Li2Lu5O4(BO3)3 crystallizes in the monoclinic P2_1/m space group. There are two inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(1), one O(9), and three equivalent O(6) atoms to form distorted LiO5 trigonal bipyramids that share  a cornercorner with one Lu(3)O6 octahedra,  a cornercorner with one Lu(1)O7 pentagonal bipyramid, corners with two equivalent Li(1)O5 trigonal bipyramids, edges with two equivalent Lu(1)O7 pentagonal bipyramids, and edges with two equivalent Li(1)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 14°. In the second Li site, Li(2) is bonded in a trigonal non-coplanar geometry to one O(13) and two equivalent O(2) atoms. There are five inequivalent Lu sites. In the first Lu site, Lu(1) is bonded to one O(4), one O(6), two equivalent O(9), and three equivalent O(8) atoms to form distorted LuO7 pentagonal bipyramids that share  a cornercorner with one Lu(4)O7 pentagonal bipyramid,  a cornercorner with one Li(1)O5 trigonal bipyramid, edges with two equivalent Lu(4)O7 pentagonal bipyramids, edges with four equivalent Lu(1)O7 pentagonal bipyramids, and edges with two equivalent Li(1)O5 trigonal bipyramids. In the second Lu site, Lu(2) is bonded to one O(11), one O(7), two equivalent O(5), and three equivalent O(3) atoms to form distorted LuO7 pentagonal bipyramids that share  a cornercorner with one Lu(3)O6 octahedra, edges with two equivalent Lu(3)O6 octahedra,  an edgeedge with one Lu(4)O7 pentagonal bipyramid, and edges with four equivalent Lu(2)O7 pentagonal bipyramids. The corner-sharing octahedral tilt angles are 51°. In the third Lu site, Lu(3) is bonded to one O(1), one O(3), two equivalent O(11), and two equivalent O(13) atoms to form distorted LuO6 octahedra that share  a cornercorner with one Lu(2)O7 pentagonal bipyramid, corners with two equivalent Lu(4)O7 pentagonal bipyramids,  a cornercorner with one Li(1)O5 trigonal bipyramid, edges with two equivalent Lu(3)O6 octahedra, and edges with two equivalent Lu(2)O7 pentagonal bipyramids. In the fourth Lu site, Lu(4) is bonded to one O(11), one O(7), one O(8), two equivalent O(10), and two equivalent O(4) atoms to form distorted LuO7 pentagonal bipyramids that share corners with two equivalent Lu(3)O6 octahedra,  a cornercorner with one Lu(1)O7 pentagonal bipyramid,  an edgeedge with one Lu(2)O7 pentagonal bipyramid, edges with two equivalent Lu(1)O7 pentagonal bipyramids, and edges with two equivalent Lu(4)O7 pentagonal bipyramids. The corner-sharing octahedral tilt angles are 60°. In the fifth Lu site, Lu(5) is bonded in a 7-coordinate geometry to one O(10), one O(2), one O(5), two equivalent O(12), and two equivalent O(7) atoms. There are three inequivalent B sites. In the first B site, B(1) is bonded in a trigonal planar geometry to one O(12), one O(13), and one O(5) atom. In the second B site, B(2) is bonded in a trigonal planar geometry to one O(10), one O(2), and one O(9) atom. In the third B site, B(3) is bonded in a trigonal planar geometry to one O(1), one O(4), and one O(6) atom. There are thirteen inequivalent O sites. In the first O site, O(1) is bonded in a 3-coordinate geometry to one Li(1), one Lu(3), and one B(3) atom. In the second O site, O(2) is bonded to two equivalent Li(2), one Lu(5), and one B(2) atom to form distorted OLi2LuB tetrahedra that share corners with two equivalent O(2)Li2LuB tetrahedra and corners with two equivalent O(7)Lu4 tetrahedra. In the third O site, O(3) is bonded to one Lu(3) and three equivalent Lu(2) atoms to form a mixture of edge and corner-sharing OLu4 tetrahedra. In the fourth O site, O(4) is bonded in a distorted single-bond geometry to one Lu(1), two equivalent Lu(4), and one B(3) atom. In the fifth O site, O(5) is bonded in a 4-coordinate geometry to one Lu(5), two equivalent Lu(2), and one B(1) atom. In the sixth O site, O(6) is bonded to three equivalent Li(1), one Lu(1), and one B(3) atom to form distorted OLi3LuB trigonal bipyramids that share corners with three equivalent O(8)Lu4 tetrahedra, corners with two equivalent O(6)Li3LuB trigonal bipyramids, and edges with two equivalent O(6)Li3LuB trigonal bipyramids. In the seventh O site, O(7) is bonded to one Lu(2), one Lu(4), and two equivalent Lu(5) atoms to form OLu4 tetrahedra that share  a cornercorner with one O(8)Lu4 tetrahedra, corners with two equivalent O(2)Li2LuB tetrahedra, corners with two equivalent O(7)Lu4 tetrahedra, corners with three equivalent O(3)Lu4 tetrahedra, and  an edgeedge with one O(11)Lu4 tetrahedra. In the eighth O site, O(8) is bonded to one Lu(4) and three equivalent Lu(1) atoms to form OLu4 tetrahedra that share  a cornercorner with one O(11)Lu4 tetrahedra,  a cornercorner with one O(7)Lu4 tetrahedra, corners with two equivalent O(8)Lu4 tetrahedra, corners with three equivalent O(6)Li3LuB trigonal bipyramids, and edges with two equivalent O(8)Lu4 tetrahedra. In the ninth O site, O(9) is bonded in a 4-coordinate geometry to one Li(1), two equivalent Lu(1), and one B(2) atom. In the tenth O site, O(10) is bonded in a 4-coordinate geometry to one Lu(5), two equivalent Lu(4), and one B(2) atom. In the eleventh O site, O(11) is bonded to one Lu(2), one Lu(4), and two equivalent Lu(3) atoms to form a mixture of edge and corner-sharing OLu4 tetrahedra. In the twelfth O site, O(12) is bonded in a 3-coordinate geometry to two equivalent Lu(5) and one B(1) atom. In the thirteenth O site, O(13) is bonded in a 4-coordinate geometry to one Li(2), two equivalent Lu(3), and one B(1) atom.
Li2Lu5O4(BO3)3 crystallizes in the monoclinic P2_1/m space group. There are two inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(1), one O(9), and three equivalent O(6) atoms to form distorted LiO5 trigonal bipyramids that share  a cornercorner with one Lu(3)O6 octahedra,  a cornercorner with one Lu(1)O7 pentagonal bipyramid, corners with two equivalent Li(1)O5 trigonal bipyramids, edges with two equivalent Lu(1)O7 pentagonal bipyramids, and edges with two equivalent Li(1)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 14°. The Li(1)-O(1) bond length is 2.03 Å. The Li(1)-O(9) bond length is 2.10 Å. There are two shorter (2.07 Å) and one longer (2.26 Å) Li(1)-O(6) bond length. In the second Li site, Li(2) is bonded in a trigonal non-coplanar geometry to one O(13) and two equivalent O(2) atoms. The Li(2)-O(13) bond length is 1.91 Å. Both Li(2)-O(2) bond lengths are 1.97 Å. There are five inequivalent Lu sites. In the first Lu site, Lu(1) is bonded to one O(4), one O(6), two equivalent O(9), and three equivalent O(8) atoms to form distorted LuO7 pentagonal bipyramids that share  a cornercorner with one Lu(4)O7 pentagonal bipyramid,  a cornercorner with one Li(1)O5 trigonal bipyramid, edges with two equivalent Lu(4)O7 pentagonal bipyramids, edges with four equivalent Lu(1)O7 pentagonal bipyramids, and edges with two equivalent Li(1)O5 trigonal bipyramids. The Lu(1)-O(4) bond length is 2.37 Å. The Lu(1)-O(6) bond length is 2.28 Å. Both Lu(1)-O(9) bond lengths are 2.33 Å. There are two shorter (2.16 Å) and one longer (2.19 Å) Lu(1)-O(8) bond length. In the second Lu site, Lu(2) is bonded to one O(11), one O(7), two equivalent O(5), and three equivalent O(3) atoms to form distorted LuO7 pentagonal bipyramids that share  a cornercorner with one Lu(3)O6 octahedra, edges with two equivalent Lu(3)O6 octahedra,  an edgeedge with one Lu(4)O7 pentagonal bipyramid, and edges with four equivalent Lu(2)O7 pentagonal bipyramids. The corner-sharing octahedral tilt angles are 51°. The Lu(2)-O(11) bond length is 2.29 Å. The Lu(2)-O(7) bond length is 2.20 Å. Both Lu(2)-O(5) bond lengths are 2.43 Å. There are two shorter (2.15 Å) and one longer (2.19 Å) Lu(2)-O(3) bond length. In the third Lu site, Lu(3) is bonded to one O(1), one O(3), two equivalent O(11), and two equivalent O(13) atoms to form distorted LuO6 octahedra that share  a cornercorner with one Lu(2)O7 pentagonal bipyramid, corners with two equivalent Lu(4)O7 pentagonal bipyramids,  a cornercorner with one Li(1)O5 trigonal bipyramid, edges with two equivalent Lu(3)O6 octahedra, and edges with two equivalent Lu(2)O7 pentagonal bipyramids. The Lu(3)-O(1) bond length is 2.23 Å. The Lu(3)-O(3) bond length is 2.12 Å. Both Lu(3)-O(11) bond lengths are 2.15 Å. Both Lu(3)-O(13) bond lengths are 2.31 Å. In the fourth Lu site, Lu(4) is bonded to one O(11), one O(7), one O(8), two equivalent O(10), and two equivalent O(4) atoms to form distorted LuO7 pentagonal bipyramids that share corners with two equivalent Lu(3)O6 octahedra,  a cornercorner with one Lu(1)O7 pentagonal bipyramid,  an edgeedge with one Lu(2)O7 pentagonal bipyramid, edges with two equivalent Lu(1)O7 pentagonal bipyramids, and edges with two equivalent Lu(4)O7 pentagonal bipyramids. The corner-sharing octahedral tilt angles are 60°. The Lu(4)-O(11) bond length is 2.13 Å. The Lu(4)-O(7) bond length is 2.27 Å. The Lu(4)-O(8) bond length is 2.20 Å. Both Lu(4)-O(10) bond lengths are 2.20 Å. Both Lu(4)-O(4) bond lengths are 2.33 Å. In the fifth Lu site, Lu(5) is bonded in a 7-coordinate geometry to one O(10), one O(2), one O(5), two equivalent O(12), and two equivalent O(7) atoms. The Lu(5)-O(10) bond length is 2.56 Å. The Lu(5)-O(2) bond length is 2.27 Å. The Lu(5)-O(5) bond length is 2.34 Å. Both Lu(5)-O(12) bond lengths are 2.28 Å. Both Lu(5)-O(7) bond lengths are 2.16 Å. There are three inequivalent B sites. In the first B site, B(1) is bonded in a trigonal planar geometry to one O(12), one O(13), and one O(5) atom. The B(1)-O(12) bond length is 1.38 Å. The B(1)-O(13) bond length is 1.39 Å. The B(1)-O(5) bond length is 1.39 Å. In the second B site, B(2) is bonded in a trigonal planar geometry to one O(10), one O(2), and one O(9) atom. The B(2)-O(10) bond length is 1.39 Å. The B(2)-O(2) bond length is 1.37 Å. The B(2)-O(9) bond length is 1.37 Å. In the third B site, B(3) is bonded in a trigonal planar geometry to one O(1), one O(4), and one O(6) atom. The B(3)-O(1) bond length is 1.36 Å. The B(3)-O(4) bond length is 1.42 Å. The B(3)-O(6) bond length is 1.38 Å. There are thirteen inequivalent O sites. In the first O site, O(1) is bonded in a 3-coordinate geometry to one Li(1), one Lu(3), and one B(3) atom. In the second O site, O(2) is bonded to two equivalent Li(2), one Lu(5), and one B(2) atom to form distorted OLi2LuB tetrahedra that share corners with two equivalent O(2)Li2LuB tetrahedra and corners with two equivalent O(7)Lu4 tetrahedra. In the third O site, O(3) is bonded to one Lu(3) and three equivalent Lu(2) atoms to form a mixture of edge and corner-sharing OLu4 tetrahedra. In the fourth O site, O(4) is bonded in a distorted single-bond geometry to one Lu(1), two equivalent Lu(4), and one B(3) atom. In the fifth O site, O(5) is bonded in a 4-coordinate geometry to one Lu(5), two equivalent Lu(2), and one B(1) atom. In the sixth O site, O(6) is bonded to three equivalent Li(1), one Lu(1), and one B(3) atom to form distorted OLi3LuB trigonal bipyramids that share corners with three equivalent O(8)Lu4 tetrahedra, corners with two equivalent O(6)Li3LuB trigonal bipyramids, and edges with two equivalent O(6)Li3LuB trigonal bipyramids. In the seventh O site, O(7) is bonded to one Lu(2), one Lu(4), and two equivalent Lu(5) atoms to form OLu4 tetrahedra that share  a cornercorner with one O(8)Lu4 tetrahedra, corners with two equivalent O(2)Li2LuB tetrahedra, corners with two equivalent O(7)Lu4 tetrahedra, corners with three equivalent O(3)Lu4 tetrahedra, and  an edgeedge with one O(11)Lu4 tetrahedra. In the eighth O site, O(8) is bonded to one Lu(4) and three equivalent Lu(1) atoms to form OLu4 tetrahedra that share  a cornercorner with one O(11)Lu4 tetrahedra,  a cornercorner with one O(7)Lu4 tetrahedra, corners with two equivalent O(8)Lu4 tetrahedra, corners with three equivalent O(6)Li3LuB trigonal bipyramids, and edges with two equivalent O(8)Lu4 tetrahedra. In the ninth O site, O(9) is bonded in a 4-coordinate geometry to one Li(1), two equivalent Lu(1), and one B(2) atom. In the tenth O site, O(10) is bonded in a 4-coordinate geometry to one Lu(5), two equivalent Lu(4), and one B(2) atom. In the eleventh O site, O(11) is bonded to one Lu(2), one Lu(4), and two equivalent Lu(3) atoms to form a mixture of edge and corner-sharing OLu4 tetrahedra. In the twelfth O site, O(12) is bonded in a 3-coordinate geometry to two equivalent Lu(5) and one B(1) atom. In the thirteenth O site, O(13) is bonded in a 4-coordinate geometry to one Li(2), two equivalent Lu(3), and one B(1) atom.