The material described by HfCrAl is Hexagonal Laves-derived structured and crystallizes in the orthorhombic Amm2 space group. There are five inequivalent Hf sites. In the first Hf site, Hf(1) is bonded in a 16-coordinate geometry to one Hf(1); three Hf(2,2); one Cr(3); two equivalent Cr(1); two equivalent Cr(2); three equivalent Al(1); and four equivalent Al(2) atoms. In the second Hf site, Hf(2) is bonded in a 16-coordinate geometry to one Hf(2); three Hf(1,1); one Cr(1); two equivalent Cr(3); four equivalent Cr(2); two equivalent Al(2); and three equivalent Al(1) atoms. In the third Hf site, Hf(2) is bonded in a 16-coordinate geometry to one Hf(2), three equivalent Hf(1), one Cr(1), two equivalent Cr(3), four equivalent Cr(2), two equivalent Al(2), and three equivalent Al(1) atoms. In the fourth Hf site, Hf(1) is bonded in a 16-coordinate geometry to one Hf(1); three Hf(2,2); one Cr(3); two equivalent Cr(1); two equivalent Cr(2); three equivalent Al(1); and four equivalent Al(2) atoms. In the fifth Hf site, Hf(2) is bonded in a 16-coordinate geometry to one Hf(2), three equivalent Hf(1), one Cr(1), two equivalent Cr(3), four equivalent Cr(2), two equivalent Al(2), and three equivalent Al(1) atoms. There are three inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to two Hf(2,2); four equivalent Hf(1); two equivalent Al(1); and four equivalent Al(2) atoms to form CrHf6Al6 cuboctahedra that share corners with two equivalent Cr(3)Hf6Al2Cr4 cuboctahedra, corners with four equivalent Cr(1)Hf6Al6 cuboctahedra, corners with four equivalent Al(1)Hf6Al2Cr4 cuboctahedra, corners with eight equivalent Cr(2)Hf6Al2Cr4 cuboctahedra, edges with two equivalent Cr(1)Hf6Al6 cuboctahedra, edges with four equivalent Cr(3)Hf6Al2Cr4 cuboctahedra, faces with four equivalent Cr(2)Hf6Al2Cr4 cuboctahedra, faces with six equivalent Al(1)Hf6Al2Cr4 cuboctahedra, and faces with eight equivalent Al(2)Hf6Al4Cr2 cuboctahedra. In the second Cr site, Cr(2) is bonded to two Hf(1,1); four Hf(2,2,2); two equivalent Cr(2); two equivalent Cr(3); and two equivalent Al(1) atoms to form distorted CrHf6Al2Cr4 cuboctahedra that share corners with four equivalent Cr(2)Hf6Al2Cr4 cuboctahedra, corners with four equivalent Cr(1)Hf6Al6 cuboctahedra, corners with four equivalent Al(1)Hf6Al2Cr4 cuboctahedra, corners with six equivalent Al(2)Hf6Al4Cr2 cuboctahedra, edges with two equivalent Cr(2)Hf6Al2Cr4 cuboctahedra, edges with four equivalent Al(2)Hf6Al4Cr2 cuboctahedra, faces with two equivalent Cr(1)Hf6Al6 cuboctahedra, faces with two equivalent Al(2)Hf6Al4Cr2 cuboctahedra, faces with four equivalent Cr(2)Hf6Al2Cr4 cuboctahedra, faces with four equivalent Cr(3)Hf6Al2Cr4 cuboctahedra, and faces with six equivalent Al(1)Hf6Al2Cr4 cuboctahedra. In the third Cr site, Cr(3) is bonded to two Hf(1,1); four Hf(2,2); four equivalent Cr(2); and two equivalent Al(1) atoms to form CrHf6Al2Cr4 cuboctahedra that share corners with two equivalent Cr(1)Hf6Al6 cuboctahedra, corners with four equivalent Cr(3)Hf6Al2Cr4 cuboctahedra, corners with four equivalent Al(1)Hf6Al2Cr4 cuboctahedra, corners with eight equivalent Al(2)Hf6Al4Cr2 cuboctahedra, edges with two equivalent Cr(3)Hf6Al2Cr4 cuboctahedra, edges with four equivalent Cr(1)Hf6Al6 cuboctahedra, faces with four equivalent Al(2)Hf6Al4Cr2 cuboctahedra, faces with six equivalent Al(1)Hf6Al2Cr4 cuboctahedra, and faces with eight equivalent Cr(2)Hf6Al2Cr4 cuboctahedra. There are two inequivalent Al sites. In the first Al site, Al(1) is bonded to three Hf(1,1); three Hf(2,2); one Cr(1); one Cr(3); two equivalent Cr(2); and two equivalent Al(2) atoms to form AlHf6Al2Cr4 cuboctahedra that share corners with two equivalent Cr(3)Hf6Al2Cr4 cuboctahedra, corners with two equivalent Cr(1)Hf6Al6 cuboctahedra, corners with four equivalent Cr(2)Hf6Al2Cr4 cuboctahedra, corners with four equivalent Al(2)Hf6Al4Cr2 cuboctahedra, edges with six equivalent Al(1)Hf6Al2Cr4 cuboctahedra, faces with two equivalent Al(1)Hf6Al2Cr4 cuboctahedra, faces with three equivalent Cr(3)Hf6Al2Cr4 cuboctahedra, faces with three equivalent Cr(1)Hf6Al6 cuboctahedra, faces with six equivalent Cr(2)Hf6Al2Cr4 cuboctahedra, and faces with six equivalent Al(2)Hf6Al4Cr2 cuboctahedra. In the second Al site, Al(2) is bonded to two Hf(2,2); four Hf(1,1); two equivalent Cr(1); two equivalent Al(1); and two equivalent Al(2) atoms to form AlHf6Al4Cr2 cuboctahedra that share corners with four equivalent Cr(3)Hf6Al2Cr4 cuboctahedra, corners with four equivalent Al(1)Hf6Al2Cr4 cuboctahedra, corners with four equivalent Al(2)Hf6Al4Cr2 cuboctahedra, corners with six equivalent Cr(2)Hf6Al2Cr4 cuboctahedra, edges with two equivalent Al(2)Hf6Al4Cr2 cuboctahedra, edges with four equivalent Cr(2)Hf6Al2Cr4 cuboctahedra, faces with two equivalent Cr(2)Hf6Al2Cr4 cuboctahedra, faces with two equivalent Cr(3)Hf6Al2Cr4 cuboctahedra, faces with four equivalent Cr(1)Hf6Al6 cuboctahedra, faces with four equivalent Al(2)Hf6Al4Cr2 cuboctahedra, and faces with six equivalent Al(1)Hf6Al2Cr4 cuboctahedra. is represented by the CIF file [CIF]
data_HfAlCr
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.126
_cell_length_b   5.125
_cell_length_c   8.486
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   60.100
_symmetry_Int_Tables_number   1
_cell_volume   193.287
_cell_formula_units_Z   4
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  0.334  0.334  0.559  1.0
  Hf  Hf1  1  0.671  0.671  0.428  1.0
  Hf  Hf2  1  0.671  0.671  0.072  1.0
  Hf  Hf3  1  0.334  0.334  0.941  1.0
  Al  Al4  1  0.994  0.994  0.490  1.0
  Al  Al5  1  0.994  0.994  0.010  1.0
  Al  Al6  1  0.832  0.342  0.750  1.0
  Al  Al7  1  0.342  0.832  0.750  1.0
  Cr  Cr8  1  0.832  0.832  0.750  1.0
  Cr  Cr9  1  0.179  0.638  0.250  1.0
  Cr  Cr10  1  0.638  0.180  0.250  1.0
  Cr  Cr11  1  0.177  0.177  0.250  1.0
[/CIF]
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The material described by HfCrAl is Hexagonal Laves-derived structured and crystallizes in the orthorhombic Amm2 space group. There are five inequivalent Hf sites. In the first Hf site, Hf(1) is bonded in a 16-coordinate geometry to one Hf(1); three Hf(2,2); one Cr(3); two equivalent Cr(1); two equivalent Cr(2); three equivalent Al(1); and four equivalent Al(2) atoms. In the second Hf site, Hf(2) is bonded in a 16-coordinate geometry to one Hf(2); three Hf(1,1); one Cr(1); two equivalent Cr(3); four equivalent Cr(2); two equivalent Al(2); and three equivalent Al(1) atoms. In the third Hf site, Hf(2) is bonded in a 16-coordinate geometry to one Hf(2), three equivalent Hf(1), one Cr(1), two equivalent Cr(3), four equivalent Cr(2), two equivalent Al(2), and three equivalent Al(1) atoms. In the fourth Hf site, Hf(1) is bonded in a 16-coordinate geometry to one Hf(1); three Hf(2,2); one Cr(3); two equivalent Cr(1); two equivalent Cr(2); three equivalent Al(1); and four equivalent Al(2) atoms. In the fifth Hf site, Hf(2) is bonded in a 16-coordinate geometry to one Hf(2), three equivalent Hf(1), one Cr(1), two equivalent Cr(3), four equivalent Cr(2), two equivalent Al(2), and three equivalent Al(1) atoms. There are three inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to two Hf(2,2); four equivalent Hf(1); two equivalent Al(1); and four equivalent Al(2) atoms to form CrHf6Al6 cuboctahedra that share corners with two equivalent Cr(3)Hf6Al2Cr4 cuboctahedra, corners with four equivalent Cr(1)Hf6Al6 cuboctahedra, corners with four equivalent Al(1)Hf6Al2Cr4 cuboctahedra, corners with eight equivalent Cr(2)Hf6Al2Cr4 cuboctahedra, edges with two equivalent Cr(1)Hf6Al6 cuboctahedra, edges with four equivalent Cr(3)Hf6Al2Cr4 cuboctahedra, faces with four equivalent Cr(2)Hf6Al2Cr4 cuboctahedra, faces with six equivalent Al(1)Hf6Al2Cr4 cuboctahedra, and faces with eight equivalent Al(2)Hf6Al4Cr2 cuboctahedra. In the second Cr site, Cr(2) is bonded to two Hf(1,1); four Hf(2,2,2); two equivalent Cr(2); two equivalent Cr(3); and two equivalent Al(1) atoms to form distorted CrHf6Al2Cr4 cuboctahedra that share corners with four equivalent Cr(2)Hf6Al2Cr4 cuboctahedra, corners with four equivalent Cr(1)Hf6Al6 cuboctahedra, corners with four equivalent Al(1)Hf6Al2Cr4 cuboctahedra, corners with six equivalent Al(2)Hf6Al4Cr2 cuboctahedra, edges with two equivalent Cr(2)Hf6Al2Cr4 cuboctahedra, edges with four equivalent Al(2)Hf6Al4Cr2 cuboctahedra, faces with two equivalent Cr(1)Hf6Al6 cuboctahedra, faces with two equivalent Al(2)Hf6Al4Cr2 cuboctahedra, faces with four equivalent Cr(2)Hf6Al2Cr4 cuboctahedra, faces with four equivalent Cr(3)Hf6Al2Cr4 cuboctahedra, and faces with six equivalent Al(1)Hf6Al2Cr4 cuboctahedra. In the third Cr site, Cr(3) is bonded to two Hf(1,1); four Hf(2,2); four equivalent Cr(2); and two equivalent Al(1) atoms to form CrHf6Al2Cr4 cuboctahedra that share corners with two equivalent Cr(1)Hf6Al6 cuboctahedra, corners with four equivalent Cr(3)Hf6Al2Cr4 cuboctahedra, corners with four equivalent Al(1)Hf6Al2Cr4 cuboctahedra, corners with eight equivalent Al(2)Hf6Al4Cr2 cuboctahedra, edges with two equivalent Cr(3)Hf6Al2Cr4 cuboctahedra, edges with four equivalent Cr(1)Hf6Al6 cuboctahedra, faces with four equivalent Al(2)Hf6Al4Cr2 cuboctahedra, faces with six equivalent Al(1)Hf6Al2Cr4 cuboctahedra, and faces with eight equivalent Cr(2)Hf6Al2Cr4 cuboctahedra. There are two inequivalent Al sites. In the first Al site, Al(1) is bonded to three Hf(1,1); three Hf(2,2); one Cr(1); one Cr(3); two equivalent Cr(2); and two equivalent Al(2) atoms to form AlHf6Al2Cr4 cuboctahedra that share corners with two equivalent Cr(3)Hf6Al2Cr4 cuboctahedra, corners with two equivalent Cr(1)Hf6Al6 cuboctahedra, corners with four equivalent Cr(2)Hf6Al2Cr4 cuboctahedra, corners with four equivalent Al(2)Hf6Al4Cr2 cuboctahedra, edges with six equivalent Al(1)Hf6Al2Cr4 cuboctahedra, faces with two equivalent Al(1)Hf6Al2Cr4 cuboctahedra, faces with three equivalent Cr(3)Hf6Al2Cr4 cuboctahedra, faces with three equivalent Cr(1)Hf6Al6 cuboctahedra, faces with six equivalent Cr(2)Hf6Al2Cr4 cuboctahedra, and faces with six equivalent Al(2)Hf6Al4Cr2 cuboctahedra. In the second Al site, Al(2) is bonded to two Hf(2,2); four Hf(1,1); two equivalent Cr(1); two equivalent Al(1); and two equivalent Al(2) atoms to form AlHf6Al4Cr2 cuboctahedra that share corners with four equivalent Cr(3)Hf6Al2Cr4 cuboctahedra, corners with four equivalent Al(1)Hf6Al2Cr4 cuboctahedra, corners with four equivalent Al(2)Hf6Al4Cr2 cuboctahedra, corners with six equivalent Cr(2)Hf6Al2Cr4 cuboctahedra, edges with two equivalent Al(2)Hf6Al4Cr2 cuboctahedra, edges with four equivalent Cr(2)Hf6Al2Cr4 cuboctahedra, faces with two equivalent Cr(2)Hf6Al2Cr4 cuboctahedra, faces with two equivalent Cr(3)Hf6Al2Cr4 cuboctahedra, faces with four equivalent Cr(1)Hf6Al6 cuboctahedra, faces with four equivalent Al(2)Hf6Al4Cr2 cuboctahedra, and faces with six equivalent Al(1)Hf6Al2Cr4 cuboctahedra. is represented by the CIF file [CIF]
data_HfAlCr
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.126
_cell_length_b   5.125
_cell_length_c   8.486
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   60.100
_symmetry_Int_Tables_number   1
_cell_volume   193.287
_cell_formula_units_Z   4
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  0.334  0.334  0.559  1.0
  Hf  Hf1  1  0.671  0.671  0.428  1.0
  Hf  Hf2  1  0.671  0.671  0.072  1.0
  Hf  Hf3  1  0.334  0.334  0.941  1.0
  Al  Al4  1  0.994  0.994  0.490  1.0
  Al  Al5  1  0.994  0.994  0.010  1.0
  Al  Al6  1  0.832  0.342  0.750  1.0
  Al  Al7  1  0.342  0.832  0.750  1.0
  Cr  Cr8  1  0.832  0.832  0.750  1.0
  Cr  Cr9  1  0.179  0.638  0.250  1.0
  Cr  Cr10  1  0.638  0.180  0.250  1.0
  Cr  Cr11  1  0.177  0.177  0.250  1.0
[/CIF]
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