Ba4Mn2NaO9 crystallizes in the trigonal P321 space group. There are two inequivalent Na sites. In the first Na site, Na(1) is bonded in a 6-coordinate geometry to three equivalent O(4) and three equivalent O(5) atoms. In the second Na site, Na(2) is bonded in a 6-coordinate geometry to six equivalent O(3) atoms. There are three inequivalent Ba sites. In the first Ba site, Ba(1) is bonded in a 8-coordinate geometry to two equivalent O(1), two equivalent O(3), and four equivalent O(4) atoms. In the second Ba site, Ba(2) is bonded in a 10-coordinate geometry to two equivalent O(1), two equivalent O(2), two equivalent O(3), and four equivalent O(5) atoms. In the third Ba site, Ba(3) is bonded in a 9-coordinate geometry to one O(2), two equivalent O(1), two equivalent O(3), two equivalent O(4), and two equivalent O(5) atoms. There are three inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to three equivalent O(1) and three equivalent O(4) atoms to form face-sharing MnO6 octahedra. In the second Mn site, Mn(2) is bonded to three equivalent O(2) and three equivalent O(3) atoms to form face-sharing MnO6 octahedra. In the third Mn site, Mn(3) is bonded to three equivalent O(1) and three equivalent O(5) atoms to form face-sharing MnO6 octahedra. There are five inequivalent O sites. In the first O site, O(1) is bonded to one Ba(1), one Ba(2), two equivalent Ba(3), one Mn(1), and one Mn(3) atom to form a mixture of distorted face, corner, and edge-sharing OBa4Mn2 octahedra. The corner-sharing octahedral tilt angles range from 34-53°. In the second O site, O(2) is bonded to two equivalent Ba(2), two equivalent Ba(3), and two equivalent Mn(2) atoms to form a mixture of distorted face, corner, and edge-sharing OBa4Mn2 octahedra. The corner-sharing octahedral tilt angles are 53°. In the third O site, O(3) is bonded in a 6-coordinate geometry to one Na(2), one Ba(1), one Ba(2), two equivalent Ba(3), and one Mn(2) atom. In the fourth O site, O(4) is bonded in a 6-coordinate geometry to one Na(1), two equivalent Ba(1), two equivalent Ba(3), and one Mn(1) atom. In the fifth O site, O(5) is bonded in a 6-coordinate geometry to one Na(1), two equivalent Ba(2), two equivalent Ba(3), and one Mn(3) atom.
Ba4Mn2NaO9 crystallizes in the trigonal P321 space group. There are two inequivalent Na sites. In the first Na site, Na(1) is bonded in a 6-coordinate geometry to three equivalent O(4) and three equivalent O(5) atoms. All Na(1)-O(4) bond lengths are 2.42 Å. All Na(1)-O(5) bond lengths are 2.42 Å. In the second Na site, Na(2) is bonded in a 6-coordinate geometry to six equivalent O(3) atoms. All Na(2)-O(3) bond lengths are 2.46 Å. There are three inequivalent Ba sites. In the first Ba site, Ba(1) is bonded in a 8-coordinate geometry to two equivalent O(1), two equivalent O(3), and four equivalent O(4) atoms. Both Ba(1)-O(1) bond lengths are 2.79 Å. Both Ba(1)-O(3) bond lengths are 2.70 Å. There are two shorter (2.84 Å) and two longer (2.88 Å) Ba(1)-O(4) bond lengths. In the second Ba site, Ba(2) is bonded in a 10-coordinate geometry to two equivalent O(1), two equivalent O(2), two equivalent O(3), and four equivalent O(5) atoms. Both Ba(2)-O(1) bond lengths are 2.82 Å. Both Ba(2)-O(2) bond lengths are 2.88 Å. Both Ba(2)-O(3) bond lengths are 2.91 Å. There are two shorter (2.91 Å) and two longer (3.07 Å) Ba(2)-O(5) bond lengths. In the third Ba site, Ba(3) is bonded in a 9-coordinate geometry to one O(2), two equivalent O(1), two equivalent O(3), two equivalent O(4), and two equivalent O(5) atoms. The Ba(3)-O(2) bond length is 2.76 Å. There is one shorter (2.82 Å) and one longer (2.85 Å) Ba(3)-O(1) bond length. There is one shorter (2.86 Å) and one longer (2.90 Å) Ba(3)-O(3) bond length. There is one shorter (2.77 Å) and one longer (2.90 Å) Ba(3)-O(4) bond length. There is one shorter (2.67 Å) and one longer (2.93 Å) Ba(3)-O(5) bond length. There are three inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to three equivalent O(1) and three equivalent O(4) atoms to form face-sharing MnO6 octahedra. All Mn(1)-O(1) bond lengths are 2.02 Å. All Mn(1)-O(4) bond lengths are 1.91 Å. In the second Mn site, Mn(2) is bonded to three equivalent O(2) and three equivalent O(3) atoms to form face-sharing MnO6 octahedra. All Mn(2)-O(2) bond lengths are 2.00 Å. All Mn(2)-O(3) bond lengths are 1.92 Å. In the third Mn site, Mn(3) is bonded to three equivalent O(1) and three equivalent O(5) atoms to form face-sharing MnO6 octahedra. All Mn(3)-O(1) bond lengths are 2.02 Å. All Mn(3)-O(5) bond lengths are 1.89 Å. There are five inequivalent O sites. In the first O site, O(1) is bonded to one Ba(1), one Ba(2), two equivalent Ba(3), one Mn(1), and one Mn(3) atom to form a mixture of distorted face, corner, and edge-sharing OBa4Mn2 octahedra. The corner-sharing octahedral tilt angles range from 34-53°. In the second O site, O(2) is bonded to two equivalent Ba(2), two equivalent Ba(3), and two equivalent Mn(2) atoms to form a mixture of distorted face, corner, and edge-sharing OBa4Mn2 octahedra. The corner-sharing octahedral tilt angles are 53°. In the third O site, O(3) is bonded in a 6-coordinate geometry to one Na(2), one Ba(1), one Ba(2), two equivalent Ba(3), and one Mn(2) atom. In the fourth O site, O(4) is bonded in a 6-coordinate geometry to one Na(1), two equivalent Ba(1), two equivalent Ba(3), and one Mn(1) atom. In the fifth O site, O(5) is bonded in a 6-coordinate geometry to one Na(1), two equivalent Ba(2), two equivalent Ba(3), and one Mn(3) atom.