Na4BaO3 crystallizes in the monoclinic Cc space group. There are four inequivalent Na sites. In the first Na site, Na(1) is bonded in a trigonal planar geometry to one O(1), one O(2), and one O(3) atom. In the second Na site, Na(2) is bonded in a distorted trigonal planar geometry to one O(2) and two equivalent O(1) atoms. In the third Na site, Na(3) is bonded to one O(1), one O(3), and two equivalent O(2) atoms to form distorted NaO4 tetrahedra that share corners with two equivalent Na(3)O4 tetrahedra, corners with three equivalent Ba(1)O4 tetrahedra, and  an edgeedge with one Ba(1)O4 tetrahedra. In the fourth Na site, Na(4) is bonded in a 3-coordinate geometry to one O(1), one O(2), and one O(3) atom. Ba(1) is bonded to one O(1), one O(2), and two equivalent O(3) atoms to form BaO4 tetrahedra that share corners with two equivalent Ba(1)O4 tetrahedra, corners with three equivalent Na(3)O4 tetrahedra, and  an edgeedge with one Na(3)O4 tetrahedra. There are three inequivalent O sites. In the first O site, O(1) is bonded to one Na(1), one Na(3), one Na(4), two equivalent Na(2), and one Ba(1) atom to form OBaNa5 octahedra that share corners with two equivalent O(1)BaNa5 octahedra, corners with three equivalent O(2)BaNa5 octahedra, corners with three equivalent O(3)Ba2Na3 trigonal bipyramids, edges with two equivalent O(2)BaNa5 octahedra, and  an edgeedge with one O(3)Ba2Na3 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 50-56°. In the second O site, O(2) is bonded to one Na(1), one Na(2), one Na(4), two equivalent Na(3), and one Ba(1) atom to form OBaNa5 octahedra that share corners with two equivalent O(2)BaNa5 octahedra, corners with three equivalent O(1)BaNa5 octahedra, corners with four equivalent O(3)Ba2Na3 trigonal bipyramids, edges with two equivalent O(1)BaNa5 octahedra, and  an edgeedge with one O(3)Ba2Na3 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 50-61°. In the third O site, O(3) is bonded to one Na(1), one Na(3), one Na(4), and two equivalent Ba(1) atoms to form distorted OBa2Na3 trigonal bipyramids that share corners with three equivalent O(1)BaNa5 octahedra, corners with four equivalent O(2)BaNa5 octahedra, corners with two equivalent O(3)Ba2Na3 trigonal bipyramids,  an edgeedge with one O(1)BaNa5 octahedra, and  an edgeedge with one O(2)BaNa5 octahedra. The corner-sharing octahedral tilt angles range from 34-71°.
Na4BaO3 crystallizes in the monoclinic Cc space group. There are four inequivalent Na sites. In the first Na site, Na(1) is bonded in a trigonal planar geometry to one O(1), one O(2), and one O(3) atom. The Na(1)-O(1) bond length is 2.27 Å. The Na(1)-O(2) bond length is 2.42 Å. The Na(1)-O(3) bond length is 2.26 Å. In the second Na site, Na(2) is bonded in a distorted trigonal planar geometry to one O(2) and two equivalent O(1) atoms. The Na(2)-O(2) bond length is 2.29 Å. There is one shorter (2.32 Å) and one longer (2.38 Å) Na(2)-O(1) bond length. In the third Na site, Na(3) is bonded to one O(1), one O(3), and two equivalent O(2) atoms to form distorted NaO4 tetrahedra that share corners with two equivalent Na(3)O4 tetrahedra, corners with three equivalent Ba(1)O4 tetrahedra, and  an edgeedge with one Ba(1)O4 tetrahedra. The Na(3)-O(1) bond length is 2.36 Å. The Na(3)-O(3) bond length is 2.57 Å. There is one shorter (2.35 Å) and one longer (2.44 Å) Na(3)-O(2) bond length. In the fourth Na site, Na(4) is bonded in a 3-coordinate geometry to one O(1), one O(2), and one O(3) atom. The Na(4)-O(1) bond length is 2.44 Å. The Na(4)-O(2) bond length is 2.26 Å. The Na(4)-O(3) bond length is 2.25 Å. Ba(1) is bonded to one O(1), one O(2), and two equivalent O(3) atoms to form BaO4 tetrahedra that share corners with two equivalent Ba(1)O4 tetrahedra, corners with three equivalent Na(3)O4 tetrahedra, and  an edgeedge with one Na(3)O4 tetrahedra. The Ba(1)-O(1) bond length is 2.62 Å. The Ba(1)-O(2) bond length is 2.60 Å. There is one shorter (2.64 Å) and one longer (2.66 Å) Ba(1)-O(3) bond length. There are three inequivalent O sites. In the first O site, O(1) is bonded to one Na(1), one Na(3), one Na(4), two equivalent Na(2), and one Ba(1) atom to form OBaNa5 octahedra that share corners with two equivalent O(1)BaNa5 octahedra, corners with three equivalent O(2)BaNa5 octahedra, corners with three equivalent O(3)Ba2Na3 trigonal bipyramids, edges with two equivalent O(2)BaNa5 octahedra, and  an edgeedge with one O(3)Ba2Na3 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 50-56°. In the second O site, O(2) is bonded to one Na(1), one Na(2), one Na(4), two equivalent Na(3), and one Ba(1) atom to form OBaNa5 octahedra that share corners with two equivalent O(2)BaNa5 octahedra, corners with three equivalent O(1)BaNa5 octahedra, corners with four equivalent O(3)Ba2Na3 trigonal bipyramids, edges with two equivalent O(1)BaNa5 octahedra, and  an edgeedge with one O(3)Ba2Na3 trigonal bipyramid. The corner-sharing octahedral tilt angles range from 50-61°. In the third O site, O(3) is bonded to one Na(1), one Na(3), one Na(4), and two equivalent Ba(1) atoms to form distorted OBa2Na3 trigonal bipyramids that share corners with three equivalent O(1)BaNa5 octahedra, corners with four equivalent O(2)BaNa5 octahedra, corners with two equivalent O(3)Ba2Na3 trigonal bipyramids,  an edgeedge with one O(1)BaNa5 octahedra, and  an edgeedge with one O(2)BaNa5 octahedra. The corner-sharing octahedral tilt angles range from 34-71°.