MgFe3Co5O16 crystallizes in the triclinic P1 space group. Mg(1) 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 MgO6 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 48-53°. 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 Mg(1)O6 octahedra, corners with two equivalent Co(5)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 range from 52-53°. 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,  a cornercorner with one Co(5)O4 tetrahedra,  an edgeedge with one Mg(1)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 50-51°. 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,  a cornercorner with one Co(5)O4 tetrahedra,  an edgeedge with one Mg(1)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 are 52°. 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 Mg(1)O6 octahedra, corners with two equivalent Co(5)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 48-51°. 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, corners with three equivalent Co(5)O4 tetrahedra,  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 50-52°. 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 Mg(1)O6 octahedra, corners with two equivalent Co(5)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 48-51°. 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,  a cornercorner with one Co(5)O4 tetrahedra,  an edgeedge with one Mg(1)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 range from 50-52°. In the fifth Co site, Co(5) is bonded to one O(13), one O(2), one O(7), and one O(8) atom to form CoO4 tetrahedra that share  a cornercorner with one Fe(2)O6 octahedra,  a cornercorner with one Fe(3)O6 octahedra,  a cornercorner with one Co(4)O6 octahedra, corners with two equivalent Fe(1)O6 octahedra, corners with two equivalent Co(1)O6 octahedra, corners with two equivalent Co(3)O6 octahedra, and corners with three equivalent Co(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-67°. 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 to one Co(1), one Co(2), one Co(3), and one Co(5) atom to form a mixture of corner and edge-sharing OCo4 tetrahedra. 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 distorted T-shaped 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 to one Fe(1), one Co(1), one Co(2), and one Co(5) atom to form distorted OFeCo3 tetrahedra that share  a cornercorner with one O(2)Co4 tetrahedra,  a cornercorner with one O(8)FeCo3 tetrahedra,  an edgeedge with one O(2)Co4 tetrahedra, and  an edgeedge with one O(8)FeCo3 tetrahedra. In the eighth O site, O(8) is bonded to one Fe(1), one Co(2), one Co(3), and one Co(5) atom to form distorted OFeCo3 tetrahedra that share  a cornercorner with one O(2)Co4 tetrahedra,  a cornercorner with one O(7)FeCo3 tetrahedra,  an edgeedge with one O(2)Co4 tetrahedra, and  an edgeedge with one O(7)FeCo3 tetrahedra. In the ninth O site, O(9) is bonded in a distorted trigonal planar geometry to one Mg(1), one Co(1), and one Co(3) 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 trigonal non-coplanar geometry to one Mg(1), one Fe(2), and one Co(4) atom. In the twelfth O site, O(12) is bonded in a distorted trigonal non-coplanar geometry to one Mg(1), one Fe(3), and one Co(4) atom. In the thirteenth O site, O(13) is bonded in a rectangular see-saw-like geometry to one Fe(2), one Fe(3), one Co(4), and one Co(5) atom. In the fourteenth O site, O(14) is bonded in a distorted trigonal planar geometry to one Mg(1), one Fe(1), and one Co(1) atom. In the fifteenth O site, O(15) is bonded in a distorted trigonal non-coplanar geometry to one Mg(1), one Fe(2), and one Fe(3) atom. In the sixteenth O site, O(16) is bonded in a distorted trigonal planar geometry to one Mg(1), one Fe(1), and one Co(3) atom.
MgFe3Co5O16 crystallizes in the triclinic P1 space group. Mg(1) 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 MgO6 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 48-53°. The Mg(1)-O(11) bond length is 2.11 Å. The Mg(1)-O(12) bond length is 2.12 Å. The Mg(1)-O(14) bond length is 2.04 Å. The Mg(1)-O(15) bond length is 2.18 Å. The Mg(1)-O(16) bond length is 2.04 Å. The Mg(1)-O(9) bond length is 2.23 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 Mg(1)O6 octahedra, corners with two equivalent Co(5)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 range from 52-53°. The Fe(1)-O(14) bond length is 1.93 Å. The Fe(1)-O(16) bond length is 1.93 Å. The Fe(1)-O(3) bond length is 1.93 Å. The Fe(1)-O(4) bond length is 1.97 Å. The Fe(1)-O(7) bond length is 2.09 Å. The Fe(1)-O(8) bond length is 2.09 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,  a cornercorner with one Co(5)O4 tetrahedra,  an edgeedge with one Mg(1)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 50-51°. The Fe(2)-O(1) bond length is 2.05 Å. The Fe(2)-O(10) bond length is 1.96 Å. The Fe(2)-O(11) bond length is 1.91 Å. The Fe(2)-O(13) bond length is 2.04 Å. The Fe(2)-O(15) bond length is 1.89 Å. The Fe(2)-O(5) bond length is 1.94 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,  a cornercorner with one Co(5)O4 tetrahedra,  an edgeedge with one Mg(1)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 are 52°. The Fe(3)-O(10) bond length is 1.99 Å. The Fe(3)-O(12) bond length is 1.91 Å. The Fe(3)-O(13) bond length is 2.04 Å. The Fe(3)-O(15) bond length is 1.90 Å. The Fe(3)-O(5) bond length is 1.94 Å. The Fe(3)-O(6) bond length is 2.00 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 Mg(1)O6 octahedra, corners with two equivalent Co(5)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 48-51°. The Co(1)-O(14) bond length is 1.80 Å. The Co(1)-O(2) bond length is 1.98 Å. The Co(1)-O(3) bond length is 1.92 Å. The Co(1)-O(4) bond length is 1.89 Å. The Co(1)-O(7) bond length is 1.96 Å. The Co(1)-O(9) bond length is 1.84 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, corners with three equivalent Co(5)O4 tetrahedra,  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 50-52°. The Co(2)-O(1) bond length is 1.86 Å. The Co(2)-O(10) bond length is 1.88 Å. The Co(2)-O(2) bond length is 2.01 Å. The Co(2)-O(6) bond length is 1.91 Å. The Co(2)-O(7) bond length is 1.98 Å. The Co(2)-O(8) bond length is 1.99 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 Mg(1)O6 octahedra, corners with two equivalent Co(5)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 48-51°. The Co(3)-O(16) bond length is 1.80 Å. The Co(3)-O(2) bond length is 1.98 Å. The Co(3)-O(3) bond length is 1.92 Å. The Co(3)-O(4) bond length is 1.91 Å. The Co(3)-O(8) bond length is 1.95 Å. The Co(3)-O(9) bond length is 1.84 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,  a cornercorner with one Co(5)O4 tetrahedra,  an edgeedge with one Mg(1)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 range from 50-52°. The Co(4)-O(1) bond length is 1.95 Å. The Co(4)-O(11) bond length is 1.84 Å. The Co(4)-O(12) bond length is 1.86 Å. The Co(4)-O(13) bond length is 1.91 Å. The Co(4)-O(5) bond length is 1.88 Å. The Co(4)-O(6) bond length is 1.90 Å. In the fifth Co site, Co(5) is bonded to one O(13), one O(2), one O(7), and one O(8) atom to form CoO4 tetrahedra that share  a cornercorner with one Fe(2)O6 octahedra,  a cornercorner with one Fe(3)O6 octahedra,  a cornercorner with one Co(4)O6 octahedra, corners with two equivalent Fe(1)O6 octahedra, corners with two equivalent Co(1)O6 octahedra, corners with two equivalent Co(3)O6 octahedra, and corners with three equivalent Co(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-67°. The Co(5)-O(13) bond length is 1.84 Å. The Co(5)-O(2) bond length is 1.95 Å. The Co(5)-O(7) bond length is 1.86 Å. The Co(5)-O(8) bond length is 1.86 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 to one Co(1), one Co(2), one Co(3), and one Co(5) atom to form a mixture of corner and edge-sharing OCo4 tetrahedra. 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 distorted T-shaped 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 to one Fe(1), one Co(1), one Co(2), and one Co(5) atom to form distorted OFeCo3 tetrahedra that share  a cornercorner with one O(2)Co4 tetrahedra,  a cornercorner with one O(8)FeCo3 tetrahedra,  an edgeedge with one O(2)Co4 tetrahedra, and  an edgeedge with one O(8)FeCo3 tetrahedra. In the eighth O site, O(8) is bonded to one Fe(1), one Co(2), one Co(3), and one Co(5) atom to form distorted OFeCo3 tetrahedra that share  a cornercorner with one O(2)Co4 tetrahedra,  a cornercorner with one O(7)FeCo3 tetrahedra,  an edgeedge with one O(2)Co4 tetrahedra, and  an edgeedge with one O(7)FeCo3 tetrahedra. In the ninth O site, O(9) is bonded in a distorted trigonal planar geometry to one Mg(1), one Co(1), and one Co(3) 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 trigonal non-coplanar geometry to one Mg(1), one Fe(2), and one Co(4) atom. In the twelfth O site, O(12) is bonded in a distorted trigonal non-coplanar geometry to one Mg(1), one Fe(3), and one Co(4) atom. In the thirteenth O site, O(13) is bonded in a rectangular see-saw-like geometry to one Fe(2), one Fe(3), one Co(4), and one Co(5) atom. In the fourteenth O site, O(14) is bonded in a distorted trigonal planar geometry to one Mg(1), one Fe(1), and one Co(1) atom. In the fifteenth O site, O(15) is bonded in a distorted trigonal non-coplanar geometry to one Mg(1), one Fe(2), and one Fe(3) atom. In the sixteenth O site, O(16) is bonded in a distorted trigonal planar geometry to one Mg(1), one Fe(1), and one Co(3) atom.