Ba5Gd8Mn4O21 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 Gd sites. In the first Gd site, Gd(1) is bonded in a 7-coordinate geometry to one O(3), two equivalent O(2), and four equivalent O(1) atoms. In the second Gd site, Gd(2) is bonded to one O(4), two equivalent O(1), and four equivalent O(2) atoms to form distorted GdO7 pentagonal bipyramids that share  a cornercorner with one Gd(2)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 Gd(2)O7 pentagonal bipyramids. 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 Gd(2)O7 pentagonal bipyramids and edges with two equivalent Gd(2)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 Gd(2), two equivalent Gd(1), and one Mn(1) atom. In the second O site, O(2) is bonded to one Ba(1), one Ba(2), one Gd(1), two equivalent Gd(2), and one Mn(1) atom to form distorted OBa2Gd3Mn octahedra that share  a cornercorner with one O(4)Ba2Gd4 octahedra, corners with three equivalent O(3)Ba4GdMn octahedra, corners with six equivalent O(2)Ba2Gd3Mn octahedra, edges with two equivalent O(2)Ba2Gd3Mn octahedra,  a faceface with one O(4)Ba2Gd4 octahedra,  a faceface with one O(3)Ba4GdMn octahedra, and faces with two equivalent O(2)Ba2Gd3Mn 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 Gd(1), and one Mn(1) atom to form distorted OBa4GdMn octahedra that share corners with two equivalent O(3)Ba4GdMn octahedra, corners with six equivalent O(2)Ba2Gd3Mn octahedra, edges with five equivalent O(3)Ba4GdMn octahedra, and faces with two equivalent O(2)Ba2Gd3Mn octahedra. The corner-sharing octahedral tilt angles range from 7-58°. In the fourth O site, O(4) is bonded to two equivalent Ba(2) and four equivalent Gd(2) atoms to form OBa2Gd4 octahedra that share corners with two equivalent O(4)Ba2Gd4 octahedra, corners with eight equivalent O(2)Ba2Gd3Mn octahedra, and faces with eight equivalent O(2)Ba2Gd3Mn octahedra. The corner-sharing octahedral tilt angles range from 0-61°.
Ba5Gd8Mn4O21 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 3.00 Å. All Ba(1)-O(1) bond lengths are 3.31 Å. There are a spread of Ba(1)-O(3) bond distances ranging from 2.67-2.93 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 2.93 Å. All Ba(2)-O(2) bond lengths are 2.99 Å. There are two inequivalent Gd sites. In the first Gd site, Gd(1) is bonded in a 7-coordinate geometry to one O(3), two equivalent O(2), and four equivalent O(1) atoms. The Gd(1)-O(3) bond length is 2.61 Å. Both Gd(1)-O(2) bond lengths are 2.47 Å. There are two shorter (2.31 Å) and two longer (2.38 Å) Gd(1)-O(1) bond lengths. In the second Gd site, Gd(2) is bonded to one O(4), two equivalent O(1), and four equivalent O(2) atoms to form distorted GdO7 pentagonal bipyramids that share  a cornercorner with one Gd(2)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 Gd(2)O7 pentagonal bipyramids. The Gd(2)-O(4) bond length is 2.37 Å. Both Gd(2)-O(1) bond lengths are 2.36 Å. There are two shorter (2.34 Å) and two longer (2.49 Å) Gd(2)-O(2) 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 Gd(2)O7 pentagonal bipyramids and edges with two equivalent Gd(2)O7 pentagonal bipyramids. The Mn(1)-O(3) bond length is 2.07 Å. Both Mn(1)-O(1) bond lengths are 2.12 Å. Both Mn(1)-O(2) bond lengths are 2.17 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 Gd(2), two equivalent Gd(1), and one Mn(1) atom. In the second O site, O(2) is bonded to one Ba(1), one Ba(2), one Gd(1), two equivalent Gd(2), and one Mn(1) atom to form distorted OBa2Gd3Mn octahedra that share  a cornercorner with one O(4)Ba2Gd4 octahedra, corners with three equivalent O(3)Ba4GdMn octahedra, corners with six equivalent O(2)Ba2Gd3Mn octahedra, edges with two equivalent O(2)Ba2Gd3Mn octahedra,  a faceface with one O(4)Ba2Gd4 octahedra,  a faceface with one O(3)Ba4GdMn octahedra, and faces with two equivalent O(2)Ba2Gd3Mn 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 Gd(1), and one Mn(1) atom to form distorted OBa4GdMn octahedra that share corners with two equivalent O(3)Ba4GdMn octahedra, corners with six equivalent O(2)Ba2Gd3Mn octahedra, edges with five equivalent O(3)Ba4GdMn octahedra, and faces with two equivalent O(2)Ba2Gd3Mn octahedra. The corner-sharing octahedral tilt angles range from 7-58°. In the fourth O site, O(4) is bonded to two equivalent Ba(2) and four equivalent Gd(2) atoms to form OBa2Gd4 octahedra that share corners with two equivalent O(4)Ba2Gd4 octahedra, corners with eight equivalent O(2)Ba2Gd3Mn octahedra, and faces with eight equivalent O(2)Ba2Gd3Mn octahedra. The corner-sharing octahedral tilt angles range from 0-61°.