Ba4Lu6O13 crystallizes in the triclinic P1 space group. There are eight inequivalent Ba sites. In the first Ba site, Ba(1) is bonded in a 9-coordinate geometry to one O(11), one O(23), one O(24), one O(25), one O(5), one O(8), one O(9), and two equivalent O(26) atoms. In the second Ba site, Ba(2) is bonded in a 9-coordinate geometry to one O(12), one O(24), one O(3), one O(5), one O(7), one O(8), one O(9), and two equivalent O(6) atoms. In the third Ba site, Ba(3) is bonded in a 9-coordinate geometry to one O(10), one O(14), one O(15), one O(18), one O(6), one O(8), one O(9), and two equivalent O(12) atoms. In the fourth Ba site, Ba(4) is bonded in a 9-coordinate geometry to one O(13), one O(14), one O(15), one O(17), one O(26), one O(8), one O(9), and two equivalent O(11) atoms. In the fifth Ba site, Ba(5) is bonded in a 9-coordinate geometry to one O(12), one O(14), one O(15), one O(16), one O(20), one O(21), one O(3), and two equivalent O(18) atoms. In the sixth Ba site, Ba(6) is bonded in a 9-coordinate geometry to one O(11), one O(14), one O(15), one O(19), one O(20), one O(21), one O(23), and two equivalent O(17) atoms. In the seventh Ba site, Ba(7) is bonded in a 9-coordinate geometry to one O(17), one O(20), one O(21), one O(22), one O(24), one O(26), one O(5), and two equivalent O(23) atoms. In the eighth Ba site, Ba(8) is bonded in a 9-coordinate geometry to one O(18), one O(20), one O(21), one O(24), one O(4), one O(5), one O(6), and two equivalent O(3) atoms. There are twelve inequivalent Lu sites. In the first Lu site, Lu(1) is bonded to one O(1), one O(13), one O(2), one O(3), and one O(4) atom to form distorted LuO5 trigonal bipyramids that share  a cornercorner with one Lu(11)O6 octahedra,  a cornercorner with one Lu(3)O5 trigonal bipyramid,  a cornercorner with one Lu(9)O5 trigonal bipyramid, corners with two equivalent Lu(7)O5 trigonal bipyramids,  an edgeedge with one Lu(12)O5 trigonal bipyramid, and edges with two equivalent Lu(6)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 9°. In the second Lu site, Lu(2) is bonded to one O(24), one O(26), one O(5), one O(6), one O(8), and one O(9) atom to form LuO6 octahedra that share corners with two equivalent Lu(11)O6 octahedra, corners with two equivalent Lu(5)O6 octahedra,  a cornercorner with one Lu(12)O5 trigonal bipyramid, and  a cornercorner with one Lu(3)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 2-7°. In the third Lu site, Lu(3) is bonded to one O(10), one O(19), one O(4), one O(6), and one O(7) atom to form LuO5 trigonal bipyramids that share  a cornercorner with one Lu(2)O6 octahedra,  a cornercorner with one Lu(1)O5 trigonal bipyramid,  a cornercorner with one Lu(6)O5 trigonal bipyramid, corners with two equivalent Lu(4)O5 trigonal bipyramids, corners with two equivalent Lu(9)O5 trigonal bipyramids, and  an edgeedge with one Lu(10)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles are 10°. In the fourth Lu site, Lu(4) is bonded to one O(10), one O(12), one O(16), one O(22), and one O(7) atom to form distorted LuO5 trigonal bipyramids that share  a cornercorner with one Lu(5)O6 octahedra,  a cornercorner with one Lu(12)O5 trigonal bipyramid,  a cornercorner with one Lu(7)O5 trigonal bipyramid, corners with two equivalent Lu(10)O5 trigonal bipyramids, corners with two equivalent Lu(3)O5 trigonal bipyramids, and  an edgeedge with one Lu(9)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles are 10°. In the fifth Lu site, Lu(5) is bonded to one O(11), one O(12), one O(14), one O(15), one O(8), and one O(9) atom to form LuO6 octahedra that share corners with two equivalent Lu(2)O6 octahedra, corners with two equivalent Lu(8)O6 octahedra,  a cornercorner with one Lu(4)O5 trigonal bipyramid, and  a cornercorner with one Lu(6)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 2-7°. In the sixth Lu site, Lu(6) is bonded to one O(1), one O(11), one O(13), one O(2), and one O(4) atom to form distorted LuO5 trigonal bipyramids that share  a cornercorner with one Lu(5)O6 octahedra,  a cornercorner with one Lu(3)O5 trigonal bipyramid,  a cornercorner with one Lu(9)O5 trigonal bipyramid, corners with two equivalent Lu(12)O5 trigonal bipyramids,  an edgeedge with one Lu(7)O5 trigonal bipyramid, and edges with two equivalent Lu(1)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 7°. In the seventh Lu site, Lu(7) is bonded to one O(1), one O(16), one O(18), one O(2), and one O(25) atom to form distorted LuO5 trigonal bipyramids that share  a cornercorner with one Lu(8)O6 octahedra,  a cornercorner with one Lu(10)O5 trigonal bipyramid,  a cornercorner with one Lu(4)O5 trigonal bipyramid, corners with two equivalent Lu(1)O5 trigonal bipyramids,  an edgeedge with one Lu(6)O5 trigonal bipyramid, and edges with two equivalent Lu(12)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 7°. In the eighth Lu site, Lu(8) is bonded to one O(14), one O(15), one O(17), one O(18), one O(20), and one O(21) atom to form LuO6 octahedra that share corners with two equivalent Lu(11)O6 octahedra, corners with two equivalent Lu(5)O6 octahedra,  a cornercorner with one Lu(7)O5 trigonal bipyramid, and  a cornercorner with one Lu(9)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 4-7°. In the ninth Lu site, Lu(9) is bonded to one O(13), one O(17), one O(19), one O(22), and one O(7) atom to form LuO5 trigonal bipyramids that share  a cornercorner with one Lu(8)O6 octahedra,  a cornercorner with one Lu(1)O5 trigonal bipyramid,  a cornercorner with one Lu(6)O5 trigonal bipyramid, corners with two equivalent Lu(10)O5 trigonal bipyramids, corners with two equivalent Lu(3)O5 trigonal bipyramids, and  an edgeedge with one Lu(4)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles are 11°. In the tenth Lu site, Lu(10) is bonded to one O(10), one O(19), one O(22), one O(23), and one O(25) atom to form distorted LuO5 trigonal bipyramids that share  a cornercorner with one Lu(11)O6 octahedra,  a cornercorner with one Lu(12)O5 trigonal bipyramid,  a cornercorner with one Lu(7)O5 trigonal bipyramid, corners with two equivalent Lu(4)O5 trigonal bipyramids, corners with two equivalent Lu(9)O5 trigonal bipyramids, and  an edgeedge with one Lu(3)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles are 12°. In the eleventh Lu site, Lu(11) is bonded to one O(20), one O(21), one O(23), one O(24), one O(3), and one O(5) atom to form LuO6 octahedra that share corners with two equivalent Lu(2)O6 octahedra, corners with two equivalent Lu(8)O6 octahedra,  a cornercorner with one Lu(1)O5 trigonal bipyramid, and  a cornercorner with one Lu(10)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 4-7°. In the twelfth Lu site, Lu(12) is bonded to one O(1), one O(16), one O(2), one O(25), and one O(26) atom to form distorted LuO5 trigonal bipyramids that share  a cornercorner with one Lu(2)O6 octahedra,  a cornercorner with one Lu(10)O5 trigonal bipyramid,  a cornercorner with one Lu(4)O5 trigonal bipyramid, corners with two equivalent Lu(6)O5 trigonal bipyramids,  an edgeedge with one Lu(1)O5 trigonal bipyramid, and edges with two equivalent Lu(7)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 7°. There are twenty-six inequivalent O sites. In the first O site, O(1) is bonded to one Lu(1), one Lu(12), one Lu(6), and one Lu(7) atom to form distorted edge-sharing OLu4 trigonal pyramids. In the second O site, O(2) is bonded to one Lu(1), one Lu(12), one Lu(6), and one Lu(7) atom to form distorted edge-sharing OLu4 trigonal pyramids. In the third O site, O(3) is bonded in a 6-coordinate geometry to one Ba(2), one Ba(5), two equivalent Ba(8), one Lu(1), and one Lu(11) atom. In the fourth O site, O(4) is bonded in a 4-coordinate geometry to one Ba(8), one Lu(1), one Lu(3), and one Lu(6) atom. In the fifth O site, O(5) is bonded to one Ba(1), one Ba(2), one Ba(7), one Ba(8), one Lu(11), and one Lu(2) atom to form distorted OBa4Lu2 octahedra that share  a cornercorner with one O(21)Ba4Lu2 octahedra,  a cornercorner with one O(9)Ba4Lu2 octahedra,  a cornercorner with one O(22)BaLu3 tetrahedra,  a cornercorner with one O(7)BaLu3 tetrahedra,  an edgeedge with one O(21)Ba4Lu2 octahedra,  an edgeedge with one O(9)Ba4Lu2 octahedra,  a faceface with one O(20)Ba4Lu2 octahedra,  a faceface with one O(8)Ba4Lu2 octahedra, and faces with two equivalent O(24)Ba4Lu2 octahedra. The corner-sharing octahedral tilt angles range from 2-4°. In the sixth O site, O(6) is bonded in a 6-coordinate geometry to one Ba(3), one Ba(8), two equivalent Ba(2), one Lu(2), and one Lu(3) atom. In the seventh O site, O(7) is bonded to one Ba(2), one Lu(3), one Lu(4), and one Lu(9) atom to form distorted OBaLu3 tetrahedra that share  a cornercorner with one O(24)Ba4Lu2 octahedra,  a cornercorner with one O(5)Ba4Lu2 octahedra,  a cornercorner with one O(8)Ba4Lu2 octahedra,  a cornercorner with one O(9)Ba4Lu2 octahedra, corners with two equivalent O(10)BaLu3 tetrahedra, corners with two equivalent O(19)BaLu3 tetrahedra, and  an edgeedge with one O(22)BaLu3 tetrahedra. The corner-sharing octahedral tilt angles range from 26-70°. In the eighth O site, O(8) is bonded to one Ba(1), one Ba(2), one Ba(3), one Ba(4), one Lu(2), and one Lu(5) atom to form distorted OBa4Lu2 octahedra that share  a cornercorner with one O(14)Ba4Lu2 octahedra,  a cornercorner with one O(24)Ba4Lu2 octahedra,  a cornercorner with one O(10)BaLu3 tetrahedra,  a cornercorner with one O(7)BaLu3 tetrahedra,  an edgeedge with one O(14)Ba4Lu2 octahedra,  an edgeedge with one O(24)Ba4Lu2 octahedra,  a faceface with one O(15)Ba4Lu2 octahedra,  a faceface with one O(5)Ba4Lu2 octahedra, and faces with two equivalent O(9)Ba4Lu2 octahedra. The corner-sharing octahedral tilt angles range from 3-5°. In the ninth O site, O(9) is bonded to one Ba(1), one Ba(2), one Ba(3), one Ba(4), one Lu(2), and one Lu(5) atom to form distorted OBa4Lu2 octahedra that share  a cornercorner with one O(15)Ba4Lu2 octahedra,  a cornercorner with one O(5)Ba4Lu2 octahedra,  a cornercorner with one O(10)BaLu3 tetrahedra,  a cornercorner with one O(7)BaLu3 tetrahedra,  an edgeedge with one O(15)Ba4Lu2 octahedra,  an edgeedge with one O(5)Ba4Lu2 octahedra,  a faceface with one O(14)Ba4Lu2 octahedra,  a faceface with one O(24)Ba4Lu2 octahedra, and faces with two equivalent O(8)Ba4Lu2 octahedra. The corner-sharing octahedral tilt angles range from 2-4°. In the tenth O site, O(10) is bonded to one Ba(3), one Lu(10), one Lu(3), and one Lu(4) atom to form distorted OBaLu3 tetrahedra that share  a cornercorner with one O(14)Ba4Lu2 octahedra,  a cornercorner with one O(15)Ba4Lu2 octahedra,  a cornercorner with one O(8)Ba4Lu2 octahedra,  a cornercorner with one O(9)Ba4Lu2 octahedra, corners with two equivalent O(22)BaLu3 tetrahedra, corners with two equivalent O(7)BaLu3 tetrahedra, and  an edgeedge with one O(19)BaLu3 tetrahedra. The corner-sharing octahedral tilt angles range from 25-70°. In the eleventh O site, O(11) is bonded in a 6-coordinate geometry to one Ba(1), one Ba(6), two equivalent Ba(4), one Lu(5), and one Lu(6) atom. In the twelfth O site, O(12) is bonded in a 6-coordinate geometry to one Ba(2), one Ba(5), two equivalent Ba(3), one Lu(4), and one Lu(5) atom. In the thirteenth O site, O(13) is bonded in a 4-coordinate geometry to one Ba(4), one Lu(1), one Lu(6), and one Lu(9) atom. In the fourteenth O site, O(14) is bonded to one Ba(3), one Ba(4), one Ba(5), one Ba(6), one Lu(5), and one Lu(8) atom to form distorted OBa4Lu2 octahedra that share  a cornercorner with one O(20)Ba4Lu2 octahedra,  a cornercorner with one O(8)Ba4Lu2 octahedra,  a cornercorner with one O(10)BaLu3 tetrahedra,  a cornercorner with one O(19)BaLu3 tetrahedra,  an edgeedge with one O(20)Ba4Lu2 octahedra,  an edgeedge with one O(8)Ba4Lu2 octahedra,  a faceface with one O(21)Ba4Lu2 octahedra,  a faceface with one O(9)Ba4Lu2 octahedra, and faces with two equivalent O(15)Ba4Lu2 octahedra. The corner-sharing octahedral tilt angles range from 4-5°. In the fifteenth O site, O(15) is bonded to one Ba(3), one Ba(4), one Ba(5), one Ba(6), one Lu(5), and one Lu(8) atom to form distorted OBa4Lu2 octahedra that share  a cornercorner with one O(21)Ba4Lu2 octahedra,  a cornercorner with one O(9)Ba4Lu2 octahedra,  a cornercorner with one O(10)BaLu3 tetrahedra,  a cornercorner with one O(19)BaLu3 tetrahedra,  an edgeedge with one O(21)Ba4Lu2 octahedra,  an edgeedge with one O(9)Ba4Lu2 octahedra,  a faceface with one O(20)Ba4Lu2 octahedra,  a faceface with one O(8)Ba4Lu2 octahedra, and faces with two equivalent O(14)Ba4Lu2 octahedra. The corner-sharing octahedral tilt angles range from 3-4°. In the sixteenth O site, O(16) is bonded in a 4-coordinate geometry to one Ba(5), one Lu(12), one Lu(4), and one Lu(7) atom. In the seventeenth O site, O(17) is bonded in a 6-coordinate geometry to one Ba(4), one Ba(7), two equivalent Ba(6), one Lu(8), and one Lu(9) atom. In the eighteenth O site, O(18) is bonded in a 6-coordinate geometry to one Ba(3), one Ba(8), two equivalent Ba(5), one Lu(7), and one Lu(8) atom. In the nineteenth O site, O(19) is bonded to one Ba(6), one Lu(10), one Lu(3), and one Lu(9) atom to form distorted OBaLu3 tetrahedra that share  a cornercorner with one O(14)Ba4Lu2 octahedra,  a cornercorner with one O(15)Ba4Lu2 octahedra,  a cornercorner with one O(20)Ba4Lu2 octahedra,  a cornercorner with one O(21)Ba4Lu2 octahedra, corners with two equivalent O(22)BaLu3 tetrahedra, corners with two equivalent O(7)BaLu3 tetrahedra, and  an edgeedge with one O(10)BaLu3 tetrahedra. The corner-sharing octahedral tilt angles range from 26-69°. In the twentieth O site, O(20) is bonded to one Ba(5), one Ba(6), one Ba(7), one Ba(8), one Lu(11), and one Lu(8) atom to form distorted OBa4Lu2 octahedra that share  a cornercorner with one O(14)Ba4Lu2 octahedra,  a cornercorner with one O(24)Ba4Lu2 octahedra,  a cornercorner with one O(19)BaLu3 tetrahedra,  a cornercorner with one O(22)BaLu3 tetrahedra,  an edgeedge with one O(14)Ba4Lu2 octahedra,  an edgeedge with one O(24)Ba4Lu2 octahedra,  a faceface with one O(15)Ba4Lu2 octahedra,  a faceface with one O(5)Ba4Lu2 octahedra, and faces with two equivalent O(21)Ba4Lu2 octahedra. The corner-sharing octahedral tilt angles range from 3-4°. In the twenty-first O site, O(21) is bonded to one Ba(5), one Ba(6), one Ba(7), one Ba(8), one Lu(11), and one Lu(8) atom to form distorted OBa4Lu2 octahedra that share  a cornercorner with one O(15)Ba4Lu2 octahedra,  a cornercorner with one O(5)Ba4Lu2 octahedra,  a cornercorner with one O(19)BaLu3 tetrahedra,  a cornercorner with one O(22)BaLu3 tetrahedra,  an edgeedge with one O(15)Ba4Lu2 octahedra,  an edgeedge with one O(5)Ba4Lu2 octahedra,  a faceface with one O(14)Ba4Lu2 octahedra,  a faceface with one O(24)Ba4Lu2 octahedra, and faces with two equivalent O(20)Ba4Lu2 octahedra. The corner-sharing octahedral tilt angles range from 3-4°. In the twenty-second O site, O(22) is bonded to one Ba(7), one Lu(10), one Lu(4), and one Lu(9) atom to form distorted OBaLu3 tetrahedra that share  a cornercorner with one O(20)Ba4Lu2 octahedra,  a cornercorner with one O(21)Ba4Lu2 octahedra,  a cornercorner with one O(24)Ba4Lu2 octahedra,  a cornercorner with one O(5)Ba4Lu2 octahedra, corners with two equivalent O(10)BaLu3 tetrahedra, corners with two equivalent O(19)BaLu3 tetrahedra, and  an edgeedge with one O(7)BaLu3 tetrahedra. The corner-sharing octahedral tilt angles range from 25-70°. In the twenty-third O site, O(23) is bonded in a 6-coordinate geometry to one Ba(1), one Ba(6), two equivalent Ba(7), one Lu(10), and one Lu(11) atom. In the twenty-fourth O site, O(24) is bonded to one Ba(1), one Ba(2), one Ba(7), one Ba(8), one Lu(11), and one Lu(2) atom to form distorted OBa4Lu2 octahedra that share  a cornercorner with one O(20)Ba4Lu2 octahedra,  a cornercorner with one O(8)Ba4Lu2 octahedra,  a cornercorner with one O(22)BaLu3 tetrahedra,  a cornercorner with one O(7)BaLu3 tetrahedra,  an edgeedge with one O(20)Ba4Lu2 octahedra,  an edgeedge with one O(8)Ba4Lu2 octahedra,  a faceface with one O(21)Ba4Lu2 octahedra,  a faceface with one O(9)Ba4Lu2 octahedra, and faces with two equivalent O(5)Ba4Lu2 octahedra. The corner-sharing octahedral tilt angles are 3°. In the twenty-fifth O site, O(25) is bonded in a 4-coordinate geometry to one Ba(1), one Lu(10), one Lu(12), and one Lu(7) atom. In the twenty-sixth O site, O(26) is bonded in a 6-coordinate geometry to one Ba(4), one Ba(7), two equivalent Ba(1), one Lu(12), and one Lu(2) atom.
Ba4Lu6O13 crystallizes in the triclinic P1 space group. There are eight inequivalent Ba sites. In the first Ba site, Ba(1) is bonded in a 9-coordinate geometry to one O(11), one O(23), one O(24), one O(25), one O(5), one O(8), one O(9), and two equivalent O(26) atoms. The Ba(1)-O(11) bond length is 3.18 Å. The Ba(1)-O(23) bond length is 3.04 Å. The Ba(1)-O(24) bond length is 2.74 Å. The Ba(1)-O(25) bond length is 3.10 Å. The Ba(1)-O(5) bond length is 2.91 Å. The Ba(1)-O(8) bond length is 2.83 Å. The Ba(1)-O(9) bond length is 2.79 Å. There is one shorter (2.96 Å) and one longer (3.13 Å) Ba(1)-O(26) bond length. In the second Ba site, Ba(2) is bonded in a 9-coordinate geometry to one O(12), one O(24), one O(3), one O(5), one O(7), one O(8), one O(9), and two equivalent O(6) atoms. The Ba(2)-O(12) bond length is 3.00 Å. The Ba(2)-O(24) bond length is 2.91 Å. The Ba(2)-O(3) bond length is 3.16 Å. The Ba(2)-O(5) bond length is 2.73 Å. The Ba(2)-O(7) bond length is 2.65 Å. The Ba(2)-O(8) bond length is 2.84 Å. The Ba(2)-O(9) bond length is 2.88 Å. There is one shorter (2.87 Å) and one longer (3.16 Å) Ba(2)-O(6) bond length. In the third Ba site, Ba(3) is bonded in a 9-coordinate geometry to one O(10), one O(14), one O(15), one O(18), one O(6), one O(8), one O(9), and two equivalent O(12) atoms. The Ba(3)-O(10) bond length is 2.66 Å. The Ba(3)-O(14) bond length is 2.74 Å. The Ba(3)-O(15) bond length is 2.90 Å. The Ba(3)-O(18) bond length is 3.09 Å. The Ba(3)-O(6) bond length is 2.99 Å. The Ba(3)-O(8) bond length is 2.85 Å. The Ba(3)-O(9) bond length is 2.90 Å. There is one shorter (2.89 Å) and one longer (3.15 Å) Ba(3)-O(12) bond length. In the fourth Ba site, Ba(4) is bonded in a 9-coordinate geometry to one O(13), one O(14), one O(15), one O(17), one O(26), one O(8), one O(9), and two equivalent O(11) atoms. The Ba(4)-O(13) bond length is 3.05 Å. The Ba(4)-O(14) bond length is 2.89 Å. The Ba(4)-O(15) bond length is 2.74 Å. The Ba(4)-O(17) bond length is 3.00 Å. The Ba(4)-O(26) bond length is 3.20 Å. The Ba(4)-O(8) bond length is 2.86 Å. The Ba(4)-O(9) bond length is 2.81 Å. There is one shorter (2.95 Å) and one longer (3.14 Å) Ba(4)-O(11) bond length. In the fifth Ba site, Ba(5) is bonded in a 9-coordinate geometry to one O(12), one O(14), one O(15), one O(16), one O(20), one O(21), one O(3), and two equivalent O(18) atoms. The Ba(5)-O(12) bond length is 2.99 Å. The Ba(5)-O(14) bond length is 2.74 Å. The Ba(5)-O(15) bond length is 2.91 Å. The Ba(5)-O(16) bond length is 3.06 Å. The Ba(5)-O(20) bond length is 2.82 Å. The Ba(5)-O(21) bond length is 2.86 Å. The Ba(5)-O(3) bond length is 3.20 Å. There is one shorter (2.97 Å) and one longer (3.12 Å) Ba(5)-O(18) bond length. In the sixth Ba site, Ba(6) is bonded in a 9-coordinate geometry to one O(11), one O(14), one O(15), one O(19), one O(20), one O(21), one O(23), and two equivalent O(17) atoms. The Ba(6)-O(11) bond length is 3.15 Å. The Ba(6)-O(14) bond length is 2.91 Å. The Ba(6)-O(15) bond length is 2.74 Å. The Ba(6)-O(19) bond length is 2.65 Å. The Ba(6)-O(20) bond length is 2.83 Å. The Ba(6)-O(21) bond length is 2.88 Å. The Ba(6)-O(23) bond length is 2.98 Å. There is one shorter (2.87 Å) and one longer (3.17 Å) Ba(6)-O(17) bond length. In the seventh Ba site, Ba(7) is bonded in a 9-coordinate geometry to one O(17), one O(20), one O(21), one O(22), one O(24), one O(26), one O(5), and two equivalent O(23) atoms. The Ba(7)-O(17) bond length is 3.00 Å. The Ba(7)-O(20) bond length is 2.87 Å. The Ba(7)-O(21) bond length is 2.85 Å. The Ba(7)-O(22) bond length is 2.66 Å. The Ba(7)-O(24) bond length is 2.75 Å. The Ba(7)-O(26) bond length is 3.13 Å. The Ba(7)-O(5) bond length is 2.92 Å. There is one shorter (2.84 Å) and one longer (3.19 Å) Ba(7)-O(23) bond length. In the eighth Ba site, Ba(8) is bonded in a 9-coordinate geometry to one O(18), one O(20), one O(21), one O(24), one O(4), one O(5), one O(6), and two equivalent O(3) atoms. The Ba(8)-O(18) bond length is 3.22 Å. The Ba(8)-O(20) bond length is 2.84 Å. The Ba(8)-O(21) bond length is 2.82 Å. The Ba(8)-O(24) bond length is 2.92 Å. The Ba(8)-O(4) bond length is 3.06 Å. The Ba(8)-O(5) bond length is 2.73 Å. The Ba(8)-O(6) bond length is 3.05 Å. There is one shorter (3.03 Å) and one longer (3.06 Å) Ba(8)-O(3) bond length. There are twelve inequivalent Lu sites. In the first Lu site, Lu(1) is bonded to one O(1), one O(13), one O(2), one O(3), and one O(4) atom to form distorted LuO5 trigonal bipyramids that share  a cornercorner with one Lu(11)O6 octahedra,  a cornercorner with one Lu(3)O5 trigonal bipyramid,  a cornercorner with one Lu(9)O5 trigonal bipyramid, corners with two equivalent Lu(7)O5 trigonal bipyramids,  an edgeedge with one Lu(12)O5 trigonal bipyramid, and edges with two equivalent Lu(6)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 9°. The Lu(1)-O(1) bond length is 2.35 Å. The Lu(1)-O(13) bond length is 2.17 Å. The Lu(1)-O(2) bond length is 2.22 Å. The Lu(1)-O(3) bond length is 2.08 Å. The Lu(1)-O(4) bond length is 2.20 Å. In the second Lu site, Lu(2) is bonded to one O(24), one O(26), one O(5), one O(6), one O(8), and one O(9) atom to form LuO6 octahedra that share corners with two equivalent Lu(11)O6 octahedra, corners with two equivalent Lu(5)O6 octahedra,  a cornercorner with one Lu(12)O5 trigonal bipyramid, and  a cornercorner with one Lu(3)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 2-7°. The Lu(2)-O(24) bond length is 2.14 Å. The Lu(2)-O(26) bond length is 2.42 Å. The Lu(2)-O(5) bond length is 2.15 Å. The Lu(2)-O(6) bond length is 2.26 Å. The Lu(2)-O(8) bond length is 2.13 Å. The Lu(2)-O(9) bond length is 2.13 Å. In the third Lu site, Lu(3) is bonded to one O(10), one O(19), one O(4), one O(6), and one O(7) atom to form LuO5 trigonal bipyramids that share  a cornercorner with one Lu(2)O6 octahedra,  a cornercorner with one Lu(1)O5 trigonal bipyramid,  a cornercorner with one Lu(6)O5 trigonal bipyramid, corners with two equivalent Lu(4)O5 trigonal bipyramids, corners with two equivalent Lu(9)O5 trigonal bipyramids, and  an edgeedge with one Lu(10)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles are 10°. The Lu(3)-O(10) bond length is 2.28 Å. The Lu(3)-O(19) bond length is 2.27 Å. The Lu(3)-O(4) bond length is 2.25 Å. The Lu(3)-O(6) bond length is 2.09 Å. The Lu(3)-O(7) bond length is 2.18 Å. In the fourth Lu site, Lu(4) is bonded to one O(10), one O(12), one O(16), one O(22), and one O(7) atom to form distorted LuO5 trigonal bipyramids that share  a cornercorner with one Lu(5)O6 octahedra,  a cornercorner with one Lu(12)O5 trigonal bipyramid,  a cornercorner with one Lu(7)O5 trigonal bipyramid, corners with two equivalent Lu(10)O5 trigonal bipyramids, corners with two equivalent Lu(3)O5 trigonal bipyramids, and  an edgeedge with one Lu(9)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles are 10°. The Lu(4)-O(10) bond length is 2.18 Å. The Lu(4)-O(12) bond length is 2.09 Å. The Lu(4)-O(16) bond length is 2.25 Å. The Lu(4)-O(22) bond length is 2.28 Å. The Lu(4)-O(7) bond length is 2.29 Å. In the fifth Lu site, Lu(5) is bonded to one O(11), one O(12), one O(14), one O(15), one O(8), and one O(9) atom to form LuO6 octahedra that share corners with two equivalent Lu(2)O6 octahedra, corners with two equivalent Lu(8)O6 octahedra,  a cornercorner with one Lu(4)O5 trigonal bipyramid, and  a cornercorner with one Lu(6)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 2-7°. The Lu(5)-O(11) bond length is 2.40 Å. The Lu(5)-O(12) bond length is 2.28 Å. The Lu(5)-O(14) bond length is 2.14 Å. The Lu(5)-O(15) bond length is 2.14 Å. The Lu(5)-O(8) bond length is 2.13 Å. The Lu(5)-O(9) bond length is 2.13 Å. In the sixth Lu site, Lu(6) is bonded to one O(1), one O(11), one O(13), one O(2), and one O(4) atom to form distorted LuO5 trigonal bipyramids that share  a cornercorner with one Lu(5)O6 octahedra,  a cornercorner with one Lu(3)O5 trigonal bipyramid,  a cornercorner with one Lu(9)O5 trigonal bipyramid, corners with two equivalent Lu(12)O5 trigonal bipyramids,  an edgeedge with one Lu(7)O5 trigonal bipyramid, and edges with two equivalent Lu(1)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 7°. The Lu(6)-O(1) bond length is 2.21 Å. The Lu(6)-O(11) bond length is 2.08 Å. The Lu(6)-O(13) bond length is 2.20 Å. The Lu(6)-O(2) bond length is 2.34 Å. The Lu(6)-O(4) bond length is 2.17 Å. In the seventh Lu site, Lu(7) is bonded to one O(1), one O(16), one O(18), one O(2), and one O(25) atom to form distorted LuO5 trigonal bipyramids that share  a cornercorner with one Lu(8)O6 octahedra,  a cornercorner with one Lu(10)O5 trigonal bipyramid,  a cornercorner with one Lu(4)O5 trigonal bipyramid, corners with two equivalent Lu(1)O5 trigonal bipyramids,  an edgeedge with one Lu(6)O5 trigonal bipyramid, and edges with two equivalent Lu(12)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 7°. The Lu(7)-O(1) bond length is 2.22 Å. The Lu(7)-O(16) bond length is 2.19 Å. The Lu(7)-O(18) bond length is 2.08 Å. The Lu(7)-O(2) bond length is 2.36 Å. The Lu(7)-O(25) bond length is 2.16 Å. In the eighth Lu site, Lu(8) is bonded to one O(14), one O(15), one O(17), one O(18), one O(20), and one O(21) atom to form LuO6 octahedra that share corners with two equivalent Lu(11)O6 octahedra, corners with two equivalent Lu(5)O6 octahedra,  a cornercorner with one Lu(7)O5 trigonal bipyramid, and  a cornercorner with one Lu(9)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 4-7°. The Lu(8)-O(14) bond length is 2.14 Å. The Lu(8)-O(15) bond length is 2.15 Å. The Lu(8)-O(17) bond length is 2.26 Å. The Lu(8)-O(18) bond length is 2.42 Å. The Lu(8)-O(20) bond length is 2.13 Å. The Lu(8)-O(21) bond length is 2.13 Å. In the ninth Lu site, Lu(9) is bonded to one O(13), one O(17), one O(19), one O(22), and one O(7) atom to form LuO5 trigonal bipyramids that share  a cornercorner with one Lu(8)O6 octahedra,  a cornercorner with one Lu(1)O5 trigonal bipyramid,  a cornercorner with one Lu(6)O5 trigonal bipyramid, corners with two equivalent Lu(10)O5 trigonal bipyramids, corners with two equivalent Lu(3)O5 trigonal bipyramids, and  an edgeedge with one Lu(4)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles are 11°. The Lu(9)-O(13) bond length is 2.24 Å. The Lu(9)-O(17) bond length is 2.09 Å. The Lu(9)-O(19) bond length is 2.17 Å. The Lu(9)-O(22) bond length is 2.29 Å. The Lu(9)-O(7) bond length is 2.27 Å. In the tenth Lu site, Lu(10) is bonded to one O(10), one O(19), one O(22), one O(23), and one O(25) atom to form distorted LuO5 trigonal bipyramids that share  a cornercorner with one Lu(11)O6 octahedra,  a cornercorner with one Lu(12)O5 trigonal bipyramid,  a cornercorner with one Lu(7)O5 trigonal bipyramid, corners with two equivalent Lu(4)O5 trigonal bipyramids, corners with two equivalent Lu(9)O5 trigonal bipyramids, and  an edgeedge with one Lu(3)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles are 12°. The Lu(10)-O(10) bond length is 2.26 Å. The Lu(10)-O(19) bond length is 2.30 Å. The Lu(10)-O(22) bond length is 2.17 Å. The Lu(10)-O(23) bond length is 2.09 Å. The Lu(10)-O(25) bond length is 2.24 Å. In the eleventh Lu site, Lu(11) is bonded to one O(20), one O(21), one O(23), one O(24), one O(3), and one O(5) atom to form LuO6 octahedra that share corners with two equivalent Lu(2)O6 octahedra, corners with two equivalent Lu(8)O6 octahedra,  a cornercorner with one Lu(1)O5 trigonal bipyramid, and  a cornercorner with one Lu(10)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 4-7°. The Lu(11)-O(20) bond length is 2.13 Å. The Lu(11)-O(21) bond length is 2.13 Å. The Lu(11)-O(23) bond length is 2.26 Å. The Lu(11)-O(24) bond length is 2.14 Å. The Lu(11)-O(3) bond length is 2.43 Å. The Lu(11)-O(5) bond length is 2.14 Å. In the twelfth Lu site, Lu(12) is bonded to one O(1), one O(16), one O(2), one O(25), and one O(26) atom to form distorted LuO5 trigonal bipyramids that share  a cornercorner with one Lu(2)O6 octahedra,  a cornercorner with one Lu(10)O5 trigonal bipyramid,  a cornercorner with one Lu(4)O5 trigonal bipyramid, corners with two equivalent Lu(6)O5 trigonal bipyramids,  an edgeedge with one Lu(1)O5 trigonal bipyramid, and edges with two equivalent Lu(7)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 7°. The Lu(12)-O(1) bond length is 2.34 Å. The Lu(12)-O(16) bond length is 2.17 Å. The Lu(12)-O(2) bond length is 2.21 Å. The Lu(12)-O(25) bond length is 2.20 Å. The Lu(12)-O(26) bond length is 2.08 Å. There are twenty-six inequivalent O sites. In the first O site, O(1) is bonded to one Lu(1), one Lu(12), one Lu(6), and one Lu(7) atom to form distorted edge-sharing OLu4 trigonal pyramids. In the second O site, O(2) is bonded to one Lu(1), one Lu(12), one Lu(6), and one Lu(7) atom to form distorted edge-sharing OLu4 trigonal pyramids. In the third O site, O(3) is bonded in a 6-coordinate geometry to one Ba(2), one Ba(5), two equivalent Ba(8), one Lu(1), and one Lu(11) atom. In the fourth O site, O(4) is bonded in a 4-coordinate geometry to one Ba(8), one Lu(1), one Lu(3), and one Lu(6) atom. In the fifth O site, O(5) is bonded to one Ba(1), one Ba(2), one Ba(7), one Ba(8), one Lu(11), and one Lu(2) atom to form distorted OBa4Lu2 octahedra that share  a cornercorner with one O(21)Ba4Lu2 octahedra,  a cornercorner with one O(9)Ba4Lu2 octahedra,  a cornercorner with one O(22)BaLu3 tetrahedra,  a cornercorner with one O(7)BaLu3 tetrahedra,  an edgeedge with one O(21)Ba4Lu2 octahedra,  an edgeedge with one O(9)Ba4Lu2 octahedra,  a faceface with one O(20)Ba4Lu2 octahedra,  a faceface with one O(8)Ba4Lu2 octahedra, and faces with two equivalent O(24)Ba4Lu2 octahedra. The corner-sharing octahedral tilt angles range from 2-4°. In the sixth O site, O(6) is bonded in a 6-coordinate geometry to one Ba(3), one Ba(8), two equivalent Ba(2), one Lu(2), and one Lu(3) atom. In the seventh O site, O(7) is bonded to one Ba(2), one Lu(3), one Lu(4), and one Lu(9) atom to form distorted OBaLu3 tetrahedra that share  a cornercorner with one O(24)Ba4Lu2 octahedra,  a cornercorner with one O(5)Ba4Lu2 octahedra,  a cornercorner with one O(8)Ba4Lu2 octahedra,  a cornercorner with one O(9)Ba4Lu2 octahedra, corners with two equivalent O(10)BaLu3 tetrahedra, corners with two equivalent O(19)BaLu3 tetrahedra, and  an edgeedge with one O(22)BaLu3 tetrahedra. The corner-sharing octahedral tilt angles range from 26-70°. In the eighth O site, O(8) is bonded to one Ba(1), one Ba(2), one Ba(3), one Ba(4), one Lu(2), and one Lu(5) atom to form distorted OBa4Lu2 octahedra that share  a cornercorner with one O(14)Ba4Lu2 octahedra,  a cornercorner with one O(24)Ba4Lu2 octahedra,  a cornercorner with one O(10)BaLu3 tetrahedra,  a cornercorner with one O(7)BaLu3 tetrahedra,  an edgeedge with one O(14)Ba4Lu2 octahedra,  an edgeedge with one O(24)Ba4Lu2 octahedra,  a faceface with one O(15)Ba4Lu2 octahedra,  a faceface with one O(5)Ba4Lu2 octahedra, and faces with two equivalent O(9)Ba4Lu2 octahedra. The corner-sharing octahedral tilt angles range from 3-5°. In the ninth O site, O(9) is bonded to one Ba(1), one Ba(2), one Ba(3), one Ba(4), one Lu(2), and one Lu(5) atom to form distorted OBa4Lu2 octahedra that share  a cornercorner with one O(15)Ba4Lu2 octahedra,  a cornercorner with one O(5)Ba4Lu2 octahedra,  a cornercorner with one O(10)BaLu3 tetrahedra,  a cornercorner with one O(7)BaLu3 tetrahedra,  an edgeedge with one O(15)Ba4Lu2 octahedra,  an edgeedge with one O(5)Ba4Lu2 octahedra,  a faceface with one O(14)Ba4Lu2 octahedra,  a faceface with one O(24)Ba4Lu2 octahedra, and faces with two equivalent O(8)Ba4Lu2 octahedra. The corner-sharing octahedral tilt angles range from 2-4°. In the tenth O site, O(10) is bonded to one Ba(3), one Lu(10), one Lu(3), and one Lu(4) atom to form distorted OBaLu3 tetrahedra that share  a cornercorner with one O(14)Ba4Lu2 octahedra,  a cornercorner with one O(15)Ba4Lu2 octahedra,  a cornercorner with one O(8)Ba4Lu2 octahedra,  a cornercorner with one O(9)Ba4Lu2 octahedra, corners with two equivalent O(22)BaLu3 tetrahedra, corners with two equivalent O(7)BaLu3 tetrahedra, and  an edgeedge with one O(19)BaLu3 tetrahedra. The corner-sharing octahedral tilt angles range from 25-70°. In the eleventh O site, O(11) is bonded in a 6-coordinate geometry to one Ba(1), one Ba(6), two equivalent Ba(4), one Lu(5), and one Lu(6) atom. In the twelfth O site, O(12) is bonded in a 6-coordinate geometry to one Ba(2), one Ba(5), two equivalent Ba(3), one Lu(4), and one Lu(5) atom. In the thirteenth O site, O(13) is bonded in a 4-coordinate geometry to one Ba(4), one Lu(1), one Lu(6), and one Lu(9) atom. In the fourteenth O site, O(14) is bonded to one Ba(3), one Ba(4), one Ba(5), one Ba(6), one Lu(5), and one Lu(8) atom to form distorted OBa4Lu2 octahedra that share  a cornercorner with one O(20)Ba4Lu2 octahedra,  a cornercorner with one O(8)Ba4Lu2 octahedra,  a cornercorner with one O(10)BaLu3 tetrahedra,  a cornercorner with one O(19)BaLu3 tetrahedra,  an edgeedge with one O(20)Ba4Lu2 octahedra,  an edgeedge with one O(8)Ba4Lu2 octahedra,  a faceface with one O(21)Ba4Lu2 octahedra,  a faceface with one O(9)Ba4Lu2 octahedra, and faces with two equivalent O(15)Ba4Lu2 octahedra. The corner-sharing octahedral tilt angles range from 4-5°. In the fifteenth O site, O(15) is bonded to one Ba(3), one Ba(4), one Ba(5), one Ba(6), one Lu(5), and one Lu(8) atom to form distorted OBa4Lu2 octahedra that share  a cornercorner with one O(21)Ba4Lu2 octahedra,  a cornercorner with one O(9)Ba4Lu2 octahedra,  a cornercorner with one O(10)BaLu3 tetrahedra,  a cornercorner with one O(19)BaLu3 tetrahedra,  an edgeedge with one O(21)Ba4Lu2 octahedra,  an edgeedge with one O(9)Ba4Lu2 octahedra,  a faceface with one O(20)Ba4Lu2 octahedra,  a faceface with one O(8)Ba4Lu2 octahedra, and faces with two equivalent O(14)Ba4Lu2 octahedra. The corner-sharing octahedral tilt angles range from 3-4°. In the sixteenth O site, O(16) is bonded in a 4-coordinate geometry to one Ba(5), one Lu(12), one Lu(4), and one Lu(7) atom. In the seventeenth O site, O(17) is bonded in a 6-coordinate geometry to one Ba(4), one Ba(7), two equivalent Ba(6), one Lu(8), and one Lu(9) atom. In the eighteenth O site, O(18) is bonded in a 6-coordinate geometry to one Ba(3), one Ba(8), two equivalent Ba(5), one Lu(7), and one Lu(8) atom. In the nineteenth O site, O(19) is bonded to one Ba(6), one Lu(10), one Lu(3), and one Lu(9) atom to form distorted OBaLu3 tetrahedra that share  a cornercorner with one O(14)Ba4Lu2 octahedra,  a cornercorner with one O(15)Ba4Lu2 octahedra,  a cornercorner with one O(20)Ba4Lu2 octahedra,  a cornercorner with one O(21)Ba4Lu2 octahedra, corners with two equivalent O(22)BaLu3 tetrahedra, corners with two equivalent O(7)BaLu3 tetrahedra, and  an edgeedge with one O(10)BaLu3 tetrahedra. The corner-sharing octahedral tilt angles range from 26-69°. In the twentieth O site, O(20) is bonded to one Ba(5), one Ba(6), one Ba(7), one Ba(8), one Lu(11), and one Lu(8) atom to form distorted OBa4Lu2 octahedra that share  a cornercorner with one O(14)Ba4Lu2 octahedra,  a cornercorner with one O(24)Ba4Lu2 octahedra,  a cornercorner with one O(19)BaLu3 tetrahedra,  a cornercorner with one O(22)BaLu3 tetrahedra,  an edgeedge with one O(14)Ba4Lu2 octahedra,  an edgeedge with one O(24)Ba4Lu2 octahedra,  a faceface with one O(15)Ba4Lu2 octahedra,  a faceface with one O(5)Ba4Lu2 octahedra, and faces with two equivalent O(21)Ba4Lu2 octahedra. The corner-sharing octahedral tilt angles range from 3-4°. In the twenty-first O site, O(21) is bonded to one Ba(5), one Ba(6), one Ba(7), one Ba(8), one Lu(11), and one Lu(8) atom to form distorted OBa4Lu2 octahedra that share  a cornercorner with one O(15)Ba4Lu2 octahedra,  a cornercorner with one O(5)Ba4Lu2 octahedra,  a cornercorner with one O(19)BaLu3 tetrahedra,  a cornercorner with one O(22)BaLu3 tetrahedra,  an edgeedge with one O(15)Ba4Lu2 octahedra,  an edgeedge with one O(5)Ba4Lu2 octahedra,  a faceface with one O(14)Ba4Lu2 octahedra,  a faceface with one O(24)Ba4Lu2 octahedra, and faces with two equivalent O(20)Ba4Lu2 octahedra. The corner-sharing octahedral tilt angles range from 3-4°. In the twenty-second O site, O(22) is bonded to one Ba(7), one Lu(10), one Lu(4), and one Lu(9) atom to form distorted OBaLu3 tetrahedra that share  a cornercorner with one O(20)Ba4Lu2 octahedra,  a cornercorner with one O(21)Ba4Lu2 octahedra,  a cornercorner with one O(24)Ba4Lu2 octahedra,  a cornercorner with one O(5)Ba4Lu2 octahedra, corners with two equivalent O(10)BaLu3 tetrahedra, corners with two equivalent O(19)BaLu3 tetrahedra, and  an edgeedge with one O(7)BaLu3 tetrahedra. The corner-sharing octahedral tilt angles range from 25-70°. In the twenty-third O site, O(23) is bonded in a 6-coordinate geometry to one Ba(1), one Ba(6), two equivalent Ba(7), one Lu(10), and one Lu(11) atom. In the twenty-fourth O site, O(24) is bonded to one Ba(1), one Ba(2), one Ba(7), one Ba(8), one Lu(11), and one Lu(2) atom to form distorted OBa4Lu2 octahedra that share  a cornercorner with one O(20)Ba4Lu2 octahedra,  a cornercorner with one O(8)Ba4Lu2 octahedra,  a cornercorner with one O(22)BaLu3 tetrahedra,  a cornercorner with one O(7)BaLu3 tetrahedra,  an edgeedge with one O(20)Ba4Lu2 octahedra,  an edgeedge with one O(8)Ba4Lu2 octahedra,  a faceface with one O(21)Ba4Lu2 octahedra,  a faceface with one O(9)Ba4Lu2 octahedra, and faces with two equivalent O(5)Ba4Lu2 octahedra. The corner-sharing octahedral tilt angles are 3°. In the twenty-fifth O site, O(25) is bonded in a 4-coordinate geometry to one Ba(1), one Lu(10), one Lu(12), and one Lu(7) atom. In the twenty-sixth O site, O(26) is bonded in a 6-coordinate geometry to one Ba(4), one Ba(7), two equivalent Ba(1), one Lu(12), and one Lu(2) atom.