Mg(Fe2O3)4 crystallizes in the triclinic P1 space group. Mg(1) is bonded to one O(1), one O(12), one O(2), one O(7), one O(8), and one O(9) atom to form MgO6 octahedra that share corners with two equivalent Fe(1)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra,  a cornercorner with one Fe(6)O5 trigonal bipyramid,  an edgeedge with one Fe(8)O6 octahedra, edges with two equivalent Fe(3)O6 octahedra, edges with two equivalent Fe(4)O6 octahedra, and  an edgeedge with one Fe(6)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 32-49°. There are eight inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to one O(1), one O(11), one O(3), one O(4), one O(5), and one O(9) atom to form distorted FeO6 octahedra that share  a cornercorner with one Fe(4)O6 octahedra, corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent Fe(3)O6 octahedra, corners with four equivalent Fe(8)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra, and  a faceface with one Fe(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 41-57°. In the second Fe site, Fe(2) is bonded to one O(10), one O(12), one O(2), one O(3), one O(4), and one O(6) atom to form distorted FeO6 octahedra that share  a cornercorner with one Fe(3)O6 octahedra, corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent Fe(4)O6 octahedra, corners with two equivalent Fe(8)O6 octahedra,  a cornercorner with one Fe(6)O5 trigonal bipyramid,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(6)O5 trigonal bipyramid, and  a faceface with one Fe(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 32-63°. In the third Fe site, Fe(3) is bonded to one O(1), one O(10), one O(12), one O(2), one O(3), and one O(7) atom to form FeO6 octahedra that share  a cornercorner with one Fe(2)O6 octahedra, corners with two equivalent Fe(1)O6 octahedra, corners with three equivalent Fe(6)O5 trigonal bipyramids,  an edgeedge with one Fe(4)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, and  a faceface with one Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 44-52°. In the fourth Fe site, Fe(4) is bonded to one O(1), one O(11), one O(2), one O(4), one O(8), and one O(9) atom to form FeO6 octahedra that share  a cornercorner with one Fe(1)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra,  a cornercorner with one Fe(6)O5 trigonal bipyramid,  an edgeedge with one Fe(3)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Fe(8)O6 octahedra, and  a faceface with one Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 48-57°. In the fifth Fe site, Fe(5) is bonded in a 5-coordinate geometry to one O(1), one O(11), one O(5), one O(7), one O(8), and one O(9) atom. In the sixth Fe site, Fe(6) is bonded to one O(10), one O(12), one O(6), one O(7), and one O(8) atom to form distorted FeO5 trigonal bipyramids that share  a cornercorner with one Mg(1)O6 octahedra,  a cornercorner with one Fe(2)O6 octahedra,  a cornercorner with one Fe(4)O6 octahedra, corners with two equivalent Fe(8)O6 octahedra, corners with three equivalent Fe(3)O6 octahedra,  an edgeedge with one Mg(1)O6 octahedra, and  an edgeedge with one Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 32-68°. In the seventh Fe site, Fe(7) is bonded in a 4-coordinate geometry to one O(12), one O(3), one O(5), one O(6), and one O(9) atom. In the eighth Fe site, Fe(8) is bonded to one O(11), one O(4), one O(5), one O(6), one O(8), and one O(9) atom to form distorted FeO6 octahedra that share corners with two equivalent Fe(2)O6 octahedra, corners with four equivalent Fe(1)O6 octahedra, corners with two equivalent Fe(6)O5 trigonal bipyramids,  an edgeedge with one Mg(1)O6 octahedra, and edges with two equivalent Fe(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 43-63°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a 5-coordinate geometry to one Mg(1), one Fe(1), one Fe(3), one Fe(4), and one Fe(5) atom. In the second O site, O(2) is bonded to one Mg(1), one Fe(2), one Fe(3), and one Fe(4) atom to form distorted OMgFe3 trigonal pyramids that share  a cornercorner with one O(12)MgFe4 trigonal bipyramid, corners with two equivalent O(8)MgFe4 trigonal bipyramids,  a cornercorner with one O(6)Fe4 trigonal pyramid, corners with two equivalent O(4)Fe4 trigonal pyramids,  an edgeedge with one O(12)MgFe4 trigonal bipyramid,  an edgeedge with one O(3)Fe4 trigonal pyramid, and  an edgeedge with one O(7)MgFe3 trigonal pyramid. In the third O site, O(3) is bonded to one Fe(1), one Fe(2), one Fe(3), and one Fe(7) atom to form OFe4 trigonal pyramids that share corners with two equivalent O(5)Fe4 tetrahedra,  a cornercorner with one O(12)MgFe4 trigonal bipyramid,  a cornercorner with one O(7)MgFe3 trigonal pyramid,  an edgeedge with one O(12)MgFe4 trigonal bipyramid,  an edgeedge with one O(4)Fe4 trigonal pyramid,  an edgeedge with one O(6)Fe4 trigonal pyramid, and  an edgeedge with one O(2)MgFe3 trigonal pyramid. In the fourth O site, O(4) is bonded to one Fe(1), one Fe(2), one Fe(4), and one Fe(8) atom to form distorted OFe4 trigonal pyramids that share corners with two equivalent O(5)Fe4 tetrahedra,  a cornercorner with one O(12)MgFe4 trigonal bipyramid, corners with two equivalent O(6)Fe4 trigonal pyramids, corners with two equivalent O(2)MgFe3 trigonal pyramids,  an edgeedge with one O(8)MgFe4 trigonal bipyramid, and  an edgeedge with one O(3)Fe4 trigonal pyramid. In the fifth O site, O(5) is bonded to one Fe(1), one Fe(5), one Fe(7), and one Fe(8) atom to form distorted OFe4 tetrahedra that share  a cornercorner with one O(12)MgFe4 trigonal bipyramid,  a cornercorner with one O(7)MgFe3 trigonal pyramid, corners with two equivalent O(3)Fe4 trigonal pyramids, corners with two equivalent O(4)Fe4 trigonal pyramids, corners with two equivalent O(6)Fe4 trigonal pyramids, and  an edgeedge with one O(8)MgFe4 trigonal bipyramid. In the sixth O site, O(6) is bonded to one Fe(2), one Fe(6), one Fe(7), and one Fe(8) atom to form OFe4 trigonal pyramids that share corners with two equivalent O(5)Fe4 tetrahedra,  a cornercorner with one O(12)MgFe4 trigonal bipyramid, corners with two equivalent O(8)MgFe4 trigonal bipyramids,  a cornercorner with one O(2)MgFe3 trigonal pyramid,  a cornercorner with one O(7)MgFe3 trigonal pyramid, corners with two equivalent O(4)Fe4 trigonal pyramids,  an edgeedge with one O(12)MgFe4 trigonal bipyramid, and  an edgeedge with one O(3)Fe4 trigonal pyramid. In the seventh O site, O(7) is bonded to one Mg(1), one Fe(3), one Fe(5), and one Fe(6) atom to form distorted OMgFe3 trigonal pyramids that share  a cornercorner with one O(5)Fe4 tetrahedra,  a cornercorner with one O(8)MgFe4 trigonal bipyramid, corners with three equivalent O(12)MgFe4 trigonal bipyramids,  a cornercorner with one O(3)Fe4 trigonal pyramid,  a cornercorner with one O(6)Fe4 trigonal pyramid,  an edgeedge with one O(8)MgFe4 trigonal bipyramid, and  an edgeedge with one O(2)MgFe3 trigonal pyramid. In the eighth O site, O(8) is bonded to one Mg(1), one Fe(4), one Fe(5), one Fe(6), and one Fe(8) atom to form distorted OMgFe4 trigonal bipyramids that share  a cornercorner with one O(7)MgFe3 trigonal pyramid, corners with two equivalent O(6)Fe4 trigonal pyramids, corners with two equivalent O(2)MgFe3 trigonal pyramids,  an edgeedge with one O(5)Fe4 tetrahedra,  an edgeedge with one O(12)MgFe4 trigonal bipyramid,  an edgeedge with one O(4)Fe4 trigonal pyramid, and  an edgeedge with one O(7)MgFe3 trigonal pyramid. In the ninth O site, O(9) is bonded in a 6-coordinate geometry to one Mg(1), one Fe(1), one Fe(4), one Fe(5), one Fe(7), and one Fe(8) atom. In the tenth O site, O(10) is bonded in a trigonal planar geometry to one Fe(2), one Fe(3), and one Fe(6) atom. In the eleventh O site, O(11) is bonded in a 4-coordinate geometry to one Fe(1), one Fe(4), one Fe(5), and one Fe(8) atom. In the twelfth O site, O(12) is bonded to one Mg(1), one Fe(2), one Fe(3), one Fe(6), and one Fe(7) atom to form distorted OMgFe4 trigonal bipyramids that share  a cornercorner with one O(5)Fe4 tetrahedra,  a cornercorner with one O(3)Fe4 trigonal pyramid,  a cornercorner with one O(4)Fe4 trigonal pyramid,  a cornercorner with one O(6)Fe4 trigonal pyramid,  a cornercorner with one O(2)MgFe3 trigonal pyramid, corners with three equivalent O(7)MgFe3 trigonal pyramids,  an edgeedge with one O(8)MgFe4 trigonal bipyramid,  an edgeedge with one O(3)Fe4 trigonal pyramid,  an edgeedge with one O(6)Fe4 trigonal pyramid, and  an edgeedge with one O(2)MgFe3 trigonal pyramid.
Mg(Fe2O3)4 crystallizes in the triclinic P1 space group. Mg(1) is bonded to one O(1), one O(12), one O(2), one O(7), one O(8), and one O(9) atom to form MgO6 octahedra that share corners with two equivalent Fe(1)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra,  a cornercorner with one Fe(6)O5 trigonal bipyramid,  an edgeedge with one Fe(8)O6 octahedra, edges with two equivalent Fe(3)O6 octahedra, edges with two equivalent Fe(4)O6 octahedra, and  an edgeedge with one Fe(6)O5 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 32-49°. The Mg(1)-O(1) bond length is 2.08 Å. The Mg(1)-O(12) bond length is 2.08 Å. The Mg(1)-O(2) bond length is 2.05 Å. The Mg(1)-O(7) bond length is 2.07 Å. The Mg(1)-O(8) bond length is 2.08 Å. The Mg(1)-O(9) bond length is 2.23 Å. There are eight inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to one O(1), one O(11), one O(3), one O(4), one O(5), and one O(9) atom to form distorted FeO6 octahedra that share  a cornercorner with one Fe(4)O6 octahedra, corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent Fe(3)O6 octahedra, corners with four equivalent Fe(8)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra, and  a faceface with one Fe(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 41-57°. The Fe(1)-O(1) bond length is 2.12 Å. The Fe(1)-O(11) bond length is 2.03 Å. The Fe(1)-O(3) bond length is 2.02 Å. The Fe(1)-O(4) bond length is 2.07 Å. The Fe(1)-O(5) bond length is 1.97 Å. The Fe(1)-O(9) bond length is 2.34 Å. In the second Fe site, Fe(2) is bonded to one O(10), one O(12), one O(2), one O(3), one O(4), and one O(6) atom to form distorted FeO6 octahedra that share  a cornercorner with one Fe(3)O6 octahedra, corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent Fe(4)O6 octahedra, corners with two equivalent Fe(8)O6 octahedra,  a cornercorner with one Fe(6)O5 trigonal bipyramid,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(6)O5 trigonal bipyramid, and  a faceface with one Fe(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 32-63°. The Fe(2)-O(10) bond length is 1.97 Å. The Fe(2)-O(12) bond length is 2.18 Å. The Fe(2)-O(2) bond length is 2.19 Å. The Fe(2)-O(3) bond length is 2.07 Å. The Fe(2)-O(4) bond length is 2.06 Å. The Fe(2)-O(6) bond length is 1.96 Å. In the third Fe site, Fe(3) is bonded to one O(1), one O(10), one O(12), one O(2), one O(3), and one O(7) atom to form FeO6 octahedra that share  a cornercorner with one Fe(2)O6 octahedra, corners with two equivalent Fe(1)O6 octahedra, corners with three equivalent Fe(6)O5 trigonal bipyramids,  an edgeedge with one Fe(4)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, and  a faceface with one Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 44-52°. The Fe(3)-O(1) bond length is 2.09 Å. The Fe(3)-O(10) bond length is 1.96 Å. The Fe(3)-O(12) bond length is 2.21 Å. The Fe(3)-O(2) bond length is 2.12 Å. The Fe(3)-O(3) bond length is 2.06 Å. The Fe(3)-O(7) bond length is 2.07 Å. In the fourth Fe site, Fe(4) is bonded to one O(1), one O(11), one O(2), one O(4), one O(8), and one O(9) atom to form FeO6 octahedra that share  a cornercorner with one Fe(1)O6 octahedra, corners with two equivalent Fe(2)O6 octahedra,  a cornercorner with one Fe(6)O5 trigonal bipyramid,  an edgeedge with one Fe(3)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Fe(8)O6 octahedra, and  a faceface with one Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 48-57°. The Fe(4)-O(1) bond length is 2.13 Å. The Fe(4)-O(11) bond length is 2.01 Å. The Fe(4)-O(2) bond length is 2.02 Å. The Fe(4)-O(4) bond length is 2.12 Å. The Fe(4)-O(8) bond length is 2.11 Å. The Fe(4)-O(9) bond length is 2.20 Å. In the fifth Fe site, Fe(5) is bonded in a 5-coordinate geometry to one O(1), one O(11), one O(5), one O(7), one O(8), and one O(9) atom. The Fe(5)-O(1) bond length is 2.61 Å. The Fe(5)-O(11) bond length is 1.97 Å. The Fe(5)-O(5) bond length is 1.97 Å. The Fe(5)-O(7) bond length is 1.99 Å. The Fe(5)-O(8) bond length is 2.05 Å. The Fe(5)-O(9) bond length is 2.05 Å. In the sixth Fe site, Fe(6) is bonded to one O(10), one O(12), one O(6), one O(7), and one O(8) atom to form distorted FeO5 trigonal bipyramids that share  a cornercorner with one Mg(1)O6 octahedra,  a cornercorner with one Fe(2)O6 octahedra,  a cornercorner with one Fe(4)O6 octahedra, corners with two equivalent Fe(8)O6 octahedra, corners with three equivalent Fe(3)O6 octahedra,  an edgeedge with one Mg(1)O6 octahedra, and  an edgeedge with one Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 32-68°. The Fe(6)-O(10) bond length is 1.90 Å. The Fe(6)-O(12) bond length is 2.12 Å. The Fe(6)-O(6) bond length is 1.95 Å. The Fe(6)-O(7) bond length is 1.96 Å. The Fe(6)-O(8) bond length is 2.12 Å. In the seventh Fe site, Fe(7) is bonded in a 4-coordinate geometry to one O(12), one O(3), one O(5), one O(6), and one O(9) atom. The Fe(7)-O(12) bond length is 2.01 Å. The Fe(7)-O(3) bond length is 2.05 Å. The Fe(7)-O(5) bond length is 2.01 Å. The Fe(7)-O(6) bond length is 2.20 Å. The Fe(7)-O(9) bond length is 2.61 Å. In the eighth Fe site, Fe(8) is bonded to one O(11), one O(4), one O(5), one O(6), one O(8), and one O(9) atom to form distorted FeO6 octahedra that share corners with two equivalent Fe(2)O6 octahedra, corners with four equivalent Fe(1)O6 octahedra, corners with two equivalent Fe(6)O5 trigonal bipyramids,  an edgeedge with one Mg(1)O6 octahedra, and edges with two equivalent Fe(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 43-63°. The Fe(8)-O(11) bond length is 2.25 Å. The Fe(8)-O(4) bond length is 2.10 Å. The Fe(8)-O(5) bond length is 2.21 Å. The Fe(8)-O(6) bond length is 2.04 Å. The Fe(8)-O(8) bond length is 2.30 Å. The Fe(8)-O(9) bond length is 2.25 Å. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a 5-coordinate geometry to one Mg(1), one Fe(1), one Fe(3), one Fe(4), and one Fe(5) atom. In the second O site, O(2) is bonded to one Mg(1), one Fe(2), one Fe(3), and one Fe(4) atom to form distorted OMgFe3 trigonal pyramids that share  a cornercorner with one O(12)MgFe4 trigonal bipyramid, corners with two equivalent O(8)MgFe4 trigonal bipyramids,  a cornercorner with one O(6)Fe4 trigonal pyramid, corners with two equivalent O(4)Fe4 trigonal pyramids,  an edgeedge with one O(12)MgFe4 trigonal bipyramid,  an edgeedge with one O(3)Fe4 trigonal pyramid, and  an edgeedge with one O(7)MgFe3 trigonal pyramid. In the third O site, O(3) is bonded to one Fe(1), one Fe(2), one Fe(3), and one Fe(7) atom to form OFe4 trigonal pyramids that share corners with two equivalent O(5)Fe4 tetrahedra,  a cornercorner with one O(12)MgFe4 trigonal bipyramid,  a cornercorner with one O(7)MgFe3 trigonal pyramid,  an edgeedge with one O(12)MgFe4 trigonal bipyramid,  an edgeedge with one O(4)Fe4 trigonal pyramid,  an edgeedge with one O(6)Fe4 trigonal pyramid, and  an edgeedge with one O(2)MgFe3 trigonal pyramid. In the fourth O site, O(4) is bonded to one Fe(1), one Fe(2), one Fe(4), and one Fe(8) atom to form distorted OFe4 trigonal pyramids that share corners with two equivalent O(5)Fe4 tetrahedra,  a cornercorner with one O(12)MgFe4 trigonal bipyramid, corners with two equivalent O(6)Fe4 trigonal pyramids, corners with two equivalent O(2)MgFe3 trigonal pyramids,  an edgeedge with one O(8)MgFe4 trigonal bipyramid, and  an edgeedge with one O(3)Fe4 trigonal pyramid. In the fifth O site, O(5) is bonded to one Fe(1), one Fe(5), one Fe(7), and one Fe(8) atom to form distorted OFe4 tetrahedra that share  a cornercorner with one O(12)MgFe4 trigonal bipyramid,  a cornercorner with one O(7)MgFe3 trigonal pyramid, corners with two equivalent O(3)Fe4 trigonal pyramids, corners with two equivalent O(4)Fe4 trigonal pyramids, corners with two equivalent O(6)Fe4 trigonal pyramids, and  an edgeedge with one O(8)MgFe4 trigonal bipyramid. In the sixth O site, O(6) is bonded to one Fe(2), one Fe(6), one Fe(7), and one Fe(8) atom to form OFe4 trigonal pyramids that share corners with two equivalent O(5)Fe4 tetrahedra,  a cornercorner with one O(12)MgFe4 trigonal bipyramid, corners with two equivalent O(8)MgFe4 trigonal bipyramids,  a cornercorner with one O(2)MgFe3 trigonal pyramid,  a cornercorner with one O(7)MgFe3 trigonal pyramid, corners with two equivalent O(4)Fe4 trigonal pyramids,  an edgeedge with one O(12)MgFe4 trigonal bipyramid, and  an edgeedge with one O(3)Fe4 trigonal pyramid. In the seventh O site, O(7) is bonded to one Mg(1), one Fe(3), one Fe(5), and one Fe(6) atom to form distorted OMgFe3 trigonal pyramids that share  a cornercorner with one O(5)Fe4 tetrahedra,  a cornercorner with one O(8)MgFe4 trigonal bipyramid, corners with three equivalent O(12)MgFe4 trigonal bipyramids,  a cornercorner with one O(3)Fe4 trigonal pyramid,  a cornercorner with one O(6)Fe4 trigonal pyramid,  an edgeedge with one O(8)MgFe4 trigonal bipyramid, and  an edgeedge with one O(2)MgFe3 trigonal pyramid. In the eighth O site, O(8) is bonded to one Mg(1), one Fe(4), one Fe(5), one Fe(6), and one Fe(8) atom to form distorted OMgFe4 trigonal bipyramids that share  a cornercorner with one O(7)MgFe3 trigonal pyramid, corners with two equivalent O(6)Fe4 trigonal pyramids, corners with two equivalent O(2)MgFe3 trigonal pyramids,  an edgeedge with one O(5)Fe4 tetrahedra,  an edgeedge with one O(12)MgFe4 trigonal bipyramid,  an edgeedge with one O(4)Fe4 trigonal pyramid, and  an edgeedge with one O(7)MgFe3 trigonal pyramid. In the ninth O site, O(9) is bonded in a 6-coordinate geometry to one Mg(1), one Fe(1), one Fe(4), one Fe(5), one Fe(7), and one Fe(8) atom. In the tenth O site, O(10) is bonded in a trigonal planar geometry to one Fe(2), one Fe(3), and one Fe(6) atom. In the eleventh O site, O(11) is bonded in a 4-coordinate geometry to one Fe(1), one Fe(4), one Fe(5), and one Fe(8) atom. In the twelfth O site, O(12) is bonded to one Mg(1), one Fe(2), one Fe(3), one Fe(6), and one Fe(7) atom to form distorted OMgFe4 trigonal bipyramids that share  a cornercorner with one O(5)Fe4 tetrahedra,  a cornercorner with one O(3)Fe4 trigonal pyramid,  a cornercorner with one O(4)Fe4 trigonal pyramid,  a cornercorner with one O(6)Fe4 trigonal pyramid,  a cornercorner with one O(2)MgFe3 trigonal pyramid, corners with three equivalent O(7)MgFe3 trigonal pyramids,  an edgeedge with one O(8)MgFe4 trigonal bipyramid,  an edgeedge with one O(3)Fe4 trigonal pyramid,  an edgeedge with one O(6)Fe4 trigonal pyramid, and  an edgeedge with one O(2)MgFe3 trigonal pyramid.