MgFe3Co5O16 crystallizes in the triclinic P1 space group. Mg(1) is bonded to one O(11), one O(12), one O(15), and one O(3) atom to form MgO4 tetrahedra that share  a cornercorner with one Fe(1)O6 octahedra,  a cornercorner with one Co(1)O6 octahedra,  a cornercorner with one Co(3)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, corners with two equivalent Fe(3)O6 octahedra, corners with two equivalent Co(4)O6 octahedra, and corners with three equivalent Co(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-67°. 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,  a cornercorner with one Mg(1)O4 tetrahedra,  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 are 50°. 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 Co(2)O6 octahedra, corners with two equivalent Mg(1)O4 tetrahedra,  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 49-50°. 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 Co(2)O6 octahedra, corners with two equivalent Mg(1)O4 tetrahedra,  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 49-50°. 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,  a cornercorner with one Mg(1)O4 tetrahedra,  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, and  an edgeedge with one Co(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 48-50°. 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,  a cornercorner with one Mg(1)O4 tetrahedra,  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, corners with two equivalent Mg(1)O4 tetrahedra,  an edgeedge with one Co(5)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, and edges with two equivalent Fe(3)O6 octahedra. The corner-sharing octahedral tilt angles are 48°. 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, corners with three equivalent Mg(1)O4 tetrahedra,  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 50-52°. There are sixteen inequivalent O sites. In the first O site, O(1) is bonded in a distorted trigonal planar geometry to 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 to one Mg(1), one Fe(1), one Co(1), and one Co(3) atom to form distorted OMgFeCo2 tetrahedra that share  a cornercorner with one O(15)MgFe2Co tetrahedra,  a cornercorner with one O(11)MgFeCo2 tetrahedra, and  a cornercorner with one O(12)MgFeCo2 tetrahedra. In the fourth O site, O(4) is bonded in a distorted trigonal non-coplanar geometry to 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 trigonal planar geometry to one Fe(3), one Co(2), and one Co(4) atom. In the seventh O site, O(7) is bonded in a distorted trigonal non-coplanar geometry to one Fe(1), one Co(1), and one Co(2) atom. In the eighth O site, O(8) is bonded in a distorted trigonal non-coplanar geometry to one Fe(1), one Co(2), and one Co(3) atom. In the ninth O site, O(9) is bonded in a distorted 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 to one Mg(1), one Fe(2), one Co(4), and one Co(5) atom to form distorted OMgFeCo2 tetrahedra that share  a cornercorner with one O(15)MgFe2Co tetrahedra,  a cornercorner with one O(12)MgFeCo2 tetrahedra,  a cornercorner with one O(3)MgFeCo2 tetrahedra,  an edgeedge with one O(15)MgFe2Co tetrahedra, and  an edgeedge with one O(12)MgFeCo2 tetrahedra. In the twelfth O site, O(12) is bonded to one Mg(1), one Fe(3), one Co(4), and one Co(5) atom to form distorted OMgFeCo2 tetrahedra that share  a cornercorner with one O(15)MgFe2Co tetrahedra,  a cornercorner with one O(11)MgFeCo2 tetrahedra,  a cornercorner with one O(3)MgFeCo2 tetrahedra,  an edgeedge with one O(15)MgFe2Co tetrahedra, and  an edgeedge with one O(11)MgFeCo2 tetrahedra. In the thirteenth O site, O(13) is bonded in a distorted trigonal non-coplanar geometry to 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 to one Mg(1), one Fe(2), one Fe(3), and one Co(5) atom to form a mixture of distorted corner and edge-sharing OMgFe2Co tetrahedra. 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(11), one O(12), one O(15), and one O(3) atom to form MgO4 tetrahedra that share  a cornercorner with one Fe(1)O6 octahedra,  a cornercorner with one Co(1)O6 octahedra,  a cornercorner with one Co(3)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, corners with two equivalent Fe(3)O6 octahedra, corners with two equivalent Co(4)O6 octahedra, and corners with three equivalent Co(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-67°. The Mg(1)-O(11) bond length is 1.95 Å. The Mg(1)-O(12) bond length is 1.96 Å. The Mg(1)-O(15) bond length is 1.93 Å. The Mg(1)-O(3) bond length is 1.98 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,  a cornercorner with one Mg(1)O4 tetrahedra,  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 are 50°. The Fe(1)-O(14) bond length is 2.01 Å. The Fe(1)-O(16) bond length is 2.00 Å. The Fe(1)-O(3) bond length is 2.02 Å. The Fe(1)-O(4) bond length is 1.95 Å. The Fe(1)-O(7) bond length is 2.02 Å. The Fe(1)-O(8) bond length is 2.02 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 Co(2)O6 octahedra, corners with two equivalent Mg(1)O4 tetrahedra,  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 49-50°. The Fe(2)-O(1) bond length is 2.04 Å. The Fe(2)-O(10) bond length is 1.95 Å. The Fe(2)-O(11) bond length is 2.07 Å. The Fe(2)-O(13) bond length is 1.97 Å. The Fe(2)-O(15) bond length is 2.01 Å. The Fe(2)-O(5) bond length is 1.97 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 Co(2)O6 octahedra, corners with two equivalent Mg(1)O4 tetrahedra,  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 49-50°. The Fe(3)-O(10) bond length is 1.94 Å. The Fe(3)-O(12) bond length is 2.08 Å. The Fe(3)-O(13) bond length is 1.96 Å. The Fe(3)-O(15) bond length is 2.00 Å. The Fe(3)-O(5) bond length is 1.97 Å. The Fe(3)-O(6) bond length is 2.04 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,  a cornercorner with one Mg(1)O4 tetrahedra,  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 1.90 Å. The Co(1)-O(2) bond length is 1.92 Å. The Co(1)-O(3) bond length is 1.94 Å. The Co(1)-O(4) bond length is 1.91 Å. The Co(1)-O(7) bond length is 1.88 Å. The Co(1)-O(9) bond length is 1.87 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, and  an edgeedge with one Co(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 48-50°. The Co(2)-O(1) bond length is 1.89 Å. The Co(2)-O(10) bond length is 1.88 Å. The Co(2)-O(2) bond length is 1.90 Å. The Co(2)-O(6) bond length is 1.89 Å. The Co(2)-O(7) bond length is 1.88 Å. The Co(2)-O(8) bond length is 1.88 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,  a cornercorner with one Mg(1)O4 tetrahedra,  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 1.90 Å. The Co(3)-O(2) bond length is 1.92 Å. The Co(3)-O(3) bond length is 1.93 Å. The Co(3)-O(4) bond length is 1.91 Å. The Co(3)-O(8) bond length is 1.88 Å. The Co(3)-O(9) bond length is 1.87 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, corners with two equivalent Mg(1)O4 tetrahedra,  an edgeedge with one Co(5)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, and edges with two equivalent Fe(3)O6 octahedra. The corner-sharing octahedral tilt angles are 48°. The Co(4)-O(1) bond length is 1.91 Å. The Co(4)-O(11) bond length is 2.05 Å. The Co(4)-O(12) bond length is 2.07 Å. The Co(4)-O(13) bond length is 1.85 Å. The Co(4)-O(5) bond length is 1.85 Å. The Co(4)-O(6) bond length is 1.92 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, corners with three equivalent Mg(1)O4 tetrahedra,  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 50-52°. The Co(5)-O(11) bond length is 1.97 Å. The Co(5)-O(12) bond length is 1.95 Å. The Co(5)-O(14) bond length is 1.90 Å. The Co(5)-O(15) bond length is 2.02 Å. The Co(5)-O(16) bond length is 1.92 Å. The Co(5)-O(9) bond length is 2.17 Å. There are sixteen inequivalent O sites. In the first O site, O(1) is bonded in a distorted trigonal planar geometry to 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 to one Mg(1), one Fe(1), one Co(1), and one Co(3) atom to form distorted OMgFeCo2 tetrahedra that share  a cornercorner with one O(15)MgFe2Co tetrahedra,  a cornercorner with one O(11)MgFeCo2 tetrahedra, and  a cornercorner with one O(12)MgFeCo2 tetrahedra. In the fourth O site, O(4) is bonded in a distorted trigonal non-coplanar geometry to 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 trigonal planar geometry to one Fe(3), one Co(2), and one Co(4) atom. In the seventh O site, O(7) is bonded in a distorted trigonal non-coplanar geometry to one Fe(1), one Co(1), and one Co(2) atom. In the eighth O site, O(8) is bonded in a distorted trigonal non-coplanar geometry to one Fe(1), one Co(2), and one Co(3) atom. In the ninth O site, O(9) is bonded in a distorted 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 to one Mg(1), one Fe(2), one Co(4), and one Co(5) atom to form distorted OMgFeCo2 tetrahedra that share  a cornercorner with one O(15)MgFe2Co tetrahedra,  a cornercorner with one O(12)MgFeCo2 tetrahedra,  a cornercorner with one O(3)MgFeCo2 tetrahedra,  an edgeedge with one O(15)MgFe2Co tetrahedra, and  an edgeedge with one O(12)MgFeCo2 tetrahedra. In the twelfth O site, O(12) is bonded to one Mg(1), one Fe(3), one Co(4), and one Co(5) atom to form distorted OMgFeCo2 tetrahedra that share  a cornercorner with one O(15)MgFe2Co tetrahedra,  a cornercorner with one O(11)MgFeCo2 tetrahedra,  a cornercorner with one O(3)MgFeCo2 tetrahedra,  an edgeedge with one O(15)MgFe2Co tetrahedra, and  an edgeedge with one O(11)MgFeCo2 tetrahedra. In the thirteenth O site, O(13) is bonded in a distorted trigonal non-coplanar geometry to 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 to one Mg(1), one Fe(2), one Fe(3), and one Co(5) atom to form a mixture of distorted corner and edge-sharing OMgFe2Co tetrahedra. 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.