Na4FeO5 crystallizes in the tetragonal P4 space group. There are four inequivalent Na sites. In the first Na site, Na(1) is bonded to one O(1), one O(5), one O(7), and three equivalent O(8) atoms to form distorted NaO6 octahedra that share corners with two equivalent Na(3)O6 octahedra, corners with three equivalent Na(1)O6 octahedra,  a cornercorner with one Fe(4)O5 square pyramid,  an edgeedge with one Fe(1)O6 octahedra, edges with three equivalent Na(1)O6 octahedra, edges with three equivalent Na(2)O6 octahedra, edges with three equivalent Na(4)O6 octahedra,  an edgeedge with one Fe(3)O5 square pyramid, and  an edgeedge with one Fe(4)O5 square pyramid. The corner-sharing octahedral tilt angles range from 11-24°. In the second Na site, Na(2) is bonded to one O(2), one O(6), one O(8), and three equivalent O(5) atoms to form distorted NaO6 octahedra that share  a cornercorner with one Fe(1)O6 octahedra, corners with two equivalent Na(4)O6 octahedra, corners with three equivalent Na(2)O6 octahedra,  a cornercorner with one Fe(4)O5 square pyramid,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra, edges with three equivalent Na(1)O6 octahedra, edges with three equivalent Na(2)O6 octahedra, and edges with three equivalent Na(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 6-27°. In the third Na site, Na(3) is bonded to one O(3), one O(5), one O(7), and three equivalent O(6) atoms to form distorted NaO6 octahedra that share  a cornercorner with one Fe(2)O6 octahedra, corners with two equivalent Na(1)O6 octahedra, corners with three equivalent Na(3)O6 octahedra,  a cornercorner with one Fe(3)O5 square pyramid,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra, edges with three equivalent Na(2)O6 octahedra, edges with three equivalent Na(3)O6 octahedra, and edges with three equivalent Na(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 6-27°. In the fourth Na site, Na(4) is bonded to one O(4), one O(6), one O(8), and three equivalent O(7) atoms to form distorted NaO6 octahedra that share corners with two equivalent Na(2)O6 octahedra, corners with three equivalent Na(4)O6 octahedra,  a cornercorner with one Fe(3)O5 square pyramid,  an edgeedge with one Fe(2)O6 octahedra, edges with three equivalent Na(1)O6 octahedra, edges with three equivalent Na(3)O6 octahedra, edges with three equivalent Na(4)O6 octahedra,  an edgeedge with one Fe(3)O5 square pyramid, and  an edgeedge with one Fe(4)O5 square pyramid. The corner-sharing octahedral tilt angles range from 12-24°. There are four inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to one O(1), one O(3), and four equivalent O(5) atoms to form FeO6 octahedra that share corners with four equivalent Na(2)O6 octahedra,  a cornercorner with one Fe(3)O5 square pyramid, edges with four equivalent Na(1)O6 octahedra, edges with four equivalent Na(2)O6 octahedra, and edges with four equivalent Na(3)O6 octahedra. The corner-sharing octahedral tilt angles are 6°. In the second Fe site, Fe(2) is bonded to one O(2), one O(4), and four equivalent O(6) atoms to form FeO6 octahedra that share corners with four equivalent Na(3)O6 octahedra,  a cornercorner with one Fe(4)O5 square pyramid, edges with four equivalent Na(2)O6 octahedra, edges with four equivalent Na(3)O6 octahedra, and edges with four equivalent Na(4)O6 octahedra. The corner-sharing octahedral tilt angles are 6°. In the third Fe site, Fe(3) is bonded to one O(1) and four equivalent O(7) atoms to form FeO5 square pyramids that share  a cornercorner with one Fe(1)O6 octahedra, corners with four equivalent Na(3)O6 octahedra, corners with four equivalent Na(4)O6 octahedra, edges with four equivalent Na(1)O6 octahedra, and edges with four equivalent Na(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-72°. In the fourth Fe site, Fe(4) is bonded to one O(4) and four equivalent O(8) atoms to form FeO5 square pyramids that share  a cornercorner with one Fe(2)O6 octahedra, corners with four equivalent Na(1)O6 octahedra, corners with four equivalent Na(2)O6 octahedra, edges with four equivalent Na(1)O6 octahedra, and edges with four equivalent Na(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-72°. There are eight inequivalent O sites. In the first O site, O(1) is bonded to four equivalent Na(1), one Fe(1), and one Fe(3) atom to form corner-sharing ONa4Fe2 octahedra. In the second O site, O(2) is bonded to four equivalent Na(2) and one Fe(2) atom to form distorted corner-sharing ONa4Fe trigonal bipyramids. The corner-sharing octahedra are not tilted. In the third O site, O(3) is bonded to four equivalent Na(3) and one Fe(1) atom to form distorted corner-sharing ONa4Fe trigonal bipyramids. The corner-sharing octahedra are not tilted. In the fourth O site, O(4) is bonded to four equivalent Na(4), one Fe(2), and one Fe(4) atom to form corner-sharing ONa4Fe2 octahedra. In the fifth O site, O(5) is bonded in a 6-coordinate geometry to one Na(1), one Na(3), three equivalent Na(2), and one Fe(1) atom. In the sixth O site, O(6) is bonded in a 6-coordinate geometry to one Na(2), one Na(4), three equivalent Na(3), and one Fe(2) atom. In the seventh O site, O(7) is bonded in a 6-coordinate geometry to one Na(1), one Na(3), three equivalent Na(4), and one Fe(3) atom. In the eighth O site, O(8) is bonded in a 6-coordinate geometry to one Na(2), one Na(4), three equivalent Na(1), and one Fe(4) atom.
Na4FeO5 crystallizes in the tetragonal P4 space group. There are four inequivalent Na sites. In the first Na site, Na(1) is bonded to one O(1), one O(5), one O(7), and three equivalent O(8) atoms to form distorted NaO6 octahedra that share corners with two equivalent Na(3)O6 octahedra, corners with three equivalent Na(1)O6 octahedra,  a cornercorner with one Fe(4)O5 square pyramid,  an edgeedge with one Fe(1)O6 octahedra, edges with three equivalent Na(1)O6 octahedra, edges with three equivalent Na(2)O6 octahedra, edges with three equivalent Na(4)O6 octahedra,  an edgeedge with one Fe(3)O5 square pyramid, and  an edgeedge with one Fe(4)O5 square pyramid. The corner-sharing octahedral tilt angles range from 11-24°. The Na(1)-O(1) bond length is 2.33 Å. The Na(1)-O(5) bond length is 2.32 Å. The Na(1)-O(7) bond length is 2.36 Å. There are a spread of Na(1)-O(8) bond distances ranging from 2.33-2.89 Å. In the second Na site, Na(2) is bonded to one O(2), one O(6), one O(8), and three equivalent O(5) atoms to form distorted NaO6 octahedra that share  a cornercorner with one Fe(1)O6 octahedra, corners with two equivalent Na(4)O6 octahedra, corners with three equivalent Na(2)O6 octahedra,  a cornercorner with one Fe(4)O5 square pyramid,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra, edges with three equivalent Na(1)O6 octahedra, edges with three equivalent Na(2)O6 octahedra, and edges with three equivalent Na(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 6-27°. The Na(2)-O(2) bond length is 2.34 Å. The Na(2)-O(6) bond length is 2.42 Å. The Na(2)-O(8) bond length is 2.40 Å. There are a spread of Na(2)-O(5) bond distances ranging from 2.36-2.84 Å. In the third Na site, Na(3) is bonded to one O(3), one O(5), one O(7), and three equivalent O(6) atoms to form distorted NaO6 octahedra that share  a cornercorner with one Fe(2)O6 octahedra, corners with two equivalent Na(1)O6 octahedra, corners with three equivalent Na(3)O6 octahedra,  a cornercorner with one Fe(3)O5 square pyramid,  an edgeedge with one Fe(1)O6 octahedra,  an edgeedge with one Fe(2)O6 octahedra, edges with three equivalent Na(2)O6 octahedra, edges with three equivalent Na(3)O6 octahedra, and edges with three equivalent Na(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 6-27°. The Na(3)-O(3) bond length is 2.33 Å. The Na(3)-O(5) bond length is 2.41 Å. The Na(3)-O(7) bond length is 2.40 Å. There are a spread of Na(3)-O(6) bond distances ranging from 2.37-2.83 Å. In the fourth Na site, Na(4) is bonded to one O(4), one O(6), one O(8), and three equivalent O(7) atoms to form distorted NaO6 octahedra that share corners with two equivalent Na(2)O6 octahedra, corners with three equivalent Na(4)O6 octahedra,  a cornercorner with one Fe(3)O5 square pyramid,  an edgeedge with one Fe(2)O6 octahedra, edges with three equivalent Na(1)O6 octahedra, edges with three equivalent Na(3)O6 octahedra, edges with three equivalent Na(4)O6 octahedra,  an edgeedge with one Fe(3)O5 square pyramid, and  an edgeedge with one Fe(4)O5 square pyramid. The corner-sharing octahedral tilt angles range from 12-24°. The Na(4)-O(4) bond length is 2.34 Å. The Na(4)-O(6) bond length is 2.33 Å. The Na(4)-O(8) bond length is 2.35 Å. There are a spread of Na(4)-O(7) bond distances ranging from 2.33-2.90 Å. There are four inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to one O(1), one O(3), and four equivalent O(5) atoms to form FeO6 octahedra that share corners with four equivalent Na(2)O6 octahedra,  a cornercorner with one Fe(3)O5 square pyramid, edges with four equivalent Na(1)O6 octahedra, edges with four equivalent Na(2)O6 octahedra, and edges with four equivalent Na(3)O6 octahedra. The corner-sharing octahedral tilt angles are 6°. The Fe(1)-O(1) bond length is 2.02 Å. The Fe(1)-O(3) bond length is 1.87 Å. All Fe(1)-O(5) bond lengths are 1.88 Å. In the second Fe site, Fe(2) is bonded to one O(2), one O(4), and four equivalent O(6) atoms to form FeO6 octahedra that share corners with four equivalent Na(3)O6 octahedra,  a cornercorner with one Fe(4)O5 square pyramid, edges with four equivalent Na(2)O6 octahedra, edges with four equivalent Na(3)O6 octahedra, and edges with four equivalent Na(4)O6 octahedra. The corner-sharing octahedral tilt angles are 6°. The Fe(2)-O(2) bond length is 1.87 Å. The Fe(2)-O(4) bond length is 2.00 Å. All Fe(2)-O(6) bond lengths are 1.89 Å. In the third Fe site, Fe(3) is bonded to one O(1) and four equivalent O(7) atoms to form FeO5 square pyramids that share  a cornercorner with one Fe(1)O6 octahedra, corners with four equivalent Na(3)O6 octahedra, corners with four equivalent Na(4)O6 octahedra, edges with four equivalent Na(1)O6 octahedra, and edges with four equivalent Na(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-72°. The Fe(3)-O(1) bond length is 2.29 Å. All Fe(3)-O(7) bond lengths are 1.84 Å. In the fourth Fe site, Fe(4) is bonded to one O(4) and four equivalent O(8) atoms to form FeO5 square pyramids that share  a cornercorner with one Fe(2)O6 octahedra, corners with four equivalent Na(1)O6 octahedra, corners with four equivalent Na(2)O6 octahedra, edges with four equivalent Na(1)O6 octahedra, and edges with four equivalent Na(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-72°. The Fe(4)-O(4) bond length is 2.31 Å. All Fe(4)-O(8) bond lengths are 1.84 Å. There are eight inequivalent O sites. In the first O site, O(1) is bonded to four equivalent Na(1), one Fe(1), and one Fe(3) atom to form corner-sharing ONa4Fe2 octahedra. In the second O site, O(2) is bonded to four equivalent Na(2) and one Fe(2) atom to form distorted corner-sharing ONa4Fe trigonal bipyramids. The corner-sharing octahedra are not tilted. In the third O site, O(3) is bonded to four equivalent Na(3) and one Fe(1) atom to form distorted corner-sharing ONa4Fe trigonal bipyramids. The corner-sharing octahedra are not tilted. In the fourth O site, O(4) is bonded to four equivalent Na(4), one Fe(2), and one Fe(4) atom to form corner-sharing ONa4Fe2 octahedra. In the fifth O site, O(5) is bonded in a 6-coordinate geometry to one Na(1), one Na(3), three equivalent Na(2), and one Fe(1) atom. In the sixth O site, O(6) is bonded in a 6-coordinate geometry to one Na(2), one Na(4), three equivalent Na(3), and one Fe(2) atom. In the seventh O site, O(7) is bonded in a 6-coordinate geometry to one Na(1), one Na(3), three equivalent Na(4), and one Fe(3) atom. In the eighth O site, O(8) is bonded in a 6-coordinate geometry to one Na(2), one Na(4), three equivalent Na(1), and one Fe(4) atom.