The material structure described by 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. is represented by the Crystallographic Information File (CIF) [CIF]
data_Ti16CuS32
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   23.157
_cell_length_b   23.157
_cell_length_c   23.157
_cell_angle_alpha   17.352
_cell_angle_beta   17.352
_cell_angle_gamma   17.352
_symmetry_Int_Tables_number   1
_cell_volume   963.891
_cell_formula_units_Z   1
loop_
 _symmetry_equiv_pos_site_id
 _symmetry_equiv_pos_as_xyz
  1  'x, y, z'
loop_
 _atom_site_type_symbol
 _atom_site_label
 _atom_site_symmetry_multiplicity
 _atom_site_fract_x
 _atom_site_fract_y
 _atom_site_fract_z
 _atom_site_occupancy
  Ti  Ti0  1  0.872  0.872  0.382  1.0
  Ti  Ti1  1  0.126  0.624  0.624  1.0
  Ti  Ti2  1  0.382  0.872  0.872  1.0
  Ti  Ti3  1  0.998  0.998  0.998  1.0
  Ti  Ti4  1  0.751  0.751  0.751  1.0
  Ti  Ti5  1  0.872  0.382  0.872  1.0
  Ti  Ti6  1  0.624  0.624  0.126  1.0
  Ti  Ti7  1  0.624  0.126  0.624  1.0
  Ti  Ti8  1  0.500  0.500  0.500  1.0
  Ti  Ti9  1  0.375  0.874  0.375  1.0
  Ti  Ti10  1  0.375  0.375  0.874  1.0
  Ti  Ti11  1  0.123  0.627  0.123  1.0
  Ti  Ti12  1  0.874  0.375  0.375  1.0
  Ti  Ti13  1  0.627  0.123  0.123  1.0
  Ti  Ti14  1  0.249  0.249  0.249  1.0
  Ti  Ti15  1  0.123  0.123  0.627  1.0
  Cu  Cu16  1  0.344  0.344  0.344  1.0
  S  S17  1  0.181  0.702  0.181  1.0
  S  S18  1  0.702  0.181  0.181  1.0
  S  S19  1  0.688  0.688  0.688  1.0
  S  S20  1  0.055  0.566  0.566  1.0
  S  S21  1  0.566  0.566  0.055  1.0
  S  S22  1  0.566  0.055  0.566  1.0
  S  S23  1  0.181  0.181  0.702  1.0
  S  S24  1  0.933  0.933  0.446  1.0
  S  S25  1  0.446  0.933  0.933  1.0
  S  S26  1  0.196  0.684  0.684  1.0
  S  S27  1  0.812  0.812  0.812  1.0
  S  S28  1  0.062  0.062  0.062  1.0
  S  S29  1  0.438  0.438  0.438  1.0
  S  S30  1  0.316  0.316  0.804  1.0
  S  S31  1  0.316  0.804  0.316  1.0
  S  S32  1  0.067  0.554  0.067  1.0
  S  S33  1  0.933  0.446  0.933  1.0
  S  S34  1  0.684  0.196  0.684  1.0
  S  S35  1  0.684  0.684  0.196  1.0
  S  S36  1  0.562  0.562  0.562  1.0
  S  S37  1  0.188  0.188  0.188  1.0
  S  S38  1  0.804  0.316  0.316  1.0
  S  S39  1  0.554  0.067  0.067  1.0
  S  S40  1  0.938  0.938  0.938  1.0
  S  S41  1  0.817  0.817  0.304  1.0
  S  S42  1  0.067  0.067  0.554  1.0
  S  S43  1  0.434  0.946  0.434  1.0
  S  S44  1  0.434  0.434  0.946  1.0
  S  S45  1  0.946  0.434  0.434  1.0
  S  S46  1  0.311  0.311  0.311  1.0
  S  S47  1  0.304  0.817  0.817  1.0
  S  S48  1  0.817  0.304  0.817  1.0
[/CIF]
.
The material structure described by 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. is represented by the Crystallographic Information File (CIF) [CIF]
data_Ti16CuS32
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   23.157
_cell_length_b   23.157
_cell_length_c   23.157
_cell_angle_alpha   17.352
_cell_angle_beta   17.352
_cell_angle_gamma   17.352
_symmetry_Int_Tables_number   1
_cell_volume   963.891
_cell_formula_units_Z   1
loop_
 _symmetry_equiv_pos_site_id
 _symmetry_equiv_pos_as_xyz
  1  'x, y, z'
loop_
 _atom_site_type_symbol
 _atom_site_label
 _atom_site_symmetry_multiplicity
 _atom_site_fract_x
 _atom_site_fract_y
 _atom_site_fract_z
 _atom_site_occupancy
  Ti  Ti0  1  0.872  0.872  0.382  1.0
  Ti  Ti1  1  0.126  0.624  0.624  1.0
  Ti  Ti2  1  0.382  0.872  0.872  1.0
  Ti  Ti3  1  0.998  0.998  0.998  1.0
  Ti  Ti4  1  0.751  0.751  0.751  1.0
  Ti  Ti5  1  0.872  0.382  0.872  1.0
  Ti  Ti6  1  0.624  0.624  0.126  1.0
  Ti  Ti7  1  0.624  0.126  0.624  1.0
  Ti  Ti8  1  0.500  0.500  0.500  1.0
  Ti  Ti9  1  0.375  0.874  0.375  1.0
  Ti  Ti10  1  0.375  0.375  0.874  1.0
  Ti  Ti11  1  0.123  0.627  0.123  1.0
  Ti  Ti12  1  0.874  0.375  0.375  1.0
  Ti  Ti13  1  0.627  0.123  0.123  1.0
  Ti  Ti14  1  0.249  0.249  0.249  1.0
  Ti  Ti15  1  0.123  0.123  0.627  1.0
  Cu  Cu16  1  0.344  0.344  0.344  1.0
  S  S17  1  0.181  0.702  0.181  1.0
  S  S18  1  0.702  0.181  0.181  1.0
  S  S19  1  0.688  0.688  0.688  1.0
  S  S20  1  0.055  0.566  0.566  1.0
  S  S21  1  0.566  0.566  0.055  1.0
  S  S22  1  0.566  0.055  0.566  1.0
  S  S23  1  0.181  0.181  0.702  1.0
  S  S24  1  0.933  0.933  0.446  1.0
  S  S25  1  0.446  0.933  0.933  1.0
  S  S26  1  0.196  0.684  0.684  1.0
  S  S27  1  0.812  0.812  0.812  1.0
  S  S28  1  0.062  0.062  0.062  1.0
  S  S29  1  0.438  0.438  0.438  1.0
  S  S30  1  0.316  0.316  0.804  1.0
  S  S31  1  0.316  0.804  0.316  1.0
  S  S32  1  0.067  0.554  0.067  1.0
  S  S33  1  0.933  0.446  0.933  1.0
  S  S34  1  0.684  0.196  0.684  1.0
  S  S35  1  0.684  0.684  0.196  1.0
  S  S36  1  0.562  0.562  0.562  1.0
  S  S37  1  0.188  0.188  0.188  1.0
  S  S38  1  0.804  0.316  0.316  1.0
  S  S39  1  0.554  0.067  0.067  1.0
  S  S40  1  0.938  0.938  0.938  1.0
  S  S41  1  0.817  0.817  0.304  1.0
  S  S42  1  0.067  0.067  0.554  1.0
  S  S43  1  0.434  0.946  0.434  1.0
  S  S44  1  0.434  0.434  0.946  1.0
  S  S45  1  0.946  0.434  0.434  1.0
  S  S46  1  0.311  0.311  0.311  1.0
  S  S47  1  0.304  0.817  0.817  1.0
  S  S48  1  0.817  0.304  0.817  1.0
[/CIF]
.