MgLu4Ti2O10 crystallizes in the monoclinic Pm space group. Mg(1) is bonded to one O(4) and four equivalent O(1) atoms to form distorted MgO5 square pyramids that share corners with four equivalent Lu(1)O6 pentagonal pyramids, edges with two equivalent Mg(1)O5 square pyramids, and faces with two equivalent Ti(1)O6 pentagonal pyramids. There are two inequivalent Lu sites. In the first Lu site, Lu(1) is bonded to one O(1), one O(3), one O(5), one O(6), and two equivalent O(2) atoms to form distorted LuO6 pentagonal pyramids that share  a cornercorner with one Ti(2)O6 octahedra, corners with three equivalent Lu(1)O6 pentagonal pyramids, corners with two equivalent Mg(1)O5 square pyramids, edges with two equivalent Ti(2)O6 octahedra, and  an edgeedge with one Ti(1)O6 pentagonal pyramid. The corner-sharing octahedral tilt angles are 29°. In the second Lu site, Lu(2) is bonded in a 6-coordinate geometry to one O(1), one O(2), one O(4), one O(6), and two equivalent O(5) atoms. There are two inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to two equivalent O(1), two equivalent O(4), and two equivalent O(5) atoms to form TiO6 pentagonal pyramids that share corners with two equivalent Ti(1)O6 pentagonal pyramids, edges with two equivalent Lu(1)O6 pentagonal pyramids, and faces with two equivalent Mg(1)O5 square pyramids. In the second Ti site, Ti(2) is bonded to two equivalent O(2), two equivalent O(3), and two equivalent O(6) atoms to form distorted TiO6 octahedra that share corners with two equivalent Ti(2)O6 octahedra, corners with two equivalent Lu(1)O6 pentagonal pyramids, and edges with four equivalent Lu(1)O6 pentagonal pyramids. The corner-sharing octahedral tilt angles are 34°. There are six inequivalent O sites. In the first O site, O(1) is bonded to two equivalent Mg(1), one Lu(1), one Lu(2), and one Ti(1) atom to form OLu2Mg2Ti trigonal bipyramids that share  a cornercorner with one O(3)Lu2Ti2 tetrahedra, corners with three equivalent O(5)Lu3Ti tetrahedra,  a cornercorner with one O(4)Lu2MgTi2 trigonal bipyramid, corners with four equivalent O(1)Lu2Mg2Ti trigonal bipyramids, corners with three equivalent O(2)Lu3Ti trigonal pyramids,  an edgeedge with one O(5)Lu3Ti tetrahedra, edges with two equivalent O(4)Lu2MgTi2 trigonal bipyramids, and  a faceface with one O(1)Lu2Mg2Ti trigonal bipyramid. In the second O site, O(2) is bonded to one Lu(2), two equivalent Lu(1), and one Ti(2) atom to form OLu3Ti trigonal pyramids that share  a cornercorner with one O(4)Lu2MgTi2 trigonal bipyramid, corners with three equivalent O(1)Lu2Mg2Ti trigonal bipyramids, corners with three equivalent O(2)Lu3Ti trigonal pyramids, edges with two equivalent O(3)Lu2Ti2 tetrahedra, and edges with two equivalent O(5)Lu3Ti tetrahedra. In the third O site, O(3) is bonded to two equivalent Lu(1) and two equivalent Ti(2) atoms to form distorted OLu2Ti2 tetrahedra that share corners with two equivalent O(3)Lu2Ti2 tetrahedra, corners with two equivalent O(5)Lu3Ti tetrahedra, corners with two equivalent O(1)Lu2Mg2Ti trigonal bipyramids, and edges with four equivalent O(2)Lu3Ti trigonal pyramids. In the fourth O site, O(4) is bonded to one Mg(1), two equivalent Lu(2), and two equivalent Ti(1) atoms to form OLu2MgTi2 trigonal bipyramids that share corners with two equivalent O(1)Lu2Mg2Ti trigonal bipyramids, corners with two equivalent O(4)Lu2MgTi2 trigonal bipyramids, corners with two equivalent O(2)Lu3Ti trigonal pyramids, edges with four equivalent O(5)Lu3Ti tetrahedra, and edges with four equivalent O(1)Lu2Mg2Ti trigonal bipyramids. In the fifth O site, O(5) is bonded to one Lu(1), two equivalent Lu(2), and one Ti(1) atom to form OLu3Ti tetrahedra that share  a cornercorner with one O(3)Lu2Ti2 tetrahedra, corners with three equivalent O(5)Lu3Ti tetrahedra, corners with three equivalent O(1)Lu2Mg2Ti trigonal bipyramids,  an edgeedge with one O(1)Lu2Mg2Ti trigonal bipyramid, edges with two equivalent O(4)Lu2MgTi2 trigonal bipyramids, and edges with two equivalent O(2)Lu3Ti trigonal pyramids. In the sixth O site, O(6) is bonded in a distorted trigonal non-coplanar geometry to one Lu(1), one Lu(2), and one Ti(2) atom.
MgLu4Ti2O10 crystallizes in the monoclinic Pm space group. Mg(1) is bonded to one O(4) and four equivalent O(1) atoms to form distorted MgO5 square pyramids that share corners with four equivalent Lu(1)O6 pentagonal pyramids, edges with two equivalent Mg(1)O5 square pyramids, and faces with two equivalent Ti(1)O6 pentagonal pyramids. The Mg(1)-O(4) bond length is 2.05 Å. There are two shorter (2.37 Å) and two longer (2.47 Å) Mg(1)-O(1) bond lengths. There are two inequivalent Lu sites. In the first Lu site, Lu(1) is bonded to one O(1), one O(3), one O(5), one O(6), and two equivalent O(2) atoms to form distorted LuO6 pentagonal pyramids that share  a cornercorner with one Ti(2)O6 octahedra, corners with three equivalent Lu(1)O6 pentagonal pyramids, corners with two equivalent Mg(1)O5 square pyramids, edges with two equivalent Ti(2)O6 octahedra, and  an edgeedge with one Ti(1)O6 pentagonal pyramid. The corner-sharing octahedral tilt angles are 29°. The Lu(1)-O(1) bond length is 2.30 Å. The Lu(1)-O(3) bond length is 2.31 Å. The Lu(1)-O(5) bond length is 2.26 Å. The Lu(1)-O(6) bond length is 2.15 Å. Both Lu(1)-O(2) bond lengths are 2.14 Å. In the second Lu site, Lu(2) is bonded in a 6-coordinate geometry to one O(1), one O(2), one O(4), one O(6), and two equivalent O(5) atoms. The Lu(2)-O(1) bond length is 2.18 Å. The Lu(2)-O(2) bond length is 2.29 Å. The Lu(2)-O(4) bond length is 2.52 Å. The Lu(2)-O(6) bond length is 2.14 Å. Both Lu(2)-O(5) bond lengths are 2.14 Å. There are two inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to two equivalent O(1), two equivalent O(4), and two equivalent O(5) atoms to form TiO6 pentagonal pyramids that share corners with two equivalent Ti(1)O6 pentagonal pyramids, edges with two equivalent Lu(1)O6 pentagonal pyramids, and faces with two equivalent Mg(1)O5 square pyramids. Both Ti(1)-O(1) bond lengths are 2.22 Å. There is one shorter (2.02 Å) and one longer (2.03 Å) Ti(1)-O(4) bond length. Both Ti(1)-O(5) bond lengths are 2.05 Å. In the second Ti site, Ti(2) is bonded to two equivalent O(2), two equivalent O(3), and two equivalent O(6) atoms to form distorted TiO6 octahedra that share corners with two equivalent Ti(2)O6 octahedra, corners with two equivalent Lu(1)O6 pentagonal pyramids, and edges with four equivalent Lu(1)O6 pentagonal pyramids. The corner-sharing octahedral tilt angles are 34°. Both Ti(2)-O(2) bond lengths are 2.12 Å. Both Ti(2)-O(3) bond lengths are 2.11 Å. Both Ti(2)-O(6) bond lengths are 1.92 Å. There are six inequivalent O sites. In the first O site, O(1) is bonded to two equivalent Mg(1), one Lu(1), one Lu(2), and one Ti(1) atom to form OLu2Mg2Ti trigonal bipyramids that share  a cornercorner with one O(3)Lu2Ti2 tetrahedra, corners with three equivalent O(5)Lu3Ti tetrahedra,  a cornercorner with one O(4)Lu2MgTi2 trigonal bipyramid, corners with four equivalent O(1)Lu2Mg2Ti trigonal bipyramids, corners with three equivalent O(2)Lu3Ti trigonal pyramids,  an edgeedge with one O(5)Lu3Ti tetrahedra, edges with two equivalent O(4)Lu2MgTi2 trigonal bipyramids, and  a faceface with one O(1)Lu2Mg2Ti trigonal bipyramid. In the second O site, O(2) is bonded to one Lu(2), two equivalent Lu(1), and one Ti(2) atom to form OLu3Ti trigonal pyramids that share  a cornercorner with one O(4)Lu2MgTi2 trigonal bipyramid, corners with three equivalent O(1)Lu2Mg2Ti trigonal bipyramids, corners with three equivalent O(2)Lu3Ti trigonal pyramids, edges with two equivalent O(3)Lu2Ti2 tetrahedra, and edges with two equivalent O(5)Lu3Ti tetrahedra. In the third O site, O(3) is bonded to two equivalent Lu(1) and two equivalent Ti(2) atoms to form distorted OLu2Ti2 tetrahedra that share corners with two equivalent O(3)Lu2Ti2 tetrahedra, corners with two equivalent O(5)Lu3Ti tetrahedra, corners with two equivalent O(1)Lu2Mg2Ti trigonal bipyramids, and edges with four equivalent O(2)Lu3Ti trigonal pyramids. In the fourth O site, O(4) is bonded to one Mg(1), two equivalent Lu(2), and two equivalent Ti(1) atoms to form OLu2MgTi2 trigonal bipyramids that share corners with two equivalent O(1)Lu2Mg2Ti trigonal bipyramids, corners with two equivalent O(4)Lu2MgTi2 trigonal bipyramids, corners with two equivalent O(2)Lu3Ti trigonal pyramids, edges with four equivalent O(5)Lu3Ti tetrahedra, and edges with four equivalent O(1)Lu2Mg2Ti trigonal bipyramids. In the fifth O site, O(5) is bonded to one Lu(1), two equivalent Lu(2), and one Ti(1) atom to form OLu3Ti tetrahedra that share  a cornercorner with one O(3)Lu2Ti2 tetrahedra, corners with three equivalent O(5)Lu3Ti tetrahedra, corners with three equivalent O(1)Lu2Mg2Ti trigonal bipyramids,  an edgeedge with one O(1)Lu2Mg2Ti trigonal bipyramid, edges with two equivalent O(4)Lu2MgTi2 trigonal bipyramids, and edges with two equivalent O(2)Lu3Ti trigonal pyramids. In the sixth O site, O(6) is bonded in a distorted trigonal non-coplanar geometry to one Lu(1), one Lu(2), and one Ti(2) atom.