MgFe3Co5O16 crystallizes in the monoclinic Cm space group. Mg(1) is bonded to one O(4), one O(8), and two equivalent O(6) atoms to form MgO4 tetrahedra that share  a cornercorner with one Co(2)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, and corners with four equivalent Co(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-66°. There are two inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to one O(3), one O(5), two equivalent O(11), and two equivalent O(9) atoms to form distorted FeO6 octahedra that share corners with three equivalent Co(3)O6 octahedra, corners with four equivalent Co(1)O6 octahedra,  an edgeedge with one Co(2)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 3-60°. In the second Fe site, Fe(2) is bonded to one O(1), one O(10), one O(12), one O(5), one O(8), and one O(9) atom to form FeO6 octahedra that share  a cornercorner with one Mg(1)O4 tetrahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, edges with two equivalent Co(2)O6 octahedra, and edges with two equivalent Co(3)O6 octahedra. There are four inequivalent Co sites. In the first Co site, Co(1) is bonded to one O(11), one O(2), one O(3), one O(4), one O(6), and one O(7) atom to form distorted CoO6 octahedra that share corners with two equivalent Fe(1)O6 octahedra, corners with two equivalent Co(4)O6 octahedra, corners with two equivalent Mg(1)O4 tetrahedra, and edges with two equivalent Co(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 47-60°. In the second Co site, Co(2) is bonded to one O(12), one O(8), two equivalent O(1), and two equivalent O(9) atoms to form CoO6 octahedra that share corners with three equivalent Co(4)O6 octahedra,  a cornercorner with one Mg(1)O4 tetrahedra,  an edgeedge with one Fe(1)O6 octahedra, edges with two equivalent Co(3)O6 octahedra, and edges with four equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 9-18°. In the third Co site, Co(3) is bonded to one O(10), one O(5), two equivalent O(1), and two equivalent O(9) atoms to form CoO6 octahedra that share corners with three equivalent Fe(1)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra, edges with two equivalent Co(2)O6 octahedra, and edges with four equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 3-25°. In the fourth Co site, Co(4) is bonded to one O(12), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form CoO6 octahedra that share corners with three equivalent Co(2)O6 octahedra, corners with four equivalent Co(1)O6 octahedra,  an edgeedge with one Co(3)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, and edges with two equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 9-56°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a distorted trigonal non-coplanar geometry to one Fe(2), one Co(2), and one Co(3) atom. In the second O site, O(2) is bonded in a water-like geometry to two equivalent Co(1) atoms. In the third O site, O(3) is bonded in a trigonal planar geometry to one Fe(1) and two equivalent Co(1) atoms. In the fourth O site, O(4) is bonded in a trigonal planar geometry to one Mg(1) and two equivalent Co(1) atoms. In the fifth O site, O(5) is bonded in a rectangular see-saw-like geometry to one Fe(1), two equivalent Fe(2), and one Co(3) atom. In the sixth O site, O(6) is bonded in a bent 120 degrees geometry to one Mg(1) and one Co(1) atom. In the seventh O site, O(7) is bonded in a trigonal planar geometry to one Co(4) and two equivalent Co(1) atoms. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Mg(1), two equivalent Fe(2), and one Co(2) atom. In the ninth O site, O(9) is bonded to one Fe(1), one Fe(2), one Co(2), one Co(3), and one Co(4) atom to form edge-sharing OFe2Co3 square pyramids. In the tenth O site, O(10) is bonded in a distorted trigonal non-coplanar geometry to two equivalent Fe(2) and one Co(3) atom. In the eleventh O site, O(11) is bonded in a distorted trigonal planar geometry to one Fe(1), one Co(1), and one Co(4) atom. In the twelfth O site, O(12) is bonded in a rectangular see-saw-like geometry to two equivalent Fe(2), one Co(2), and one Co(4) atom.
MgFe3Co5O16 crystallizes in the monoclinic Cm space group. Mg(1) is bonded to one O(4), one O(8), and two equivalent O(6) atoms to form MgO4 tetrahedra that share  a cornercorner with one Co(2)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, and corners with four equivalent Co(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-66°. The Mg(1)-O(4) bond length is 1.99 Å. The Mg(1)-O(8) bond length is 2.00 Å. Both Mg(1)-O(6) bond lengths are 2.01 Å. There are two inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to one O(3), one O(5), two equivalent O(11), and two equivalent O(9) atoms to form distorted FeO6 octahedra that share corners with three equivalent Co(3)O6 octahedra, corners with four equivalent Co(1)O6 octahedra,  an edgeedge with one Co(2)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 3-60°. The Fe(1)-O(3) bond length is 1.99 Å. The Fe(1)-O(5) bond length is 2.08 Å. Both Fe(1)-O(11) bond lengths are 1.89 Å. Both Fe(1)-O(9) bond lengths are 2.34 Å. In the second Fe site, Fe(2) is bonded to one O(1), one O(10), one O(12), one O(5), one O(8), and one O(9) atom to form FeO6 octahedra that share  a cornercorner with one Mg(1)O4 tetrahedra,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra, edges with two equivalent Fe(2)O6 octahedra, edges with two equivalent Co(2)O6 octahedra, and edges with two equivalent Co(3)O6 octahedra. The Fe(2)-O(1) bond length is 1.93 Å. The Fe(2)-O(10) bond length is 1.96 Å. The Fe(2)-O(12) bond length is 2.07 Å. The Fe(2)-O(5) bond length is 2.03 Å. The Fe(2)-O(8) bond length is 1.98 Å. The Fe(2)-O(9) bond length is 2.08 Å. There are four inequivalent Co sites. In the first Co site, Co(1) is bonded to one O(11), one O(2), one O(3), one O(4), one O(6), and one O(7) atom to form distorted CoO6 octahedra that share corners with two equivalent Fe(1)O6 octahedra, corners with two equivalent Co(4)O6 octahedra, corners with two equivalent Mg(1)O4 tetrahedra, and edges with two equivalent Co(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 47-60°. The Co(1)-O(11) bond length is 2.10 Å. The Co(1)-O(2) bond length is 1.84 Å. The Co(1)-O(3) bond length is 1.88 Å. The Co(1)-O(4) bond length is 1.90 Å. The Co(1)-O(6) bond length is 1.67 Å. The Co(1)-O(7) bond length is 1.98 Å. In the second Co site, Co(2) is bonded to one O(12), one O(8), two equivalent O(1), and two equivalent O(9) atoms to form CoO6 octahedra that share corners with three equivalent Co(4)O6 octahedra,  a cornercorner with one Mg(1)O4 tetrahedra,  an edgeedge with one Fe(1)O6 octahedra, edges with two equivalent Co(3)O6 octahedra, and edges with four equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 9-18°. The Co(2)-O(12) bond length is 1.93 Å. The Co(2)-O(8) bond length is 2.00 Å. Both Co(2)-O(1) bond lengths are 1.95 Å. Both Co(2)-O(9) bond lengths are 2.11 Å. In the third Co site, Co(3) is bonded to one O(10), one O(5), two equivalent O(1), and two equivalent O(9) atoms to form CoO6 octahedra that share corners with three equivalent Fe(1)O6 octahedra,  an edgeedge with one Co(4)O6 octahedra, edges with two equivalent Co(2)O6 octahedra, and edges with four equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 3-25°. The Co(3)-O(10) bond length is 1.84 Å. The Co(3)-O(5) bond length is 1.94 Å. Both Co(3)-O(1) bond lengths are 1.87 Å. Both Co(3)-O(9) bond lengths are 1.98 Å. In the fourth Co site, Co(4) is bonded to one O(12), one O(7), two equivalent O(11), and two equivalent O(9) atoms to form CoO6 octahedra that share corners with three equivalent Co(2)O6 octahedra, corners with four equivalent Co(1)O6 octahedra,  an edgeedge with one Co(3)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, and edges with two equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 9-56°. The Co(4)-O(12) bond length is 1.98 Å. The Co(4)-O(7) bond length is 1.89 Å. Both Co(4)-O(11) bond lengths are 1.83 Å. Both Co(4)-O(9) bond lengths are 2.09 Å. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a distorted trigonal non-coplanar geometry to one Fe(2), one Co(2), and one Co(3) atom. In the second O site, O(2) is bonded in a water-like geometry to two equivalent Co(1) atoms. In the third O site, O(3) is bonded in a trigonal planar geometry to one Fe(1) and two equivalent Co(1) atoms. In the fourth O site, O(4) is bonded in a trigonal planar geometry to one Mg(1) and two equivalent Co(1) atoms. In the fifth O site, O(5) is bonded in a rectangular see-saw-like geometry to one Fe(1), two equivalent Fe(2), and one Co(3) atom. In the sixth O site, O(6) is bonded in a bent 120 degrees geometry to one Mg(1) and one Co(1) atom. In the seventh O site, O(7) is bonded in a trigonal planar geometry to one Co(4) and two equivalent Co(1) atoms. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Mg(1), two equivalent Fe(2), and one Co(2) atom. In the ninth O site, O(9) is bonded to one Fe(1), one Fe(2), one Co(2), one Co(3), and one Co(4) atom to form edge-sharing OFe2Co3 square pyramids. In the tenth O site, O(10) is bonded in a distorted trigonal non-coplanar geometry to two equivalent Fe(2) and one Co(3) atom. In the eleventh O site, O(11) is bonded in a distorted trigonal planar geometry to one Fe(1), one Co(1), and one Co(4) atom. In the twelfth O site, O(12) is bonded in a rectangular see-saw-like geometry to two equivalent Fe(2), one Co(2), and one Co(4) atom.