Ba4MgYb8(CoO5)4 crystallizes in the monoclinic Pm space group. There are four inequivalent Ba sites. In the first Ba site, Ba(1) is bonded in a 9-coordinate geometry to one O(4), two equivalent O(3), two equivalent O(6), two equivalent O(8), and two equivalent O(9) atoms. In the second Ba site, Ba(2) is bonded in a 11-coordinate geometry to one O(3), two equivalent O(10), two equivalent O(4), two equivalent O(5), two equivalent O(7), and two equivalent O(9) atoms. In the third Ba site, Ba(3) is bonded in a 7-coordinate geometry to one O(2), two equivalent O(1), two equivalent O(6), and two equivalent O(8) atoms. In the fourth Ba site, Ba(4) is bonded in a 9-coordinate geometry to one O(1), two equivalent O(11), two equivalent O(2), two equivalent O(5), and two equivalent O(7) atoms. Mg(1) is bonded in a 6-coordinate geometry to two equivalent O(11), two equivalent O(12), and two equivalent O(5) atoms. There are eight inequivalent Yb sites. In the first Yb site, Yb(1) is bonded in a 7-coordinate geometry to one O(1), two equivalent O(11), two equivalent O(12), and two equivalent O(6) atoms. In the second Yb site, Yb(2) is bonded in a 7-coordinate geometry to one O(2), two equivalent O(11), two equivalent O(12), and two equivalent O(5) atoms. In the third Yb site, Yb(3) is bonded to one O(3), two equivalent O(10), two equivalent O(8), and two equivalent O(9) atoms to form distorted YbO7 pentagonal bipyramids that share corners with two equivalent Co(4)O5 square pyramids,  a cornercorner with one Co(3)O5 trigonal bipyramid, corners with two equivalent Co(1)O5 trigonal bipyramids, and  an edgeedge with one Co(3)O5 trigonal bipyramid. In the fourth Yb site, Yb(4) is bonded in a 7-coordinate geometry to one O(4), two equivalent O(10), two equivalent O(7), and two equivalent O(9) atoms. In the fifth Yb site, Yb(5) is bonded in a 7-coordinate geometry to one O(1), two equivalent O(10), two equivalent O(6), and two equivalent O(8) atoms. In the sixth Yb site, Yb(6) is bonded in a 7-coordinate geometry to one O(2), two equivalent O(5), two equivalent O(7), and two equivalent O(9) atoms. In the seventh Yb site, Yb(7) is bonded in a 7-coordinate geometry to one O(3), two equivalent O(12), two equivalent O(6), and two equivalent O(8) atoms. In the eighth Yb site, Yb(8) is bonded in a 7-coordinate geometry to one O(4), two equivalent O(11), two equivalent O(5), and two equivalent O(7) atoms. There are four inequivalent Co sites. In the first Co site, Co(1) is bonded to one O(1), two equivalent O(12), and two equivalent O(8) atoms to form distorted CoO5 trigonal bipyramids that share corners with two equivalent Yb(3)O7 pentagonal bipyramids. In the second Co site, Co(2) is bonded in a distorted trigonal bipyramidal geometry to one O(2), two equivalent O(11), and two equivalent O(7) atoms. In the third Co site, Co(3) is bonded to one O(3), two equivalent O(10), and two equivalent O(6) atoms to form CoO5 trigonal bipyramids that share  a cornercorner with one Yb(3)O7 pentagonal bipyramid and  an edgeedge with one Yb(3)O7 pentagonal bipyramid. In the fourth Co site, Co(4) is bonded to one O(4), two equivalent O(5), and two equivalent O(9) atoms to form distorted CoO5 square pyramids that share corners with two equivalent Yb(3)O7 pentagonal bipyramids. There are twelve inequivalent O sites. In the first O site, O(1) is bonded to one Ba(4), two equivalent Ba(3), one Yb(1), one Yb(5), and one Co(1) atom to form distorted OBa3Yb2Co octahedra that share corners with two equivalent O(7)Ba2Yb3Co octahedra, corners with two equivalent O(8)Ba2Yb3Co octahedra, corners with two equivalent O(1)Ba3Yb2Co octahedra, edges with two equivalent O(2)Ba3Yb2Co octahedra, and faces with two equivalent O(8)Ba2Yb3Co octahedra. The corner-sharing octahedral tilt angles range from 5-57°. In the second O site, O(2) is bonded to one Ba(3), two equivalent Ba(4), one Yb(2), one Yb(6), and one Co(2) atom to form distorted OBa3Yb2Co octahedra that share corners with two equivalent O(7)Ba2Yb3Co octahedra, corners with two equivalent O(8)Ba2Yb3Co octahedra, corners with two equivalent O(2)Ba3Yb2Co octahedra, edges with two equivalent O(1)Ba3Yb2Co octahedra, and faces with two equivalent O(7)Ba2Yb3Co octahedra. The corner-sharing octahedral tilt angles range from 10-60°. In the third O site, O(3) is bonded to one Ba(2), two equivalent Ba(1), one Yb(3), one Yb(7), and one Co(3) atom to form distorted OBa3Yb2Co octahedra that share corners with two equivalent O(7)Ba2Yb3Co octahedra, corners with two equivalent O(8)Ba2Yb3Co octahedra, corners with two equivalent O(3)Ba3Yb2Co octahedra, edges with two equivalent O(4)Ba3Yb2Co octahedra, and faces with two equivalent O(8)Ba2Yb3Co octahedra. The corner-sharing octahedral tilt angles range from 10-56°. In the fourth O site, O(4) is bonded to one Ba(1), two equivalent Ba(2), one Yb(4), one Yb(8), and one Co(4) atom to form distorted OBa3Yb2Co octahedra that share corners with two equivalent O(7)Ba2Yb3Co octahedra, corners with two equivalent O(8)Ba2Yb3Co octahedra, corners with two equivalent O(4)Ba3Yb2Co octahedra, edges with two equivalent O(3)Ba3Yb2Co octahedra, and faces with two equivalent O(7)Ba2Yb3Co octahedra. The corner-sharing octahedral tilt angles range from 13-55°. In the fifth O site, O(5) is bonded in a 7-coordinate geometry to one Ba(2), one Ba(4), one Mg(1), one Yb(2), one Yb(6), one Yb(8), and one Co(4) atom. In the sixth O site, O(6) is bonded in a 6-coordinate geometry to one Ba(1), one Ba(3), one Yb(1), one Yb(5), one Yb(7), and one Co(3) atom. In the seventh O site, O(7) is bonded to one Ba(2), one Ba(4), one Yb(4), one Yb(6), one Yb(8), and one Co(2) atom to form distorted OBa2Yb3Co octahedra that share  a cornercorner with one O(1)Ba3Yb2Co octahedra,  a cornercorner with one O(2)Ba3Yb2Co octahedra,  a cornercorner with one O(3)Ba3Yb2Co octahedra,  a cornercorner with one O(4)Ba3Yb2Co octahedra,  a faceface with one O(2)Ba3Yb2Co octahedra,  a faceface with one O(4)Ba3Yb2Co octahedra, and faces with two equivalent O(7)Ba2Yb3Co octahedra. The corner-sharing octahedral tilt angles range from 42-55°. In the eighth O site, O(8) is bonded to one Ba(1), one Ba(3), one Yb(3), one Yb(5), one Yb(7), and one Co(1) atom to form distorted OBa2Yb3Co octahedra that share  a cornercorner with one O(1)Ba3Yb2Co octahedra,  a cornercorner with one O(2)Ba3Yb2Co octahedra,  a cornercorner with one O(3)Ba3Yb2Co octahedra,  a cornercorner with one O(4)Ba3Yb2Co octahedra,  a faceface with one O(1)Ba3Yb2Co octahedra,  a faceface with one O(3)Ba3Yb2Co octahedra, and faces with two equivalent O(8)Ba2Yb3Co octahedra. The corner-sharing octahedral tilt angles range from 43-60°. In the ninth O site, O(9) is bonded in a 4-coordinate geometry to one Ba(1), one Ba(2), one Yb(3), one Yb(4), one Yb(6), and one Co(4) atom. In the tenth O site, O(10) is bonded in a 4-coordinate geometry to one Ba(2), one Yb(3), one Yb(4), one Yb(5), and one Co(3) atom. In the eleventh O site, O(11) is bonded in a 5-coordinate geometry to one Ba(4), one Mg(1), one Yb(1), one Yb(2), one Yb(8), and one Co(2) atom. In the twelfth O site, O(12) is bonded in a 5-coordinate geometry to one Mg(1), one Yb(1), one Yb(2), one Yb(7), and one Co(1) atom.
Ba4MgYb8(CoO5)4 crystallizes in the monoclinic Pm space group. There are four inequivalent Ba sites. In the first Ba site, Ba(1) is bonded in a 9-coordinate geometry to one O(4), two equivalent O(3), two equivalent O(6), two equivalent O(8), and two equivalent O(9) atoms. The Ba(1)-O(4) bond length is 2.64 Å. Both Ba(1)-O(3) bond lengths are 2.86 Å. Both Ba(1)-O(6) bond lengths are 3.00 Å. Both Ba(1)-O(8) bond lengths are 2.79 Å. Both Ba(1)-O(9) bond lengths are 3.02 Å. In the second Ba site, Ba(2) is bonded in a 11-coordinate geometry to one O(3), two equivalent O(10), two equivalent O(4), two equivalent O(5), two equivalent O(7), and two equivalent O(9) atoms. The Ba(2)-O(3) bond length is 2.65 Å. Both Ba(2)-O(10) bond lengths are 2.94 Å. Both Ba(2)-O(4) bond lengths are 2.87 Å. Both Ba(2)-O(5) bond lengths are 3.26 Å. Both Ba(2)-O(7) bond lengths are 2.78 Å. Both Ba(2)-O(9) bond lengths are 3.29 Å. In the third Ba site, Ba(3) is bonded in a 7-coordinate geometry to one O(2), two equivalent O(1), two equivalent O(6), and two equivalent O(8) atoms. The Ba(3)-O(2) bond length is 2.67 Å. Both Ba(3)-O(1) bond lengths are 2.85 Å. Both Ba(3)-O(6) bond lengths are 2.81 Å. Both Ba(3)-O(8) bond lengths are 2.85 Å. In the fourth Ba site, Ba(4) is bonded in a 9-coordinate geometry to one O(1), two equivalent O(11), two equivalent O(2), two equivalent O(5), and two equivalent O(7) atoms. The Ba(4)-O(1) bond length is 2.63 Å. Both Ba(4)-O(11) bond lengths are 2.94 Å. Both Ba(4)-O(2) bond lengths are 2.86 Å. Both Ba(4)-O(5) bond lengths are 2.99 Å. Both Ba(4)-O(7) bond lengths are 2.77 Å. Mg(1) is bonded in a 6-coordinate geometry to two equivalent O(11), two equivalent O(12), and two equivalent O(5) atoms. Both Mg(1)-O(11) bond lengths are 2.24 Å. Both Mg(1)-O(12) bond lengths are 2.08 Å. Both Mg(1)-O(5) bond lengths are 2.25 Å. There are eight inequivalent Yb sites. In the first Yb site, Yb(1) is bonded in a 7-coordinate geometry to one O(1), two equivalent O(11), two equivalent O(12), and two equivalent O(6) atoms. The Yb(1)-O(1) bond length is 2.27 Å. Both Yb(1)-O(11) bond lengths are 2.51 Å. Both Yb(1)-O(12) bond lengths are 2.56 Å. Both Yb(1)-O(6) bond lengths are 2.28 Å. In the second Yb site, Yb(2) is bonded in a 7-coordinate geometry to one O(2), two equivalent O(11), two equivalent O(12), and two equivalent O(5) atoms. The Yb(2)-O(2) bond length is 2.62 Å. Both Yb(2)-O(11) bond lengths are 2.36 Å. Both Yb(2)-O(12) bond lengths are 2.29 Å. Both Yb(2)-O(5) bond lengths are 2.40 Å. In the third Yb site, Yb(3) is bonded to one O(3), two equivalent O(10), two equivalent O(8), and two equivalent O(9) atoms to form distorted YbO7 pentagonal bipyramids that share corners with two equivalent Co(4)O5 square pyramids,  a cornercorner with one Co(3)O5 trigonal bipyramid, corners with two equivalent Co(1)O5 trigonal bipyramids, and  an edgeedge with one Co(3)O5 trigonal bipyramid. The Yb(3)-O(3) bond length is 2.49 Å. Both Yb(3)-O(10) bond lengths are 2.44 Å. Both Yb(3)-O(8) bond lengths are 2.40 Å. Both Yb(3)-O(9) bond lengths are 2.44 Å. In the fourth Yb site, Yb(4) is bonded in a 7-coordinate geometry to one O(4), two equivalent O(10), two equivalent O(7), and two equivalent O(9) atoms. The Yb(4)-O(4) bond length is 2.68 Å. Both Yb(4)-O(10) bond lengths are 2.37 Å. Both Yb(4)-O(7) bond lengths are 2.39 Å. Both Yb(4)-O(9) bond lengths are 2.39 Å. In the fifth Yb site, Yb(5) is bonded in a 7-coordinate geometry to one O(1), two equivalent O(10), two equivalent O(6), and two equivalent O(8) atoms. The Yb(5)-O(1) bond length is 2.42 Å. Both Yb(5)-O(10) bond lengths are 2.31 Å. Both Yb(5)-O(6) bond lengths are 2.41 Å. Both Yb(5)-O(8) bond lengths are 2.40 Å. In the sixth Yb site, Yb(6) is bonded in a 7-coordinate geometry to one O(2), two equivalent O(5), two equivalent O(7), and two equivalent O(9) atoms. The Yb(6)-O(2) bond length is 2.45 Å. Both Yb(6)-O(5) bond lengths are 2.43 Å. Both Yb(6)-O(7) bond lengths are 2.35 Å. Both Yb(6)-O(9) bond lengths are 2.32 Å. In the seventh Yb site, Yb(7) is bonded in a 7-coordinate geometry to one O(3), two equivalent O(12), two equivalent O(6), and two equivalent O(8) atoms. The Yb(7)-O(3) bond length is 2.44 Å. Both Yb(7)-O(12) bond lengths are 2.38 Å. Both Yb(7)-O(6) bond lengths are 2.44 Å. Both Yb(7)-O(8) bond lengths are 2.35 Å. In the eighth Yb site, Yb(8) is bonded in a 7-coordinate geometry to one O(4), two equivalent O(11), two equivalent O(5), and two equivalent O(7) atoms. The Yb(8)-O(4) bond length is 2.22 Å. Both Yb(8)-O(11) bond lengths are 2.35 Å. Both Yb(8)-O(5) bond lengths are 2.54 Å. Both Yb(8)-O(7) bond lengths are 2.22 Å. There are four inequivalent Co sites. In the first Co site, Co(1) is bonded to one O(1), two equivalent O(12), and two equivalent O(8) atoms to form distorted CoO5 trigonal bipyramids that share corners with two equivalent Yb(3)O7 pentagonal bipyramids. The Co(1)-O(1) bond length is 1.84 Å. Both Co(1)-O(12) bond lengths are 2.00 Å. Both Co(1)-O(8) bond lengths are 2.02 Å. In the second Co site, Co(2) is bonded in a distorted trigonal bipyramidal geometry to one O(2), two equivalent O(11), and two equivalent O(7) atoms. The Co(2)-O(2) bond length is 1.81 Å. Both Co(2)-O(11) bond lengths are 2.05 Å. Both Co(2)-O(7) bond lengths are 2.06 Å. In the third Co site, Co(3) is bonded to one O(3), two equivalent O(10), and two equivalent O(6) atoms to form CoO5 trigonal bipyramids that share  a cornercorner with one Yb(3)O7 pentagonal bipyramid and  an edgeedge with one Yb(3)O7 pentagonal bipyramid. The Co(3)-O(3) bond length is 1.85 Å. Both Co(3)-O(10) bond lengths are 1.89 Å. Both Co(3)-O(6) bond lengths are 1.91 Å. In the fourth Co site, Co(4) is bonded to one O(4), two equivalent O(5), and two equivalent O(9) atoms to form distorted CoO5 square pyramids that share corners with two equivalent Yb(3)O7 pentagonal bipyramids. The Co(4)-O(4) bond length is 1.86 Å. Both Co(4)-O(5) bond lengths are 1.94 Å. Both Co(4)-O(9) bond lengths are 1.88 Å. There are twelve inequivalent O sites. In the first O site, O(1) is bonded to one Ba(4), two equivalent Ba(3), one Yb(1), one Yb(5), and one Co(1) atom to form distorted OBa3Yb2Co octahedra that share corners with two equivalent O(7)Ba2Yb3Co octahedra, corners with two equivalent O(8)Ba2Yb3Co octahedra, corners with two equivalent O(1)Ba3Yb2Co octahedra, edges with two equivalent O(2)Ba3Yb2Co octahedra, and faces with two equivalent O(8)Ba2Yb3Co octahedra. The corner-sharing octahedral tilt angles range from 5-57°. In the second O site, O(2) is bonded to one Ba(3), two equivalent Ba(4), one Yb(2), one Yb(6), and one Co(2) atom to form distorted OBa3Yb2Co octahedra that share corners with two equivalent O(7)Ba2Yb3Co octahedra, corners with two equivalent O(8)Ba2Yb3Co octahedra, corners with two equivalent O(2)Ba3Yb2Co octahedra, edges with two equivalent O(1)Ba3Yb2Co octahedra, and faces with two equivalent O(7)Ba2Yb3Co octahedra. The corner-sharing octahedral tilt angles range from 10-60°. In the third O site, O(3) is bonded to one Ba(2), two equivalent Ba(1), one Yb(3), one Yb(7), and one Co(3) atom to form distorted OBa3Yb2Co octahedra that share corners with two equivalent O(7)Ba2Yb3Co octahedra, corners with two equivalent O(8)Ba2Yb3Co octahedra, corners with two equivalent O(3)Ba3Yb2Co octahedra, edges with two equivalent O(4)Ba3Yb2Co octahedra, and faces with two equivalent O(8)Ba2Yb3Co octahedra. The corner-sharing octahedral tilt angles range from 10-56°. In the fourth O site, O(4) is bonded to one Ba(1), two equivalent Ba(2), one Yb(4), one Yb(8), and one Co(4) atom to form distorted OBa3Yb2Co octahedra that share corners with two equivalent O(7)Ba2Yb3Co octahedra, corners with two equivalent O(8)Ba2Yb3Co octahedra, corners with two equivalent O(4)Ba3Yb2Co octahedra, edges with two equivalent O(3)Ba3Yb2Co octahedra, and faces with two equivalent O(7)Ba2Yb3Co octahedra. The corner-sharing octahedral tilt angles range from 13-55°. In the fifth O site, O(5) is bonded in a 7-coordinate geometry to one Ba(2), one Ba(4), one Mg(1), one Yb(2), one Yb(6), one Yb(8), and one Co(4) atom. In the sixth O site, O(6) is bonded in a 6-coordinate geometry to one Ba(1), one Ba(3), one Yb(1), one Yb(5), one Yb(7), and one Co(3) atom. In the seventh O site, O(7) is bonded to one Ba(2), one Ba(4), one Yb(4), one Yb(6), one Yb(8), and one Co(2) atom to form distorted OBa2Yb3Co octahedra that share  a cornercorner with one O(1)Ba3Yb2Co octahedra,  a cornercorner with one O(2)Ba3Yb2Co octahedra,  a cornercorner with one O(3)Ba3Yb2Co octahedra,  a cornercorner with one O(4)Ba3Yb2Co octahedra,  a faceface with one O(2)Ba3Yb2Co octahedra,  a faceface with one O(4)Ba3Yb2Co octahedra, and faces with two equivalent O(7)Ba2Yb3Co octahedra. The corner-sharing octahedral tilt angles range from 42-55°. In the eighth O site, O(8) is bonded to one Ba(1), one Ba(3), one Yb(3), one Yb(5), one Yb(7), and one Co(1) atom to form distorted OBa2Yb3Co octahedra that share  a cornercorner with one O(1)Ba3Yb2Co octahedra,  a cornercorner with one O(2)Ba3Yb2Co octahedra,  a cornercorner with one O(3)Ba3Yb2Co octahedra,  a cornercorner with one O(4)Ba3Yb2Co octahedra,  a faceface with one O(1)Ba3Yb2Co octahedra,  a faceface with one O(3)Ba3Yb2Co octahedra, and faces with two equivalent O(8)Ba2Yb3Co octahedra. The corner-sharing octahedral tilt angles range from 43-60°. In the ninth O site, O(9) is bonded in a 4-coordinate geometry to one Ba(1), one Ba(2), one Yb(3), one Yb(4), one Yb(6), and one Co(4) atom. In the tenth O site, O(10) is bonded in a 4-coordinate geometry to one Ba(2), one Yb(3), one Yb(4), one Yb(5), and one Co(3) atom. In the eleventh O site, O(11) is bonded in a 5-coordinate geometry to one Ba(4), one Mg(1), one Yb(1), one Yb(2), one Yb(8), and one Co(2) atom. In the twelfth O site, O(12) is bonded in a 5-coordinate geometry to one Mg(1), one Yb(1), one Yb(2), one Yb(7), and one Co(1) atom.