The material structure described by Hf3Al4C6 crystallizes in the trigonal R-3m space group. There are two inequivalent Hf sites. In the first Hf site, Hf(1) is bonded to three equivalent C(1) and three equivalent C(3) atoms to form HfC6 octahedra that share corners with three equivalent Hf(2)C6 octahedra, corners with three equivalent Al(1)C4 tetrahedra, edges with three equivalent Hf(2)C6 octahedra, edges with six equivalent Hf(1)C6 octahedra, and edges with three equivalent Al(1)C4 tetrahedra. The corner-sharing octahedral tilt angles are 1°. In the second Hf site, Hf(2) is bonded to six equivalent C(1) atoms to form a mixture of edge and corner-sharing HfC6 octahedra. The corner-sharing octahedral tilt angles are 1°. There are two inequivalent Al sites. In the first Al site, Al(1) is bonded to one C(2) and three equivalent C(3) atoms to form AlC4 tetrahedra that share corners with three equivalent Hf(1)C6 octahedra, corners with six equivalent Al(1)C4 tetrahedra, corners with four equivalent Al(2)C4 trigonal pyramids, and edges with three equivalent Hf(1)C6 octahedra. The corner-sharing octahedral tilt angles are 10°. In the second Al site, Al(2) is bonded to four equivalent C(2) atoms to form a mixture of distorted edge and corner-sharing AlC4 trigonal pyramids. There are three inequivalent C sites. In the first C site, C(1) is bonded to three equivalent Hf(1) and three equivalent Hf(2) atoms to form CHf6 octahedra that share corners with three equivalent C(3)Hf3Al3 octahedra, corners with three equivalent C(1)Hf6 octahedra, edges with three equivalent C(3)Hf3Al3 octahedra, and edges with nine equivalent C(1)Hf6 octahedra. The corner-sharing octahedral tilt angles range from 0-1°. In the second C site, C(2) is bonded to one Al(1) and four equivalent Al(2) atoms to form CAl5 trigonal bipyramids that share corners with three equivalent C(3)Hf3Al3 octahedra, corners with six equivalent C(2)Al5 trigonal bipyramids, and edges with three equivalent C(2)Al5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 65°. In the third C site, C(3) is bonded to three equivalent Hf(1) and three equivalent Al(1) atoms to form CHf3Al3 octahedra that share corners with three equivalent C(1)Hf6 octahedra, corners with three equivalent C(2)Al5 trigonal bipyramids, edges with three equivalent C(1)Hf6 octahedra, and edges with six equivalent C(3)Hf3Al3 octahedra. The corner-sharing octahedral tilt angles are 1°. is represented by the Crystallographic Information File (CIF) [CIF]
data_Hf3(Al2C3)2
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   16.416
_cell_length_b   16.416
_cell_length_c   16.416
_cell_angle_alpha   11.638
_cell_angle_beta   11.638
_cell_angle_gamma   11.638
_symmetry_Int_Tables_number   1
_cell_volume   156.443
_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  0.388  0.388  0.388  1.0
  Hf  Hf1  1  0.612  0.612  0.612  1.0
  Hf  Hf2  1  0.000  0.000  0.000  1.0
  Al  Al3  1  0.768  0.768  0.768  1.0
  Al  Al4  1  0.148  0.148  0.148  1.0
  Al  Al5  1  0.232  0.232  0.232  1.0
  Al  Al6  1  0.852  0.852  0.852  1.0
  C  C7  1  0.694  0.694  0.694  1.0
  C  C8  1  0.808  0.808  0.808  1.0
  C  C9  1  0.918  0.918  0.918  1.0
  C  C10  1  0.306  0.306  0.306  1.0
  C  C11  1  0.082  0.082  0.082  1.0
  C  C12  1  0.192  0.192  0.192  1.0
[/CIF]
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The material structure described by Hf3Al4C6 crystallizes in the trigonal R-3m space group. There are two inequivalent Hf sites. In the first Hf site, Hf(1) is bonded to three equivalent C(1) and three equivalent C(3) atoms to form HfC6 octahedra that share corners with three equivalent Hf(2)C6 octahedra, corners with three equivalent Al(1)C4 tetrahedra, edges with three equivalent Hf(2)C6 octahedra, edges with six equivalent Hf(1)C6 octahedra, and edges with three equivalent Al(1)C4 tetrahedra. The corner-sharing octahedral tilt angles are 1°. In the second Hf site, Hf(2) is bonded to six equivalent C(1) atoms to form a mixture of edge and corner-sharing HfC6 octahedra. The corner-sharing octahedral tilt angles are 1°. There are two inequivalent Al sites. In the first Al site, Al(1) is bonded to one C(2) and three equivalent C(3) atoms to form AlC4 tetrahedra that share corners with three equivalent Hf(1)C6 octahedra, corners with six equivalent Al(1)C4 tetrahedra, corners with four equivalent Al(2)C4 trigonal pyramids, and edges with three equivalent Hf(1)C6 octahedra. The corner-sharing octahedral tilt angles are 10°. In the second Al site, Al(2) is bonded to four equivalent C(2) atoms to form a mixture of distorted edge and corner-sharing AlC4 trigonal pyramids. There are three inequivalent C sites. In the first C site, C(1) is bonded to three equivalent Hf(1) and three equivalent Hf(2) atoms to form CHf6 octahedra that share corners with three equivalent C(3)Hf3Al3 octahedra, corners with three equivalent C(1)Hf6 octahedra, edges with three equivalent C(3)Hf3Al3 octahedra, and edges with nine equivalent C(1)Hf6 octahedra. The corner-sharing octahedral tilt angles range from 0-1°. In the second C site, C(2) is bonded to one Al(1) and four equivalent Al(2) atoms to form CAl5 trigonal bipyramids that share corners with three equivalent C(3)Hf3Al3 octahedra, corners with six equivalent C(2)Al5 trigonal bipyramids, and edges with three equivalent C(2)Al5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 65°. In the third C site, C(3) is bonded to three equivalent Hf(1) and three equivalent Al(1) atoms to form CHf3Al3 octahedra that share corners with three equivalent C(1)Hf6 octahedra, corners with three equivalent C(2)Al5 trigonal bipyramids, edges with three equivalent C(1)Hf6 octahedra, and edges with six equivalent C(3)Hf3Al3 octahedra. The corner-sharing octahedral tilt angles are 1°. is represented by the Crystallographic Information File (CIF) [CIF]
data_Hf3(Al2C3)2
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   16.416
_cell_length_b   16.416
_cell_length_c   16.416
_cell_angle_alpha   11.638
_cell_angle_beta   11.638
_cell_angle_gamma   11.638
_symmetry_Int_Tables_number   1
_cell_volume   156.443
_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  0.388  0.388  0.388  1.0
  Hf  Hf1  1  0.612  0.612  0.612  1.0
  Hf  Hf2  1  0.000  0.000  0.000  1.0
  Al  Al3  1  0.768  0.768  0.768  1.0
  Al  Al4  1  0.148  0.148  0.148  1.0
  Al  Al5  1  0.232  0.232  0.232  1.0
  Al  Al6  1  0.852  0.852  0.852  1.0
  C  C7  1  0.694  0.694  0.694  1.0
  C  C8  1  0.808  0.808  0.808  1.0
  C  C9  1  0.918  0.918  0.918  1.0
  C  C10  1  0.306  0.306  0.306  1.0
  C  C11  1  0.082  0.082  0.082  1.0
  C  C12  1  0.192  0.192  0.192  1.0
[/CIF]
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