NaMgFe5O8 crystallizes in the monoclinic Cm space group. Na(1) is bonded in a 5-coordinate geometry to one O(5), two equivalent O(1), and two equivalent O(4) atoms. Mg(1) is bonded to one O(2), one O(6), and two equivalent O(4) atoms to form MgO4 tetrahedra that share corners with two equivalent Fe(2)O4 tetrahedra. There are four inequivalent Fe sites. In the first Fe site, Fe(1) is bonded in a 6-coordinate geometry to one O(1), one O(2), one O(3), one O(4), one O(5), and one O(6) atom. In the second Fe site, Fe(2) is bonded to one O(3), one O(5), and two equivalent O(4) atoms to form FeO4 tetrahedra that share corners with two equivalent Mg(1)O4 tetrahedra. In the third Fe site, Fe(3) is bonded in a 5-coordinate geometry to one O(3), two equivalent O(1), and two equivalent O(4) atoms. In the fourth Fe site, Fe(4) is bonded in a 5-coordinate geometry to one O(2), one O(5), one O(6), and two equivalent O(1) atoms. There are six inequivalent O sites. In the first O site, O(1) is bonded to one Na(1), one Fe(1), one Fe(3), and one Fe(4) atom to form ONaFe3 tetrahedra that share  a cornercorner with one O(1)NaFe3 tetrahedra,  a cornercorner with one O(5)NaFe4 trigonal bipyramid, corners with five equivalent O(4)NaMgFe3 trigonal bipyramids,  an edgeedge with one O(1)NaFe3 tetrahedra, and  an edgeedge with one O(5)NaFe4 trigonal bipyramid. In the second O site, O(2) is bonded in a 4-coordinate geometry to one Mg(1), one Fe(4), and two equivalent Fe(1) atoms. In the third O site, O(3) is bonded in a 2-coordinate geometry to one Fe(2), one Fe(3), and two equivalent Fe(1) atoms. In the fourth O site, O(4) is bonded to one Na(1), one Mg(1), one Fe(1), one Fe(2), and one Fe(3) atom to form distorted ONaMgFe3 trigonal bipyramids that share corners with five equivalent O(1)NaFe3 tetrahedra,  a cornercorner with one O(5)NaFe4 trigonal bipyramid,  a cornercorner with one O(4)NaMgFe3 trigonal bipyramid,  an edgeedge with one O(5)NaFe4 trigonal bipyramid, and  a faceface with one O(4)NaMgFe3 trigonal bipyramid. In the fifth O site, O(5) is bonded to one Na(1), one Fe(2), one Fe(4), and two equivalent Fe(1) atoms to form ONaFe4 trigonal bipyramids that share corners with two equivalent O(1)NaFe3 tetrahedra, corners with two equivalent O(4)NaMgFe3 trigonal bipyramids, edges with two equivalent O(1)NaFe3 tetrahedra, and edges with two equivalent O(4)NaMgFe3 trigonal bipyramids. In the sixth O site, O(6) is bonded in a 4-coordinate geometry to one Mg(1), one Fe(4), and two equivalent Fe(1) atoms.
NaMgFe5O8 crystallizes in the monoclinic Cm space group. Na(1) is bonded in a 5-coordinate geometry to one O(5), two equivalent O(1), and two equivalent O(4) atoms. The Na(1)-O(5) bond length is 2.13 Å. Both Na(1)-O(1) bond lengths are 2.17 Å. Both Na(1)-O(4) bond lengths are 2.35 Å. Mg(1) is bonded to one O(2), one O(6), and two equivalent O(4) atoms to form MgO4 tetrahedra that share corners with two equivalent Fe(2)O4 tetrahedra. The Mg(1)-O(2) bond length is 1.96 Å. The Mg(1)-O(6) bond length is 1.94 Å. Both Mg(1)-O(4) bond lengths are 2.07 Å. There are four inequivalent Fe sites. In the first Fe site, Fe(1) is bonded in a 6-coordinate geometry to one O(1), one O(2), one O(3), one O(4), one O(5), and one O(6) atom. The Fe(1)-O(1) bond length is 2.00 Å. The Fe(1)-O(2) bond length is 2.04 Å. The Fe(1)-O(3) bond length is 2.64 Å. The Fe(1)-O(4) bond length is 2.22 Å. The Fe(1)-O(5) bond length is 2.23 Å. The Fe(1)-O(6) bond length is 2.04 Å. In the second Fe site, Fe(2) is bonded to one O(3), one O(5), and two equivalent O(4) atoms to form FeO4 tetrahedra that share corners with two equivalent Mg(1)O4 tetrahedra. The Fe(2)-O(3) bond length is 1.99 Å. The Fe(2)-O(5) bond length is 1.92 Å. Both Fe(2)-O(4) bond lengths are 2.00 Å. In the third Fe site, Fe(3) is bonded in a 5-coordinate geometry to one O(3), two equivalent O(1), and two equivalent O(4) atoms. The Fe(3)-O(3) bond length is 1.93 Å. Both Fe(3)-O(1) bond lengths are 1.94 Å. Both Fe(3)-O(4) bond lengths are 2.15 Å. In the fourth Fe site, Fe(4) is bonded in a 5-coordinate geometry to one O(2), one O(5), one O(6), and two equivalent O(1) atoms. The Fe(4)-O(2) bond length is 2.40 Å. The Fe(4)-O(5) bond length is 2.25 Å. The Fe(4)-O(6) bond length is 2.23 Å. Both Fe(4)-O(1) bond lengths are 1.94 Å. There are six inequivalent O sites. In the first O site, O(1) is bonded to one Na(1), one Fe(1), one Fe(3), and one Fe(4) atom to form ONaFe3 tetrahedra that share  a cornercorner with one O(1)NaFe3 tetrahedra,  a cornercorner with one O(5)NaFe4 trigonal bipyramid, corners with five equivalent O(4)NaMgFe3 trigonal bipyramids,  an edgeedge with one O(1)NaFe3 tetrahedra, and  an edgeedge with one O(5)NaFe4 trigonal bipyramid. In the second O site, O(2) is bonded in a 4-coordinate geometry to one Mg(1), one Fe(4), and two equivalent Fe(1) atoms. In the third O site, O(3) is bonded in a 2-coordinate geometry to one Fe(2), one Fe(3), and two equivalent Fe(1) atoms. In the fourth O site, O(4) is bonded to one Na(1), one Mg(1), one Fe(1), one Fe(2), and one Fe(3) atom to form distorted ONaMgFe3 trigonal bipyramids that share corners with five equivalent O(1)NaFe3 tetrahedra,  a cornercorner with one O(5)NaFe4 trigonal bipyramid,  a cornercorner with one O(4)NaMgFe3 trigonal bipyramid,  an edgeedge with one O(5)NaFe4 trigonal bipyramid, and  a faceface with one O(4)NaMgFe3 trigonal bipyramid. In the fifth O site, O(5) is bonded to one Na(1), one Fe(2), one Fe(4), and two equivalent Fe(1) atoms to form ONaFe4 trigonal bipyramids that share corners with two equivalent O(1)NaFe3 tetrahedra, corners with two equivalent O(4)NaMgFe3 trigonal bipyramids, edges with two equivalent O(1)NaFe3 tetrahedra, and edges with two equivalent O(4)NaMgFe3 trigonal bipyramids. In the sixth O site, O(6) is bonded in a 4-coordinate geometry to one Mg(1), one Fe(4), and two equivalent Fe(1) atoms.