The crystal structure described by Hf3TaFe8 is Hexagonal Laves-derived structured and crystallizes in the trigonal P3m1 space group. There are three inequivalent Hf sites. In the first Hf site, Hf(1) is bonded in a 16-coordinate geometry to one Hf(2), three equivalent Ta(1), three equivalent Fe(1), three equivalent Fe(3), and six equivalent Fe(4) atoms. In the second Hf site, Hf(2) is bonded in a 12-coordinate geometry to one Hf(1), three equivalent Hf(3), three equivalent Fe(2), three equivalent Fe(3), and six equivalent Fe(4) atoms. In the third Hf site, Hf(3) is bonded in a 16-coordinate geometry to three equivalent Hf(2), one Ta(1), three equivalent Fe(2), three equivalent Fe(4), and six equivalent Fe(3) atoms. Ta(1) is bonded in a 16-coordinate geometry to one Hf(3), three equivalent Hf(1), three equivalent Fe(1), three equivalent Fe(4), and six equivalent Fe(3) atoms. There are four inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to three equivalent Hf(1), three equivalent Ta(1), three equivalent Fe(3), and three equivalent Fe(4) atoms to form FeHf3Ta3Fe6 cuboctahedra that share corners with six equivalent Fe(3)Hf4Ta2Fe6 cuboctahedra, corners with six equivalent Fe(4)Hf5TaFe6 cuboctahedra, edges with six equivalent Fe(1)Hf3Ta3Fe6 cuboctahedra, faces with two equivalent Fe(2)Hf6Fe6 cuboctahedra, faces with nine equivalent Fe(3)Hf4Ta2Fe6 cuboctahedra, and faces with nine equivalent Fe(4)Hf5TaFe6 cuboctahedra. In the second Fe site, Fe(2) is bonded to three equivalent Hf(2), three equivalent Hf(3), three equivalent Fe(3), and three equivalent Fe(4) atoms to form FeHf6Fe6 cuboctahedra that share corners with six equivalent Fe(3)Hf4Ta2Fe6 cuboctahedra, corners with six equivalent Fe(4)Hf5TaFe6 cuboctahedra, edges with six equivalent Fe(2)Hf6Fe6 cuboctahedra, faces with two equivalent Fe(1)Hf3Ta3Fe6 cuboctahedra, faces with nine equivalent Fe(3)Hf4Ta2Fe6 cuboctahedra, and faces with nine equivalent Fe(4)Hf5TaFe6 cuboctahedra. In the third Fe site, Fe(3) is bonded to one Hf(1), one Hf(2), two equivalent Hf(3), two equivalent Ta(1), one Fe(1), one Fe(2), and four equivalent Fe(3) atoms to form FeHf4Ta2Fe6 cuboctahedra that share corners with two equivalent Fe(1)Hf3Ta3Fe6 cuboctahedra, corners with two equivalent Fe(2)Hf6Fe6 cuboctahedra, corners with four equivalent Fe(3)Hf4Ta2Fe6 cuboctahedra, corners with ten equivalent Fe(4)Hf5TaFe6 cuboctahedra, edges with two equivalent Fe(3)Hf4Ta2Fe6 cuboctahedra, edges with four equivalent Fe(4)Hf5TaFe6 cuboctahedra, faces with three equivalent Fe(1)Hf3Ta3Fe6 cuboctahedra, faces with three equivalent Fe(2)Hf6Fe6 cuboctahedra, faces with four equivalent Fe(4)Hf5TaFe6 cuboctahedra, and faces with eight equivalent Fe(3)Hf4Ta2Fe6 cuboctahedra. In the fourth Fe site, Fe(4) is bonded to one Hf(3), two equivalent Hf(1), two equivalent Hf(2), one Ta(1), one Fe(1), one Fe(2), and four equivalent Fe(4) atoms to form FeHf5TaFe6 cuboctahedra that share corners with two equivalent Fe(1)Hf3Ta3Fe6 cuboctahedra, corners with two equivalent Fe(2)Hf6Fe6 cuboctahedra, corners with four equivalent Fe(4)Hf5TaFe6 cuboctahedra, corners with ten equivalent Fe(3)Hf4Ta2Fe6 cuboctahedra, edges with two equivalent Fe(4)Hf5TaFe6 cuboctahedra, edges with four equivalent Fe(3)Hf4Ta2Fe6 cuboctahedra, faces with three equivalent Fe(1)Hf3Ta3Fe6 cuboctahedra, faces with three equivalent Fe(2)Hf6Fe6 cuboctahedra, faces with four equivalent Fe(3)Hf4Ta2Fe6 cuboctahedra, and faces with eight equivalent Fe(4)Hf5TaFe6 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Hf3TaFe8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   4.944
_cell_length_b   4.944
_cell_length_c   8.063
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   119.999
_symmetry_Int_Tables_number   1
_cell_volume   170.640
_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
  Hf  Hf0  1  0.333  0.667  0.441  1.0
  Hf  Hf1  1  0.333  0.667  0.061  1.0
  Hf  Hf2  1  0.667  0.333  0.935  1.0
  Ta  Ta3  1  0.667  0.333  0.560  1.0
  Fe  Fe4  1  1.000  0.000  0.500  1.0
  Fe  Fe5  1  1.000  1.000  0.000  1.0
  Fe  Fe6  1  0.168  0.336  0.748  1.0
  Fe  Fe7  1  0.168  0.832  0.748  1.0
  Fe  Fe8  1  0.664  0.832  0.748  1.0
  Fe  Fe9  1  0.832  0.664  0.252  1.0
  Fe  Fe10  1  0.832  0.168  0.252  1.0
  Fe  Fe11  1  0.336  0.168  0.252  1.0
[/CIF]
.
The crystal structure described by Hf3TaFe8 is Hexagonal Laves-derived structured and crystallizes in the trigonal P3m1 space group. There are three inequivalent Hf sites. In the first Hf site, Hf(1) is bonded in a 16-coordinate geometry to one Hf(2), three equivalent Ta(1), three equivalent Fe(1), three equivalent Fe(3), and six equivalent Fe(4) atoms. In the second Hf site, Hf(2) is bonded in a 12-coordinate geometry to one Hf(1), three equivalent Hf(3), three equivalent Fe(2), three equivalent Fe(3), and six equivalent Fe(4) atoms. In the third Hf site, Hf(3) is bonded in a 16-coordinate geometry to three equivalent Hf(2), one Ta(1), three equivalent Fe(2), three equivalent Fe(4), and six equivalent Fe(3) atoms. Ta(1) is bonded in a 16-coordinate geometry to one Hf(3), three equivalent Hf(1), three equivalent Fe(1), three equivalent Fe(4), and six equivalent Fe(3) atoms. There are four inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to three equivalent Hf(1), three equivalent Ta(1), three equivalent Fe(3), and three equivalent Fe(4) atoms to form FeHf3Ta3Fe6 cuboctahedra that share corners with six equivalent Fe(3)Hf4Ta2Fe6 cuboctahedra, corners with six equivalent Fe(4)Hf5TaFe6 cuboctahedra, edges with six equivalent Fe(1)Hf3Ta3Fe6 cuboctahedra, faces with two equivalent Fe(2)Hf6Fe6 cuboctahedra, faces with nine equivalent Fe(3)Hf4Ta2Fe6 cuboctahedra, and faces with nine equivalent Fe(4)Hf5TaFe6 cuboctahedra. In the second Fe site, Fe(2) is bonded to three equivalent Hf(2), three equivalent Hf(3), three equivalent Fe(3), and three equivalent Fe(4) atoms to form FeHf6Fe6 cuboctahedra that share corners with six equivalent Fe(3)Hf4Ta2Fe6 cuboctahedra, corners with six equivalent Fe(4)Hf5TaFe6 cuboctahedra, edges with six equivalent Fe(2)Hf6Fe6 cuboctahedra, faces with two equivalent Fe(1)Hf3Ta3Fe6 cuboctahedra, faces with nine equivalent Fe(3)Hf4Ta2Fe6 cuboctahedra, and faces with nine equivalent Fe(4)Hf5TaFe6 cuboctahedra. In the third Fe site, Fe(3) is bonded to one Hf(1), one Hf(2), two equivalent Hf(3), two equivalent Ta(1), one Fe(1), one Fe(2), and four equivalent Fe(3) atoms to form FeHf4Ta2Fe6 cuboctahedra that share corners with two equivalent Fe(1)Hf3Ta3Fe6 cuboctahedra, corners with two equivalent Fe(2)Hf6Fe6 cuboctahedra, corners with four equivalent Fe(3)Hf4Ta2Fe6 cuboctahedra, corners with ten equivalent Fe(4)Hf5TaFe6 cuboctahedra, edges with two equivalent Fe(3)Hf4Ta2Fe6 cuboctahedra, edges with four equivalent Fe(4)Hf5TaFe6 cuboctahedra, faces with three equivalent Fe(1)Hf3Ta3Fe6 cuboctahedra, faces with three equivalent Fe(2)Hf6Fe6 cuboctahedra, faces with four equivalent Fe(4)Hf5TaFe6 cuboctahedra, and faces with eight equivalent Fe(3)Hf4Ta2Fe6 cuboctahedra. In the fourth Fe site, Fe(4) is bonded to one Hf(3), two equivalent Hf(1), two equivalent Hf(2), one Ta(1), one Fe(1), one Fe(2), and four equivalent Fe(4) atoms to form FeHf5TaFe6 cuboctahedra that share corners with two equivalent Fe(1)Hf3Ta3Fe6 cuboctahedra, corners with two equivalent Fe(2)Hf6Fe6 cuboctahedra, corners with four equivalent Fe(4)Hf5TaFe6 cuboctahedra, corners with ten equivalent Fe(3)Hf4Ta2Fe6 cuboctahedra, edges with two equivalent Fe(4)Hf5TaFe6 cuboctahedra, edges with four equivalent Fe(3)Hf4Ta2Fe6 cuboctahedra, faces with three equivalent Fe(1)Hf3Ta3Fe6 cuboctahedra, faces with three equivalent Fe(2)Hf6Fe6 cuboctahedra, faces with four equivalent Fe(3)Hf4Ta2Fe6 cuboctahedra, and faces with eight equivalent Fe(4)Hf5TaFe6 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_Hf3TaFe8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   4.944
_cell_length_b   4.944
_cell_length_c   8.063
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   119.999
_symmetry_Int_Tables_number   1
_cell_volume   170.640
_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
  Hf  Hf0  1  0.333  0.667  0.441  1.0
  Hf  Hf1  1  0.333  0.667  0.061  1.0
  Hf  Hf2  1  0.667  0.333  0.935  1.0
  Ta  Ta3  1  0.667  0.333  0.560  1.0
  Fe  Fe4  1  1.000  0.000  0.500  1.0
  Fe  Fe5  1  1.000  1.000  0.000  1.0
  Fe  Fe6  1  0.168  0.336  0.748  1.0
  Fe  Fe7  1  0.168  0.832  0.748  1.0
  Fe  Fe8  1  0.664  0.832  0.748  1.0
  Fe  Fe9  1  0.832  0.664  0.252  1.0
  Fe  Fe10  1  0.832  0.168  0.252  1.0
  Fe  Fe11  1  0.336  0.168  0.252  1.0
[/CIF]
.