MgLu2S4 is Spinel-like structured and crystallizes in the orthorhombic Pnma space group. Mg(1) is bonded to one S(2), one S(3), and two equivalent S(1) atoms to form MgS4 tetrahedra that share corners with two equivalent Lu(1)S6 octahedra, corners with four equivalent Lu(2)S6 octahedra,  an edgeedge with one Lu(2)S6 octahedra, and edges with two equivalent Lu(1)S6 octahedra. The corner-sharing octahedral tilt angles range from 61-67°. There are two inequivalent Lu sites. In the first Lu site, Lu(1) is bonded to two equivalent S(1), two equivalent S(2), and two equivalent S(3) atoms to form LuS6 octahedra that share corners with four equivalent Lu(2)S6 octahedra, corners with two equivalent Mg(1)S4 tetrahedra, edges with two equivalent Lu(1)S6 octahedra, edges with two equivalent Lu(2)S6 octahedra, and edges with two equivalent Mg(1)S4 tetrahedra. The corner-sharing octahedral tilt angles range from 50-54°. In the second Lu site, Lu(2) is bonded to one S(2), one S(3), and four equivalent S(1) atoms to form LuS6 octahedra that share corners with four equivalent Lu(1)S6 octahedra, corners with four equivalent Lu(2)S6 octahedra, corners with four equivalent Mg(1)S4 tetrahedra, edges with two equivalent Lu(1)S6 octahedra, and  an edgeedge with one Mg(1)S4 tetrahedra. The corner-sharing octahedral tilt angles range from 47-54°. There are three inequivalent S sites. In the first S site, S(1) is bonded in a rectangular see-saw-like geometry to one Mg(1), one Lu(1), and two equivalent Lu(2) atoms. In the second S site, S(2) is bonded in a rectangular see-saw-like geometry to one Mg(1), one Lu(2), and two equivalent Lu(1) atoms. In the third S site, S(3) is bonded to one Mg(1), one Lu(2), and two equivalent Lu(1) atoms to form distorted corner-sharing SLu3Mg tetrahedra.
MgLu2S4 is Spinel-like structured and crystallizes in the orthorhombic Pnma space group. Mg(1) is bonded to one S(2), one S(3), and two equivalent S(1) atoms to form MgS4 tetrahedra that share corners with two equivalent Lu(1)S6 octahedra, corners with four equivalent Lu(2)S6 octahedra,  an edgeedge with one Lu(2)S6 octahedra, and edges with two equivalent Lu(1)S6 octahedra. The corner-sharing octahedral tilt angles range from 61-67°. The Mg(1)-S(2) bond length is 2.47 Å. The Mg(1)-S(3) bond length is 2.39 Å. Both Mg(1)-S(1) bond lengths are 2.45 Å. There are two inequivalent Lu sites. In the first Lu site, Lu(1) is bonded to two equivalent S(1), two equivalent S(2), and two equivalent S(3) atoms to form LuS6 octahedra that share corners with four equivalent Lu(2)S6 octahedra, corners with two equivalent Mg(1)S4 tetrahedra, edges with two equivalent Lu(1)S6 octahedra, edges with two equivalent Lu(2)S6 octahedra, and edges with two equivalent Mg(1)S4 tetrahedra. The corner-sharing octahedral tilt angles range from 50-54°. Both Lu(1)-S(1) bond lengths are 2.73 Å. Both Lu(1)-S(2) bond lengths are 2.70 Å. Both Lu(1)-S(3) bond lengths are 2.63 Å. In the second Lu site, Lu(2) is bonded to one S(2), one S(3), and four equivalent S(1) atoms to form LuS6 octahedra that share corners with four equivalent Lu(1)S6 octahedra, corners with four equivalent Lu(2)S6 octahedra, corners with four equivalent Mg(1)S4 tetrahedra, edges with two equivalent Lu(1)S6 octahedra, and  an edgeedge with one Mg(1)S4 tetrahedra. The corner-sharing octahedral tilt angles range from 47-54°. The Lu(2)-S(2) bond length is 2.66 Å. The Lu(2)-S(3) bond length is 2.67 Å. There are two shorter (2.72 Å) and two longer (2.80 Å) Lu(2)-S(1) bond lengths. There are three inequivalent S sites. In the first S site, S(1) is bonded in a rectangular see-saw-like geometry to one Mg(1), one Lu(1), and two equivalent Lu(2) atoms. In the second S site, S(2) is bonded in a rectangular see-saw-like geometry to one Mg(1), one Lu(2), and two equivalent Lu(1) atoms. In the third S site, S(3) is bonded to one Mg(1), one Lu(2), and two equivalent Lu(1) atoms to form distorted corner-sharing SLu3Mg tetrahedra.