Ti16CuS32 crystallizes in the trigonal R3m space group. There are eight inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one S(2), one S(7), two equivalent S(1), and two equivalent S(3) atoms to form TiS6 octahedra that share corners with two equivalent Cu(1)S4 tetrahedra,  an edgeedge with one Ti(3)S6 octahedra,  an edgeedge with one Ti(4)S6 octahedra, and edges with four equivalent Ti(1)S6 octahedra. In the second Ti site, Ti(2) is bonded to one S(6), one S(8), two equivalent S(4), and two equivalent S(9) atoms to form edge-sharing TiS6 octahedra. In the third Ti site, Ti(3) is bonded to three equivalent S(1) and three equivalent S(14) atoms to form TiS6 octahedra that share corners with three equivalent Cu(1)S4 tetrahedra, edges with three equivalent Ti(1)S6 octahedra, and edges with three equivalent Ti(7)S6 octahedra. In the fourth Ti site, Ti(4) is bonded to three equivalent S(3) and three equivalent S(4) atoms to form edge-sharing TiS6 octahedra. In the fifth Ti site, Ti(5) is bonded to three equivalent S(5) and three equivalent S(9) atoms to form edge-sharing TiS6 octahedra. In the sixth Ti site, Ti(6) is bonded to one S(11), one S(12), two equivalent S(10), and two equivalent S(5) atoms to form edge-sharing TiS6 octahedra. In the seventh Ti site, Ti(7) is bonded to one S(13), one S(16), two equivalent S(14), and two equivalent S(15) atoms to form TiS6 octahedra that share  a cornercorner with one Cu(1)S4 tetrahedra,  an edgeedge with one Ti(3)S6 octahedra,  an edgeedge with one Ti(8)S6 octahedra, and edges with four equivalent Ti(7)S6 octahedra. In the eighth Ti site, Ti(8) is bonded to three equivalent S(10) and three equivalent S(15) atoms to form edge-sharing TiS6 octahedra. Cu(1) is bonded to one S(16) and three equivalent S(1) atoms to form CuS4 tetrahedra that share corners with three equivalent Ti(3)S6 octahedra, corners with three equivalent Ti(7)S6 octahedra, and corners with six equivalent Ti(1)S6 octahedra. The corner-sharing octahedral tilt angles range from 56-58°. There are sixteen inequivalent S sites. In the first S site, S(1) is bonded to one Ti(3), two equivalent Ti(1), and one Cu(1) atom to form a mixture of distorted corner and edge-sharing STi3Cu trigonal pyramids. In the second S site, S(2) is bonded in a distorted T-shaped geometry to three equivalent Ti(1) atoms. In the third S site, S(3) is bonded in a distorted T-shaped geometry to one Ti(4) and two equivalent Ti(1) atoms. In the fourth S site, S(4) is bonded in a distorted T-shaped geometry to one Ti(4) and two equivalent Ti(2) atoms. In the fifth S site, S(5) is bonded in a distorted T-shaped geometry to one Ti(5) and two equivalent Ti(6) atoms. In the sixth S site, S(6) is bonded in a distorted T-shaped geometry to three equivalent Ti(2) atoms. In the seventh S site, S(7) is bonded in a distorted T-shaped geometry to three equivalent Ti(1) atoms. In the eighth S site, S(8) is bonded in a distorted T-shaped geometry to three equivalent Ti(2) atoms. In the ninth S site, S(9) is bonded in a distorted T-shaped geometry to one Ti(5) and two equivalent Ti(2) atoms. In the tenth S site, S(10) is bonded in a distorted T-shaped geometry to one Ti(8) and two equivalent Ti(6) atoms. In the eleventh S site, S(11) is bonded in a distorted T-shaped geometry to three equivalent Ti(6) atoms. In the twelfth S site, S(12) is bonded in a distorted T-shaped geometry to three equivalent Ti(6) atoms. In the thirteenth S site, S(13) is bonded in a distorted T-shaped geometry to three equivalent Ti(7) atoms. In the fourteenth S site, S(14) is bonded in a distorted T-shaped geometry to one Ti(3) and two equivalent Ti(7) atoms. In the fifteenth S site, S(15) is bonded in a distorted T-shaped geometry to one Ti(8) and two equivalent Ti(7) atoms. In the sixteenth S site, S(16) is bonded in a rectangular see-saw-like geometry to three equivalent Ti(7) and one Cu(1) atom.
Ti16CuS32 crystallizes in the trigonal R3m space group. There are eight inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one S(2), one S(7), two equivalent S(1), and two equivalent S(3) atoms to form TiS6 octahedra that share corners with two equivalent Cu(1)S4 tetrahedra,  an edgeedge with one Ti(3)S6 octahedra,  an edgeedge with one Ti(4)S6 octahedra, and edges with four equivalent Ti(1)S6 octahedra. The Ti(1)-S(2) bond length is 2.43 Å. The Ti(1)-S(7) bond length is 2.43 Å. Both Ti(1)-S(1) bond lengths are 2.47 Å. Both Ti(1)-S(3) bond lengths are 2.39 Å. In the second Ti site, Ti(2) is bonded to one S(6), one S(8), two equivalent S(4), and two equivalent S(9) atoms to form edge-sharing TiS6 octahedra. The Ti(2)-S(6) bond length is 2.44 Å. The Ti(2)-S(8) bond length is 2.44 Å. Both Ti(2)-S(4) bond lengths are 2.45 Å. Both Ti(2)-S(9) bond lengths are 2.43 Å. In the third Ti site, Ti(3) is bonded to three equivalent S(1) and three equivalent S(14) atoms to form TiS6 octahedra that share corners with three equivalent Cu(1)S4 tetrahedra, edges with three equivalent Ti(1)S6 octahedra, and edges with three equivalent Ti(7)S6 octahedra. All Ti(3)-S(1) bond lengths are 2.48 Å. All Ti(3)-S(14) bond lengths are 2.37 Å. In the fourth Ti site, Ti(4) is bonded to three equivalent S(3) and three equivalent S(4) atoms to form edge-sharing TiS6 octahedra. All Ti(4)-S(3) bond lengths are 2.49 Å. All Ti(4)-S(4) bond lengths are 2.39 Å. In the fifth Ti site, Ti(5) is bonded to three equivalent S(5) and three equivalent S(9) atoms to form edge-sharing TiS6 octahedra. All Ti(5)-S(5) bond lengths are 2.44 Å. All Ti(5)-S(9) bond lengths are 2.45 Å. In the sixth Ti site, Ti(6) is bonded to one S(11), one S(12), two equivalent S(10), and two equivalent S(5) atoms to form edge-sharing TiS6 octahedra. The Ti(6)-S(11) bond length is 2.44 Å. The Ti(6)-S(12) bond length is 2.44 Å. Both Ti(6)-S(10) bond lengths are 2.45 Å. Both Ti(6)-S(5) bond lengths are 2.43 Å. In the seventh Ti site, Ti(7) is bonded to one S(13), one S(16), two equivalent S(14), and two equivalent S(15) atoms to form TiS6 octahedra that share  a cornercorner with one Cu(1)S4 tetrahedra,  an edgeedge with one Ti(3)S6 octahedra,  an edgeedge with one Ti(8)S6 octahedra, and edges with four equivalent Ti(7)S6 octahedra. The Ti(7)-S(13) bond length is 2.41 Å. The Ti(7)-S(16) bond length is 2.46 Å. Both Ti(7)-S(14) bond lengths are 2.46 Å. Both Ti(7)-S(15) bond lengths are 2.42 Å. In the eighth Ti site, Ti(8) is bonded to three equivalent S(10) and three equivalent S(15) atoms to form edge-sharing TiS6 octahedra. All Ti(8)-S(10) bond lengths are 2.41 Å. All Ti(8)-S(15) bond lengths are 2.47 Å. Cu(1) is bonded to one S(16) and three equivalent S(1) atoms to form CuS4 tetrahedra that share corners with three equivalent Ti(3)S6 octahedra, corners with three equivalent Ti(7)S6 octahedra, and corners with six equivalent Ti(1)S6 octahedra. The corner-sharing octahedral tilt angles range from 56-58°. The Cu(1)-S(16) bond length is 2.22 Å. All Cu(1)-S(1) bond lengths are 2.23 Å. There are sixteen inequivalent S sites. In the first S site, S(1) is bonded to one Ti(3), two equivalent Ti(1), and one Cu(1) atom to form a mixture of distorted corner and edge-sharing STi3Cu trigonal pyramids. In the second S site, S(2) is bonded in a distorted T-shaped geometry to three equivalent Ti(1) atoms. In the third S site, S(3) is bonded in a distorted T-shaped geometry to one Ti(4) and two equivalent Ti(1) atoms. In the fourth S site, S(4) is bonded in a distorted T-shaped geometry to one Ti(4) and two equivalent Ti(2) atoms. In the fifth S site, S(5) is bonded in a distorted T-shaped geometry to one Ti(5) and two equivalent Ti(6) atoms. In the sixth S site, S(6) is bonded in a distorted T-shaped geometry to three equivalent Ti(2) atoms. In the seventh S site, S(7) is bonded in a distorted T-shaped geometry to three equivalent Ti(1) atoms. In the eighth S site, S(8) is bonded in a distorted T-shaped geometry to three equivalent Ti(2) atoms. In the ninth S site, S(9) is bonded in a distorted T-shaped geometry to one Ti(5) and two equivalent Ti(2) atoms. In the tenth S site, S(10) is bonded in a distorted T-shaped geometry to one Ti(8) and two equivalent Ti(6) atoms. In the eleventh S site, S(11) is bonded in a distorted T-shaped geometry to three equivalent Ti(6) atoms. In the twelfth S site, S(12) is bonded in a distorted T-shaped geometry to three equivalent Ti(6) atoms. In the thirteenth S site, S(13) is bonded in a distorted T-shaped geometry to three equivalent Ti(7) atoms. In the fourteenth S site, S(14) is bonded in a distorted T-shaped geometry to one Ti(3) and two equivalent Ti(7) atoms. In the fifteenth S site, S(15) is bonded in a distorted T-shaped geometry to one Ti(8) and two equivalent Ti(7) atoms. In the sixteenth S site, S(16) is bonded in a rectangular see-saw-like geometry to three equivalent Ti(7) and one Cu(1) atom.