LiLu4(CoO3)4 crystallizes in the triclinic P1 space group. Li(1) is bonded to one Lu(1), one O(11), one O(6), one O(7), and one O(9) atom to form LiLuO4 tetrahedra that share corners with two equivalent Co(1)O6 octahedra, corners with two equivalent Co(2)O6 octahedra, and  an edgeedge with one Co(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 29-67°. There are four inequivalent Lu sites. In the first Lu site, Lu(1) is bonded in a 9-coordinate geometry to one Li(1), one O(1), one O(11), one O(3), one O(4), one O(5), one O(6), one O(7), and one O(9) atom. In the second Lu site, Lu(2) is bonded in a 8-coordinate geometry to one O(11), one O(12), one O(3), one O(5), one O(6), one O(7), one O(8), and one O(9) atom. In the third Lu site, Lu(3) is bonded in a 8-coordinate geometry to one O(1), one O(10), one O(12), one O(2), one O(4), one O(7), one O(8), and one O(9) atom. In the fourth Lu site, Lu(4) is bonded in a 8-coordinate geometry to one O(1), one O(10), one O(12), one O(2), one O(3), one O(4), one O(5), and one O(8) atom. There are four inequivalent Co sites. In the first Co site, Co(1) is bonded to one O(1), one O(2), one O(5), one O(6), one O(8), and one O(9) atom to form CoO6 octahedra that share corners with two equivalent Co(2)O6 octahedra and corners with two equivalent Li(1)LuO4 tetrahedra. The corner-sharing octahedral tilt angles are 48°. In the second Co site, Co(2) is bonded to one O(12), one O(2), one O(3), one O(4), one O(6), and one O(7) atom to form CoO6 octahedra that share corners with two equivalent Co(1)O6 octahedra, corners with four equivalent Co(3)O6 octahedra, and corners with two equivalent Li(1)LuO4 tetrahedra. The corner-sharing octahedral tilt angles range from 36-48°. In the third Co site, Co(3) is bonded to one O(10), one O(11), one O(12), one O(3), one O(4), and one O(7) atom to form distorted CoO6 octahedra that share corners with four equivalent Co(2)O6 octahedra and  an edgeedge with one Li(1)LuO4 tetrahedra. The corner-sharing octahedral tilt angles range from 36-45°. In the fourth Co site, Co(4) is bonded in a 6-coordinate geometry to one O(1), one O(10), one O(11), one O(5), one O(8), and one O(9) atom. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a 5-coordinate geometry to one Lu(1), one Lu(3), one Lu(4), one Co(1), and one Co(4) atom. In the second O site, O(2) is bonded to one Lu(3), one Lu(4), one Co(1), and one Co(2) atom to form distorted corner-sharing OLu2Co2 trigonal pyramids. In the third O site, O(3) is bonded in a 5-coordinate geometry to one Lu(1), one Lu(2), one Lu(4), one Co(2), and one Co(3) atom. In the fourth O site, O(4) is bonded in a 5-coordinate geometry to one Lu(1), one Lu(3), one Lu(4), one Co(2), and one Co(3) atom. In the fifth O site, O(5) is bonded in a 5-coordinate geometry to one Lu(1), one Lu(2), one Lu(4), one Co(1), and one Co(4) atom. In the sixth O site, O(6) is bonded in a 5-coordinate geometry to one Li(1), one Lu(1), one Lu(2), one Co(1), and one Co(2) atom. In the seventh O site, O(7) is bonded in a 6-coordinate geometry to one Li(1), one Lu(1), one Lu(2), one Lu(3), one Co(2), and one Co(3) atom. In the eighth O site, O(8) is bonded in a 5-coordinate geometry to one Lu(2), one Lu(3), one Lu(4), one Co(1), and one Co(4) atom. In the ninth O site, O(9) is bonded in a 6-coordinate geometry to one Li(1), one Lu(1), one Lu(2), one Lu(3), one Co(1), and one Co(4) atom. In the tenth O site, O(10) is bonded to one Lu(3), one Lu(4), one Co(3), and one Co(4) atom to form distorted corner-sharing OLu2Co2 trigonal pyramids. In the eleventh O site, O(11) is bonded in a 5-coordinate geometry to one Li(1), one Lu(1), one Lu(2), one Co(3), and one Co(4) atom. In the twelfth O site, O(12) is bonded in a 5-coordinate geometry to one Lu(2), one Lu(3), one Lu(4), one Co(2), and one Co(3) atom.
LiLu4(CoO3)4 crystallizes in the triclinic P1 space group. Li(1) is bonded to one Lu(1), one O(11), one O(6), one O(7), and one O(9) atom to form LiLuO4 tetrahedra that share corners with two equivalent Co(1)O6 octahedra, corners with two equivalent Co(2)O6 octahedra, and  an edgeedge with one Co(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 29-67°. The Li(1)-Lu(1) bond length is 2.32 Å. The Li(1)-O(11) bond length is 1.74 Å. The Li(1)-O(6) bond length is 1.84 Å. The Li(1)-O(7) bond length is 1.92 Å. The Li(1)-O(9) bond length is 1.92 Å. There are four inequivalent Lu sites. In the first Lu site, Lu(1) is bonded in a 9-coordinate geometry to one Li(1), one O(1), one O(11), one O(3), one O(4), one O(5), one O(6), one O(7), and one O(9) atom. The Lu(1)-O(1) bond length is 2.71 Å. The Lu(1)-O(11) bond length is 2.13 Å. The Lu(1)-O(3) bond length is 2.25 Å. The Lu(1)-O(4) bond length is 2.61 Å. The Lu(1)-O(5) bond length is 2.27 Å. The Lu(1)-O(6) bond length is 2.29 Å. The Lu(1)-O(7) bond length is 2.31 Å. The Lu(1)-O(9) bond length is 2.33 Å. In the second Lu site, Lu(2) is bonded in a 8-coordinate geometry to one O(11), one O(12), one O(3), one O(5), one O(6), one O(7), one O(8), and one O(9) atom. The Lu(2)-O(11) bond length is 2.20 Å. The Lu(2)-O(12) bond length is 2.62 Å. The Lu(2)-O(3) bond length is 2.22 Å. The Lu(2)-O(5) bond length is 2.27 Å. The Lu(2)-O(6) bond length is 2.29 Å. The Lu(2)-O(7) bond length is 2.40 Å. The Lu(2)-O(8) bond length is 2.67 Å. The Lu(2)-O(9) bond length is 2.40 Å. In the third Lu site, Lu(3) is bonded in a 8-coordinate geometry to one O(1), one O(10), one O(12), one O(2), one O(4), one O(7), one O(8), and one O(9) atom. The Lu(3)-O(1) bond length is 2.26 Å. The Lu(3)-O(10) bond length is 2.24 Å. The Lu(3)-O(12) bond length is 2.50 Å. The Lu(3)-O(2) bond length is 2.14 Å. The Lu(3)-O(4) bond length is 2.24 Å. The Lu(3)-O(7) bond length is 2.62 Å. The Lu(3)-O(8) bond length is 2.47 Å. The Lu(3)-O(9) bond length is 2.70 Å. In the fourth Lu site, Lu(4) is bonded in a 8-coordinate geometry to one O(1), one O(10), one O(12), one O(2), one O(3), one O(4), one O(5), and one O(8) atom. The Lu(4)-O(1) bond length is 2.42 Å. The Lu(4)-O(10) bond length is 2.19 Å. The Lu(4)-O(12) bond length is 2.25 Å. The Lu(4)-O(2) bond length is 2.25 Å. The Lu(4)-O(3) bond length is 2.61 Å. The Lu(4)-O(4) bond length is 2.43 Å. The Lu(4)-O(5) bond length is 2.61 Å. The Lu(4)-O(8) bond length is 2.29 Å. There are four inequivalent Co sites. In the first Co site, Co(1) is bonded to one O(1), one O(2), one O(5), one O(6), one O(8), and one O(9) atom to form CoO6 octahedra that share corners with two equivalent Co(2)O6 octahedra and corners with two equivalent Li(1)LuO4 tetrahedra. The corner-sharing octahedral tilt angles are 48°. The Co(1)-O(1) bond length is 1.90 Å. The Co(1)-O(2) bond length is 2.03 Å. The Co(1)-O(5) bond length is 2.24 Å. The Co(1)-O(6) bond length is 2.05 Å. The Co(1)-O(8) bond length is 2.13 Å. The Co(1)-O(9) bond length is 1.95 Å. In the second Co site, Co(2) is bonded to one O(12), one O(2), one O(3), one O(4), one O(6), and one O(7) atom to form CoO6 octahedra that share corners with two equivalent Co(1)O6 octahedra, corners with four equivalent Co(3)O6 octahedra, and corners with two equivalent Li(1)LuO4 tetrahedra. The corner-sharing octahedral tilt angles range from 36-48°. The Co(2)-O(12) bond length is 2.09 Å. The Co(2)-O(2) bond length is 2.03 Å. The Co(2)-O(3) bond length is 2.19 Å. The Co(2)-O(4) bond length is 1.92 Å. The Co(2)-O(6) bond length is 2.05 Å. The Co(2)-O(7) bond length is 1.98 Å. In the third Co site, Co(3) is bonded to one O(10), one O(11), one O(12), one O(3), one O(4), and one O(7) atom to form distorted CoO6 octahedra that share corners with four equivalent Co(2)O6 octahedra and  an edgeedge with one Li(1)LuO4 tetrahedra. The corner-sharing octahedral tilt angles range from 36-45°. The Co(3)-O(10) bond length is 1.97 Å. The Co(3)-O(11) bond length is 2.14 Å. The Co(3)-O(12) bond length is 2.00 Å. The Co(3)-O(3) bond length is 2.01 Å. The Co(3)-O(4) bond length is 2.15 Å. The Co(3)-O(7) bond length is 2.30 Å. In the fourth Co site, Co(4) is bonded in a 6-coordinate geometry to one O(1), one O(10), one O(11), one O(5), one O(8), and one O(9) atom. The Co(4)-O(1) bond length is 2.17 Å. The Co(4)-O(10) bond length is 1.90 Å. The Co(4)-O(11) bond length is 2.00 Å. The Co(4)-O(5) bond length is 1.95 Å. The Co(4)-O(8) bond length is 1.94 Å. The Co(4)-O(9) bond length is 2.34 Å. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a 5-coordinate geometry to one Lu(1), one Lu(3), one Lu(4), one Co(1), and one Co(4) atom. In the second O site, O(2) is bonded to one Lu(3), one Lu(4), one Co(1), and one Co(2) atom to form distorted corner-sharing OLu2Co2 trigonal pyramids. In the third O site, O(3) is bonded in a 5-coordinate geometry to one Lu(1), one Lu(2), one Lu(4), one Co(2), and one Co(3) atom. In the fourth O site, O(4) is bonded in a 5-coordinate geometry to one Lu(1), one Lu(3), one Lu(4), one Co(2), and one Co(3) atom. In the fifth O site, O(5) is bonded in a 5-coordinate geometry to one Lu(1), one Lu(2), one Lu(4), one Co(1), and one Co(4) atom. In the sixth O site, O(6) is bonded in a 5-coordinate geometry to one Li(1), one Lu(1), one Lu(2), one Co(1), and one Co(2) atom. In the seventh O site, O(7) is bonded in a 6-coordinate geometry to one Li(1), one Lu(1), one Lu(2), one Lu(3), one Co(2), and one Co(3) atom. In the eighth O site, O(8) is bonded in a 5-coordinate geometry to one Lu(2), one Lu(3), one Lu(4), one Co(1), and one Co(4) atom. In the ninth O site, O(9) is bonded in a 6-coordinate geometry to one Li(1), one Lu(1), one Lu(2), one Lu(3), one Co(1), and one Co(4) atom. In the tenth O site, O(10) is bonded to one Lu(3), one Lu(4), one Co(3), and one Co(4) atom to form distorted corner-sharing OLu2Co2 trigonal pyramids. In the eleventh O site, O(11) is bonded in a 5-coordinate geometry to one Li(1), one Lu(1), one Lu(2), one Co(3), and one Co(4) atom. In the twelfth O site, O(12) is bonded in a 5-coordinate geometry to one Lu(2), one Lu(3), one Lu(4), one Co(2), and one Co(3) atom.