The crystal structure described by Cr8CuCd3S16 is Spinel-derived structured and crystallizes in the trigonal R3m space group. There are four inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one S(3), one S(7), two equivalent S(1), and two equivalent S(5) atoms to form CrS6 octahedra that share  a cornercorner with one Cd(1)S4 tetrahedra,  a cornercorner with one Cd(3)S4 tetrahedra, corners with two equivalent Cu(1)S4 tetrahedra, corners with two equivalent Cd(2)S4 tetrahedra,  an edgeedge with one Cr(3)S6 octahedra,  an edgeedge with one Cr(4)S6 octahedra, and edges with four equivalent Cr(1)S6 octahedra. In the second Cr site, Cr(2) is bonded to one S(4), one S(8), two equivalent S(2), and two equivalent S(6) atoms to form CrS6 octahedra that share  a cornercorner with one Cu(1)S4 tetrahedra,  a cornercorner with one Cd(2)S4 tetrahedra, corners with two equivalent Cd(1)S4 tetrahedra, corners with two equivalent Cd(3)S4 tetrahedra,  an edgeedge with one Cr(3)S6 octahedra,  an edgeedge with one Cr(4)S6 octahedra, and edges with four equivalent Cr(2)S6 octahedra. In the third Cr site, Cr(3) is bonded to three equivalent S(2) and three equivalent S(5) atoms to form CrS6 octahedra that share corners with three equivalent Cu(1)S4 tetrahedra, corners with three equivalent Cd(3)S4 tetrahedra, edges with three equivalent Cr(1)S6 octahedra, and edges with three equivalent Cr(2)S6 octahedra. In the fourth Cr site, Cr(4) is bonded to three equivalent S(1) and three equivalent S(6) atoms to form CrS6 octahedra that share corners with three equivalent Cd(1)S4 tetrahedra, corners with three equivalent Cd(2)S4 tetrahedra, edges with three equivalent Cr(1)S6 octahedra, and edges with three equivalent Cr(2)S6 octahedra. Cu(1) is bonded to one S(8) and three equivalent S(5) atoms to form CuS4 tetrahedra that share corners with three equivalent Cr(2)S6 octahedra, corners with three equivalent Cr(3)S6 octahedra, and corners with six equivalent Cr(1)S6 octahedra. The corner-sharing octahedral tilt angles range from 54-59°. There are three inequivalent Cd sites. In the first Cd site, Cd(1) is bonded to one S(7) and three equivalent S(6) atoms to form CdS4 tetrahedra that share corners with three equivalent Cr(1)S6 octahedra, corners with three equivalent Cr(4)S6 octahedra, and corners with six equivalent Cr(2)S6 octahedra. The corner-sharing octahedral tilt angles range from 60-61°. In the second Cd site, Cd(2) is bonded to one S(4) and three equivalent S(1) atoms to form CdS4 tetrahedra that share corners with three equivalent Cr(2)S6 octahedra, corners with three equivalent Cr(4)S6 octahedra, and corners with six equivalent Cr(1)S6 octahedra. The corner-sharing octahedral tilt angles range from 60-61°. In the third Cd site, Cd(3) is bonded to one S(3) and three equivalent S(2) atoms to form CdS4 tetrahedra that share corners with three equivalent Cr(1)S6 octahedra, corners with three equivalent Cr(3)S6 octahedra, and corners with six equivalent Cr(2)S6 octahedra. The corner-sharing octahedral tilt angles range from 59-62°. There are eight inequivalent S sites. In the first S site, S(1) is bonded to one Cr(4), two equivalent Cr(1), and one Cd(2) atom to form a mixture of distorted corner and edge-sharing SCr3Cd tetrahedra. In the second S site, S(2) is bonded to one Cr(3), two equivalent Cr(2), and one Cd(3) atom to form SCr3Cd tetrahedra that share  a cornercorner with one S(3)Cr3Cd tetrahedra, corners with two equivalent S(2)Cr3Cd tetrahedra, corners with four equivalent S(6)Cr3Cd tetrahedra, corners with two equivalent S(8)Cr3Cu trigonal pyramids,  an edgeedge with one S(4)Cr3Cd tetrahedra, and edges with two equivalent S(2)Cr3Cd tetrahedra. In the third S site, S(3) is bonded to three equivalent Cr(1) and one Cd(3) atom to form a mixture of corner and edge-sharing SCr3Cd tetrahedra. In the fourth S site, S(4) is bonded to three equivalent Cr(2) and one Cd(2) atom to form distorted SCr3Cd tetrahedra that share corners with three equivalent S(1)Cr3Cd tetrahedra, corners with six equivalent S(6)Cr3Cd tetrahedra, corners with three equivalent S(8)Cr3Cu trigonal pyramids, and edges with three equivalent S(2)Cr3Cd tetrahedra. In the fifth S site, S(5) is bonded in a rectangular see-saw-like geometry to one Cr(3), two equivalent Cr(1), and one Cu(1) atom. In the sixth S site, S(6) is bonded to one Cr(4), two equivalent Cr(2), and one Cd(1) atom to form distorted SCr3Cd tetrahedra that share  a cornercorner with one S(7)Cr3Cd tetrahedra, corners with two equivalent S(4)Cr3Cd tetrahedra, corners with two equivalent S(6)Cr3Cd tetrahedra, corners with three equivalent S(1)Cr3Cd tetrahedra, corners with four equivalent S(2)Cr3Cd tetrahedra, edges with two equivalent S(6)Cr3Cd tetrahedra, and  an edgeedge with one S(8)Cr3Cu trigonal pyramid. In the seventh S site, S(7) is bonded to three equivalent Cr(1) and one Cd(1) atom to form distorted corner-sharing SCr3Cd tetrahedra. In the eighth S site, S(8) is bonded to three equivalent Cr(2) and one Cu(1) atom to form a mixture of distorted corner and edge-sharing SCr3Cu trigonal pyramids. is represented by the CIF file [CIF]
data_Cr8Cd3CuS16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   12.412
_cell_length_b   12.412
_cell_length_c   12.412
_cell_angle_alpha   33.899
_cell_angle_beta   33.899
_cell_angle_gamma   33.899
_symmetry_Int_Tables_number   1
_cell_volume   530.051
_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
  Cr  Cr0  1  0.566  0.063  0.566  1.0
  Cr  Cr1  1  0.062  0.558  0.062  1.0
  Cr  Cr2  1  0.063  0.566  0.566  1.0
  Cr  Cr3  1  0.558  0.062  0.062  1.0
  Cr  Cr4  1  0.809  0.809  0.809  1.0
  Cr  Cr5  1  0.313  0.313  0.313  1.0
  Cr  Cr6  1  0.566  0.566  0.063  1.0
  Cr  Cr7  1  0.062  0.062  0.558  1.0
  Cd  Cd8  1  0.625  0.625  0.625  1.0
  Cd  Cd9  1  0.001  0.001  0.001  1.0
  Cd  Cd10  1  0.501  0.501  0.501  1.0
  Cu  Cu11  1  0.125  0.125  0.125  1.0
  S  S12  1  0.213  0.648  0.213  1.0
  S  S13  1  0.711  0.145  0.711  1.0
  S  S14  1  0.648  0.213  0.213  1.0
  S  S15  1  0.145  0.711  0.711  1.0
  S  S16  1  0.431  0.431  0.431  1.0
  S  S17  1  0.929  0.929  0.929  1.0
  S  S18  1  0.213  0.213  0.648  1.0
  S  S19  1  0.711  0.711  0.145  1.0
  S  S20  1  0.926  0.457  0.926  1.0
  S  S21  1  0.413  0.976  0.413  1.0
  S  S22  1  0.457  0.926  0.926  1.0
  S  S23  1  0.976  0.413  0.413  1.0
  S  S24  1  0.697  0.697  0.697  1.0
  S  S25  1  0.191  0.191  0.191  1.0
  S  S26  1  0.926  0.926  0.457  1.0
  S  S27  1  0.413  0.413  0.976  1.0
[/CIF]
.
The crystal structure described by Cr8CuCd3S16 is Spinel-derived structured and crystallizes in the trigonal R3m space group. There are four inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one S(3), one S(7), two equivalent S(1), and two equivalent S(5) atoms to form CrS6 octahedra that share  a cornercorner with one Cd(1)S4 tetrahedra,  a cornercorner with one Cd(3)S4 tetrahedra, corners with two equivalent Cu(1)S4 tetrahedra, corners with two equivalent Cd(2)S4 tetrahedra,  an edgeedge with one Cr(3)S6 octahedra,  an edgeedge with one Cr(4)S6 octahedra, and edges with four equivalent Cr(1)S6 octahedra. In the second Cr site, Cr(2) is bonded to one S(4), one S(8), two equivalent S(2), and two equivalent S(6) atoms to form CrS6 octahedra that share  a cornercorner with one Cu(1)S4 tetrahedra,  a cornercorner with one Cd(2)S4 tetrahedra, corners with two equivalent Cd(1)S4 tetrahedra, corners with two equivalent Cd(3)S4 tetrahedra,  an edgeedge with one Cr(3)S6 octahedra,  an edgeedge with one Cr(4)S6 octahedra, and edges with four equivalent Cr(2)S6 octahedra. In the third Cr site, Cr(3) is bonded to three equivalent S(2) and three equivalent S(5) atoms to form CrS6 octahedra that share corners with three equivalent Cu(1)S4 tetrahedra, corners with three equivalent Cd(3)S4 tetrahedra, edges with three equivalent Cr(1)S6 octahedra, and edges with three equivalent Cr(2)S6 octahedra. In the fourth Cr site, Cr(4) is bonded to three equivalent S(1) and three equivalent S(6) atoms to form CrS6 octahedra that share corners with three equivalent Cd(1)S4 tetrahedra, corners with three equivalent Cd(2)S4 tetrahedra, edges with three equivalent Cr(1)S6 octahedra, and edges with three equivalent Cr(2)S6 octahedra. Cu(1) is bonded to one S(8) and three equivalent S(5) atoms to form CuS4 tetrahedra that share corners with three equivalent Cr(2)S6 octahedra, corners with three equivalent Cr(3)S6 octahedra, and corners with six equivalent Cr(1)S6 octahedra. The corner-sharing octahedral tilt angles range from 54-59°. There are three inequivalent Cd sites. In the first Cd site, Cd(1) is bonded to one S(7) and three equivalent S(6) atoms to form CdS4 tetrahedra that share corners with three equivalent Cr(1)S6 octahedra, corners with three equivalent Cr(4)S6 octahedra, and corners with six equivalent Cr(2)S6 octahedra. The corner-sharing octahedral tilt angles range from 60-61°. In the second Cd site, Cd(2) is bonded to one S(4) and three equivalent S(1) atoms to form CdS4 tetrahedra that share corners with three equivalent Cr(2)S6 octahedra, corners with three equivalent Cr(4)S6 octahedra, and corners with six equivalent Cr(1)S6 octahedra. The corner-sharing octahedral tilt angles range from 60-61°. In the third Cd site, Cd(3) is bonded to one S(3) and three equivalent S(2) atoms to form CdS4 tetrahedra that share corners with three equivalent Cr(1)S6 octahedra, corners with three equivalent Cr(3)S6 octahedra, and corners with six equivalent Cr(2)S6 octahedra. The corner-sharing octahedral tilt angles range from 59-62°. There are eight inequivalent S sites. In the first S site, S(1) is bonded to one Cr(4), two equivalent Cr(1), and one Cd(2) atom to form a mixture of distorted corner and edge-sharing SCr3Cd tetrahedra. In the second S site, S(2) is bonded to one Cr(3), two equivalent Cr(2), and one Cd(3) atom to form SCr3Cd tetrahedra that share  a cornercorner with one S(3)Cr3Cd tetrahedra, corners with two equivalent S(2)Cr3Cd tetrahedra, corners with four equivalent S(6)Cr3Cd tetrahedra, corners with two equivalent S(8)Cr3Cu trigonal pyramids,  an edgeedge with one S(4)Cr3Cd tetrahedra, and edges with two equivalent S(2)Cr3Cd tetrahedra. In the third S site, S(3) is bonded to three equivalent Cr(1) and one Cd(3) atom to form a mixture of corner and edge-sharing SCr3Cd tetrahedra. In the fourth S site, S(4) is bonded to three equivalent Cr(2) and one Cd(2) atom to form distorted SCr3Cd tetrahedra that share corners with three equivalent S(1)Cr3Cd tetrahedra, corners with six equivalent S(6)Cr3Cd tetrahedra, corners with three equivalent S(8)Cr3Cu trigonal pyramids, and edges with three equivalent S(2)Cr3Cd tetrahedra. In the fifth S site, S(5) is bonded in a rectangular see-saw-like geometry to one Cr(3), two equivalent Cr(1), and one Cu(1) atom. In the sixth S site, S(6) is bonded to one Cr(4), two equivalent Cr(2), and one Cd(1) atom to form distorted SCr3Cd tetrahedra that share  a cornercorner with one S(7)Cr3Cd tetrahedra, corners with two equivalent S(4)Cr3Cd tetrahedra, corners with two equivalent S(6)Cr3Cd tetrahedra, corners with three equivalent S(1)Cr3Cd tetrahedra, corners with four equivalent S(2)Cr3Cd tetrahedra, edges with two equivalent S(6)Cr3Cd tetrahedra, and  an edgeedge with one S(8)Cr3Cu trigonal pyramid. In the seventh S site, S(7) is bonded to three equivalent Cr(1) and one Cd(1) atom to form distorted corner-sharing SCr3Cd tetrahedra. In the eighth S site, S(8) is bonded to three equivalent Cr(2) and one Cu(1) atom to form a mixture of distorted corner and edge-sharing SCr3Cu trigonal pyramids. is represented by the CIF file [CIF]
data_Cr8Cd3CuS16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   12.412
_cell_length_b   12.412
_cell_length_c   12.412
_cell_angle_alpha   33.899
_cell_angle_beta   33.899
_cell_angle_gamma   33.899
_symmetry_Int_Tables_number   1
_cell_volume   530.051
_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
  Cr  Cr0  1  0.566  0.063  0.566  1.0
  Cr  Cr1  1  0.062  0.558  0.062  1.0
  Cr  Cr2  1  0.063  0.566  0.566  1.0
  Cr  Cr3  1  0.558  0.062  0.062  1.0
  Cr  Cr4  1  0.809  0.809  0.809  1.0
  Cr  Cr5  1  0.313  0.313  0.313  1.0
  Cr  Cr6  1  0.566  0.566  0.063  1.0
  Cr  Cr7  1  0.062  0.062  0.558  1.0
  Cd  Cd8  1  0.625  0.625  0.625  1.0
  Cd  Cd9  1  0.001  0.001  0.001  1.0
  Cd  Cd10  1  0.501  0.501  0.501  1.0
  Cu  Cu11  1  0.125  0.125  0.125  1.0
  S  S12  1  0.213  0.648  0.213  1.0
  S  S13  1  0.711  0.145  0.711  1.0
  S  S14  1  0.648  0.213  0.213  1.0
  S  S15  1  0.145  0.711  0.711  1.0
  S  S16  1  0.431  0.431  0.431  1.0
  S  S17  1  0.929  0.929  0.929  1.0
  S  S18  1  0.213  0.213  0.648  1.0
  S  S19  1  0.711  0.711  0.145  1.0
  S  S20  1  0.926  0.457  0.926  1.0
  S  S21  1  0.413  0.976  0.413  1.0
  S  S22  1  0.457  0.926  0.926  1.0
  S  S23  1  0.976  0.413  0.413  1.0
  S  S24  1  0.697  0.697  0.697  1.0
  S  S25  1  0.191  0.191  0.191  1.0
  S  S26  1  0.926  0.926  0.457  1.0
  S  S27  1  0.413  0.413  0.976  1.0
[/CIF]
.