MgFe4(CoO4)2 crystallizes in the monoclinic Cm space group. Mg(1) is bonded to one O(5), one O(6), and two equivalent O(2) atoms to form distorted MgO4 tetrahedra that share corners with three equivalent Co(1)O6 octahedra, corners with three equivalent Co(2)O6 octahedra, corners with four equivalent Fe(1)O6 octahedra, and  an edgeedge with one Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 12-69°. There are three inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to one O(5), one O(6), two equivalent O(2), and two equivalent O(4) atoms to form distorted FeO6 octahedra that share corners with two equivalent Co(1)O6 octahedra, corners with two equivalent Co(2)O6 octahedra, corners with four equivalent Mg(1)O4 tetrahedra, edges with two equivalent Fe(2)O6 octahedra,  a faceface with one Co(1)O6 octahedra, and  a faceface with one Co(2)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(3), two equivalent O(2), and two equivalent O(4) atoms to form FeO6 octahedra that share corners with two equivalent Co(1)O6 octahedra, corners with two equivalent Co(2)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra,  an edgeedge with one Mg(1)O4 tetrahedra,  a faceface with one Co(1)O6 octahedra, and  a faceface with one Co(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 44-49°. In the third Fe site, Fe(3) is bonded in a 5-coordinate geometry to one O(1), one O(3), one O(4), one O(5), and one O(6) atom. There are two inequivalent Co sites. In the first Co site, Co(1) is bonded to one O(1), one O(6), two equivalent O(2), and two equivalent O(4) atoms to form distorted CoO6 octahedra that share corners with two equivalent Fe(1)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, corners with three equivalent Mg(1)O4 tetrahedra, edges with two equivalent Co(2)O6 octahedra,  a faceface with one Fe(1)O6 octahedra, and  a faceface with one Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 44-53°. In the second Co site, Co(2) is bonded to one O(3), one O(5), two equivalent O(2), and two equivalent O(4) atoms to form distorted CoO6 octahedra that share corners with two equivalent Fe(1)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, corners with three equivalent Mg(1)O4 tetrahedra, edges with two equivalent Co(1)O6 octahedra,  a faceface with one Fe(1)O6 octahedra, and  a faceface with one Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 49-52°. There are six inequivalent O sites. In the first O site, O(1) is bonded to one Fe(2), two equivalent Fe(3), and one Co(1) atom to form OFe3Co tetrahedra that share  a cornercorner with one O(3)Fe3Co tetrahedra, corners with two equivalent O(5)MgFe3Co trigonal bipyramids, corners with three equivalent O(6)MgFe3Co trigonal bipyramids, corners with four equivalent O(2)MgFe2Co2 trigonal bipyramids, and  an edgeedge with one O(3)Fe3Co tetrahedra. In the second O site, O(2) is bonded to one Mg(1), one Fe(1), one Fe(2), one Co(1), and one Co(2) atom to form distorted OMgFe2Co2 trigonal bipyramids that share corners with two equivalent O(1)Fe3Co tetrahedra, corners with two equivalent O(3)Fe3Co tetrahedra,  a cornercorner with one O(5)MgFe3Co trigonal bipyramid,  a cornercorner with one O(6)MgFe3Co trigonal bipyramid,  an edgeedge with one O(2)MgFe2Co2 trigonal bipyramid,  an edgeedge with one O(5)MgFe3Co trigonal bipyramid,  an edgeedge with one O(6)MgFe3Co trigonal bipyramid, and  a faceface with one O(2)MgFe2Co2 trigonal bipyramid. In the third O site, O(3) is bonded to one Fe(2), two equivalent Fe(3), and one Co(2) atom to form distorted OFe3Co tetrahedra that share  a cornercorner with one O(1)Fe3Co tetrahedra, corners with two equivalent O(6)MgFe3Co trigonal bipyramids, corners with three equivalent O(5)MgFe3Co trigonal bipyramids, corners with four equivalent O(2)MgFe2Co2 trigonal bipyramids, and  an edgeedge with one O(1)Fe3Co tetrahedra. In the fourth O site, O(4) is bonded in a 5-coordinate geometry to one Fe(1), one Fe(2), one Fe(3), one Co(1), and one Co(2) atom. In the fifth O site, O(5) is bonded to one Mg(1), one Fe(1), two equivalent Fe(3), and one Co(2) atom to form OMgFe3Co trigonal bipyramids that share corners with two equivalent O(1)Fe3Co tetrahedra, corners with three equivalent O(3)Fe3Co tetrahedra,  a cornercorner with one O(6)MgFe3Co trigonal bipyramid, corners with two equivalent O(2)MgFe2Co2 trigonal bipyramids, edges with two equivalent O(2)MgFe2Co2 trigonal bipyramids, and  a faceface with one O(6)MgFe3Co trigonal bipyramid. In the sixth O site, O(6) is bonded to one Mg(1), one Fe(1), two equivalent Fe(3), and one Co(1) atom to form OMgFe3Co trigonal bipyramids that share corners with two equivalent O(3)Fe3Co tetrahedra, corners with three equivalent O(1)Fe3Co tetrahedra,  a cornercorner with one O(5)MgFe3Co trigonal bipyramid, corners with two equivalent O(2)MgFe2Co2 trigonal bipyramids, edges with two equivalent O(2)MgFe2Co2 trigonal bipyramids, and  a faceface with one O(5)MgFe3Co trigonal bipyramid.
MgFe4(CoO4)2 crystallizes in the monoclinic Cm space group. Mg(1) is bonded to one O(5), one O(6), and two equivalent O(2) atoms to form distorted MgO4 tetrahedra that share corners with three equivalent Co(1)O6 octahedra, corners with three equivalent Co(2)O6 octahedra, corners with four equivalent Fe(1)O6 octahedra, and  an edgeedge with one Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 12-69°. The Mg(1)-O(5) bond length is 2.04 Å. The Mg(1)-O(6) bond length is 2.03 Å. Both Mg(1)-O(2) bond lengths are 1.99 Å. There are three inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to one O(5), one O(6), two equivalent O(2), and two equivalent O(4) atoms to form distorted FeO6 octahedra that share corners with two equivalent Co(1)O6 octahedra, corners with two equivalent Co(2)O6 octahedra, corners with four equivalent Mg(1)O4 tetrahedra, edges with two equivalent Fe(2)O6 octahedra,  a faceface with one Co(1)O6 octahedra, and  a faceface with one Co(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-53°. The Fe(1)-O(5) bond length is 2.01 Å. The Fe(1)-O(6) bond length is 2.02 Å. Both Fe(1)-O(2) bond lengths are 2.34 Å. Both Fe(1)-O(4) bond lengths are 2.02 Å. In the second Fe site, Fe(2) is bonded to one O(1), one O(3), two equivalent O(2), and two equivalent O(4) atoms to form FeO6 octahedra that share corners with two equivalent Co(1)O6 octahedra, corners with two equivalent Co(2)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra,  an edgeedge with one Mg(1)O4 tetrahedra,  a faceface with one Co(1)O6 octahedra, and  a faceface with one Co(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 44-49°. The Fe(2)-O(1) bond length is 1.98 Å. The Fe(2)-O(3) bond length is 1.99 Å. Both Fe(2)-O(2) bond lengths are 2.15 Å. Both Fe(2)-O(4) bond lengths are 2.06 Å. In the third Fe site, Fe(3) is bonded in a 5-coordinate geometry to one O(1), one O(3), one O(4), one O(5), and one O(6) atom. The Fe(3)-O(1) bond length is 2.03 Å. The Fe(3)-O(3) bond length is 2.03 Å. The Fe(3)-O(4) bond length is 2.07 Å. The Fe(3)-O(5) bond length is 2.22 Å. The Fe(3)-O(6) bond length is 2.18 Å. There are two inequivalent Co sites. In the first Co site, Co(1) is bonded to one O(1), one O(6), two equivalent O(2), and two equivalent O(4) atoms to form distorted CoO6 octahedra that share corners with two equivalent Fe(1)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, corners with three equivalent Mg(1)O4 tetrahedra, edges with two equivalent Co(2)O6 octahedra,  a faceface with one Fe(1)O6 octahedra, and  a faceface with one Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 44-53°. The Co(1)-O(1) bond length is 2.01 Å. The Co(1)-O(6) bond length is 2.11 Å. Both Co(1)-O(2) bond lengths are 2.12 Å. Both Co(1)-O(4) bond lengths are 2.45 Å. In the second Co site, Co(2) is bonded to one O(3), one O(5), two equivalent O(2), and two equivalent O(4) atoms to form distorted CoO6 octahedra that share corners with two equivalent Fe(1)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra, corners with three equivalent Mg(1)O4 tetrahedra, edges with two equivalent Co(1)O6 octahedra,  a faceface with one Fe(1)O6 octahedra, and  a faceface with one Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 49-52°. The Co(2)-O(3) bond length is 2.00 Å. The Co(2)-O(5) bond length is 2.06 Å. Both Co(2)-O(2) bond lengths are 2.19 Å. Both Co(2)-O(4) bond lengths are 2.35 Å. There are six inequivalent O sites. In the first O site, O(1) is bonded to one Fe(2), two equivalent Fe(3), and one Co(1) atom to form OFe3Co tetrahedra that share  a cornercorner with one O(3)Fe3Co tetrahedra, corners with two equivalent O(5)MgFe3Co trigonal bipyramids, corners with three equivalent O(6)MgFe3Co trigonal bipyramids, corners with four equivalent O(2)MgFe2Co2 trigonal bipyramids, and  an edgeedge with one O(3)Fe3Co tetrahedra. In the second O site, O(2) is bonded to one Mg(1), one Fe(1), one Fe(2), one Co(1), and one Co(2) atom to form distorted OMgFe2Co2 trigonal bipyramids that share corners with two equivalent O(1)Fe3Co tetrahedra, corners with two equivalent O(3)Fe3Co tetrahedra,  a cornercorner with one O(5)MgFe3Co trigonal bipyramid,  a cornercorner with one O(6)MgFe3Co trigonal bipyramid,  an edgeedge with one O(2)MgFe2Co2 trigonal bipyramid,  an edgeedge with one O(5)MgFe3Co trigonal bipyramid,  an edgeedge with one O(6)MgFe3Co trigonal bipyramid, and  a faceface with one O(2)MgFe2Co2 trigonal bipyramid. In the third O site, O(3) is bonded to one Fe(2), two equivalent Fe(3), and one Co(2) atom to form distorted OFe3Co tetrahedra that share  a cornercorner with one O(1)Fe3Co tetrahedra, corners with two equivalent O(6)MgFe3Co trigonal bipyramids, corners with three equivalent O(5)MgFe3Co trigonal bipyramids, corners with four equivalent O(2)MgFe2Co2 trigonal bipyramids, and  an edgeedge with one O(1)Fe3Co tetrahedra. In the fourth O site, O(4) is bonded in a 5-coordinate geometry to one Fe(1), one Fe(2), one Fe(3), one Co(1), and one Co(2) atom. In the fifth O site, O(5) is bonded to one Mg(1), one Fe(1), two equivalent Fe(3), and one Co(2) atom to form OMgFe3Co trigonal bipyramids that share corners with two equivalent O(1)Fe3Co tetrahedra, corners with three equivalent O(3)Fe3Co tetrahedra,  a cornercorner with one O(6)MgFe3Co trigonal bipyramid, corners with two equivalent O(2)MgFe2Co2 trigonal bipyramids, edges with two equivalent O(2)MgFe2Co2 trigonal bipyramids, and  a faceface with one O(6)MgFe3Co trigonal bipyramid. In the sixth O site, O(6) is bonded to one Mg(1), one Fe(1), two equivalent Fe(3), and one Co(1) atom to form OMgFe3Co trigonal bipyramids that share corners with two equivalent O(3)Fe3Co tetrahedra, corners with three equivalent O(1)Fe3Co tetrahedra,  a cornercorner with one O(5)MgFe3Co trigonal bipyramid, corners with two equivalent O(2)MgFe2Co2 trigonal bipyramids, edges with two equivalent O(2)MgFe2Co2 trigonal bipyramids, and  a faceface with one O(5)MgFe3Co trigonal bipyramid.