Ba4Lu6O13 crystallizes in the orthorhombic Iba2 space group. There are two inequivalent Ba sites. In the first Ba site, Ba(1) is bonded in a 9-coordinate geometry to one O(3), one O(5), two equivalent O(4), two equivalent O(7), and three equivalent O(2) atoms. In the second Ba site, Ba(2) is bonded in a 9-coordinate geometry to one O(2), one O(6), two equivalent O(4), two equivalent O(7), and three equivalent O(5) atoms. There are three inequivalent Lu sites. In the first Lu site, Lu(1) is bonded to one O(2), two equivalent O(1), and two equivalent O(3) atoms to form distorted LuO5 trigonal bipyramids that share  a cornercorner with one Lu(2)O6 octahedra, corners with two equivalent Lu(1)O5 trigonal bipyramids, corners with two equivalent Lu(3)O5 trigonal bipyramids, and edges with three equivalent Lu(1)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 8°. In the second Lu site, Lu(2) is bonded to one O(2), one O(5), two equivalent O(4), and two equivalent O(7) atoms to form LuO6 octahedra that share corners with four equivalent Lu(2)O6 octahedra,  a cornercorner with one Lu(1)O5 trigonal bipyramid, and  a cornercorner with one Lu(3)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 4-7°. In the third Lu site, Lu(3) is bonded to one O(3), one O(5), and three equivalent O(6) atoms to form distorted LuO5 trigonal bipyramids that share  a cornercorner with one Lu(2)O6 octahedra, corners with two equivalent Lu(1)O5 trigonal bipyramids, corners with four equivalent Lu(3)O5 trigonal bipyramids, and  an edgeedge with one Lu(3)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles are 11°. There are seven inequivalent O sites. In the first O site, O(1) is bonded to four equivalent Lu(1) atoms to form distorted edge-sharing OLu4 trigonal pyramids. In the second O site, O(2) is bonded in a 6-coordinate geometry to one Ba(2), three equivalent Ba(1), one Lu(1), and one Lu(2) atom. In the third O site, O(3) is bonded in a 4-coordinate geometry to one Ba(1), one Lu(3), and two equivalent Lu(1) atoms. In the fourth O site, O(4) is bonded to two equivalent Ba(1), two equivalent Ba(2), and two equivalent Lu(2) atoms to form distorted OBa4Lu2 octahedra that share corners with two equivalent O(7)Ba4Lu2 octahedra, corners with two equivalent O(6)BaLu3 tetrahedra, edges with two equivalent O(7)Ba4Lu2 octahedra, faces with two equivalent O(4)Ba4Lu2 octahedra, and faces with two equivalent O(7)Ba4Lu2 octahedra. The corner-sharing octahedral tilt angles range from 3-4°. In the fifth O site, O(5) is bonded in a 6-coordinate geometry to one Ba(1), three equivalent Ba(2), one Lu(2), and one Lu(3) atom. In the sixth O site, O(6) is bonded to one Ba(2) and three equivalent Lu(3) atoms to form distorted OBaLu3 tetrahedra that share corners with two equivalent O(4)Ba4Lu2 octahedra, corners with two equivalent O(7)Ba4Lu2 octahedra, corners with four equivalent O(6)BaLu3 tetrahedra, and  an edgeedge with one O(6)BaLu3 tetrahedra. The corner-sharing octahedral tilt angles range from 26-70°. In the seventh O site, O(7) is bonded to two equivalent Ba(1), two equivalent Ba(2), and two equivalent Lu(2) atoms to form distorted OBa4Lu2 octahedra that share corners with two equivalent O(4)Ba4Lu2 octahedra, corners with two equivalent O(6)BaLu3 tetrahedra, edges with two equivalent O(4)Ba4Lu2 octahedra, faces with two equivalent O(4)Ba4Lu2 octahedra, and faces with two equivalent O(7)Ba4Lu2 octahedra. The corner-sharing octahedral tilt angles range from 3-4°.
Ba4Lu6O13 crystallizes in the orthorhombic Iba2 space group. There are two inequivalent Ba sites. In the first Ba site, Ba(1) is bonded in a 9-coordinate geometry to one O(3), one O(5), two equivalent O(4), two equivalent O(7), and three equivalent O(2) atoms. The Ba(1)-O(3) bond length is 3.06 Å. The Ba(1)-O(5) bond length is 3.02 Å. There is one shorter (2.74 Å) and one longer (2.90 Å) Ba(1)-O(4) bond length. There is one shorter (2.82 Å) and one longer (2.83 Å) Ba(1)-O(7) bond length. There are a spread of Ba(1)-O(2) bond distances ranging from 2.99-3.19 Å. In the second Ba site, Ba(2) is bonded in a 9-coordinate geometry to one O(2), one O(6), two equivalent O(4), two equivalent O(7), and three equivalent O(5) atoms. The Ba(2)-O(2) bond length is 3.15 Å. The Ba(2)-O(6) bond length is 2.65 Å. There is one shorter (2.74 Å) and one longer (2.92 Å) Ba(2)-O(4) bond length. There is one shorter (2.85 Å) and one longer (2.86 Å) Ba(2)-O(7) bond length. There are a spread of Ba(2)-O(5) bond distances ranging from 2.87-3.17 Å. There are three inequivalent Lu sites. In the first Lu site, Lu(1) is bonded to one O(2), two equivalent O(1), and two equivalent O(3) atoms to form distorted LuO5 trigonal bipyramids that share  a cornercorner with one Lu(2)O6 octahedra, corners with two equivalent Lu(1)O5 trigonal bipyramids, corners with two equivalent Lu(3)O5 trigonal bipyramids, and edges with three equivalent Lu(1)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 8°. The Lu(1)-O(2) bond length is 2.08 Å. There is one shorter (2.21 Å) and one longer (2.35 Å) Lu(1)-O(1) bond length. There is one shorter (2.17 Å) and one longer (2.20 Å) Lu(1)-O(3) bond length. In the second Lu site, Lu(2) is bonded to one O(2), one O(5), two equivalent O(4), and two equivalent O(7) atoms to form LuO6 octahedra that share corners with four equivalent Lu(2)O6 octahedra,  a cornercorner with one Lu(1)O5 trigonal bipyramid, and  a cornercorner with one Lu(3)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 4-7°. The Lu(2)-O(2) bond length is 2.42 Å. The Lu(2)-O(5) bond length is 2.27 Å. There is one shorter (2.14 Å) and one longer (2.15 Å) Lu(2)-O(4) bond length. Both Lu(2)-O(7) bond lengths are 2.13 Å. In the third Lu site, Lu(3) is bonded to one O(3), one O(5), and three equivalent O(6) atoms to form distorted LuO5 trigonal bipyramids that share  a cornercorner with one Lu(2)O6 octahedra, corners with two equivalent Lu(1)O5 trigonal bipyramids, corners with four equivalent Lu(3)O5 trigonal bipyramids, and  an edgeedge with one Lu(3)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles are 11°. The Lu(3)-O(3) bond length is 2.25 Å. The Lu(3)-O(5) bond length is 2.08 Å. There are a spread of Lu(3)-O(6) bond distances ranging from 2.18-2.30 Å. There are seven inequivalent O sites. In the first O site, O(1) is bonded to four equivalent Lu(1) atoms to form distorted edge-sharing OLu4 trigonal pyramids. In the second O site, O(2) is bonded in a 6-coordinate geometry to one Ba(2), three equivalent Ba(1), one Lu(1), and one Lu(2) atom. In the third O site, O(3) is bonded in a 4-coordinate geometry to one Ba(1), one Lu(3), and two equivalent Lu(1) atoms. In the fourth O site, O(4) is bonded to two equivalent Ba(1), two equivalent Ba(2), and two equivalent Lu(2) atoms to form distorted OBa4Lu2 octahedra that share corners with two equivalent O(7)Ba4Lu2 octahedra, corners with two equivalent O(6)BaLu3 tetrahedra, edges with two equivalent O(7)Ba4Lu2 octahedra, faces with two equivalent O(4)Ba4Lu2 octahedra, and faces with two equivalent O(7)Ba4Lu2 octahedra. The corner-sharing octahedral tilt angles range from 3-4°. In the fifth O site, O(5) is bonded in a 6-coordinate geometry to one Ba(1), three equivalent Ba(2), one Lu(2), and one Lu(3) atom. In the sixth O site, O(6) is bonded to one Ba(2) and three equivalent Lu(3) atoms to form distorted OBaLu3 tetrahedra that share corners with two equivalent O(4)Ba4Lu2 octahedra, corners with two equivalent O(7)Ba4Lu2 octahedra, corners with four equivalent O(6)BaLu3 tetrahedra, and  an edgeedge with one O(6)BaLu3 tetrahedra. The corner-sharing octahedral tilt angles range from 26-70°. In the seventh O site, O(7) is bonded to two equivalent Ba(1), two equivalent Ba(2), and two equivalent Lu(2) atoms to form distorted OBa4Lu2 octahedra that share corners with two equivalent O(4)Ba4Lu2 octahedra, corners with two equivalent O(6)BaLu3 tetrahedra, edges with two equivalent O(4)Ba4Lu2 octahedra, faces with two equivalent O(4)Ba4Lu2 octahedra, and faces with two equivalent O(7)Ba4Lu2 octahedra. The corner-sharing octahedral tilt angles range from 3-4°.