(1) atom. In the eighth O site, O(3) is bonded in a 5-coordinate geometry to one Ba(3), two equivalent Ba(2), one Lu(1), and one Al(1) atom.