Ba5Nd8Mn4O21 crystallizes in the tetragonal I4/m space group. There are two inequivalent Ba sites. In the first Ba site, Ba(1) is bonded in a 10-coordinate geometry to two equivalent O(2), four equivalent O(1), and four equivalent O(3) atoms. In the second Ba site, Ba(2) is bonded in a distorted q6 geometry to two equivalent O(4) and eight equivalent O(2) atoms. There are two inequivalent Nd sites. In the first Nd site, Nd(1) is bonded to one O(4), two equivalent O(1), and four equivalent O(2) atoms to form distorted NdO7 pentagonal bipyramids that share  a cornercorner with one Nd(1)O7 pentagonal bipyramid, corners with two equivalent Mn(1)O5 trigonal bipyramids, edges with two equivalent Mn(1)O5 trigonal bipyramids, and faces with two equivalent Nd(1)O7 pentagonal bipyramids. In the second Nd site, Nd(2) is bonded in a 7-coordinate geometry to one O(3), two equivalent O(2), and four equivalent O(1) atoms. Mn(1) is bonded to one O(3), two equivalent O(1), and two equivalent O(2) atoms to form distorted MnO5 trigonal bipyramids that share corners with two equivalent Nd(1)O7 pentagonal bipyramids and edges with two equivalent Nd(1)O7 pentagonal bipyramids. There are four inequivalent O sites. In the first O site, O(1) is bonded in a 4-coordinate geometry to two equivalent Ba(1), one Nd(1), two equivalent Nd(2), and one Mn(1) atom. In the second O site, O(2) is bonded to one Ba(1), one Ba(2), one Nd(2), two equivalent Nd(1), and one Mn(1) atom to form distorted OBa2Nd3Mn octahedra that share  a cornercorner with one O(4)Ba2Nd4 octahedra, corners with three equivalent O(3)Ba4NdMn octahedra, corners with six equivalent O(2)Ba2Nd3Mn octahedra, edges with two equivalent O(2)Ba2Nd3Mn octahedra,  a faceface with one O(4)Ba2Nd4 octahedra,  a faceface with one O(3)Ba4NdMn octahedra, and faces with two equivalent O(2)Ba2Nd3Mn octahedra. The corner-sharing octahedral tilt angles range from 0-76°. In the third O site, O(3) is bonded to four equivalent Ba(1), one Nd(2), and one Mn(1) atom to form distorted OBa4NdMn octahedra that share corners with two equivalent O(3)Ba4NdMn octahedra, corners with six equivalent O(2)Ba2Nd3Mn octahedra, edges with five equivalent O(3)Ba4NdMn octahedra, and faces with two equivalent O(2)Ba2Nd3Mn octahedra. The corner-sharing octahedral tilt angles range from 7-57°. In the fourth O site, O(4) is bonded to two equivalent Ba(2) and four equivalent Nd(1) atoms to form OBa2Nd4 octahedra that share corners with two equivalent O(4)Ba2Nd4 octahedra, corners with eight equivalent O(2)Ba2Nd3Mn octahedra, and faces with eight equivalent O(2)Ba2Nd3Mn octahedra. The corner-sharing octahedral tilt angles range from 0-61°.
Ba5Nd8Mn4O21 crystallizes in the tetragonal I4/m space group. There are two inequivalent Ba sites. In the first Ba site, Ba(1) is bonded in a 10-coordinate geometry to two equivalent O(2), four equivalent O(1), and four equivalent O(3) atoms. Both Ba(1)-O(2) bond lengths are 3.07 Å. There are two shorter (3.34 Å) and two longer (3.37 Å) Ba(1)-O(1) bond lengths. There are a spread of Ba(1)-O(3) bond distances ranging from 2.67-2.98 Å. In the second Ba site, Ba(2) is bonded in a distorted q6 geometry to two equivalent O(4) and eight equivalent O(2) atoms. Both Ba(2)-O(4) bond lengths are 2.97 Å. All Ba(2)-O(2) bond lengths are 3.04 Å. There are two inequivalent Nd sites. In the first Nd site, Nd(1) is bonded to one O(4), two equivalent O(1), and four equivalent O(2) atoms to form distorted NdO7 pentagonal bipyramids that share  a cornercorner with one Nd(1)O7 pentagonal bipyramid, corners with two equivalent Mn(1)O5 trigonal bipyramids, edges with two equivalent Mn(1)O5 trigonal bipyramids, and faces with two equivalent Nd(1)O7 pentagonal bipyramids. The Nd(1)-O(4) bond length is 2.43 Å. Both Nd(1)-O(1) bond lengths are 2.41 Å. There are two shorter (2.43 Å) and two longer (2.51 Å) Nd(1)-O(2) bond lengths. In the second Nd site, Nd(2) is bonded in a 7-coordinate geometry to one O(3), two equivalent O(2), and four equivalent O(1) atoms. The Nd(2)-O(3) bond length is 2.71 Å. Both Nd(2)-O(2) bond lengths are 2.50 Å. There are two shorter (2.38 Å) and two longer (2.43 Å) Nd(2)-O(1) bond lengths. Mn(1) is bonded to one O(3), two equivalent O(1), and two equivalent O(2) atoms to form distorted MnO5 trigonal bipyramids that share corners with two equivalent Nd(1)O7 pentagonal bipyramids and edges with two equivalent Nd(1)O7 pentagonal bipyramids. The Mn(1)-O(3) bond length is 2.08 Å. Both Mn(1)-O(1) bond lengths are 2.13 Å. Both Mn(1)-O(2) bond lengths are 2.20 Å. There are four inequivalent O sites. In the first O site, O(1) is bonded in a 4-coordinate geometry to two equivalent Ba(1), one Nd(1), two equivalent Nd(2), and one Mn(1) atom. In the second O site, O(2) is bonded to one Ba(1), one Ba(2), one Nd(2), two equivalent Nd(1), and one Mn(1) atom to form distorted OBa2Nd3Mn octahedra that share  a cornercorner with one O(4)Ba2Nd4 octahedra, corners with three equivalent O(3)Ba4NdMn octahedra, corners with six equivalent O(2)Ba2Nd3Mn octahedra, edges with two equivalent O(2)Ba2Nd3Mn octahedra,  a faceface with one O(4)Ba2Nd4 octahedra,  a faceface with one O(3)Ba4NdMn octahedra, and faces with two equivalent O(2)Ba2Nd3Mn octahedra. The corner-sharing octahedral tilt angles range from 0-76°. In the third O site, O(3) is bonded to four equivalent Ba(1), one Nd(2), and one Mn(1) atom to form distorted OBa4NdMn octahedra that share corners with two equivalent O(3)Ba4NdMn octahedra, corners with six equivalent O(2)Ba2Nd3Mn octahedra, edges with five equivalent O(3)Ba4NdMn octahedra, and faces with two equivalent O(2)Ba2Nd3Mn octahedra. The corner-sharing octahedral tilt angles range from 7-57°. In the fourth O site, O(4) is bonded to two equivalent Ba(2) and four equivalent Nd(1) atoms to form OBa2Nd4 octahedra that share corners with two equivalent O(4)Ba2Nd4 octahedra, corners with eight equivalent O(2)Ba2Nd3Mn octahedra, and faces with eight equivalent O(2)Ba2Nd3Mn octahedra. The corner-sharing octahedral tilt angles range from 0-61°.