Ba5Lu8Ni4O21 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(1), four equivalent O(2), and four equivalent O(4) atoms. In the second Ba site, Ba(2) is bonded in a distorted q6 geometry to two equivalent O(3) and eight equivalent O(1) atoms. There are two inequivalent Lu sites. In the first Lu site, Lu(1) is bonded to one O(3), two equivalent O(2), and four equivalent O(1) atoms to form distorted LuO7 pentagonal bipyramids that share  a cornercorner with one Lu(1)O7 pentagonal bipyramid, corners with two equivalent Lu(2)O7 pentagonal bipyramids, corners with two equivalent Ni(1)O5 trigonal bipyramids, edges with three equivalent Lu(2)O7 pentagonal bipyramids, edges with two equivalent Ni(1)O5 trigonal bipyramids, and faces with two equivalent Lu(1)O7 pentagonal bipyramids. In the second Lu site, Lu(2) is bonded to one O(4), two equivalent O(1), and four equivalent O(2) atoms to form distorted LuO7 pentagonal bipyramids that share corners with two equivalent Lu(1)O7 pentagonal bipyramids, corners with two equivalent Ni(1)O5 trigonal bipyramids, edges with two equivalent Lu(2)O7 pentagonal bipyramids, edges with three equivalent Lu(1)O7 pentagonal bipyramids,  an edgeedge with one Ni(1)O5 trigonal bipyramid, and  a faceface with one Ni(1)O5 trigonal bipyramid. Ni(1) is bonded to one O(4), two equivalent O(1), and two equivalent O(2) atoms to form NiO5 trigonal bipyramids that share corners with two equivalent Lu(1)O7 pentagonal bipyramids, corners with two equivalent Lu(2)O7 pentagonal bipyramids,  an edgeedge with one Lu(2)O7 pentagonal bipyramid, edges with two equivalent Lu(1)O7 pentagonal bipyramids, and  a faceface with one Lu(2)O7 pentagonal bipyramid. There are four inequivalent O sites. In the first O site, O(1) is bonded to one Ba(1), one Ba(2), one Lu(2), two equivalent Lu(1), and one Ni(1) atom to form distorted OBa2Lu3Ni octahedra that share  a cornercorner with one O(3)Ba2Lu4 octahedra, corners with three equivalent O(4)Ba4LuNi octahedra, corners with six equivalent O(1)Ba2Lu3Ni octahedra, edges with two equivalent O(1)Ba2Lu3Ni octahedra,  a faceface with one O(3)Ba2Lu4 octahedra,  a faceface with one O(4)Ba4LuNi octahedra, and faces with two equivalent O(1)Ba2Lu3Ni octahedra. The corner-sharing octahedral tilt angles range from 0-76°. In the second O site, O(2) is bonded in a 4-coordinate geometry to two equivalent Ba(1), one Lu(1), two equivalent Lu(2), and one Ni(1) atom. In the third O site, O(3) is bonded to two equivalent Ba(2) and four equivalent Lu(1) atoms to form OBa2Lu4 octahedra that share corners with two equivalent O(3)Ba2Lu4 octahedra, corners with eight equivalent O(1)Ba2Lu3Ni octahedra, and faces with eight equivalent O(1)Ba2Lu3Ni octahedra. The corner-sharing octahedral tilt angles range from 0-60°. In the fourth O site, O(4) is bonded to four equivalent Ba(1), one Lu(2), and one Ni(1) atom to form distorted OBa4LuNi octahedra that share corners with two equivalent O(4)Ba4LuNi octahedra, corners with six equivalent O(1)Ba2Lu3Ni octahedra, edges with five equivalent O(4)Ba4LuNi octahedra, and faces with two equivalent O(1)Ba2Lu3Ni octahedra. The corner-sharing octahedral tilt angles range from 4-61°.
Ba5Lu8Ni4O21 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(1), four equivalent O(2), and four equivalent O(4) atoms. Both Ba(1)-O(1) bond lengths are 2.86 Å. There are two shorter (3.13 Å) and two longer (3.23 Å) Ba(1)-O(2) bond lengths. There are a spread of Ba(1)-O(4) bond distances ranging from 2.69-2.83 Å. In the second Ba site, Ba(2) is bonded in a distorted q6 geometry to two equivalent O(3) and eight equivalent O(1) atoms. Both Ba(2)-O(3) bond lengths are 2.83 Å. All Ba(2)-O(1) bond lengths are 2.88 Å. There are two inequivalent Lu sites. In the first Lu site, Lu(1) is bonded to one O(3), two equivalent O(2), and four equivalent O(1) atoms to form distorted LuO7 pentagonal bipyramids that share  a cornercorner with one Lu(1)O7 pentagonal bipyramid, corners with two equivalent Lu(2)O7 pentagonal bipyramids, corners with two equivalent Ni(1)O5 trigonal bipyramids, edges with three equivalent Lu(2)O7 pentagonal bipyramids, edges with two equivalent Ni(1)O5 trigonal bipyramids, and faces with two equivalent Lu(1)O7 pentagonal bipyramids. The Lu(1)-O(3) bond length is 2.28 Å. Both Lu(1)-O(2) bond lengths are 2.26 Å. There are two shorter (2.25 Å) and two longer (2.39 Å) Lu(1)-O(1) bond lengths. In the second Lu site, Lu(2) is bonded to one O(4), two equivalent O(1), and four equivalent O(2) atoms to form distorted LuO7 pentagonal bipyramids that share corners with two equivalent Lu(1)O7 pentagonal bipyramids, corners with two equivalent Ni(1)O5 trigonal bipyramids, edges with two equivalent Lu(2)O7 pentagonal bipyramids, edges with three equivalent Lu(1)O7 pentagonal bipyramids,  an edgeedge with one Ni(1)O5 trigonal bipyramid, and  a faceface with one Ni(1)O5 trigonal bipyramid. The Lu(2)-O(4) bond length is 2.35 Å. Both Lu(2)-O(1) bond lengths are 2.37 Å. There are two shorter (2.23 Å) and two longer (2.32 Å) Lu(2)-O(2) bond lengths. Ni(1) is bonded to one O(4), two equivalent O(1), and two equivalent O(2) atoms to form NiO5 trigonal bipyramids that share corners with two equivalent Lu(1)O7 pentagonal bipyramids, corners with two equivalent Lu(2)O7 pentagonal bipyramids,  an edgeedge with one Lu(2)O7 pentagonal bipyramid, edges with two equivalent Lu(1)O7 pentagonal bipyramids, and  a faceface with one Lu(2)O7 pentagonal bipyramid. The Ni(1)-O(4) bond length is 2.01 Å. Both Ni(1)-O(1) bond lengths are 2.08 Å. Both Ni(1)-O(2) bond lengths are 2.04 Å. There are four inequivalent O sites. In the first O site, O(1) is bonded to one Ba(1), one Ba(2), one Lu(2), two equivalent Lu(1), and one Ni(1) atom to form distorted OBa2Lu3Ni octahedra that share  a cornercorner with one O(3)Ba2Lu4 octahedra, corners with three equivalent O(4)Ba4LuNi octahedra, corners with six equivalent O(1)Ba2Lu3Ni octahedra, edges with two equivalent O(1)Ba2Lu3Ni octahedra,  a faceface with one O(3)Ba2Lu4 octahedra,  a faceface with one O(4)Ba4LuNi octahedra, and faces with two equivalent O(1)Ba2Lu3Ni octahedra. The corner-sharing octahedral tilt angles range from 0-76°. In the second O site, O(2) is bonded in a 4-coordinate geometry to two equivalent Ba(1), one Lu(1), two equivalent Lu(2), and one Ni(1) atom. In the third O site, O(3) is bonded to two equivalent Ba(2) and four equivalent Lu(1) atoms to form OBa2Lu4 octahedra that share corners with two equivalent O(3)Ba2Lu4 octahedra, corners with eight equivalent O(1)Ba2Lu3Ni octahedra, and faces with eight equivalent O(1)Ba2Lu3Ni octahedra. The corner-sharing octahedral tilt angles range from 0-60°. In the fourth O site, O(4) is bonded to four equivalent Ba(1), one Lu(2), and one Ni(1) atom to form distorted OBa4LuNi octahedra that share corners with two equivalent O(4)Ba4LuNi octahedra, corners with six equivalent O(1)Ba2Lu3Ni octahedra, edges with five equivalent O(4)Ba4LuNi octahedra, and faces with two equivalent O(1)Ba2Lu3Ni octahedra. The corner-sharing octahedral tilt angles range from 4-61°.