The crystal structure described by Ba7Cd31 crystallizes in the hexagonal P-6m2 space group. There are four inequivalent Ba sites. In the first Ba site, Ba(1) is bonded in a 20-coordinate geometry to two equivalent Cd(3); six Cd(1,1,1,1); six equivalent Cd(2); and six equivalent Cd(5) atoms. In the second Ba site, Ba(2) is bonded in a 20-coordinate geometry to two equivalent Cd(4); six Cd(1,1,1,1); six equivalent Cd(2); and six equivalent Cd(6) atoms. In the third Ba site, Ba(3) is bonded in a 16-coordinate geometry to two equivalent Cd(2), two equivalent Cd(3), two equivalent Cd(4), two equivalent Cd(7), four equivalent Cd(5), and four equivalent Cd(6) atoms. In the fourth Ba site, Ba(4) is bonded in a 15-coordinate geometry to three equivalent Cd(5); three equivalent Cd(6); three equivalent Cd(7); and six Cd(1,1,1,1) atoms. There are ten inequivalent Cd sites. In the first Cd site, Cd(7) is bonded in a 8-coordinate geometry to two equivalent Ba(3), two equivalent Ba(4), two equivalent Cd(5), and two equivalent Cd(7) atoms. In the second Cd site, Cd(1) is bonded to one Ba(1); one Ba(2); two equivalent Ba(4); two Cd(1,1); two equivalent Cd(2); two equivalent Cd(5); and two equivalent Cd(6) atoms to form a mixture of corner, edge, and face-sharing CdBa4Cd8 cuboctahedra. In the third Cd site, Cd(1) is bonded to one Ba(1); one Ba(2); two equivalent Ba(4); two Cd(1,1); two equivalent Cd(2); two equivalent Cd(5); and two equivalent Cd(6) atoms to form a mixture of corner, edge, and face-sharing CdBa4Cd8 cuboctahedra. In the fourth Cd site, Cd(1) is bonded to one Ba(1), one Ba(2), two equivalent Ba(4), two equivalent Cd(1), two equivalent Cd(2), two equivalent Cd(5), and two equivalent Cd(6) atoms to form a mixture of corner, edge, and face-sharing CdBa4Cd8 cuboctahedra. In the fifth Cd site, Cd(1) is bonded to one Ba(1); one Ba(2); two equivalent Ba(4); two Cd(1,1); two equivalent Cd(2); two equivalent Cd(5); and two equivalent Cd(6) atoms to form a mixture of corner, edge, and face-sharing CdBa4Cd8 cuboctahedra. In the sixth Cd site, Cd(2) is bonded in a 9-coordinate geometry to one Ba(1); one Ba(2); one Ba(3); two Cd(1,1); two equivalent Cd(5); and two equivalent Cd(6) atoms. In the seventh Cd site, Cd(3) is bonded in a distorted body-centered cubic geometry to one Ba(1), three equivalent Ba(3), one Cd(3), and three equivalent Cd(5) atoms. In the eighth Cd site, Cd(4) is bonded in a distorted body-centered cubic geometry to one Ba(2), three equivalent Ba(3), one Cd(4), and three equivalent Cd(6) atoms. In the ninth Cd site, Cd(5) is bonded in a 12-coordinate geometry to one Ba(1); one Ba(4); two equivalent Ba(3); one Cd(3); one Cd(7); two Cd(1,1); two equivalent Cd(2); and two equivalent Cd(6) atoms. In the tenth Cd site, Cd(6) is bonded in a 11-coordinate geometry to one Ba(2); one Ba(4); two equivalent Ba(3); one Cd(4); two Cd(1,1); two equivalent Cd(2); and two equivalent Cd(5) atoms. is represented by the CIF file [CIF]
data_Ba7Cd31
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   10.445
_cell_length_b   10.662
_cell_length_c   10.662
_cell_angle_alpha   60.001
_cell_angle_beta   89.999
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   1028.359
_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
  Ba  Ba0  1  0.000  0.333  0.333  1.0
  Ba  Ba1  1  1.000  0.667  0.667  1.0
  Ba  Ba2  1  0.500  0.499  0.499  1.0
  Ba  Ba3  1  0.500  0.499  0.002  1.0
  Ba  Ba4  1  0.500  0.002  0.499  1.0
  Ba  Ba5  1  0.207  0.000  0.000  1.0
  Ba  Ba6  1  0.793  0.000  0.000  1.0
  Cd  Cd7  1  0.000  0.275  0.725  1.0
  Cd  Cd8  1  0.000  0.725  0.000  1.0
  Cd  Cd9  1  1.000  0.000  0.275  1.0
  Cd  Cd10  1  1.000  0.725  0.275  1.0
  Cd  Cd11  1  0.000  0.275  0.000  1.0
  Cd  Cd12  1  0.000  0.000  0.725  1.0
  Cd  Cd13  1  0.167  0.499  0.499  1.0
  Cd  Cd14  1  0.167  0.499  0.002  1.0
  Cd  Cd15  1  0.167  0.002  0.499  1.0
  Cd  Cd16  1  0.833  0.499  0.499  1.0
  Cd  Cd17  1  0.833  0.499  0.002  1.0
  Cd  Cd18  1  0.833  0.002  0.499  1.0
  Cd  Cd19  1  0.345  0.333  0.333  1.0
  Cd  Cd20  1  0.351  0.667  0.667  1.0
  Cd  Cd21  1  0.649  0.667  0.667  1.0
  Cd  Cd22  1  0.655  0.333  0.333  1.0
  Cd  Cd23  1  0.261  0.184  0.631  1.0
  Cd  Cd24  1  0.261  0.631  0.184  1.0
  Cd  Cd25  1  0.261  0.184  0.184  1.0
  Cd  Cd26  1  0.263  0.369  0.815  1.0
  Cd  Cd27  1  0.263  0.815  0.369  1.0
  Cd  Cd28  1  0.263  0.815  0.815  1.0
  Cd  Cd29  1  0.737  0.815  0.369  1.0
  Cd  Cd30  1  0.737  0.369  0.815  1.0
  Cd  Cd31  1  0.737  0.815  0.815  1.0
  Cd  Cd32  1  0.739  0.631  0.184  1.0
  Cd  Cd33  1  0.739  0.184  0.631  1.0
  Cd  Cd34  1  0.739  0.184  0.184  1.0
  Cd  Cd35  1  0.500  0.097  0.805  1.0
  Cd  Cd36  1  0.500  0.805  0.097  1.0
  Cd  Cd37  1  0.500  0.098  0.097  1.0
[/CIF]
.
The crystal structure described by Ba7Cd31 crystallizes in the hexagonal P-6m2 space group. There are four inequivalent Ba sites. In the first Ba site, Ba(1) is bonded in a 20-coordinate geometry to two equivalent Cd(3); six Cd(1,1,1,1); six equivalent Cd(2); and six equivalent Cd(5) atoms. In the second Ba site, Ba(2) is bonded in a 20-coordinate geometry to two equivalent Cd(4); six Cd(1,1,1,1); six equivalent Cd(2); and six equivalent Cd(6) atoms. In the third Ba site, Ba(3) is bonded in a 16-coordinate geometry to two equivalent Cd(2), two equivalent Cd(3), two equivalent Cd(4), two equivalent Cd(7), four equivalent Cd(5), and four equivalent Cd(6) atoms. In the fourth Ba site, Ba(4) is bonded in a 15-coordinate geometry to three equivalent Cd(5); three equivalent Cd(6); three equivalent Cd(7); and six Cd(1,1,1,1) atoms. There are ten inequivalent Cd sites. In the first Cd site, Cd(7) is bonded in a 8-coordinate geometry to two equivalent Ba(3), two equivalent Ba(4), two equivalent Cd(5), and two equivalent Cd(7) atoms. In the second Cd site, Cd(1) is bonded to one Ba(1); one Ba(2); two equivalent Ba(4); two Cd(1,1); two equivalent Cd(2); two equivalent Cd(5); and two equivalent Cd(6) atoms to form a mixture of corner, edge, and face-sharing CdBa4Cd8 cuboctahedra. In the third Cd site, Cd(1) is bonded to one Ba(1); one Ba(2); two equivalent Ba(4); two Cd(1,1); two equivalent Cd(2); two equivalent Cd(5); and two equivalent Cd(6) atoms to form a mixture of corner, edge, and face-sharing CdBa4Cd8 cuboctahedra. In the fourth Cd site, Cd(1) is bonded to one Ba(1), one Ba(2), two equivalent Ba(4), two equivalent Cd(1), two equivalent Cd(2), two equivalent Cd(5), and two equivalent Cd(6) atoms to form a mixture of corner, edge, and face-sharing CdBa4Cd8 cuboctahedra. In the fifth Cd site, Cd(1) is bonded to one Ba(1); one Ba(2); two equivalent Ba(4); two Cd(1,1); two equivalent Cd(2); two equivalent Cd(5); and two equivalent Cd(6) atoms to form a mixture of corner, edge, and face-sharing CdBa4Cd8 cuboctahedra. In the sixth Cd site, Cd(2) is bonded in a 9-coordinate geometry to one Ba(1); one Ba(2); one Ba(3); two Cd(1,1); two equivalent Cd(5); and two equivalent Cd(6) atoms. In the seventh Cd site, Cd(3) is bonded in a distorted body-centered cubic geometry to one Ba(1), three equivalent Ba(3), one Cd(3), and three equivalent Cd(5) atoms. In the eighth Cd site, Cd(4) is bonded in a distorted body-centered cubic geometry to one Ba(2), three equivalent Ba(3), one Cd(4), and three equivalent Cd(6) atoms. In the ninth Cd site, Cd(5) is bonded in a 12-coordinate geometry to one Ba(1); one Ba(4); two equivalent Ba(3); one Cd(3); one Cd(7); two Cd(1,1); two equivalent Cd(2); and two equivalent Cd(6) atoms. In the tenth Cd site, Cd(6) is bonded in a 11-coordinate geometry to one Ba(2); one Ba(4); two equivalent Ba(3); one Cd(4); two Cd(1,1); two equivalent Cd(2); and two equivalent Cd(5) atoms. is represented by the CIF file [CIF]
data_Ba7Cd31
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   10.445
_cell_length_b   10.662
_cell_length_c   10.662
_cell_angle_alpha   60.001
_cell_angle_beta   89.999
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   1028.359
_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
  Ba  Ba0  1  0.000  0.333  0.333  1.0
  Ba  Ba1  1  1.000  0.667  0.667  1.0
  Ba  Ba2  1  0.500  0.499  0.499  1.0
  Ba  Ba3  1  0.500  0.499  0.002  1.0
  Ba  Ba4  1  0.500  0.002  0.499  1.0
  Ba  Ba5  1  0.207  0.000  0.000  1.0
  Ba  Ba6  1  0.793  0.000  0.000  1.0
  Cd  Cd7  1  0.000  0.275  0.725  1.0
  Cd  Cd8  1  0.000  0.725  0.000  1.0
  Cd  Cd9  1  1.000  0.000  0.275  1.0
  Cd  Cd10  1  1.000  0.725  0.275  1.0
  Cd  Cd11  1  0.000  0.275  0.000  1.0
  Cd  Cd12  1  0.000  0.000  0.725  1.0
  Cd  Cd13  1  0.167  0.499  0.499  1.0
  Cd  Cd14  1  0.167  0.499  0.002  1.0
  Cd  Cd15  1  0.167  0.002  0.499  1.0
  Cd  Cd16  1  0.833  0.499  0.499  1.0
  Cd  Cd17  1  0.833  0.499  0.002  1.0
  Cd  Cd18  1  0.833  0.002  0.499  1.0
  Cd  Cd19  1  0.345  0.333  0.333  1.0
  Cd  Cd20  1  0.351  0.667  0.667  1.0
  Cd  Cd21  1  0.649  0.667  0.667  1.0
  Cd  Cd22  1  0.655  0.333  0.333  1.0
  Cd  Cd23  1  0.261  0.184  0.631  1.0
  Cd  Cd24  1  0.261  0.631  0.184  1.0
  Cd  Cd25  1  0.261  0.184  0.184  1.0
  Cd  Cd26  1  0.263  0.369  0.815  1.0
  Cd  Cd27  1  0.263  0.815  0.369  1.0
  Cd  Cd28  1  0.263  0.815  0.815  1.0
  Cd  Cd29  1  0.737  0.815  0.369  1.0
  Cd  Cd30  1  0.737  0.369  0.815  1.0
  Cd  Cd31  1  0.737  0.815  0.815  1.0
  Cd  Cd32  1  0.739  0.631  0.184  1.0
  Cd  Cd33  1  0.739  0.184  0.631  1.0
  Cd  Cd34  1  0.739  0.184  0.184  1.0
  Cd  Cd35  1  0.500  0.097  0.805  1.0
  Cd  Cd36  1  0.500  0.805  0.097  1.0
  Cd  Cd37  1  0.500  0.098  0.097  1.0
[/CIF]
.