Ba5Hf4S13 is (Cubic) Perovskite-like structured and crystallizes in the tetragonal I4/mmm space group. There are three inequivalent Ba sites. In the first Ba site, Ba(1) is bonded in a 9-coordinate geometry to four equivalent S(2) and five equivalent S(4) atoms. In the second Ba site, Ba(2) is bonded to four equivalent S(1), four equivalent S(2), and four equivalent S(3) atoms to form BaS12 cuboctahedra that share corners with four equivalent Ba(2)S12 cuboctahedra, corners with four equivalent Ba(3)S12 cuboctahedra,  a faceface with one Ba(3)S12 cuboctahedra, faces with four equivalent Ba(2)S12 cuboctahedra, faces with four equivalent Hf(1)S6 octahedra, and faces with four equivalent Hf(2)S6 octahedra. In the third Ba site, Ba(3) is bonded to four equivalent S(5) and eight equivalent S(3) atoms to form BaS12 cuboctahedra that share corners with four equivalent Ba(3)S12 cuboctahedra, corners with eight equivalent Ba(2)S12 cuboctahedra, faces with two equivalent Ba(2)S12 cuboctahedra, faces with four equivalent Ba(3)S12 cuboctahedra, and faces with eight equivalent Hf(2)S6 octahedra. There are two inequivalent Hf sites. In the first Hf site, Hf(1) is bonded to one S(1), one S(4), and four equivalent S(2) atoms to form HfS6 octahedra that share  a cornercorner with one Hf(2)S6 octahedra, corners with four equivalent Hf(1)S6 octahedra, and faces with four equivalent Ba(2)S12 cuboctahedra. The corner-sharing octahedral tilt angles range from 0-6°. In the second Hf site, Hf(2) is bonded to one S(1), one S(5), and four equivalent S(3) atoms to form HfS6 octahedra that share  a cornercorner with one Hf(1)S6 octahedra, corners with five equivalent Hf(2)S6 octahedra, faces with four equivalent Ba(2)S12 cuboctahedra, and faces with four equivalent Ba(3)S12 cuboctahedra. The corner-sharing octahedral tilt angles range from 0-1°. There are five inequivalent S sites. In the first S site, S(1) is bonded in a distorted linear geometry to four equivalent Ba(2), one Hf(1), and one Hf(2) atom. In the second S site, S(2) is bonded to two equivalent Ba(1), two equivalent Ba(2), and two equivalent Hf(1) atoms to form distorted SBa4Hf2 octahedra that share corners with two equivalent S(2)Ba4Hf2 octahedra, corners with six equivalent S(4)Ba5Hf octahedra, edges with two equivalent S(2)Ba4Hf2 octahedra, faces with two equivalent S(4)Ba5Hf octahedra, and faces with four equivalent S(2)Ba4Hf2 octahedra. The corner-sharing octahedral tilt angles range from 6-52°. In the third S site, S(3) is bonded in a distorted linear geometry to two equivalent Ba(2), two equivalent Ba(3), and two equivalent Hf(2) atoms. In the fourth S site, S(4) is bonded to five equivalent Ba(1) and one Hf(1) atom to form distorted SBa5Hf octahedra that share corners with four equivalent S(4)Ba5Hf octahedra, corners with twelve equivalent S(2)Ba4Hf2 octahedra, edges with eight equivalent S(4)Ba5Hf octahedra, and faces with four equivalent S(2)Ba4Hf2 octahedra. The corner-sharing octahedral tilt angles range from 14-52°. In the fifth S site, S(5) is bonded in a distorted linear geometry to four equivalent Ba(3) and two equivalent Hf(2) atoms.
Ba5Hf4S13 is (Cubic) Perovskite-like structured and crystallizes in the tetragonal I4/mmm space group. There are three inequivalent Ba sites. In the first Ba site, Ba(1) is bonded in a 9-coordinate geometry to four equivalent S(2) and five equivalent S(4) atoms. All Ba(1)-S(2) bond lengths are 3.32 Å. There is one shorter (3.13 Å) and four longer (3.57 Å) Ba(1)-S(4) bond lengths. In the second Ba site, Ba(2) is bonded to four equivalent S(1), four equivalent S(2), and four equivalent S(3) atoms to form BaS12 cuboctahedra that share corners with four equivalent Ba(2)S12 cuboctahedra, corners with four equivalent Ba(3)S12 cuboctahedra,  a faceface with one Ba(3)S12 cuboctahedra, faces with four equivalent Ba(2)S12 cuboctahedra, faces with four equivalent Hf(1)S6 octahedra, and faces with four equivalent Hf(2)S6 octahedra. All Ba(2)-S(1) bond lengths are 3.54 Å. All Ba(2)-S(2) bond lengths are 3.58 Å. All Ba(2)-S(3) bond lengths are 3.47 Å. In the third Ba site, Ba(3) is bonded to four equivalent S(5) and eight equivalent S(3) atoms to form BaS12 cuboctahedra that share corners with four equivalent Ba(3)S12 cuboctahedra, corners with eight equivalent Ba(2)S12 cuboctahedra, faces with two equivalent Ba(2)S12 cuboctahedra, faces with four equivalent Ba(3)S12 cuboctahedra, and faces with eight equivalent Hf(2)S6 octahedra. All Ba(3)-S(5) bond lengths are 3.54 Å. All Ba(3)-S(3) bond lengths are 3.54 Å. There are two inequivalent Hf sites. In the first Hf site, Hf(1) is bonded to one S(1), one S(4), and four equivalent S(2) atoms to form HfS6 octahedra that share  a cornercorner with one Hf(2)S6 octahedra, corners with four equivalent Hf(1)S6 octahedra, and faces with four equivalent Ba(2)S12 cuboctahedra. The corner-sharing octahedral tilt angles range from 0-6°. The Hf(1)-S(1) bond length is 2.58 Å. The Hf(1)-S(4) bond length is 2.49 Å. All Hf(1)-S(2) bond lengths are 2.51 Å. In the second Hf site, Hf(2) is bonded to one S(1), one S(5), and four equivalent S(3) atoms to form HfS6 octahedra that share  a cornercorner with one Hf(1)S6 octahedra, corners with five equivalent Hf(2)S6 octahedra, faces with four equivalent Ba(2)S12 cuboctahedra, and faces with four equivalent Ba(3)S12 cuboctahedra. The corner-sharing octahedral tilt angles range from 0-1°. The Hf(2)-S(1) bond length is 2.49 Å. The Hf(2)-S(5) bond length is 2.53 Å. All Hf(2)-S(3) bond lengths are 2.50 Å. There are five inequivalent S sites. In the first S site, S(1) is bonded in a distorted linear geometry to four equivalent Ba(2), one Hf(1), and one Hf(2) atom. In the second S site, S(2) is bonded to two equivalent Ba(1), two equivalent Ba(2), and two equivalent Hf(1) atoms to form distorted SBa4Hf2 octahedra that share corners with two equivalent S(2)Ba4Hf2 octahedra, corners with six equivalent S(4)Ba5Hf octahedra, edges with two equivalent S(2)Ba4Hf2 octahedra, faces with two equivalent S(4)Ba5Hf octahedra, and faces with four equivalent S(2)Ba4Hf2 octahedra. The corner-sharing octahedral tilt angles range from 6-52°. In the third S site, S(3) is bonded in a distorted linear geometry to two equivalent Ba(2), two equivalent Ba(3), and two equivalent Hf(2) atoms. In the fourth S site, S(4) is bonded to five equivalent Ba(1) and one Hf(1) atom to form distorted SBa5Hf octahedra that share corners with four equivalent S(4)Ba5Hf octahedra, corners with twelve equivalent S(2)Ba4Hf2 octahedra, edges with eight equivalent S(4)Ba5Hf octahedra, and faces with four equivalent S(2)Ba4Hf2 octahedra. The corner-sharing octahedral tilt angles range from 14-52°. In the fifth S site, S(5) is bonded in a distorted linear geometry to four equivalent Ba(3) and two equivalent Hf(2) atoms.