Na4MgMn4O8 crystallizes in the monoclinic Pm space group. There are four inequivalent Na sites. In the first Na site, Na(1) is bonded in a distorted square co-planar geometry to two equivalent O(1) and two equivalent O(5) atoms. In the second Na site, Na(2) is bonded in a 6-coordinate geometry to one O(2), one O(8), two equivalent O(4), and two equivalent O(7) atoms. In the third Na site, Na(3) is bonded to one O(5), two equivalent O(2), and two equivalent O(6) atoms to form distorted NaO5 trigonal bipyramids that share corners with four equivalent Mn(2)O5 square pyramids,  a cornercorner with one Mg(1)O4 tetrahedra, edges with two equivalent Mn(2)O5 square pyramids, and edges with two equivalent Na(3)O5 trigonal bipyramids. In the fourth Na site, Na(4) is bonded in a 5-coordinate geometry to one O(7), two equivalent O(3), and two equivalent O(8) atoms. Mg(1) is bonded to one O(1), one O(5), and two equivalent O(3) atoms to form distorted MgO4 tetrahedra that share corners with two equivalent Mn(3)O5 square pyramids, corners with two equivalent Mg(1)O4 tetrahedra,  a cornercorner with one Na(3)O5 trigonal bipyramid, and  an edgeedge with one Mn(3)O5 square pyramid. There are four inequivalent Mn sites. In the first Mn site, Mn(1) is bonded in a 5-coordinate geometry to one O(6), two equivalent O(1), and two equivalent O(5) atoms. In the second Mn site, Mn(2) is bonded to one O(4), two equivalent O(2), and two equivalent O(6) atoms to form MnO5 square pyramids that share corners with two equivalent Mn(4)O5 square pyramids, corners with four equivalent Na(3)O5 trigonal bipyramids, edges with two equivalent Mn(2)O5 square pyramids, and edges with two equivalent Na(3)O5 trigonal bipyramids. In the third Mn site, Mn(3) is bonded to one O(7), two equivalent O(3), and two equivalent O(8) atoms to form MnO5 square pyramids that share corners with two equivalent Mg(1)O4 tetrahedra, edges with two equivalent Mn(3)O5 square pyramids, edges with two equivalent Mn(4)O5 square pyramids, and  an edgeedge with one Mg(1)O4 tetrahedra. In the fourth Mn site, Mn(4) is bonded to one O(8), two equivalent O(4), and two equivalent O(7) atoms to form a mixture of corner and edge-sharing MnO5 square pyramids. There are eight inequivalent O sites. In the first O site, O(1) is bonded to two equivalent Na(1), one Mg(1), and two equivalent Mn(1) atoms to form distorted ONa2MgMn2 trigonal bipyramids that share corners with four equivalent O(5)Na3MgMn2 octahedra, corners with two equivalent O(6)Na2Mn3 trigonal bipyramids,  an edgeedge with one O(5)Na3MgMn2 octahedra, edges with two equivalent O(1)Na2MgMn2 trigonal bipyramids, and  a faceface with one O(5)Na3MgMn2 octahedra. The corner-sharing octahedral tilt angles range from 18-44°. In the second O site, O(2) is bonded to one Na(2), two equivalent Na(3), and two equivalent Mn(2) atoms to form distorted ONa3Mn2 trigonal bipyramids that share corners with two equivalent O(5)Na3MgMn2 octahedra, corners with four equivalent O(6)Na2Mn3 trigonal bipyramids, edges with two equivalent O(6)Na2Mn3 trigonal bipyramids, and edges with two equivalent O(2)Na3Mn2 trigonal bipyramids. The corner-sharing octahedral tilt angles are 85°. In the third O site, O(3) is bonded in a 6-coordinate geometry to two equivalent Na(4), two equivalent Mg(1), and two equivalent Mn(3) atoms. In the fourth O site, O(4) is bonded in a 5-coordinate geometry to two equivalent Na(2), one Mn(2), and two equivalent Mn(4) atoms. In the fifth O site, O(5) is bonded to one Na(3), two equivalent Na(1), one Mg(1), and two equivalent Mn(1) atoms to form ONa3MgMn2 octahedra that share corners with two equivalent O(2)Na3Mn2 trigonal bipyramids, corners with four equivalent O(1)Na2MgMn2 trigonal bipyramids, corners with four equivalent O(6)Na2Mn3 trigonal bipyramids, edges with two equivalent O(5)Na3MgMn2 octahedra,  an edgeedge with one O(1)Na2MgMn2 trigonal bipyramid, and  a faceface with one O(1)Na2MgMn2 trigonal bipyramid. In the sixth O site, O(6) is bonded to two equivalent Na(3), one Mn(1), and two equivalent Mn(2) atoms to form distorted ONa2Mn3 trigonal bipyramids that share corners with four equivalent O(5)Na3MgMn2 octahedra, corners with two equivalent O(1)Na2MgMn2 trigonal bipyramids, corners with four equivalent O(2)Na3Mn2 trigonal bipyramids, edges with two equivalent O(6)Na2Mn3 trigonal bipyramids, and edges with two equivalent O(2)Na3Mn2 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 61-64°. In the seventh O site, O(7) is bonded in a 6-coordinate geometry to one Na(4), two equivalent Na(2), one Mn(3), and two equivalent Mn(4) atoms. In the eighth O site, O(8) is bonded in a 6-coordinate geometry to one Na(2), two equivalent Na(4), one Mn(4), and two equivalent Mn(3) atoms.
Na4MgMn4O8 crystallizes in the monoclinic Pm space group. There are four inequivalent Na sites. In the first Na site, Na(1) is bonded in a distorted square co-planar geometry to two equivalent O(1) and two equivalent O(5) atoms. Both Na(1)-O(1) bond lengths are 2.25 Å. Both Na(1)-O(5) bond lengths are 2.34 Å. In the second Na site, Na(2) is bonded in a 6-coordinate geometry to one O(2), one O(8), two equivalent O(4), and two equivalent O(7) atoms. The Na(2)-O(2) bond length is 2.33 Å. The Na(2)-O(8) bond length is 2.62 Å. Both Na(2)-O(4) bond lengths are 2.49 Å. Both Na(2)-O(7) bond lengths are 2.53 Å. In the third Na site, Na(3) is bonded to one O(5), two equivalent O(2), and two equivalent O(6) atoms to form distorted NaO5 trigonal bipyramids that share corners with four equivalent Mn(2)O5 square pyramids,  a cornercorner with one Mg(1)O4 tetrahedra, edges with two equivalent Mn(2)O5 square pyramids, and edges with two equivalent Na(3)O5 trigonal bipyramids. The Na(3)-O(5) bond length is 2.51 Å. Both Na(3)-O(2) bond lengths are 2.48 Å. Both Na(3)-O(6) bond lengths are 2.46 Å. In the fourth Na site, Na(4) is bonded in a 5-coordinate geometry to one O(7), two equivalent O(3), and two equivalent O(8) atoms. The Na(4)-O(7) bond length is 2.45 Å. Both Na(4)-O(3) bond lengths are 2.70 Å. Both Na(4)-O(8) bond lengths are 2.32 Å. Mg(1) is bonded to one O(1), one O(5), and two equivalent O(3) atoms to form distorted MgO4 tetrahedra that share corners with two equivalent Mn(3)O5 square pyramids, corners with two equivalent Mg(1)O4 tetrahedra,  a cornercorner with one Na(3)O5 trigonal bipyramid, and  an edgeedge with one Mn(3)O5 square pyramid. The Mg(1)-O(1) bond length is 1.95 Å. The Mg(1)-O(5) bond length is 2.05 Å. Both Mg(1)-O(3) bond lengths are 2.00 Å. There are four inequivalent Mn sites. In the first Mn site, Mn(1) is bonded in a 5-coordinate geometry to one O(6), two equivalent O(1), and two equivalent O(5) atoms. The Mn(1)-O(6) bond length is 2.16 Å. Both Mn(1)-O(1) bond lengths are 2.17 Å. Both Mn(1)-O(5) bond lengths are 2.17 Å. In the second Mn site, Mn(2) is bonded to one O(4), two equivalent O(2), and two equivalent O(6) atoms to form MnO5 square pyramids that share corners with two equivalent Mn(4)O5 square pyramids, corners with four equivalent Na(3)O5 trigonal bipyramids, edges with two equivalent Mn(2)O5 square pyramids, and edges with two equivalent Na(3)O5 trigonal bipyramids. The Mn(2)-O(4) bond length is 2.13 Å. Both Mn(2)-O(2) bond lengths are 1.98 Å. Both Mn(2)-O(6) bond lengths are 2.01 Å. In the third Mn site, Mn(3) is bonded to one O(7), two equivalent O(3), and two equivalent O(8) atoms to form MnO5 square pyramids that share corners with two equivalent Mg(1)O4 tetrahedra, edges with two equivalent Mn(3)O5 square pyramids, edges with two equivalent Mn(4)O5 square pyramids, and  an edgeedge with one Mg(1)O4 tetrahedra. The Mn(3)-O(7) bond length is 2.28 Å. Both Mn(3)-O(3) bond lengths are 2.24 Å. Both Mn(3)-O(8) bond lengths are 2.09 Å. In the fourth Mn site, Mn(4) is bonded to one O(8), two equivalent O(4), and two equivalent O(7) atoms to form a mixture of corner and edge-sharing MnO5 square pyramids. The Mn(4)-O(8) bond length is 2.25 Å. Both Mn(4)-O(4) bond lengths are 1.99 Å. Both Mn(4)-O(7) bond lengths are 2.03 Å. There are eight inequivalent O sites. In the first O site, O(1) is bonded to two equivalent Na(1), one Mg(1), and two equivalent Mn(1) atoms to form distorted ONa2MgMn2 trigonal bipyramids that share corners with four equivalent O(5)Na3MgMn2 octahedra, corners with two equivalent O(6)Na2Mn3 trigonal bipyramids,  an edgeedge with one O(5)Na3MgMn2 octahedra, edges with two equivalent O(1)Na2MgMn2 trigonal bipyramids, and  a faceface with one O(5)Na3MgMn2 octahedra. The corner-sharing octahedral tilt angles range from 18-44°. In the second O site, O(2) is bonded to one Na(2), two equivalent Na(3), and two equivalent Mn(2) atoms to form distorted ONa3Mn2 trigonal bipyramids that share corners with two equivalent O(5)Na3MgMn2 octahedra, corners with four equivalent O(6)Na2Mn3 trigonal bipyramids, edges with two equivalent O(6)Na2Mn3 trigonal bipyramids, and edges with two equivalent O(2)Na3Mn2 trigonal bipyramids. The corner-sharing octahedral tilt angles are 85°. In the third O site, O(3) is bonded in a 6-coordinate geometry to two equivalent Na(4), two equivalent Mg(1), and two equivalent Mn(3) atoms. In the fourth O site, O(4) is bonded in a 5-coordinate geometry to two equivalent Na(2), one Mn(2), and two equivalent Mn(4) atoms. In the fifth O site, O(5) is bonded to one Na(3), two equivalent Na(1), one Mg(1), and two equivalent Mn(1) atoms to form ONa3MgMn2 octahedra that share corners with two equivalent O(2)Na3Mn2 trigonal bipyramids, corners with four equivalent O(1)Na2MgMn2 trigonal bipyramids, corners with four equivalent O(6)Na2Mn3 trigonal bipyramids, edges with two equivalent O(5)Na3MgMn2 octahedra,  an edgeedge with one O(1)Na2MgMn2 trigonal bipyramid, and  a faceface with one O(1)Na2MgMn2 trigonal bipyramid. In the sixth O site, O(6) is bonded to two equivalent Na(3), one Mn(1), and two equivalent Mn(2) atoms to form distorted ONa2Mn3 trigonal bipyramids that share corners with four equivalent O(5)Na3MgMn2 octahedra, corners with two equivalent O(1)Na2MgMn2 trigonal bipyramids, corners with four equivalent O(2)Na3Mn2 trigonal bipyramids, edges with two equivalent O(6)Na2Mn3 trigonal bipyramids, and edges with two equivalent O(2)Na3Mn2 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 61-64°. In the seventh O site, O(7) is bonded in a 6-coordinate geometry to one Na(4), two equivalent Na(2), one Mn(3), and two equivalent Mn(4) atoms. In the eighth O site, O(8) is bonded in a 6-coordinate geometry to one Na(2), two equivalent Na(4), one Mn(4), and two equivalent Mn(3) atoms.