BaLuCo4O7 crystallizes in the hexagonal P6_3mc space group. Ba(1) is bonded to six equivalent O(1) and six equivalent O(3) atoms to form distorted BaO12 cuboctahedra that share corners with twelve equivalent Ba(1)O12 cuboctahedra, edges with three equivalent Co(2)O4 tetrahedra, edges with nine equivalent Co(1)O4 tetrahedra, and faces with four equivalent Lu(1)O6 octahedra. Lu(1) is bonded to three equivalent O(1) and three equivalent O(3) atoms to form LuO6 octahedra that share corners with three equivalent Co(2)O4 tetrahedra, corners with nine equivalent Co(1)O4 tetrahedra, and faces with four equivalent Ba(1)O12 cuboctahedra. There are two inequivalent Co sites. In the first Co site, Co(1) is bonded to one O(1), one O(2), and two equivalent O(3) atoms to form CoO4 tetrahedra that share corners with three equivalent Lu(1)O6 octahedra, corners with two equivalent Co(2)O4 tetrahedra, corners with four equivalent Co(1)O4 tetrahedra, and edges with three equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 54-55°. In the second Co site, Co(2) is bonded to one O(2) and three equivalent O(1) atoms to form CoO4 tetrahedra that share corners with three equivalent Lu(1)O6 octahedra, corners with six equivalent Co(1)O4 tetrahedra, and edges with three equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 53°. There are three inequivalent O sites. In the first O site, O(1) is bonded in a distorted trigonal planar geometry to two equivalent Ba(1), one Lu(1), one Co(1), and one Co(2) atom. In the second O site, O(2) is bonded in a tetrahedral geometry to one Co(2) and three equivalent Co(1) atoms. In the third O site, O(3) is bonded in a 3-coordinate geometry to two equivalent Ba(1), one Lu(1), and two equivalent Co(1) atoms.
BaLuCo4O7 crystallizes in the hexagonal P6_3mc space group. Ba(1) is bonded to six equivalent O(1) and six equivalent O(3) atoms to form distorted BaO12 cuboctahedra that share corners with twelve equivalent Ba(1)O12 cuboctahedra, edges with three equivalent Co(2)O4 tetrahedra, edges with nine equivalent Co(1)O4 tetrahedra, and faces with four equivalent Lu(1)O6 octahedra. All Ba(1)-O(1) bond lengths are 3.17 Å. There are three shorter (2.91 Å) and three longer (3.42 Å) Ba(1)-O(3) bond lengths. Lu(1) is bonded to three equivalent O(1) and three equivalent O(3) atoms to form LuO6 octahedra that share corners with three equivalent Co(2)O4 tetrahedra, corners with nine equivalent Co(1)O4 tetrahedra, and faces with four equivalent Ba(1)O12 cuboctahedra. All Lu(1)-O(1) bond lengths are 2.20 Å. All Lu(1)-O(3) bond lengths are 2.24 Å. There are two inequivalent Co sites. In the first Co site, Co(1) is bonded to one O(1), one O(2), and two equivalent O(3) atoms to form CoO4 tetrahedra that share corners with three equivalent Lu(1)O6 octahedra, corners with two equivalent Co(2)O4 tetrahedra, corners with four equivalent Co(1)O4 tetrahedra, and edges with three equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles range from 54-55°. The Co(1)-O(1) bond length is 1.92 Å. The Co(1)-O(2) bond length is 1.95 Å. Both Co(1)-O(3) bond lengths are 1.94 Å. In the second Co site, Co(2) is bonded to one O(2) and three equivalent O(1) atoms to form CoO4 tetrahedra that share corners with three equivalent Lu(1)O6 octahedra, corners with six equivalent Co(1)O4 tetrahedra, and edges with three equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 53°. The Co(2)-O(2) bond length is 2.06 Å. All Co(2)-O(1) bond lengths are 1.96 Å. There are three inequivalent O sites. In the first O site, O(1) is bonded in a distorted trigonal planar geometry to two equivalent Ba(1), one Lu(1), one Co(1), and one Co(2) atom. In the second O site, O(2) is bonded in a tetrahedral geometry to one Co(2) and three equivalent Co(1) atoms. In the third O site, O(3) is bonded in a 3-coordinate geometry to two equivalent Ba(1), one Lu(1), and two equivalent Co(1) atoms.