MgFe3Co5O16 crystallizes in the triclinic P1 space group. Mg(1) is bonded to one O(1), one O(13), one O(4), one O(6), one O(7), and one O(8) atom to form MgO6 octahedra that share corners with two equivalent Fe(2)O6 octahedra, corners with two equivalent Fe(3)O6 octahedra, corners with three equivalent Fe(1)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra,  an edgeedge with one Co(3)O6 octahedra, edges with two equivalent Co(2)O6 octahedra, and  a faceface with one Co(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 11-50°. There are three inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to one O(14), one O(16), one O(3), one O(4), one O(7), and one O(8) atom to form FeO6 octahedra that share corners with two equivalent Co(5)O6 octahedra, corners with three equivalent Mg(1)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra, edges with two equivalent Co(1)O6 octahedra, and edges with two equivalent Co(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 11-52°. In the second Fe site, Fe(2) is bonded to one O(1), one O(10), one O(11), one O(13), one O(15), and one O(5) atom to form FeO6 octahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent Co(2)O6 octahedra,  an edgeedge with one Co(5)O6 octahedra, edges with two equivalent Fe(3)O6 octahedra, and edges with two equivalent Co(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 48-53°. In the third Fe site, Fe(3) is bonded to one O(10), one O(12), one O(13), one O(15), one O(5), and one O(6) atom to form FeO6 octahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent Co(2)O6 octahedra,  an edgeedge with one Co(5)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, and edges with two equivalent Co(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 48-54°. There are five inequivalent Co sites. In the first Co site, Co(1) is bonded to one O(14), one O(2), one O(3), one O(4), one O(7), and one O(9) atom to form CoO6 octahedra that share corners with two equivalent Co(5)O6 octahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, and edges with two equivalent Co(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-52°. In the second Co site, Co(2) is bonded to one O(1), one O(10), one O(2), one O(6), one O(7), and one O(8) atom to form CoO6 octahedra that share corners with two equivalent Fe(2)O6 octahedra, corners with two equivalent Fe(3)O6 octahedra, corners with two equivalent Co(4)O6 octahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra,  an edgeedge with one Co(3)O6 octahedra, and edges with two equivalent Mg(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 46-54°. In the third Co site, Co(3) is bonded to one O(16), one O(2), one O(3), one O(4), one O(8), and one O(9) atom to form CoO6 octahedra that share corners with two equivalent Co(5)O6 octahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, and edges with two equivalent Co(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-52°. In the fourth Co site, Co(4) is bonded to one O(1), one O(11), one O(12), one O(13), one O(5), and one O(6) atom to form CoO6 octahedra that share corners with two equivalent Co(2)O6 octahedra,  an edgeedge with one Co(5)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, edges with two equivalent Fe(3)O6 octahedra, and  a faceface with one Mg(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 46-47°. In the fifth Co site, Co(5) is bonded to one O(11), one O(12), one O(14), one O(15), one O(16), and one O(9) atom to form CoO6 octahedra that share corners with two equivalent Fe(1)O6 octahedra, corners with two equivalent Co(1)O6 octahedra, corners with two equivalent Co(3)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra,  an edgeedge with one Fe(3)O6 octahedra, and  an edgeedge with one Co(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-52°. There are sixteen inequivalent O sites. In the first O site, O(1) is bonded in a distorted rectangular see-saw-like geometry to one Mg(1), one Fe(2), one Co(2), and one Co(4) atom. In the second O site, O(2) is bonded in a distorted trigonal non-coplanar geometry to one Co(1), one Co(2), and one Co(3) atom. In the third O site, O(3) is bonded in a distorted trigonal non-coplanar geometry to one Fe(1), one Co(1), and one Co(3) atom. In the fourth O site, O(4) is bonded in a rectangular see-saw-like geometry to one Mg(1), one Fe(1), one Co(1), and one Co(3) atom. In the fifth O site, O(5) is bonded in a distorted trigonal non-coplanar geometry to one Fe(2), one Fe(3), and one Co(4) atom. In the sixth O site, O(6) is bonded in a distorted rectangular see-saw-like geometry to one Mg(1), one Fe(3), one Co(2), and one Co(4) atom. In the seventh O site, O(7) is bonded in a see-saw-like geometry to one Mg(1), one Fe(1), one Co(1), and one Co(2) atom. In the eighth O site, O(8) is bonded in a see-saw-like geometry to one Mg(1), one Fe(1), one Co(2), and one Co(3) atom. In the ninth O site, O(9) is bonded in a trigonal planar geometry to one Co(1), one Co(3), and one Co(5) atom. In the tenth O site, O(10) is bonded in a distorted trigonal planar geometry to one Fe(2), one Fe(3), and one Co(2) atom. In the eleventh O site, O(11) is bonded in a distorted T-shaped geometry to one Fe(2), one Co(4), and one Co(5) atom. In the twelfth O site, O(12) is bonded in a 3-coordinate geometry to one Fe(3), one Co(4), and one Co(5) atom. In the thirteenth O site, O(13) is bonded in a trigonal pyramidal geometry to one Mg(1), one Fe(2), one Fe(3), and one Co(4) atom. In the fourteenth O site, O(14) is bonded in a distorted trigonal planar geometry to one Fe(1), one Co(1), and one Co(5) atom. In the fifteenth O site, O(15) is bonded in a trigonal non-coplanar geometry to one Fe(2), one Fe(3), and one Co(5) atom. In the sixteenth O site, O(16) is bonded in a distorted trigonal planar geometry to one Fe(1), one Co(3), and one Co(5) atom.
MgFe3Co5O16 crystallizes in the triclinic P1 space group. Mg(1) is bonded to one O(1), one O(13), one O(4), one O(6), one O(7), and one O(8) atom to form MgO6 octahedra that share corners with two equivalent Fe(2)O6 octahedra, corners with two equivalent Fe(3)O6 octahedra, corners with three equivalent Fe(1)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra,  an edgeedge with one Co(3)O6 octahedra, edges with two equivalent Co(2)O6 octahedra, and  a faceface with one Co(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 11-50°. The Mg(1)-O(1) bond length is 2.11 Å. The Mg(1)-O(13) bond length is 2.03 Å. The Mg(1)-O(4) bond length is 2.00 Å. The Mg(1)-O(6) bond length is 2.10 Å. The Mg(1)-O(7) bond length is 2.00 Å. The Mg(1)-O(8) bond length is 2.01 Å. There are three inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to one O(14), one O(16), one O(3), one O(4), one O(7), and one O(8) atom to form FeO6 octahedra that share corners with two equivalent Co(5)O6 octahedra, corners with three equivalent Mg(1)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra, edges with two equivalent Co(1)O6 octahedra, and edges with two equivalent Co(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 11-52°. The Fe(1)-O(14) bond length is 1.98 Å. The Fe(1)-O(16) bond length is 1.98 Å. The Fe(1)-O(3) bond length is 1.99 Å. The Fe(1)-O(4) bond length is 1.97 Å. The Fe(1)-O(7) bond length is 2.07 Å. The Fe(1)-O(8) bond length is 2.07 Å. In the second Fe site, Fe(2) is bonded to one O(1), one O(10), one O(11), one O(13), one O(15), and one O(5) atom to form FeO6 octahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent Co(2)O6 octahedra,  an edgeedge with one Co(5)O6 octahedra, edges with two equivalent Fe(3)O6 octahedra, and edges with two equivalent Co(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 48-53°. The Fe(2)-O(1) bond length is 2.00 Å. The Fe(2)-O(10) bond length is 1.96 Å. The Fe(2)-O(11) bond length is 2.08 Å. The Fe(2)-O(13) bond length is 1.99 Å. The Fe(2)-O(15) bond length is 1.97 Å. The Fe(2)-O(5) bond length is 1.96 Å. In the third Fe site, Fe(3) is bonded to one O(10), one O(12), one O(13), one O(15), one O(5), and one O(6) atom to form FeO6 octahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent Co(2)O6 octahedra,  an edgeedge with one Co(5)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, and edges with two equivalent Co(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 48-54°. The Fe(3)-O(10) bond length is 1.99 Å. The Fe(3)-O(12) bond length is 2.11 Å. The Fe(3)-O(13) bond length is 1.99 Å. The Fe(3)-O(15) bond length is 2.04 Å. The Fe(3)-O(5) bond length is 1.95 Å. The Fe(3)-O(6) bond length is 1.98 Å. There are five inequivalent Co sites. In the first Co site, Co(1) is bonded to one O(14), one O(2), one O(3), one O(4), one O(7), and one O(9) atom to form CoO6 octahedra that share corners with two equivalent Co(5)O6 octahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, and edges with two equivalent Co(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-52°. The Co(1)-O(14) bond length is 1.84 Å. The Co(1)-O(2) bond length is 1.93 Å. The Co(1)-O(3) bond length is 1.86 Å. The Co(1)-O(4) bond length is 1.94 Å. The Co(1)-O(7) bond length is 1.93 Å. The Co(1)-O(9) bond length is 1.93 Å. In the second Co site, Co(2) is bonded to one O(1), one O(10), one O(2), one O(6), one O(7), and one O(8) atom to form CoO6 octahedra that share corners with two equivalent Fe(2)O6 octahedra, corners with two equivalent Fe(3)O6 octahedra, corners with two equivalent Co(4)O6 octahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Co(1)O6 octahedra,  an edgeedge with one Co(3)O6 octahedra, and edges with two equivalent Mg(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 46-54°. The Co(2)-O(1) bond length is 1.96 Å. The Co(2)-O(10) bond length is 1.88 Å. The Co(2)-O(2) bond length is 1.97 Å. The Co(2)-O(6) bond length is 1.95 Å. The Co(2)-O(7) bond length is 1.93 Å. The Co(2)-O(8) bond length is 1.93 Å. In the third Co site, Co(3) is bonded to one O(16), one O(2), one O(3), one O(4), one O(8), and one O(9) atom to form CoO6 octahedra that share corners with two equivalent Co(5)O6 octahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Co(2)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, and edges with two equivalent Co(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-52°. The Co(3)-O(16) bond length is 1.84 Å. The Co(3)-O(2) bond length is 1.93 Å. The Co(3)-O(3) bond length is 1.86 Å. The Co(3)-O(4) bond length is 1.94 Å. The Co(3)-O(8) bond length is 1.93 Å. The Co(3)-O(9) bond length is 1.92 Å. In the fourth Co site, Co(4) is bonded to one O(1), one O(11), one O(12), one O(13), one O(5), and one O(6) atom to form CoO6 octahedra that share corners with two equivalent Co(2)O6 octahedra,  an edgeedge with one Co(5)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, edges with two equivalent Fe(3)O6 octahedra, and  a faceface with one Mg(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 46-47°. The Co(4)-O(1) bond length is 2.07 Å. The Co(4)-O(11) bond length is 1.84 Å. The Co(4)-O(12) bond length is 1.80 Å. The Co(4)-O(13) bond length is 1.89 Å. The Co(4)-O(5) bond length is 1.81 Å. The Co(4)-O(6) bond length is 2.09 Å. In the fifth Co site, Co(5) is bonded to one O(11), one O(12), one O(14), one O(15), one O(16), and one O(9) atom to form CoO6 octahedra that share corners with two equivalent Fe(1)O6 octahedra, corners with two equivalent Co(1)O6 octahedra, corners with two equivalent Co(3)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra,  an edgeedge with one Fe(3)O6 octahedra, and  an edgeedge with one Co(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-52°. The Co(5)-O(11) bond length is 1.89 Å. The Co(5)-O(12) bond length is 1.90 Å. The Co(5)-O(14) bond length is 1.90 Å. The Co(5)-O(15) bond length is 1.87 Å. The Co(5)-O(16) bond length is 1.89 Å. The Co(5)-O(9) bond length is 1.96 Å. There are sixteen inequivalent O sites. In the first O site, O(1) is bonded in a distorted rectangular see-saw-like geometry to one Mg(1), one Fe(2), one Co(2), and one Co(4) atom. In the second O site, O(2) is bonded in a distorted trigonal non-coplanar geometry to one Co(1), one Co(2), and one Co(3) atom. In the third O site, O(3) is bonded in a distorted trigonal non-coplanar geometry to one Fe(1), one Co(1), and one Co(3) atom. In the fourth O site, O(4) is bonded in a rectangular see-saw-like geometry to one Mg(1), one Fe(1), one Co(1), and one Co(3) atom. In the fifth O site, O(5) is bonded in a distorted trigonal non-coplanar geometry to one Fe(2), one Fe(3), and one Co(4) atom. In the sixth O site, O(6) is bonded in a distorted rectangular see-saw-like geometry to one Mg(1), one Fe(3), one Co(2), and one Co(4) atom. In the seventh O site, O(7) is bonded in a see-saw-like geometry to one Mg(1), one Fe(1), one Co(1), and one Co(2) atom. In the eighth O site, O(8) is bonded in a see-saw-like geometry to one Mg(1), one Fe(1), one Co(2), and one Co(3) atom. In the ninth O site, O(9) is bonded in a trigonal planar geometry to one Co(1), one Co(3), and one Co(5) atom. In the tenth O site, O(10) is bonded in a distorted trigonal planar geometry to one Fe(2), one Fe(3), and one Co(2) atom. In the eleventh O site, O(11) is bonded in a distorted T-shaped geometry to one Fe(2), one Co(4), and one Co(5) atom. In the twelfth O site, O(12) is bonded in a 3-coordinate geometry to one Fe(3), one Co(4), and one Co(5) atom. In the thirteenth O site, O(13) is bonded in a trigonal pyramidal geometry to one Mg(1), one Fe(2), one Fe(3), and one Co(4) atom. In the fourteenth O site, O(14) is bonded in a distorted trigonal planar geometry to one Fe(1), one Co(1), and one Co(5) atom. In the fifteenth O site, O(15) is bonded in a trigonal non-coplanar geometry to one Fe(2), one Fe(3), and one Co(5) atom. In the sixteenth O site, O(16) is bonded in a distorted trigonal planar geometry to one Fe(1), one Co(3), and one Co(5) atom.