HfCrCuS4 crystallizes in the monoclinic Pm space group. There are four inequivalent Hf sites. In the first Hf site, Hf(1) is bonded to one S(10), one S(6), two equivalent S(14), and two equivalent S(5) atoms to form HfS6 octahedra that share  a cornercorner with one Hf(3)S6 octahedra, corners with two equivalent Hf(2)S6 octahedra, corners with two equivalent Cu(4)S5 square pyramids, edges with two equivalent Hf(1)S6 octahedra, edges with two equivalent Cr(1)S6 octahedra, edges with two equivalent Cr(4)S6 octahedra, and  an edgeedge with one Cu(4)S5 square pyramid. The corner-sharing octahedral tilt angles range from 55-58°. In the second Hf site, Hf(2) is bonded to one S(15), one S(5), two equivalent S(1), and two equivalent S(11) atoms to form distorted HfS6 octahedra that share  a cornercorner with one Cr(1)S6 octahedra, corners with two equivalent Hf(1)S6 octahedra, corners with two equivalent Cu(2)S5 square pyramids, edges with two equivalent Hf(2)S6 octahedra, edges with two equivalent Cr(2)S6 octahedra,  an edgeedge with one Cu(2)S5 square pyramid, and edges with two equivalent Cu(1)S5 square pyramids. The corner-sharing octahedral tilt angles range from 50-58°. In the third Hf site, Hf(3) is bonded to one S(16), one S(6), two equivalent S(12), and two equivalent S(2) atoms to form HfS6 octahedra that share  a cornercorner with one Hf(1)S6 octahedra, corners with two equivalent Cr(1)S6 octahedra, corners with two equivalent Cu(1)S5 square pyramids, edges with two equivalent Hf(3)S6 octahedra, edges with two equivalent Cr(3)S6 octahedra,  an edgeedge with one Cu(1)S5 square pyramid, and edges with two equivalent Cu(2)S5 square pyramids. The corner-sharing octahedral tilt angles are 55°. In the fourth Hf site, Hf(4) is bonded to one S(13), one S(7), two equivalent S(3), and two equivalent S(9) atoms to form HfS6 octahedra that share  a cornercorner with one Cr(2)S6 octahedra, corners with two equivalent Cr(3)S6 octahedra, corners with two equivalent Cu(4)S5 square pyramids, edges with two equivalent Hf(4)S6 octahedra, edges with two equivalent Cr(1)S6 octahedra,  an edgeedge with one Cu(4)S5 square pyramid, and edges with two equivalent Cu(3)S5 square pyramids. The corner-sharing octahedral tilt angles range from 55-57°. There are four inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one S(5), one S(9), two equivalent S(13), and two equivalent S(6) atoms to form CrS6 octahedra that share  a cornercorner with one Hf(2)S6 octahedra, corners with two equivalent Hf(3)S6 octahedra, corners with two equivalent Cu(3)S5 square pyramids, edges with two equivalent Hf(1)S6 octahedra, edges with two equivalent Hf(4)S6 octahedra, edges with two equivalent Cr(1)S6 octahedra, and  an edgeedge with one Cu(3)S5 square pyramid. The corner-sharing octahedral tilt angles range from 50-55°. In the second Cr site, Cr(2) is bonded to one S(11), one S(7), two equivalent S(15), and two equivalent S(8) atoms to form CrS6 octahedra that share  a cornercorner with one Hf(4)S6 octahedra, corners with two equivalent Cr(4)S6 octahedra, corners with two equivalent Cu(1)S5 square pyramids, edges with two equivalent Hf(2)S6 octahedra, edges with two equivalent Cr(2)S6 octahedra, edges with two equivalent Cr(3)S6 octahedra, and  an edgeedge with one Cu(1)S5 square pyramid. The corner-sharing octahedral tilt angles range from 55-59°. In the third Cr site, Cr(3) is bonded to one S(12), one S(8), two equivalent S(16), and two equivalent S(7) atoms to form CrS6 octahedra that share  a cornercorner with one Cr(4)S6 octahedra, corners with two equivalent Hf(4)S6 octahedra, corners with two equivalent Cu(2)S5 square pyramids, edges with two equivalent Hf(3)S6 octahedra, edges with two equivalent Cr(2)S6 octahedra, edges with two equivalent Cr(3)S6 octahedra, and  an edgeedge with one Cu(2)S5 square pyramid. The corner-sharing octahedral tilt angles range from 54-57°. In the fourth Cr site, Cr(4) is bonded to one S(14), one S(8), two equivalent S(10), and two equivalent S(4) atoms to form CrS6 octahedra that share  a cornercorner with one Cr(3)S6 octahedra, corners with two equivalent Cr(2)S6 octahedra, corners with two equivalent Cu(3)S5 square pyramids, edges with two equivalent Hf(1)S6 octahedra, edges with two equivalent Cr(4)S6 octahedra,  an edgeedge with one Cu(3)S5 square pyramid, and edges with two equivalent Cu(4)S5 square pyramids. The corner-sharing octahedral tilt angles range from 54-59°. There are four inequivalent Cu sites. In the first Cu site, Cu(1) is bonded to one S(1), two equivalent S(15), and two equivalent S(2) atoms to form distorted CuS5 square pyramids that share corners with two equivalent Hf(3)S6 octahedra, corners with two equivalent Cr(2)S6 octahedra,  an edgeedge with one Hf(3)S6 octahedra,  an edgeedge with one Cr(2)S6 octahedra, edges with two equivalent Hf(2)S6 octahedra, edges with two equivalent Cu(1)S5 square pyramids, and edges with two equivalent Cu(2)S5 square pyramids. The corner-sharing octahedral tilt angles range from 4-10°. In the second Cu site, Cu(2) is bonded to one S(2), two equivalent S(1), and two equivalent S(16) atoms to form CuS5 square pyramids that share corners with two equivalent Hf(2)S6 octahedra, corners with two equivalent Cr(3)S6 octahedra,  an edgeedge with one Hf(2)S6 octahedra,  an edgeedge with one Cr(3)S6 octahedra, edges with two equivalent Hf(3)S6 octahedra, edges with two equivalent Cu(1)S5 square pyramids, and edges with two equivalent Cu(2)S5 square pyramids. The corner-sharing octahedral tilt angles range from 3-11°. In the third Cu site, Cu(3) is bonded to one S(3), two equivalent S(13), and two equivalent S(4) atoms to form CuS5 square pyramids that share corners with two equivalent Cr(1)S6 octahedra, corners with two equivalent Cr(4)S6 octahedra,  an edgeedge with one Cr(1)S6 octahedra,  an edgeedge with one Cr(4)S6 octahedra, edges with two equivalent Hf(4)S6 octahedra, edges with two equivalent Cu(3)S5 square pyramids, and edges with two equivalent Cu(4)S5 square pyramids. The corner-sharing octahedral tilt angles range from 5-8°. In the fourth Cu site, Cu(4) is bonded to one S(4), two equivalent S(14), and two equivalent S(3) atoms to form CuS5 square pyramids that share corners with two equivalent Hf(1)S6 octahedra, corners with two equivalent Hf(4)S6 octahedra,  an edgeedge with one Hf(1)S6 octahedra,  an edgeedge with one Hf(4)S6 octahedra, edges with two equivalent Cr(4)S6 octahedra, edges with two equivalent Cu(3)S5 square pyramids, and edges with two equivalent Cu(4)S5 square pyramids. The corner-sharing octahedral tilt angles are 5°. There are sixteen inequivalent S sites. In the first S site, S(1) is bonded to two equivalent Hf(2), one Cu(1), and two equivalent Cu(2) atoms to form SHf2Cu3 square pyramids that share corners with two equivalent S(16)HfCr2Cu2 square pyramids,  an edgeedge with one S(16)HfCr2Cu2 square pyramid, edges with two equivalent S(1)Hf2Cu3 square pyramids, edges with two equivalent S(2)Hf2Cu3 square pyramids, and edges with two equivalent S(15)HfCr2Cu2 square pyramids. In the second S site, S(2) is bonded to two equivalent Hf(3), one Cu(2), and two equivalent Cu(1) atoms to form SHf2Cu3 square pyramids that share corners with two equivalent S(15)HfCr2Cu2 square pyramids,  an edgeedge with one S(15)HfCr2Cu2 square pyramid, edges with two equivalent S(1)Hf2Cu3 square pyramids, edges with two equivalent S(2)Hf2Cu3 square pyramids, and edges with two equivalent S(16)HfCr2Cu2 square pyramids. In the third S site, S(3) is bonded to two equivalent Hf(4), one Cu(3), and two equivalent Cu(4) atoms to form SHf2Cu3 square pyramids that share corners with two equivalent S(14)Hf2CrCu2 square pyramids,  an edgeedge with one S(14)Hf2CrCu2 square pyramid, edges with two equivalent S(4)Cr2Cu3 square pyramids, edges with two equivalent S(3)Hf2Cu3 square pyramids, and edges with two equivalent S(13)HfCr2Cu2 square pyramids. In the fourth S site, S(4) is bonded to two equivalent Cr(4), one Cu(4), and two equivalent Cu(3) atoms to form SCr2Cu3 square pyramids that share corners with two equivalent S(13)HfCr2Cu2 square pyramids,  an edgeedge with one S(13)HfCr2Cu2 square pyramid, edges with two equivalent S(4)Cr2Cu3 square pyramids, edges with two equivalent S(14)Hf2CrCu2 square pyramids, and edges with two equivalent S(3)Hf2Cu3 square pyramids. In the fifth S site, S(5) is bonded in a rectangular see-saw-like geometry to one Hf(2), two equivalent Hf(1), and one Cr(1) atom. In the sixth S site, S(6) is bonded in a rectangular see-saw-like geometry to one Hf(1), one Hf(3), and two equivalent Cr(1) atoms. In the seventh S site, S(7) is bonded in a distorted rectangular see-saw-like geometry to one Hf(4), one Cr(2), and two equivalent Cr(3) atoms. In the eighth S site, S(8) is bonded in a rectangular see-saw-like geometry to one Cr(3), one Cr(4), and two equivalent Cr(2) atoms. In the ninth S site, S(9) is bonded in a distorted T-shaped geometry to two equivalent Hf(4) and one Cr(1) atom. In the tenth S site, S(10) is bonded in a distorted T-shaped geometry to one Hf(1) and two equivalent Cr(4) atoms. In the eleventh S site, S(11) is bonded in a distorted T-shaped geometry to two equivalent Hf(2) and one Cr(2) atom. In the twelfth S site, S(12) is bonded in a distorted T-shaped geometry to two equivalent Hf(3) and one Cr(3) atom. In the thirteenth S site, S(13) is bonded to one Hf(4), two equivalent Cr(1), and two equivalent Cu(3) atoms to form SHfCr2Cu2 square pyramids that share corners with two equivalent S(4)Cr2Cu3 square pyramids,  an edgeedge with one S(4)Cr2Cu3 square pyramid, edges with two equivalent S(3)Hf2Cu3 square pyramids, and edges with two equivalent S(13)HfCr2Cu2 square pyramids. In the fourteenth S site, S(14) is bonded to two equivalent Hf(1), one Cr(4), and two equivalent Cu(4) atoms to form SHf2CrCu2 square pyramids that share corners with two equivalent S(3)Hf2Cu3 square pyramids,  an edgeedge with one S(3)Hf2Cu3 square pyramid, edges with two equivalent S(4)Cr2Cu3 square pyramids, and edges with two equivalent S(14)Hf2CrCu2 square pyramids. In the fifteenth S site, S(15) is bonded to one Hf(2), two equivalent Cr(2), and two equivalent Cu(1) atoms to form SHfCr2Cu2 square pyramids that share corners with two equivalent S(2)Hf2Cu3 square pyramids,  an edgeedge with one S(2)Hf2Cu3 square pyramid, edges with two equivalent S(1)Hf2Cu3 square pyramids, and edges with two equivalent S(15)HfCr2Cu2 square pyramids. In the sixteenth S site, S(16) is bonded to one Hf(3), two equivalent Cr(3), and two equivalent Cu(2) atoms to form SHfCr2Cu2 square pyramids that share corners with two equivalent S(1)Hf2Cu3 square pyramids,  an edgeedge with one S(1)Hf2Cu3 square pyramid, edges with two equivalent S(2)Hf2Cu3 square pyramids, and edges with two equivalent S(16)HfCr2Cu2 square pyramids.
HfCrCuS4 crystallizes in the monoclinic Pm space group. There are four inequivalent Hf sites. In the first Hf site, Hf(1) is bonded to one S(10), one S(6), two equivalent S(14), and two equivalent S(5) atoms to form HfS6 octahedra that share  a cornercorner with one Hf(3)S6 octahedra, corners with two equivalent Hf(2)S6 octahedra, corners with two equivalent Cu(4)S5 square pyramids, edges with two equivalent Hf(1)S6 octahedra, edges with two equivalent Cr(1)S6 octahedra, edges with two equivalent Cr(4)S6 octahedra, and  an edgeedge with one Cu(4)S5 square pyramid. The corner-sharing octahedral tilt angles range from 55-58°. The Hf(1)-S(10) bond length is 2.49 Å. The Hf(1)-S(6) bond length is 2.64 Å. Both Hf(1)-S(14) bond lengths are 2.52 Å. Both Hf(1)-S(5) bond lengths are 2.56 Å. In the second Hf site, Hf(2) is bonded to one S(15), one S(5), two equivalent S(1), and two equivalent S(11) atoms to form distorted HfS6 octahedra that share  a cornercorner with one Cr(1)S6 octahedra, corners with two equivalent Hf(1)S6 octahedra, corners with two equivalent Cu(2)S5 square pyramids, edges with two equivalent Hf(2)S6 octahedra, edges with two equivalent Cr(2)S6 octahedra,  an edgeedge with one Cu(2)S5 square pyramid, and edges with two equivalent Cu(1)S5 square pyramids. The corner-sharing octahedral tilt angles range from 50-58°. The Hf(2)-S(15) bond length is 2.45 Å. The Hf(2)-S(5) bond length is 2.93 Å. Both Hf(2)-S(1) bond lengths are 2.55 Å. Both Hf(2)-S(11) bond lengths are 2.49 Å. In the third Hf site, Hf(3) is bonded to one S(16), one S(6), two equivalent S(12), and two equivalent S(2) atoms to form HfS6 octahedra that share  a cornercorner with one Hf(1)S6 octahedra, corners with two equivalent Cr(1)S6 octahedra, corners with two equivalent Cu(1)S5 square pyramids, edges with two equivalent Hf(3)S6 octahedra, edges with two equivalent Cr(3)S6 octahedra,  an edgeedge with one Cu(1)S5 square pyramid, and edges with two equivalent Cu(2)S5 square pyramids. The corner-sharing octahedral tilt angles are 55°. The Hf(3)-S(16) bond length is 2.54 Å. The Hf(3)-S(6) bond length is 2.75 Å. Both Hf(3)-S(12) bond lengths are 2.49 Å. Both Hf(3)-S(2) bond lengths are 2.55 Å. In the fourth Hf site, Hf(4) is bonded to one S(13), one S(7), two equivalent S(3), and two equivalent S(9) atoms to form HfS6 octahedra that share  a cornercorner with one Cr(2)S6 octahedra, corners with two equivalent Cr(3)S6 octahedra, corners with two equivalent Cu(4)S5 square pyramids, edges with two equivalent Hf(4)S6 octahedra, edges with two equivalent Cr(1)S6 octahedra,  an edgeedge with one Cu(4)S5 square pyramid, and edges with two equivalent Cu(3)S5 square pyramids. The corner-sharing octahedral tilt angles range from 55-57°. The Hf(4)-S(13) bond length is 2.55 Å. The Hf(4)-S(7) bond length is 2.78 Å. Both Hf(4)-S(3) bond lengths are 2.53 Å. Both Hf(4)-S(9) bond lengths are 2.50 Å. There are four inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one S(5), one S(9), two equivalent S(13), and two equivalent S(6) atoms to form CrS6 octahedra that share  a cornercorner with one Hf(2)S6 octahedra, corners with two equivalent Hf(3)S6 octahedra, corners with two equivalent Cu(3)S5 square pyramids, edges with two equivalent Hf(1)S6 octahedra, edges with two equivalent Hf(4)S6 octahedra, edges with two equivalent Cr(1)S6 octahedra, and  an edgeedge with one Cu(3)S5 square pyramid. The corner-sharing octahedral tilt angles range from 50-55°. The Cr(1)-S(5) bond length is 2.51 Å. The Cr(1)-S(9) bond length is 2.43 Å. Both Cr(1)-S(13) bond lengths are 2.42 Å. Both Cr(1)-S(6) bond lengths are 2.49 Å. In the second Cr site, Cr(2) is bonded to one S(11), one S(7), two equivalent S(15), and two equivalent S(8) atoms to form CrS6 octahedra that share  a cornercorner with one Hf(4)S6 octahedra, corners with two equivalent Cr(4)S6 octahedra, corners with two equivalent Cu(1)S5 square pyramids, edges with two equivalent Hf(2)S6 octahedra, edges with two equivalent Cr(2)S6 octahedra, edges with two equivalent Cr(3)S6 octahedra, and  an edgeedge with one Cu(1)S5 square pyramid. The corner-sharing octahedral tilt angles range from 55-59°. The Cr(2)-S(11) bond length is 2.46 Å. The Cr(2)-S(7) bond length is 2.46 Å. Both Cr(2)-S(15) bond lengths are 2.49 Å. Both Cr(2)-S(8) bond lengths are 2.42 Å. In the third Cr site, Cr(3) is bonded to one S(12), one S(8), two equivalent S(16), and two equivalent S(7) atoms to form CrS6 octahedra that share  a cornercorner with one Cr(4)S6 octahedra, corners with two equivalent Hf(4)S6 octahedra, corners with two equivalent Cu(2)S5 square pyramids, edges with two equivalent Hf(3)S6 octahedra, edges with two equivalent Cr(2)S6 octahedra, edges with two equivalent Cr(3)S6 octahedra, and  an edgeedge with one Cu(2)S5 square pyramid. The corner-sharing octahedral tilt angles range from 54-57°. The Cr(3)-S(12) bond length is 2.52 Å. The Cr(3)-S(8) bond length is 2.47 Å. Both Cr(3)-S(16) bond lengths are 2.42 Å. Both Cr(3)-S(7) bond lengths are 2.45 Å. In the fourth Cr site, Cr(4) is bonded to one S(14), one S(8), two equivalent S(10), and two equivalent S(4) atoms to form CrS6 octahedra that share  a cornercorner with one Cr(3)S6 octahedra, corners with two equivalent Cr(2)S6 octahedra, corners with two equivalent Cu(3)S5 square pyramids, edges with two equivalent Hf(1)S6 octahedra, edges with two equivalent Cr(4)S6 octahedra,  an edgeedge with one Cu(3)S5 square pyramid, and edges with two equivalent Cu(4)S5 square pyramids. The corner-sharing octahedral tilt angles range from 54-59°. The Cr(4)-S(14) bond length is 2.47 Å. The Cr(4)-S(8) bond length is 2.66 Å. Both Cr(4)-S(10) bond lengths are 2.40 Å. Both Cr(4)-S(4) bond lengths are 2.44 Å. There are four inequivalent Cu sites. In the first Cu site, Cu(1) is bonded to one S(1), two equivalent S(15), and two equivalent S(2) atoms to form distorted CuS5 square pyramids that share corners with two equivalent Hf(3)S6 octahedra, corners with two equivalent Cr(2)S6 octahedra,  an edgeedge with one Hf(3)S6 octahedra,  an edgeedge with one Cr(2)S6 octahedra, edges with two equivalent Hf(2)S6 octahedra, edges with two equivalent Cu(1)S5 square pyramids, and edges with two equivalent Cu(2)S5 square pyramids. The corner-sharing octahedral tilt angles range from 4-10°. The Cu(1)-S(1) bond length is 2.33 Å. Both Cu(1)-S(15) bond lengths are 2.54 Å. Both Cu(1)-S(2) bond lengths are 2.50 Å. In the second Cu site, Cu(2) is bonded to one S(2), two equivalent S(1), and two equivalent S(16) atoms to form CuS5 square pyramids that share corners with two equivalent Hf(2)S6 octahedra, corners with two equivalent Cr(3)S6 octahedra,  an edgeedge with one Hf(2)S6 octahedra,  an edgeedge with one Cr(3)S6 octahedra, edges with two equivalent Hf(3)S6 octahedra, edges with two equivalent Cu(1)S5 square pyramids, and edges with two equivalent Cu(2)S5 square pyramids. The corner-sharing octahedral tilt angles range from 3-11°. The Cu(2)-S(2) bond length is 2.39 Å. Both Cu(2)-S(1) bond lengths are 2.50 Å. Both Cu(2)-S(16) bond lengths are 2.47 Å. In the third Cu site, Cu(3) is bonded to one S(3), two equivalent S(13), and two equivalent S(4) atoms to form CuS5 square pyramids that share corners with two equivalent Cr(1)S6 octahedra, corners with two equivalent Cr(4)S6 octahedra,  an edgeedge with one Cr(1)S6 octahedra,  an edgeedge with one Cr(4)S6 octahedra, edges with two equivalent Hf(4)S6 octahedra, edges with two equivalent Cu(3)S5 square pyramids, and edges with two equivalent Cu(4)S5 square pyramids. The corner-sharing octahedral tilt angles range from 5-8°. The Cu(3)-S(3) bond length is 2.40 Å. Both Cu(3)-S(13) bond lengths are 2.78 Å. Both Cu(3)-S(4) bond lengths are 2.37 Å. In the fourth Cu site, Cu(4) is bonded to one S(4), two equivalent S(14), and two equivalent S(3) atoms to form CuS5 square pyramids that share corners with two equivalent Hf(1)S6 octahedra, corners with two equivalent Hf(4)S6 octahedra,  an edgeedge with one Hf(1)S6 octahedra,  an edgeedge with one Hf(4)S6 octahedra, edges with two equivalent Cr(4)S6 octahedra, edges with two equivalent Cu(3)S5 square pyramids, and edges with two equivalent Cu(4)S5 square pyramids. The corner-sharing octahedral tilt angles are 5°. The Cu(4)-S(4) bond length is 2.34 Å. Both Cu(4)-S(14) bond lengths are 2.65 Å. Both Cu(4)-S(3) bond lengths are 2.38 Å. There are sixteen inequivalent S sites. In the first S site, S(1) is bonded to two equivalent Hf(2), one Cu(1), and two equivalent Cu(2) atoms to form SHf2Cu3 square pyramids that share corners with two equivalent S(16)HfCr2Cu2 square pyramids,  an edgeedge with one S(16)HfCr2Cu2 square pyramid, edges with two equivalent S(1)Hf2Cu3 square pyramids, edges with two equivalent S(2)Hf2Cu3 square pyramids, and edges with two equivalent S(15)HfCr2Cu2 square pyramids. In the second S site, S(2) is bonded to two equivalent Hf(3), one Cu(2), and two equivalent Cu(1) atoms to form SHf2Cu3 square pyramids that share corners with two equivalent S(15)HfCr2Cu2 square pyramids,  an edgeedge with one S(15)HfCr2Cu2 square pyramid, edges with two equivalent S(1)Hf2Cu3 square pyramids, edges with two equivalent S(2)Hf2Cu3 square pyramids, and edges with two equivalent S(16)HfCr2Cu2 square pyramids. In the third S site, S(3) is bonded to two equivalent Hf(4), one Cu(3), and two equivalent Cu(4) atoms to form SHf2Cu3 square pyramids that share corners with two equivalent S(14)Hf2CrCu2 square pyramids,  an edgeedge with one S(14)Hf2CrCu2 square pyramid, edges with two equivalent S(4)Cr2Cu3 square pyramids, edges with two equivalent S(3)Hf2Cu3 square pyramids, and edges with two equivalent S(13)HfCr2Cu2 square pyramids. In the fourth S site, S(4) is bonded to two equivalent Cr(4), one Cu(4), and two equivalent Cu(3) atoms to form SCr2Cu3 square pyramids that share corners with two equivalent S(13)HfCr2Cu2 square pyramids,  an edgeedge with one S(13)HfCr2Cu2 square pyramid, edges with two equivalent S(4)Cr2Cu3 square pyramids, edges with two equivalent S(14)Hf2CrCu2 square pyramids, and edges with two equivalent S(3)Hf2Cu3 square pyramids. In the fifth S site, S(5) is bonded in a rectangular see-saw-like geometry to one Hf(2), two equivalent Hf(1), and one Cr(1) atom. In the sixth S site, S(6) is bonded in a rectangular see-saw-like geometry to one Hf(1), one Hf(3), and two equivalent Cr(1) atoms. In the seventh S site, S(7) is bonded in a distorted rectangular see-saw-like geometry to one Hf(4), one Cr(2), and two equivalent Cr(3) atoms. In the eighth S site, S(8) is bonded in a rectangular see-saw-like geometry to one Cr(3), one Cr(4), and two equivalent Cr(2) atoms. In the ninth S site, S(9) is bonded in a distorted T-shaped geometry to two equivalent Hf(4) and one Cr(1) atom. In the tenth S site, S(10) is bonded in a distorted T-shaped geometry to one Hf(1) and two equivalent Cr(4) atoms. In the eleventh S site, S(11) is bonded in a distorted T-shaped geometry to two equivalent Hf(2) and one Cr(2) atom. In the twelfth S site, S(12) is bonded in a distorted T-shaped geometry to two equivalent Hf(3) and one Cr(3) atom. In the thirteenth S site, S(13) is bonded to one Hf(4), two equivalent Cr(1), and two equivalent Cu(3) atoms to form SHfCr2Cu2 square pyramids that share corners with two equivalent S(4)Cr2Cu3 square pyramids,  an edgeedge with one S(4)Cr2Cu3 square pyramid, edges with two equivalent S(3)Hf2Cu3 square pyramids, and edges with two equivalent S(13)HfCr2Cu2 square pyramids. In the fourteenth S site, S(14) is bonded to two equivalent Hf(1), one Cr(4), and two equivalent Cu(4) atoms to form SHf2CrCu2 square pyramids that share corners with two equivalent S(3)Hf2Cu3 square pyramids,  an edgeedge with one S(3)Hf2Cu3 square pyramid, edges with two equivalent S(4)Cr2Cu3 square pyramids, and edges with two equivalent S(14)Hf2CrCu2 square pyramids. In the fifteenth S site, S(15) is bonded to one Hf(2), two equivalent Cr(2), and two equivalent Cu(1) atoms to form SHfCr2Cu2 square pyramids that share corners with two equivalent S(2)Hf2Cu3 square pyramids,  an edgeedge with one S(2)Hf2Cu3 square pyramid, edges with two equivalent S(1)Hf2Cu3 square pyramids, and edges with two equivalent S(15)HfCr2Cu2 square pyramids. In the sixteenth S site, S(16) is bonded to one Hf(3), two equivalent Cr(3), and two equivalent Cu(2) atoms to form SHfCr2Cu2 square pyramids that share corners with two equivalent S(1)Hf2Cu3 square pyramids,  an edgeedge with one S(1)Hf2Cu3 square pyramid, edges with two equivalent S(2)Hf2Cu3 square pyramids, and edges with two equivalent S(16)HfCr2Cu2 square pyramids.