The material described by Eu4Zn51 crystallizes in the trigonal R-3 space group. There are two inequivalent Eu sites. In the first Eu site, Eu(1) is bonded in a 24-coordinate geometry to three equivalent Zn(1), three equivalent Zn(2), three equivalent Zn(7), three equivalent Zn(8), six equivalent Zn(3), and six equivalent Zn(5) atoms. In the second Eu site, Eu(2) is bonded in a 24-coordinate geometry to three equivalent Zn(1), three equivalent Zn(2), three equivalent Zn(7), three equivalent Zn(8), six equivalent Zn(4), and six equivalent Zn(6) atoms. There are ten inequivalent Zn sites. In the first Zn site, Zn(1) is bonded in a 11-coordinate geometry to one Eu(1), one Eu(2), one Zn(5), one Zn(8), two equivalent Zn(1), two equivalent Zn(7), and three equivalent Zn(3) atoms. In the second Zn site, Zn(2) is bonded in a 12-coordinate geometry to one Eu(1), one Eu(2), one Zn(6), one Zn(7), one Zn(9), two equivalent Zn(2), two equivalent Zn(8), and three equivalent Zn(4) atoms. In the third Zn site, Zn(3) is bonded in a 11-coordinate geometry to two equivalent Eu(1), one Zn(7), two equivalent Zn(3), three equivalent Zn(1), and three equivalent Zn(5) atoms. In the fourth Zn site, Zn(4) is bonded in a 12-coordinate geometry to two equivalent Eu(2), one Zn(8), one Zn(9), two equivalent Zn(4), three equivalent Zn(2), and three equivalent Zn(6) atoms. In the fifth Zn site, Zn(5) is bonded in a 12-coordinate geometry to two equivalent Eu(1), one Zn(1), one Zn(10), one Zn(8), two equivalent Zn(5), two equivalent Zn(7), and three equivalent Zn(3) atoms. In the sixth Zn site, Zn(6) is bonded in a 12-coordinate geometry to two equivalent Eu(2), one Zn(10), one Zn(2), one Zn(7), two equivalent Zn(6), two equivalent Zn(8), and three equivalent Zn(4) atoms. In the seventh Zn site, Zn(7) is bonded in a 12-coordinate geometry to one Eu(1), one Eu(2), one Zn(10), one Zn(2), one Zn(3), one Zn(6), two equivalent Zn(1), two equivalent Zn(5), and two equivalent Zn(8) atoms. In the eighth Zn site, Zn(8) is bonded in a 12-coordinate geometry to one Eu(1), one Eu(2), one Zn(1), one Zn(10), one Zn(4), one Zn(5), two equivalent Zn(2), two equivalent Zn(6), and two equivalent Zn(7) atoms. In the ninth Zn site, Zn(9) is bonded in a cuboctahedral geometry to six equivalent Zn(2) and six equivalent Zn(4) atoms. In the tenth Zn site, Zn(10) is bonded in a cuboctahedral geometry to three equivalent Zn(5), three equivalent Zn(6), three equivalent Zn(7), and three equivalent Zn(8) atoms. is represented by the CIF card [CIF]
data_Eu4Zn51
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.607
_cell_length_b   8.607
_cell_length_c   14.804
_cell_angle_alpha   73.101
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   894.546
_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
  Eu  Eu0  1  0.875  0.750  0.375  1.0
  Eu  Eu1  1  0.375  0.749  0.876  1.0
  Eu  Eu2  1  0.625  0.250  0.125  1.0
  Eu  Eu3  1  0.125  0.251  0.624  1.0
  Zn  Zn4  1  0.338  0.442  0.103  1.0
  Zn  Zn5  1  0.843  0.442  0.599  1.0
  Zn  Zn6  1  0.162  0.558  0.397  1.0
  Zn  Zn7  1  0.657  0.558  0.901  1.0
  Zn  Zn8  1  0.985  0.205  0.222  1.0
  Zn  Zn9  1  0.479  0.197  0.721  1.0
  Zn  Zn10  1  0.515  0.795  0.278  1.0
  Zn  Zn11  1  0.021  0.803  0.779  1.0
  Zn  Zn12  1  0.711  0.060  0.349  1.0
  Zn  Zn13  1  0.210  0.059  0.850  1.0
  Zn  Zn14  1  0.789  0.940  0.151  1.0
  Zn  Zn15  1  0.290  0.941  0.650  1.0
  Zn  Zn16  1  0.668  0.699  0.029  1.0
  Zn  Zn17  1  0.169  0.700  0.529  1.0
  Zn  Zn18  1  0.832  0.301  0.471  1.0
  Zn  Zn19  1  0.331  0.300  0.971  1.0
  Zn  Zn20  1  0.045  0.206  0.397  1.0
  Zn  Zn21  1  0.540  0.198  0.901  1.0
  Zn  Zn22  1  0.455  0.794  0.103  1.0
  Zn  Zn23  1  0.960  0.802  0.599  1.0
  Zn  Zn24  1  0.926  0.442  0.278  1.0
  Zn  Zn25  1  0.418  0.440  0.779  1.0
  Zn  Zn26  1  0.574  0.558  0.222  1.0
  Zn  Zn27  1  0.082  0.560  0.721  1.0
  Zn  Zn28  1  0.909  0.699  0.151  1.0
  Zn  Zn29  1  0.409  0.699  0.650  1.0
  Zn  Zn30  1  0.591  0.301  0.349  1.0
  Zn  Zn31  1  0.091  0.301  0.850  1.0
  Zn  Zn32  1  0.229  0.060  0.471  1.0
  Zn  Zn33  1  0.729  0.060  0.971  1.0
  Zn  Zn34  1  0.271  0.940  0.029  1.0
  Zn  Zn35  1  0.771  0.940  0.529  1.0
  Zn  Zn36  1  0.220  0.794  0.222  1.0
  Zn  Zn37  1  0.719  0.801  0.721  1.0
  Zn  Zn38  1  0.280  0.206  0.278  1.0
  Zn  Zn39  1  0.781  0.199  0.779  1.0
  Zn  Zn40  1  0.104  0.559  0.103  1.0
  Zn  Zn41  1  0.599  0.559  0.599  1.0
  Zn  Zn42  1  0.396  0.441  0.397  1.0
  Zn  Zn43  1  0.901  0.441  0.901  1.0
  Zn  Zn44  1  0.031  0.302  0.029  1.0
  Zn  Zn45  1  0.530  0.302  0.529  1.0
  Zn  Zn46  1  0.469  0.698  0.471  1.0
  Zn  Zn47  1  0.970  0.698  0.971  1.0
  Zn  Zn48  1  0.349  0.940  0.349  1.0
  Zn  Zn49  1  0.850  0.941  0.850  1.0
  Zn  Zn50  1  0.151  0.060  0.151  1.0
  Zn  Zn51  1  0.650  0.059  0.650  1.0
  Zn  Zn52  1  0.750  0.500  0.750  1.0
  Zn  Zn53  1  0.000  0.000  1.000  1.0
  Zn  Zn54  1  0.500  1.000  0.500  1.0
[/CIF]
.
The material described by Eu4Zn51 crystallizes in the trigonal R-3 space group. There are two inequivalent Eu sites. In the first Eu site, Eu(1) is bonded in a 24-coordinate geometry to three equivalent Zn(1), three equivalent Zn(2), three equivalent Zn(7), three equivalent Zn(8), six equivalent Zn(3), and six equivalent Zn(5) atoms. In the second Eu site, Eu(2) is bonded in a 24-coordinate geometry to three equivalent Zn(1), three equivalent Zn(2), three equivalent Zn(7), three equivalent Zn(8), six equivalent Zn(4), and six equivalent Zn(6) atoms. There are ten inequivalent Zn sites. In the first Zn site, Zn(1) is bonded in a 11-coordinate geometry to one Eu(1), one Eu(2), one Zn(5), one Zn(8), two equivalent Zn(1), two equivalent Zn(7), and three equivalent Zn(3) atoms. In the second Zn site, Zn(2) is bonded in a 12-coordinate geometry to one Eu(1), one Eu(2), one Zn(6), one Zn(7), one Zn(9), two equivalent Zn(2), two equivalent Zn(8), and three equivalent Zn(4) atoms. In the third Zn site, Zn(3) is bonded in a 11-coordinate geometry to two equivalent Eu(1), one Zn(7), two equivalent Zn(3), three equivalent Zn(1), and three equivalent Zn(5) atoms. In the fourth Zn site, Zn(4) is bonded in a 12-coordinate geometry to two equivalent Eu(2), one Zn(8), one Zn(9), two equivalent Zn(4), three equivalent Zn(2), and three equivalent Zn(6) atoms. In the fifth Zn site, Zn(5) is bonded in a 12-coordinate geometry to two equivalent Eu(1), one Zn(1), one Zn(10), one Zn(8), two equivalent Zn(5), two equivalent Zn(7), and three equivalent Zn(3) atoms. In the sixth Zn site, Zn(6) is bonded in a 12-coordinate geometry to two equivalent Eu(2), one Zn(10), one Zn(2), one Zn(7), two equivalent Zn(6), two equivalent Zn(8), and three equivalent Zn(4) atoms. In the seventh Zn site, Zn(7) is bonded in a 12-coordinate geometry to one Eu(1), one Eu(2), one Zn(10), one Zn(2), one Zn(3), one Zn(6), two equivalent Zn(1), two equivalent Zn(5), and two equivalent Zn(8) atoms. In the eighth Zn site, Zn(8) is bonded in a 12-coordinate geometry to one Eu(1), one Eu(2), one Zn(1), one Zn(10), one Zn(4), one Zn(5), two equivalent Zn(2), two equivalent Zn(6), and two equivalent Zn(7) atoms. In the ninth Zn site, Zn(9) is bonded in a cuboctahedral geometry to six equivalent Zn(2) and six equivalent Zn(4) atoms. In the tenth Zn site, Zn(10) is bonded in a cuboctahedral geometry to three equivalent Zn(5), three equivalent Zn(6), three equivalent Zn(7), and three equivalent Zn(8) atoms. is represented by the CIF card [CIF]
data_Eu4Zn51
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.607
_cell_length_b   8.607
_cell_length_c   14.804
_cell_angle_alpha   73.101
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   894.546
_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
  Eu  Eu0  1  0.875  0.750  0.375  1.0
  Eu  Eu1  1  0.375  0.749  0.876  1.0
  Eu  Eu2  1  0.625  0.250  0.125  1.0
  Eu  Eu3  1  0.125  0.251  0.624  1.0
  Zn  Zn4  1  0.338  0.442  0.103  1.0
  Zn  Zn5  1  0.843  0.442  0.599  1.0
  Zn  Zn6  1  0.162  0.558  0.397  1.0
  Zn  Zn7  1  0.657  0.558  0.901  1.0
  Zn  Zn8  1  0.985  0.205  0.222  1.0
  Zn  Zn9  1  0.479  0.197  0.721  1.0
  Zn  Zn10  1  0.515  0.795  0.278  1.0
  Zn  Zn11  1  0.021  0.803  0.779  1.0
  Zn  Zn12  1  0.711  0.060  0.349  1.0
  Zn  Zn13  1  0.210  0.059  0.850  1.0
  Zn  Zn14  1  0.789  0.940  0.151  1.0
  Zn  Zn15  1  0.290  0.941  0.650  1.0
  Zn  Zn16  1  0.668  0.699  0.029  1.0
  Zn  Zn17  1  0.169  0.700  0.529  1.0
  Zn  Zn18  1  0.832  0.301  0.471  1.0
  Zn  Zn19  1  0.331  0.300  0.971  1.0
  Zn  Zn20  1  0.045  0.206  0.397  1.0
  Zn  Zn21  1  0.540  0.198  0.901  1.0
  Zn  Zn22  1  0.455  0.794  0.103  1.0
  Zn  Zn23  1  0.960  0.802  0.599  1.0
  Zn  Zn24  1  0.926  0.442  0.278  1.0
  Zn  Zn25  1  0.418  0.440  0.779  1.0
  Zn  Zn26  1  0.574  0.558  0.222  1.0
  Zn  Zn27  1  0.082  0.560  0.721  1.0
  Zn  Zn28  1  0.909  0.699  0.151  1.0
  Zn  Zn29  1  0.409  0.699  0.650  1.0
  Zn  Zn30  1  0.591  0.301  0.349  1.0
  Zn  Zn31  1  0.091  0.301  0.850  1.0
  Zn  Zn32  1  0.229  0.060  0.471  1.0
  Zn  Zn33  1  0.729  0.060  0.971  1.0
  Zn  Zn34  1  0.271  0.940  0.029  1.0
  Zn  Zn35  1  0.771  0.940  0.529  1.0
  Zn  Zn36  1  0.220  0.794  0.222  1.0
  Zn  Zn37  1  0.719  0.801  0.721  1.0
  Zn  Zn38  1  0.280  0.206  0.278  1.0
  Zn  Zn39  1  0.781  0.199  0.779  1.0
  Zn  Zn40  1  0.104  0.559  0.103  1.0
  Zn  Zn41  1  0.599  0.559  0.599  1.0
  Zn  Zn42  1  0.396  0.441  0.397  1.0
  Zn  Zn43  1  0.901  0.441  0.901  1.0
  Zn  Zn44  1  0.031  0.302  0.029  1.0
  Zn  Zn45  1  0.530  0.302  0.529  1.0
  Zn  Zn46  1  0.469  0.698  0.471  1.0
  Zn  Zn47  1  0.970  0.698  0.971  1.0
  Zn  Zn48  1  0.349  0.940  0.349  1.0
  Zn  Zn49  1  0.850  0.941  0.850  1.0
  Zn  Zn50  1  0.151  0.060  0.151  1.0
  Zn  Zn51  1  0.650  0.059  0.650  1.0
  Zn  Zn52  1  0.750  0.500  0.750  1.0
  Zn  Zn53  1  0.000  0.000  1.000  1.0
  Zn  Zn54  1  0.500  1.000  0.500  1.0
[/CIF]
.