Ba5Ho2ZrAl2O13 crystallizes in the hexagonal P6_3/mmc space group. There are three inequivalent Ba sites. In the first Ba site, Ba(1) is bonded to three equivalent O(1) and nine equivalent O(2) atoms to form distorted BaO12 cuboctahedra that share corners with six equivalent Ba(1)O12 cuboctahedra, faces with three equivalent Ba(1)O12 cuboctahedra, faces with three equivalent Zr(1)O6 octahedra, faces with four equivalent Ho(1)O6 octahedra, and  a faceface with one Al(1)O4 tetrahedra. In the second Ba site, Ba(2) is bonded in a distorted q6 geometry to three equivalent O(2) and six equivalent O(1) atoms. In the third Ba site, Ba(3) is bonded in a 6-coordinate geometry to six equivalent O(1) atoms. Ho(1) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form HoO6 octahedra that share corners with three equivalent Zr(1)O6 octahedra, corners with three equivalent Al(1)O4 tetrahedra, and faces with four equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedra are not tilted. Zr(1) is bonded to six equivalent O(2) atoms to form ZrO6 octahedra that share corners with six equivalent Ho(1)O6 octahedra and faces with six equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedra are not tilted. Al(1) is bonded to one O(3) and three equivalent O(1) atoms to form AlO4 tetrahedra that share corners with three equivalent Ho(1)O6 octahedra,  a cornercorner with one Al(1)O4 tetrahedra, and  a faceface with one Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 19°. There are three inequivalent O sites. In the first O site, O(2) is bonded to one Ba(2), three equivalent Ba(1), one Ho(1), and one Zr(1) atom to form a mixture of distorted corner, edge, and face-sharing OBa4HoZr octahedra. The corner-sharing octahedral tilt angles range from 0-60°. In the second O site, O(3) is bonded in a linear geometry to two equivalent Al(1) atoms. In the third O site, O(1) is bonded in a 2-coordinate geometry to one Ba(1), one Ba(3), two equivalent Ba(2), one Ho(1), and one Al(1) atom.
Ba5Ho2ZrAl2O13 crystallizes in the hexagonal P6_3/mmc space group. There are three inequivalent Ba sites. In the first Ba site, Ba(1) is bonded to three equivalent O(1) and nine equivalent O(2) atoms to form distorted BaO12 cuboctahedra that share corners with six equivalent Ba(1)O12 cuboctahedra, faces with three equivalent Ba(1)O12 cuboctahedra, faces with three equivalent Zr(1)O6 octahedra, faces with four equivalent Ho(1)O6 octahedra, and  a faceface with one Al(1)O4 tetrahedra. All Ba(1)-O(1) bond lengths are 3.37 Å. There are three shorter (2.95 Å) and six longer (3.02 Å) Ba(1)-O(2) bond lengths. In the second Ba site, Ba(2) is bonded in a distorted q6 geometry to three equivalent O(2) and six equivalent O(1) atoms. All Ba(2)-O(2) bond lengths are 2.78 Å. All Ba(2)-O(1) bond lengths are 3.06 Å. In the third Ba site, Ba(3) is bonded in a 6-coordinate geometry to six equivalent O(1) atoms. All Ba(3)-O(1) bond lengths are 2.93 Å. Ho(1) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form HoO6 octahedra that share corners with three equivalent Zr(1)O6 octahedra, corners with three equivalent Al(1)O4 tetrahedra, and faces with four equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedra are not tilted. All Ho(1)-O(1) bond lengths are 2.27 Å. All Ho(1)-O(2) bond lengths are 2.23 Å. Zr(1) is bonded to six equivalent O(2) atoms to form ZrO6 octahedra that share corners with six equivalent Ho(1)O6 octahedra and faces with six equivalent Ba(1)O12 cuboctahedra. The corner-sharing octahedra are not tilted. All Zr(1)-O(2) bond lengths are 2.12 Å. Al(1) is bonded to one O(3) and three equivalent O(1) atoms to form AlO4 tetrahedra that share corners with three equivalent Ho(1)O6 octahedra,  a cornercorner with one Al(1)O4 tetrahedra, and  a faceface with one Ba(1)O12 cuboctahedra. The corner-sharing octahedral tilt angles are 19°. The Al(1)-O(3) bond length is 1.73 Å. All Al(1)-O(1) bond lengths are 1.78 Å. There are three inequivalent O sites. In the first O site, O(2) is bonded to one Ba(2), three equivalent Ba(1), one Ho(1), and one Zr(1) atom to form a mixture of distorted corner, edge, and face-sharing OBa4HoZr octahedra. The corner-sharing octahedral tilt angles range from 0-60°. In the second O site, O(3) is bonded in a linear geometry to two equivalent Al(1) atoms. In the third O site, O(1) is bonded in a 2-coordinate geometry to one Ba(1), one Ba(3), two equivalent Ba(2), one Ho(1), and one Al(1) atom.