The material described by Pb7Bi4Se13 crystallizes in the monoclinic C2/m space group. There are four inequivalent Pb sites. In the first Pb site, Pb(1) is bonded to two equivalent Se(2) and four equivalent Se(1) atoms to form PbSe6 octahedra that share corners with four equivalent Bi(1)Se6 octahedra, edges with two equivalent Pb(1)Se6 octahedra, edges with four equivalent Pb(3)Se6 octahedra, and edges with six equivalent Bi(1)Se6 octahedra. The corner-sharing octahedral tilt angles are 4°. In the second Pb site, Pb(2) is bonded to one Se(5), two equivalent Se(6), and three equivalent Se(3) atoms to form distorted PbSe6 octahedra that share corners with two equivalent Pb(2)Se6 octahedra, corners with two equivalent Bi(2)Se6 octahedra, edges with five equivalent Pb(2)Se6 octahedra, and edges with five equivalent Bi(2)Se6 octahedra. The corner-sharing octahedral tilt angles range from 0-6°. In the third Pb site, Pb(3) is bonded to one Se(1), one Se(7), two equivalent Se(2), and two equivalent Se(4) atoms to form PbSe6 octahedra that share  a cornercorner with one Bi(2)Se6 octahedra, corners with three equivalent Bi(1)Se6 octahedra, edges with two equivalent Pb(1)Se6 octahedra, edges with two equivalent Pb(3)Se6 octahedra, and edges with three equivalent Bi(1)Se6 octahedra. The corner-sharing octahedral tilt angles range from 2-57°. In the fourth Pb site, Pb(4) is bonded in a 7-coordinate geometry to one Se(3), two equivalent Se(4), two equivalent Se(5), and two equivalent Se(7) atoms. There are two inequivalent Bi sites. In the first Bi site, Bi(1) is bonded to one Se(4), two equivalent Se(2), and three equivalent Se(1) atoms to form BiSe6 octahedra that share corners with two equivalent Pb(1)Se6 octahedra, corners with three equivalent Pb(3)Se6 octahedra, edges with three equivalent Pb(1)Se6 octahedra, edges with three equivalent Pb(3)Se6 octahedra, and edges with four equivalent Bi(1)Se6 octahedra. The corner-sharing octahedral tilt angles range from 2-6°. In the second Bi site, Bi(2) is bonded to one Se(6), one Se(7), two equivalent Se(3), and two equivalent Se(5) atoms to form BiSe6 octahedra that share  a cornercorner with one Pb(3)Se6 octahedra,  a cornercorner with one Bi(2)Se6 octahedra, corners with two equivalent Pb(2)Se6 octahedra, edges with two equivalent Bi(2)Se6 octahedra, and edges with five equivalent Pb(2)Se6 octahedra. The corner-sharing octahedral tilt angles range from 0-57°. There are seven inequivalent Se sites. In the first Se site, Se(6) is bonded to four equivalent Pb(2) and two equivalent Bi(2) atoms to form SeBi2Pb4 octahedra that share corners with four equivalent Se(3)Bi2Pb4 octahedra, corners with two equivalent Se(7)BiPb3 tetrahedra, edges with two equivalent Se(6)Bi2Pb4 octahedra, edges with six equivalent Se(3)Bi2Pb4 octahedra, and edges with four equivalent Se(5)Bi2Pb3 square pyramids. The corner-sharing octahedral tilt angles are 2°. In the second Se site, Se(7) is bonded to one Pb(3), two equivalent Pb(4), and one Bi(2) atom to form distorted SeBiPb3 tetrahedra that share  a cornercorner with one Se(6)Bi2Pb4 octahedra,  a cornercorner with one Se(1)Bi3Pb3 octahedra, corners with two equivalent Se(2)Bi2Pb3 square pyramids, corners with four equivalent Se(5)Bi2Pb3 square pyramids, corners with two equivalent Se(7)BiPb3 tetrahedra, edges with two equivalent Se(3)Bi2Pb4 octahedra, and  an edgeedge with one Se(5)Bi2Pb3 square pyramid. The corner-sharing octahedral tilt angles range from 2-7°. In the third Se site, Se(1) is bonded to one Pb(3), two equivalent Pb(1), and three equivalent Bi(1) atoms to form SeBi3Pb3 octahedra that share corners with two equivalent Se(1)Bi3Pb3 octahedra, corners with two equivalent Se(2)Bi2Pb3 square pyramids,  a cornercorner with one Se(7)BiPb3 tetrahedra, edges with five equivalent Se(1)Bi3Pb3 octahedra, and edges with five equivalent Se(2)Bi2Pb3 square pyramids. The corner-sharing octahedra are not tilted. In the fourth Se site, Se(2) is bonded to one Pb(1), two equivalent Pb(3), and two equivalent Bi(1) atoms to form SeBi2Pb3 square pyramids that share corners with two equivalent Se(1)Bi3Pb3 octahedra,  a cornercorner with one Se(2)Bi2Pb3 square pyramid, corners with two equivalent Se(7)BiPb3 tetrahedra, edges with five equivalent Se(1)Bi3Pb3 octahedra, and edges with two equivalent Se(2)Bi2Pb3 square pyramids. The corner-sharing octahedral tilt angles are 7°. In the fifth Se site, Se(3) is bonded to one Pb(4), three equivalent Pb(2), and two equivalent Bi(2) atoms to form distorted SeBi2Pb4 octahedra that share corners with two equivalent Se(6)Bi2Pb4 octahedra, corners with three equivalent Se(5)Bi2Pb3 square pyramids, edges with three equivalent Se(6)Bi2Pb4 octahedra, edges with four equivalent Se(3)Bi2Pb4 octahedra, edges with three equivalent Se(5)Bi2Pb3 square pyramids, and edges with two equivalent Se(7)BiPb3 tetrahedra. The corner-sharing octahedral tilt angles are 2°. In the sixth Se site, Se(4) is bonded in a 3-coordinate geometry to two equivalent Pb(3), two equivalent Pb(4), and one Bi(1) atom. In the seventh Se site, Se(5) is bonded to one Pb(2), two equivalent Pb(4), and two equivalent Bi(2) atoms to form distorted SeBi2Pb3 square pyramids that share corners with three equivalent Se(3)Bi2Pb4 octahedra, corners with four equivalent Se(7)BiPb3 tetrahedra, edges with two equivalent Se(6)Bi2Pb4 octahedra, edges with three equivalent Se(3)Bi2Pb4 octahedra, edges with two equivalent Se(5)Bi2Pb3 square pyramids, and  an edgeedge with one Se(7)BiPb3 tetrahedra. The corner-sharing octahedral tilt angles range from 2-5°. is represented by the CIF file [CIF]
data_Bi4Pb7Se13
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   7.468
_cell_length_b   7.468
_cell_length_c   23.938
_cell_angle_alpha   83.000
_cell_angle_beta   83.000
_cell_angle_gamma   33.468
_symmetry_Int_Tables_number   1
_cell_volume   730.246
_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
  Bi  Bi0  1  0.248  0.248  0.913  1.0
  Bi  Bi1  1  0.752  0.752  0.087  1.0
  Bi  Bi2  1  0.061  0.061  0.623  1.0
  Bi  Bi3  1  0.939  0.939  0.377  1.0
  Pb  Pb4  1  0.500  0.500  0.000  1.0
  Pb  Pb5  1  0.353  0.353  0.542  1.0
  Pb  Pb6  1  0.647  0.647  0.458  1.0
  Pb  Pb7  1  0.989  0.989  0.837  1.0
  Pb  Pb8  1  0.011  0.011  0.163  1.0
  Pb  Pb9  1  0.767  0.767  0.718  1.0
  Pb  Pb10  1  0.233  0.233  0.282  1.0
  Se  Se11  1  0.868  0.868  0.960  1.0
  Se  Se12  1  0.132  0.132  0.040  1.0
  Se  Se13  1  0.626  0.626  0.882  1.0
  Se  Se14  1  0.374  0.374  0.118  1.0
  Se  Se15  1  0.708  0.708  0.590  1.0
  Se  Se16  1  0.292  0.292  0.410  1.0
  Se  Se17  1  0.358  0.358  0.807  1.0
  Se  Se18  1  0.642  0.642  0.193  1.0
  Se  Se19  1  0.423  0.423  0.653  1.0
  Se  Se20  1  0.577  0.577  0.347  1.0
  Se  Se21  1  0.000  0.000  0.500  1.0
  Se  Se22  1  0.123  0.123  0.730  1.0
  Se  Se23  1  0.877  0.877  0.270  1.0
[/CIF]
.
The material described by Pb7Bi4Se13 crystallizes in the monoclinic C2/m space group. There are four inequivalent Pb sites. In the first Pb site, Pb(1) is bonded to two equivalent Se(2) and four equivalent Se(1) atoms to form PbSe6 octahedra that share corners with four equivalent Bi(1)Se6 octahedra, edges with two equivalent Pb(1)Se6 octahedra, edges with four equivalent Pb(3)Se6 octahedra, and edges with six equivalent Bi(1)Se6 octahedra. The corner-sharing octahedral tilt angles are 4°. In the second Pb site, Pb(2) is bonded to one Se(5), two equivalent Se(6), and three equivalent Se(3) atoms to form distorted PbSe6 octahedra that share corners with two equivalent Pb(2)Se6 octahedra, corners with two equivalent Bi(2)Se6 octahedra, edges with five equivalent Pb(2)Se6 octahedra, and edges with five equivalent Bi(2)Se6 octahedra. The corner-sharing octahedral tilt angles range from 0-6°. In the third Pb site, Pb(3) is bonded to one Se(1), one Se(7), two equivalent Se(2), and two equivalent Se(4) atoms to form PbSe6 octahedra that share  a cornercorner with one Bi(2)Se6 octahedra, corners with three equivalent Bi(1)Se6 octahedra, edges with two equivalent Pb(1)Se6 octahedra, edges with two equivalent Pb(3)Se6 octahedra, and edges with three equivalent Bi(1)Se6 octahedra. The corner-sharing octahedral tilt angles range from 2-57°. In the fourth Pb site, Pb(4) is bonded in a 7-coordinate geometry to one Se(3), two equivalent Se(4), two equivalent Se(5), and two equivalent Se(7) atoms. There are two inequivalent Bi sites. In the first Bi site, Bi(1) is bonded to one Se(4), two equivalent Se(2), and three equivalent Se(1) atoms to form BiSe6 octahedra that share corners with two equivalent Pb(1)Se6 octahedra, corners with three equivalent Pb(3)Se6 octahedra, edges with three equivalent Pb(1)Se6 octahedra, edges with three equivalent Pb(3)Se6 octahedra, and edges with four equivalent Bi(1)Se6 octahedra. The corner-sharing octahedral tilt angles range from 2-6°. In the second Bi site, Bi(2) is bonded to one Se(6), one Se(7), two equivalent Se(3), and two equivalent Se(5) atoms to form BiSe6 octahedra that share  a cornercorner with one Pb(3)Se6 octahedra,  a cornercorner with one Bi(2)Se6 octahedra, corners with two equivalent Pb(2)Se6 octahedra, edges with two equivalent Bi(2)Se6 octahedra, and edges with five equivalent Pb(2)Se6 octahedra. The corner-sharing octahedral tilt angles range from 0-57°. There are seven inequivalent Se sites. In the first Se site, Se(6) is bonded to four equivalent Pb(2) and two equivalent Bi(2) atoms to form SeBi2Pb4 octahedra that share corners with four equivalent Se(3)Bi2Pb4 octahedra, corners with two equivalent Se(7)BiPb3 tetrahedra, edges with two equivalent Se(6)Bi2Pb4 octahedra, edges with six equivalent Se(3)Bi2Pb4 octahedra, and edges with four equivalent Se(5)Bi2Pb3 square pyramids. The corner-sharing octahedral tilt angles are 2°. In the second Se site, Se(7) is bonded to one Pb(3), two equivalent Pb(4), and one Bi(2) atom to form distorted SeBiPb3 tetrahedra that share  a cornercorner with one Se(6)Bi2Pb4 octahedra,  a cornercorner with one Se(1)Bi3Pb3 octahedra, corners with two equivalent Se(2)Bi2Pb3 square pyramids, corners with four equivalent Se(5)Bi2Pb3 square pyramids, corners with two equivalent Se(7)BiPb3 tetrahedra, edges with two equivalent Se(3)Bi2Pb4 octahedra, and  an edgeedge with one Se(5)Bi2Pb3 square pyramid. The corner-sharing octahedral tilt angles range from 2-7°. In the third Se site, Se(1) is bonded to one Pb(3), two equivalent Pb(1), and three equivalent Bi(1) atoms to form SeBi3Pb3 octahedra that share corners with two equivalent Se(1)Bi3Pb3 octahedra, corners with two equivalent Se(2)Bi2Pb3 square pyramids,  a cornercorner with one Se(7)BiPb3 tetrahedra, edges with five equivalent Se(1)Bi3Pb3 octahedra, and edges with five equivalent Se(2)Bi2Pb3 square pyramids. The corner-sharing octahedra are not tilted. In the fourth Se site, Se(2) is bonded to one Pb(1), two equivalent Pb(3), and two equivalent Bi(1) atoms to form SeBi2Pb3 square pyramids that share corners with two equivalent Se(1)Bi3Pb3 octahedra,  a cornercorner with one Se(2)Bi2Pb3 square pyramid, corners with two equivalent Se(7)BiPb3 tetrahedra, edges with five equivalent Se(1)Bi3Pb3 octahedra, and edges with two equivalent Se(2)Bi2Pb3 square pyramids. The corner-sharing octahedral tilt angles are 7°. In the fifth Se site, Se(3) is bonded to one Pb(4), three equivalent Pb(2), and two equivalent Bi(2) atoms to form distorted SeBi2Pb4 octahedra that share corners with two equivalent Se(6)Bi2Pb4 octahedra, corners with three equivalent Se(5)Bi2Pb3 square pyramids, edges with three equivalent Se(6)Bi2Pb4 octahedra, edges with four equivalent Se(3)Bi2Pb4 octahedra, edges with three equivalent Se(5)Bi2Pb3 square pyramids, and edges with two equivalent Se(7)BiPb3 tetrahedra. The corner-sharing octahedral tilt angles are 2°. In the sixth Se site, Se(4) is bonded in a 3-coordinate geometry to two equivalent Pb(3), two equivalent Pb(4), and one Bi(1) atom. In the seventh Se site, Se(5) is bonded to one Pb(2), two equivalent Pb(4), and two equivalent Bi(2) atoms to form distorted SeBi2Pb3 square pyramids that share corners with three equivalent Se(3)Bi2Pb4 octahedra, corners with four equivalent Se(7)BiPb3 tetrahedra, edges with two equivalent Se(6)Bi2Pb4 octahedra, edges with three equivalent Se(3)Bi2Pb4 octahedra, edges with two equivalent Se(5)Bi2Pb3 square pyramids, and  an edgeedge with one Se(7)BiPb3 tetrahedra. The corner-sharing octahedral tilt angles range from 2-5°. is represented by the CIF file [CIF]
data_Bi4Pb7Se13
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   7.468
_cell_length_b   7.468
_cell_length_c   23.938
_cell_angle_alpha   83.000
_cell_angle_beta   83.000
_cell_angle_gamma   33.468
_symmetry_Int_Tables_number   1
_cell_volume   730.246
_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
  Bi  Bi0  1  0.248  0.248  0.913  1.0
  Bi  Bi1  1  0.752  0.752  0.087  1.0
  Bi  Bi2  1  0.061  0.061  0.623  1.0
  Bi  Bi3  1  0.939  0.939  0.377  1.0
  Pb  Pb4  1  0.500  0.500  0.000  1.0
  Pb  Pb5  1  0.353  0.353  0.542  1.0
  Pb  Pb6  1  0.647  0.647  0.458  1.0
  Pb  Pb7  1  0.989  0.989  0.837  1.0
  Pb  Pb8  1  0.011  0.011  0.163  1.0
  Pb  Pb9  1  0.767  0.767  0.718  1.0
  Pb  Pb10  1  0.233  0.233  0.282  1.0
  Se  Se11  1  0.868  0.868  0.960  1.0
  Se  Se12  1  0.132  0.132  0.040  1.0
  Se  Se13  1  0.626  0.626  0.882  1.0
  Se  Se14  1  0.374  0.374  0.118  1.0
  Se  Se15  1  0.708  0.708  0.590  1.0
  Se  Se16  1  0.292  0.292  0.410  1.0
  Se  Se17  1  0.358  0.358  0.807  1.0
  Se  Se18  1  0.642  0.642  0.193  1.0
  Se  Se19  1  0.423  0.423  0.653  1.0
  Se  Se20  1  0.577  0.577  0.347  1.0
  Se  Se21  1  0.000  0.000  0.500  1.0
  Se  Se22  1  0.123  0.123  0.730  1.0
  Se  Se23  1  0.877  0.877  0.270  1.0
[/CIF]
.