MgLu2Cr2O8 crystallizes in the triclinic P1 space group. Mg(1) is bonded to one O(2), one O(3), one O(4), one O(5), one O(6), and one O(8) atom to form distorted MgO6 octahedra that share  a cornercorner with one Lu(1)O7 pentagonal bipyramid,  a cornercorner with one Lu(2)O7 pentagonal bipyramid,  a cornercorner with one Cr(1)O4 tetrahedra,  a cornercorner with one Cr(2)O4 tetrahedra, edges with two equivalent Lu(1)O7 pentagonal bipyramids, edges with two equivalent Lu(2)O7 pentagonal bipyramids,  an edgeedge with one Cr(1)O4 tetrahedra, and  an edgeedge with one Cr(2)O4 tetrahedra. There are two inequivalent Lu sites. In the first Lu site, Lu(1) is bonded to one O(1), one O(2), one O(4), one O(5), one O(6), one O(7), and one O(8) atom to form distorted LuO7 pentagonal bipyramids that share  a cornercorner with one Mg(1)O6 octahedra,  a cornercorner with one Cr(1)O4 tetrahedra, corners with four equivalent Cr(2)O4 tetrahedra, edges with two equivalent Mg(1)O6 octahedra, edges with three equivalent Lu(2)O7 pentagonal bipyramids, and  an edgeedge with one Cr(1)O4 tetrahedra. The corner-sharing octahedral tilt angles are 35°. In the second Lu site, Lu(2) is bonded to one O(1), one O(2), one O(3), one O(4), one O(5), one O(6), and one O(7) atom to form distorted LuO7 pentagonal bipyramids that share  a cornercorner with one Mg(1)O6 octahedra,  a cornercorner with one Cr(2)O4 tetrahedra, corners with four equivalent Cr(1)O4 tetrahedra, edges with two equivalent Mg(1)O6 octahedra, edges with three equivalent Lu(1)O7 pentagonal bipyramids, and  an edgeedge with one Cr(2)O4 tetrahedra. The corner-sharing octahedral tilt angles are 34°. There are two inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(2), one O(3), one O(6), and one O(7) atom to form CrO4 tetrahedra that share  a cornercorner with one Mg(1)O6 octahedra,  a cornercorner with one Lu(1)O7 pentagonal bipyramid, corners with four equivalent Lu(2)O7 pentagonal bipyramids,  an edgeedge with one Mg(1)O6 octahedra, and  an edgeedge with one Lu(1)O7 pentagonal bipyramid. The corner-sharing octahedral tilt angles are 64°. In the second Cr site, Cr(2) is bonded to one O(1), one O(4), one O(5), and one O(8) atom to form CrO4 tetrahedra that share  a cornercorner with one Mg(1)O6 octahedra,  a cornercorner with one Lu(2)O7 pentagonal bipyramid, corners with four equivalent Lu(1)O7 pentagonal bipyramids,  an edgeedge with one Mg(1)O6 octahedra, and  an edgeedge with one Lu(2)O7 pentagonal bipyramid. The corner-sharing octahedral tilt angles are 65°. There are eight inequivalent O sites. In the first O site, O(1) is bonded in a distorted trigonal non-coplanar geometry to one Lu(1), one Lu(2), and one Cr(2) atom. In the second O site, O(2) is bonded in a distorted rectangular see-saw-like geometry to one Mg(1), one Lu(1), one Lu(2), and one Cr(1) atom. In the third O site, O(3) is bonded in a 3-coordinate geometry to one Mg(1), one Lu(2), and one Cr(1) atom. In the fourth O site, O(4) is bonded to one Mg(1), one Lu(1), one Lu(2), and one Cr(2) atom to form distorted corner-sharing OLu2MgCr trigonal pyramids. In the fifth O site, O(5) is bonded in a 4-coordinate geometry to one Mg(1), one Lu(1), one Lu(2), and one Cr(2) atom. In the sixth O site, O(6) is bonded to one Mg(1), one Lu(1), one Lu(2), and one Cr(1) atom to form distorted corner-sharing OLu2MgCr trigonal pyramids. In the seventh O site, O(7) is bonded in a distorted trigonal non-coplanar geometry to one Lu(1), one Lu(2), and one Cr(1) atom. In the eighth O site, O(8) is bonded in a 3-coordinate geometry to one Mg(1), one Lu(1), and one Cr(2) atom.
MgLu2Cr2O8 crystallizes in the triclinic P1 space group. Mg(1) is bonded to one O(2), one O(3), one O(4), one O(5), one O(6), and one O(8) atom to form distorted MgO6 octahedra that share  a cornercorner with one Lu(1)O7 pentagonal bipyramid,  a cornercorner with one Lu(2)O7 pentagonal bipyramid,  a cornercorner with one Cr(1)O4 tetrahedra,  a cornercorner with one Cr(2)O4 tetrahedra, edges with two equivalent Lu(1)O7 pentagonal bipyramids, edges with two equivalent Lu(2)O7 pentagonal bipyramids,  an edgeedge with one Cr(1)O4 tetrahedra, and  an edgeedge with one Cr(2)O4 tetrahedra. The Mg(1)-O(2) bond length is 2.34 Å. The Mg(1)-O(3) bond length is 2.04 Å. The Mg(1)-O(4) bond length is 1.96 Å. The Mg(1)-O(5) bond length is 2.46 Å. The Mg(1)-O(6) bond length is 1.96 Å. The Mg(1)-O(8) bond length is 2.03 Å. There are two inequivalent Lu sites. In the first Lu site, Lu(1) is bonded to one O(1), one O(2), one O(4), one O(5), one O(6), one O(7), and one O(8) atom to form distorted LuO7 pentagonal bipyramids that share  a cornercorner with one Mg(1)O6 octahedra,  a cornercorner with one Cr(1)O4 tetrahedra, corners with four equivalent Cr(2)O4 tetrahedra, edges with two equivalent Mg(1)O6 octahedra, edges with three equivalent Lu(2)O7 pentagonal bipyramids, and  an edgeedge with one Cr(1)O4 tetrahedra. The corner-sharing octahedral tilt angles are 35°. The Lu(1)-O(1) bond length is 2.20 Å. The Lu(1)-O(2) bond length is 2.43 Å. The Lu(1)-O(4) bond length is 2.38 Å. The Lu(1)-O(5) bond length is 2.26 Å. The Lu(1)-O(6) bond length is 2.31 Å. The Lu(1)-O(7) bond length is 2.27 Å. The Lu(1)-O(8) bond length is 2.31 Å. In the second Lu site, Lu(2) is bonded to one O(1), one O(2), one O(3), one O(4), one O(5), one O(6), and one O(7) atom to form distorted LuO7 pentagonal bipyramids that share  a cornercorner with one Mg(1)O6 octahedra,  a cornercorner with one Cr(2)O4 tetrahedra, corners with four equivalent Cr(1)O4 tetrahedra, edges with two equivalent Mg(1)O6 octahedra, edges with three equivalent Lu(1)O7 pentagonal bipyramids, and  an edgeedge with one Cr(2)O4 tetrahedra. The corner-sharing octahedral tilt angles are 34°. The Lu(2)-O(1) bond length is 2.27 Å. The Lu(2)-O(2) bond length is 2.27 Å. The Lu(2)-O(3) bond length is 2.30 Å. The Lu(2)-O(4) bond length is 2.31 Å. The Lu(2)-O(5) bond length is 2.40 Å. The Lu(2)-O(6) bond length is 2.38 Å. The Lu(2)-O(7) bond length is 2.21 Å. There are two inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(2), one O(3), one O(6), and one O(7) atom to form CrO4 tetrahedra that share  a cornercorner with one Mg(1)O6 octahedra,  a cornercorner with one Lu(1)O7 pentagonal bipyramid, corners with four equivalent Lu(2)O7 pentagonal bipyramids,  an edgeedge with one Mg(1)O6 octahedra, and  an edgeedge with one Lu(1)O7 pentagonal bipyramid. The corner-sharing octahedral tilt angles are 64°. The Cr(1)-O(2) bond length is 1.85 Å. The Cr(1)-O(3) bond length is 1.75 Å. The Cr(1)-O(6) bond length is 1.88 Å. The Cr(1)-O(7) bond length is 1.77 Å. In the second Cr site, Cr(2) is bonded to one O(1), one O(4), one O(5), and one O(8) atom to form CrO4 tetrahedra that share  a cornercorner with one Mg(1)O6 octahedra,  a cornercorner with one Lu(2)O7 pentagonal bipyramid, corners with four equivalent Lu(1)O7 pentagonal bipyramids,  an edgeedge with one Mg(1)O6 octahedra, and  an edgeedge with one Lu(2)O7 pentagonal bipyramid. The corner-sharing octahedral tilt angles are 65°. The Cr(2)-O(1) bond length is 1.77 Å. The Cr(2)-O(4) bond length is 1.88 Å. The Cr(2)-O(5) bond length is 1.84 Å. The Cr(2)-O(8) bond length is 1.75 Å. There are eight inequivalent O sites. In the first O site, O(1) is bonded in a distorted trigonal non-coplanar geometry to one Lu(1), one Lu(2), and one Cr(2) atom. In the second O site, O(2) is bonded in a distorted rectangular see-saw-like geometry to one Mg(1), one Lu(1), one Lu(2), and one Cr(1) atom. In the third O site, O(3) is bonded in a 3-coordinate geometry to one Mg(1), one Lu(2), and one Cr(1) atom. In the fourth O site, O(4) is bonded to one Mg(1), one Lu(1), one Lu(2), and one Cr(2) atom to form distorted corner-sharing OLu2MgCr trigonal pyramids. In the fifth O site, O(5) is bonded in a 4-coordinate geometry to one Mg(1), one Lu(1), one Lu(2), and one Cr(2) atom. In the sixth O site, O(6) is bonded to one Mg(1), one Lu(1), one Lu(2), and one Cr(1) atom to form distorted corner-sharing OLu2MgCr trigonal pyramids. In the seventh O site, O(7) is bonded in a distorted trigonal non-coplanar geometry to one Lu(1), one Lu(2), and one Cr(1) atom. In the eighth O site, O(8) is bonded in a 3-coordinate geometry to one Mg(1), one Lu(1), and one Cr(2) atom.