The material described by Cr8Mn3CuS16 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 three equivalent S(3) and three equivalent S(7) atoms to form CrS6 octahedra that share corners with three equivalent Mn(2)S4 tetrahedra, corners with three equivalent Cu(1)S4 tetrahedra, edges with three equivalent Cr(3)S6 octahedra, and edges with three equivalent Cr(4)S6 octahedra. In the second Cr site, Cr(2) is bonded to three equivalent S(4) and three equivalent S(8) atoms to form CrS6 octahedra that share corners with three equivalent Mn(1)S4 tetrahedra, corners with three equivalent Mn(3)S4 tetrahedra, edges with three equivalent Cr(3)S6 octahedra, and edges with three equivalent Cr(4)S6 octahedra. In the third Cr site, Cr(3) is bonded to one S(2), one S(5), two equivalent S(3), and two equivalent S(8) atoms to form CrS6 octahedra that share  a cornercorner with one Mn(1)S4 tetrahedra,  a cornercorner with one Mn(2)S4 tetrahedra, corners with two equivalent Mn(3)S4 tetrahedra, corners with two equivalent Cu(1)S4 tetrahedra,  an edgeedge with one Cr(1)S6 octahedra,  an edgeedge with one Cr(2)S6 octahedra, and edges with four equivalent Cr(3)S6 octahedra. In the fourth Cr site, Cr(4) is bonded to one S(1), one S(6), two equivalent S(4), and two equivalent S(7) atoms to form CrS6 octahedra that share  a cornercorner with one Mn(3)S4 tetrahedra,  a cornercorner with one Cu(1)S4 tetrahedra, corners with two equivalent Mn(1)S4 tetrahedra, corners with two equivalent Mn(2)S4 tetrahedra,  an edgeedge with one Cr(1)S6 octahedra,  an edgeedge with one Cr(2)S6 octahedra, and edges with four equivalent Cr(4)S6 octahedra. There are three inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to one S(2) and three equivalent S(4) atoms to form MnS4 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(4)S6 octahedra. The corner-sharing octahedral tilt angles range from 57-58°. In the second Mn site, Mn(2) is bonded to one S(5) and three equivalent S(7) atoms to form MnS4 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(4)S6 octahedra. The corner-sharing octahedral tilt angles are 59°. In the third Mn site, Mn(3) is bonded to one S(6) and three equivalent S(8) atoms to form MnS4 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(3)S6 octahedra. The corner-sharing octahedral tilt angles range from 58-59°. Cu(1) is bonded to one S(1) and three equivalent S(3) atoms to form CuS4 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(3)S6 octahedra. The corner-sharing octahedral tilt angles range from 56-58°. There are eight inequivalent S sites. In the first S site, S(1) is bonded to three equivalent Cr(4) and one Cu(1) atom to form a mixture of distorted edge and corner-sharing SCr3Cu trigonal pyramids. In the second S site, S(2) is bonded in a distorted rectangular see-saw-like geometry to three equivalent Cr(3) and one Mn(1) atom. In the third S site, S(3) is bonded in a rectangular see-saw-like geometry to one Cr(1), two equivalent Cr(3), and one Cu(1) atom. In the fourth S site, S(4) is bonded to one Cr(2), two equivalent Cr(4), and one Mn(1) atom to form distorted SMnCr3 trigonal pyramids that share corners with two equivalent S(4)MnCr3 trigonal pyramids, corners with two equivalent S(6)MnCr3 trigonal pyramids, corners with three equivalent S(8)MnCr3 trigonal pyramids, corners with four equivalent S(7)MnCr3 trigonal pyramids,  an edgeedge with one S(1)Cr3Cu trigonal pyramid, and edges with two equivalent S(4)MnCr3 trigonal pyramids. In the fifth S site, S(5) is bonded to three equivalent Cr(3) and one Mn(2) atom to form a mixture of distorted edge and corner-sharing SMnCr3 trigonal pyramids. In the sixth S site, S(6) is bonded to three equivalent Cr(4) and one Mn(3) atom to form distorted SMnCr3 trigonal pyramids that share corners with three equivalent S(1)Cr3Cu trigonal pyramids, corners with three equivalent S(8)MnCr3 trigonal pyramids, corners with six equivalent S(4)MnCr3 trigonal pyramids, and edges with three equivalent S(7)MnCr3 trigonal pyramids. In the seventh S site, S(7) is bonded to one Cr(1), two equivalent Cr(4), and one Mn(2) atom to form distorted SMnCr3 trigonal pyramids that share  a cornercorner with one S(5)MnCr3 trigonal pyramid, corners with two equivalent S(1)Cr3Cu trigonal pyramids, corners with two equivalent S(7)MnCr3 trigonal pyramids, corners with four equivalent S(4)MnCr3 trigonal pyramids,  an edgeedge with one S(6)MnCr3 trigonal pyramid, and edges with two equivalent S(7)MnCr3 trigonal pyramids. In the eighth S site, S(8) is bonded to one Cr(2), two equivalent Cr(3), and one Mn(3) atom to form a mixture of distorted edge and corner-sharing SMnCr3 trigonal pyramids. is represented by the CIF file [CIF]
data_Mn3Cr8CuS16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   12.286
_cell_length_b   12.286
_cell_length_c   12.286
_cell_angle_alpha   33.703
_cell_angle_beta   33.703
_cell_angle_gamma   33.703
_symmetry_Int_Tables_number   1
_cell_volume   508.774
_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
  Mn  Mn0  1  0.562  0.562  0.562  1.0
  Mn  Mn1  1  0.438  0.438  0.438  1.0
  Mn  Mn2  1  0.938  0.938  0.938  1.0
  Cr  Cr3  1  0.749  0.749  0.749  1.0
  Cr  Cr4  1  0.250  0.250  0.250  1.0
  Cr  Cr5  1  0.997  0.503  0.503  1.0
  Cr  Cr6  1  0.496  0.001  0.001  1.0
  Cr  Cr7  1  0.503  0.997  0.503  1.0
  Cr  Cr8  1  0.001  0.496  0.001  1.0
  Cr  Cr9  1  0.503  0.503  0.997  1.0
  Cr  Cr10  1  0.001  0.001  0.496  1.0
  Cu  Cu11  1  0.062  0.062  0.062  1.0
  S  S12  1  0.130  0.130  0.130  1.0
  S  S13  1  0.630  0.630  0.630  1.0
  S  S14  1  0.396  0.862  0.862  1.0
  S  S15  1  0.901  0.360  0.360  1.0
  S  S16  1  0.862  0.396  0.862  1.0
  S  S17  1  0.360  0.901  0.360  1.0
  S  S18  1  0.862  0.862  0.396  1.0
  S  S19  1  0.360  0.360  0.901  1.0
  S  S20  1  0.370  0.370  0.370  1.0
  S  S21  1  0.869  0.869  0.869  1.0
  S  S22  1  0.100  0.640  0.640  1.0
  S  S23  1  0.598  0.141  0.141  1.0
  S  S24  1  0.640  0.100  0.640  1.0
  S  S25  1  0.141  0.598  0.141  1.0
  S  S26  1  0.640  0.640  0.100  1.0
  S  S27  1  0.141  0.141  0.598  1.0
[/CIF]
.
The material described by Cr8Mn3CuS16 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 three equivalent S(3) and three equivalent S(7) atoms to form CrS6 octahedra that share corners with three equivalent Mn(2)S4 tetrahedra, corners with three equivalent Cu(1)S4 tetrahedra, edges with three equivalent Cr(3)S6 octahedra, and edges with three equivalent Cr(4)S6 octahedra. In the second Cr site, Cr(2) is bonded to three equivalent S(4) and three equivalent S(8) atoms to form CrS6 octahedra that share corners with three equivalent Mn(1)S4 tetrahedra, corners with three equivalent Mn(3)S4 tetrahedra, edges with three equivalent Cr(3)S6 octahedra, and edges with three equivalent Cr(4)S6 octahedra. In the third Cr site, Cr(3) is bonded to one S(2), one S(5), two equivalent S(3), and two equivalent S(8) atoms to form CrS6 octahedra that share  a cornercorner with one Mn(1)S4 tetrahedra,  a cornercorner with one Mn(2)S4 tetrahedra, corners with two equivalent Mn(3)S4 tetrahedra, corners with two equivalent Cu(1)S4 tetrahedra,  an edgeedge with one Cr(1)S6 octahedra,  an edgeedge with one Cr(2)S6 octahedra, and edges with four equivalent Cr(3)S6 octahedra. In the fourth Cr site, Cr(4) is bonded to one S(1), one S(6), two equivalent S(4), and two equivalent S(7) atoms to form CrS6 octahedra that share  a cornercorner with one Mn(3)S4 tetrahedra,  a cornercorner with one Cu(1)S4 tetrahedra, corners with two equivalent Mn(1)S4 tetrahedra, corners with two equivalent Mn(2)S4 tetrahedra,  an edgeedge with one Cr(1)S6 octahedra,  an edgeedge with one Cr(2)S6 octahedra, and edges with four equivalent Cr(4)S6 octahedra. There are three inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to one S(2) and three equivalent S(4) atoms to form MnS4 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(4)S6 octahedra. The corner-sharing octahedral tilt angles range from 57-58°. In the second Mn site, Mn(2) is bonded to one S(5) and three equivalent S(7) atoms to form MnS4 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(4)S6 octahedra. The corner-sharing octahedral tilt angles are 59°. In the third Mn site, Mn(3) is bonded to one S(6) and three equivalent S(8) atoms to form MnS4 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(3)S6 octahedra. The corner-sharing octahedral tilt angles range from 58-59°. Cu(1) is bonded to one S(1) and three equivalent S(3) atoms to form CuS4 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(3)S6 octahedra. The corner-sharing octahedral tilt angles range from 56-58°. There are eight inequivalent S sites. In the first S site, S(1) is bonded to three equivalent Cr(4) and one Cu(1) atom to form a mixture of distorted edge and corner-sharing SCr3Cu trigonal pyramids. In the second S site, S(2) is bonded in a distorted rectangular see-saw-like geometry to three equivalent Cr(3) and one Mn(1) atom. In the third S site, S(3) is bonded in a rectangular see-saw-like geometry to one Cr(1), two equivalent Cr(3), and one Cu(1) atom. In the fourth S site, S(4) is bonded to one Cr(2), two equivalent Cr(4), and one Mn(1) atom to form distorted SMnCr3 trigonal pyramids that share corners with two equivalent S(4)MnCr3 trigonal pyramids, corners with two equivalent S(6)MnCr3 trigonal pyramids, corners with three equivalent S(8)MnCr3 trigonal pyramids, corners with four equivalent S(7)MnCr3 trigonal pyramids,  an edgeedge with one S(1)Cr3Cu trigonal pyramid, and edges with two equivalent S(4)MnCr3 trigonal pyramids. In the fifth S site, S(5) is bonded to three equivalent Cr(3) and one Mn(2) atom to form a mixture of distorted edge and corner-sharing SMnCr3 trigonal pyramids. In the sixth S site, S(6) is bonded to three equivalent Cr(4) and one Mn(3) atom to form distorted SMnCr3 trigonal pyramids that share corners with three equivalent S(1)Cr3Cu trigonal pyramids, corners with three equivalent S(8)MnCr3 trigonal pyramids, corners with six equivalent S(4)MnCr3 trigonal pyramids, and edges with three equivalent S(7)MnCr3 trigonal pyramids. In the seventh S site, S(7) is bonded to one Cr(1), two equivalent Cr(4), and one Mn(2) atom to form distorted SMnCr3 trigonal pyramids that share  a cornercorner with one S(5)MnCr3 trigonal pyramid, corners with two equivalent S(1)Cr3Cu trigonal pyramids, corners with two equivalent S(7)MnCr3 trigonal pyramids, corners with four equivalent S(4)MnCr3 trigonal pyramids,  an edgeedge with one S(6)MnCr3 trigonal pyramid, and edges with two equivalent S(7)MnCr3 trigonal pyramids. In the eighth S site, S(8) is bonded to one Cr(2), two equivalent Cr(3), and one Mn(3) atom to form a mixture of distorted edge and corner-sharing SMnCr3 trigonal pyramids. is represented by the CIF file [CIF]
data_Mn3Cr8CuS16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   12.286
_cell_length_b   12.286
_cell_length_c   12.286
_cell_angle_alpha   33.703
_cell_angle_beta   33.703
_cell_angle_gamma   33.703
_symmetry_Int_Tables_number   1
_cell_volume   508.774
_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
  Mn  Mn0  1  0.562  0.562  0.562  1.0
  Mn  Mn1  1  0.438  0.438  0.438  1.0
  Mn  Mn2  1  0.938  0.938  0.938  1.0
  Cr  Cr3  1  0.749  0.749  0.749  1.0
  Cr  Cr4  1  0.250  0.250  0.250  1.0
  Cr  Cr5  1  0.997  0.503  0.503  1.0
  Cr  Cr6  1  0.496  0.001  0.001  1.0
  Cr  Cr7  1  0.503  0.997  0.503  1.0
  Cr  Cr8  1  0.001  0.496  0.001  1.0
  Cr  Cr9  1  0.503  0.503  0.997  1.0
  Cr  Cr10  1  0.001  0.001  0.496  1.0
  Cu  Cu11  1  0.062  0.062  0.062  1.0
  S  S12  1  0.130  0.130  0.130  1.0
  S  S13  1  0.630  0.630  0.630  1.0
  S  S14  1  0.396  0.862  0.862  1.0
  S  S15  1  0.901  0.360  0.360  1.0
  S  S16  1  0.862  0.396  0.862  1.0
  S  S17  1  0.360  0.901  0.360  1.0
  S  S18  1  0.862  0.862  0.396  1.0
  S  S19  1  0.360  0.360  0.901  1.0
  S  S20  1  0.370  0.370  0.370  1.0
  S  S21  1  0.869  0.869  0.869  1.0
  S  S22  1  0.100  0.640  0.640  1.0
  S  S23  1  0.598  0.141  0.141  1.0
  S  S24  1  0.640  0.100  0.640  1.0
  S  S25  1  0.141  0.598  0.141  1.0
  S  S26  1  0.640  0.640  0.100  1.0
  S  S27  1  0.141  0.141  0.598  1.0
[/CIF]
.