The material structure described by HfCoGa is Hexagonal Laves-derived structured and crystallizes in the orthorhombic Amm2 space group. There are two inequivalent Hf sites. In the first Hf site, Hf(1) is bonded in a 16-coordinate geometry to one Hf(1), three equivalent Hf(2), three equivalent Co(1), four equivalent Co(2), one Ga(3), two equivalent Ga(1), and two equivalent Ga(2) atoms. In the second Hf site, Hf(2) is bonded in a 12-coordinate geometry to three equivalent Hf(1), two equivalent Co(2), three equivalent Co(1), one Ga(1), two equivalent Ga(3), and four equivalent Ga(2) atoms. There are two inequivalent Co sites. In the first Co site, Co(1) is bonded to three equivalent Hf(1), three equivalent Hf(2), two equivalent Co(2), one Ga(1), one Ga(3), and two equivalent Ga(2) atoms to form CoHf6Ga4Co2 cuboctahedra that share corners with two equivalent Ga(1)Hf6Co6 cuboctahedra, corners with two equivalent Ga(3)Hf6Ga4Co2 cuboctahedra, corners with four equivalent Co(2)Hf6Ga2Co4 cuboctahedra, corners with four equivalent Ga(2)Hf6Ga4Co2 cuboctahedra, edges with six equivalent Co(1)Hf6Ga4Co2 cuboctahedra, faces with two equivalent Co(1)Hf6Ga4Co2 cuboctahedra, faces with three equivalent Ga(1)Hf6Co6 cuboctahedra, faces with three equivalent Ga(3)Hf6Ga4Co2 cuboctahedra, faces with six equivalent Co(2)Hf6Ga2Co4 cuboctahedra, and faces with six equivalent Ga(2)Hf6Ga4Co2 cuboctahedra. In the second Co site, Co(2) is bonded to two equivalent Hf(2), four equivalent Hf(1), two equivalent Co(1), two equivalent Co(2), and two equivalent Ga(1) atoms to form CoHf6Ga2Co4 cuboctahedra that share corners with four equivalent Co(2)Hf6Ga2Co4 cuboctahedra, corners with four equivalent Co(1)Hf6Ga4Co2 cuboctahedra, corners with four equivalent Ga(3)Hf6Ga4Co2 cuboctahedra, corners with six equivalent Ga(2)Hf6Ga4Co2 cuboctahedra, edges with two equivalent Co(2)Hf6Ga2Co4 cuboctahedra, edges with four equivalent Ga(2)Hf6Ga4Co2 cuboctahedra, faces with two equivalent Ga(2)Hf6Ga4Co2 cuboctahedra, faces with two equivalent Ga(3)Hf6Ga4Co2 cuboctahedra, faces with four equivalent Co(2)Hf6Ga2Co4 cuboctahedra, faces with four equivalent Ga(1)Hf6Co6 cuboctahedra, and faces with six equivalent Co(1)Hf6Ga4Co2 cuboctahedra. There are three inequivalent Ga sites. In the first Ga site, Ga(1) is bonded to two equivalent Hf(2), four equivalent Hf(1), two equivalent Co(1), and four equivalent Co(2) atoms to form GaHf6Co6 cuboctahedra that share corners with two equivalent Ga(3)Hf6Ga4Co2 cuboctahedra, corners with four equivalent Co(1)Hf6Ga4Co2 cuboctahedra, corners with four equivalent Ga(1)Hf6Co6 cuboctahedra, corners with eight equivalent Ga(2)Hf6Ga4Co2 cuboctahedra, edges with two equivalent Ga(1)Hf6Co6 cuboctahedra, edges with four equivalent Ga(3)Hf6Ga4Co2 cuboctahedra, faces with four equivalent Ga(2)Hf6Ga4Co2 cuboctahedra, faces with six equivalent Co(1)Hf6Ga4Co2 cuboctahedra, and faces with eight equivalent Co(2)Hf6Ga2Co4 cuboctahedra. In the second Ga site, Ga(2) is bonded to two equivalent Hf(1), four equivalent Hf(2), two equivalent Co(1), two equivalent Ga(2), and two equivalent Ga(3) atoms to form GaHf6Ga4Co2 cuboctahedra that share corners with four equivalent Co(1)Hf6Ga4Co2 cuboctahedra, corners with four equivalent Ga(1)Hf6Co6 cuboctahedra, corners with four equivalent Ga(2)Hf6Ga4Co2 cuboctahedra, corners with six equivalent Co(2)Hf6Ga2Co4 cuboctahedra, edges with two equivalent Ga(2)Hf6Ga4Co2 cuboctahedra, edges with four equivalent Co(2)Hf6Ga2Co4 cuboctahedra, faces with two equivalent Co(2)Hf6Ga2Co4 cuboctahedra, faces with two equivalent Ga(1)Hf6Co6 cuboctahedra, faces with four equivalent Ga(2)Hf6Ga4Co2 cuboctahedra, faces with four equivalent Ga(3)Hf6Ga4Co2 cuboctahedra, and faces with six equivalent Co(1)Hf6Ga4Co2 cuboctahedra. In the third Ga site, Ga(3) is bonded to two equivalent Hf(1), four equivalent Hf(2), two equivalent Co(1), and four equivalent Ga(2) atoms to form GaHf6Ga4Co2 cuboctahedra that share corners with two equivalent Ga(1)Hf6Co6 cuboctahedra, corners with four equivalent Co(1)Hf6Ga4Co2 cuboctahedra, corners with four equivalent Ga(3)Hf6Ga4Co2 cuboctahedra, corners with eight equivalent Co(2)Hf6Ga2Co4 cuboctahedra, edges with two equivalent Ga(3)Hf6Ga4Co2 cuboctahedra, edges with four equivalent Ga(1)Hf6Co6 cuboctahedra, faces with four equivalent Co(2)Hf6Ga2Co4 cuboctahedra, faces with six equivalent Co(1)Hf6Ga4Co2 cuboctahedra, and faces with eight equivalent Ga(2)Hf6Ga4Co2 cuboctahedra. is represented by the CIF card [CIF]
data_HfGaCo
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.028
_cell_length_b   5.028
_cell_length_c   8.183
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   119.253
_symmetry_Int_Tables_number   1
_cell_volume   180.487
_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  0.666  0.181  1.0
  Hf  Hf1  1  0.662  0.338  0.289  1.0
  Hf  Hf2  1  0.662  0.338  0.711  1.0
  Hf  Hf3  1  0.334  0.666  0.819  1.0
  Ga  Ga4  1  0.840  0.160  0.000  1.0
  Ga  Ga5  1  0.167  0.335  0.500  1.0
  Ga  Ga6  1  0.665  0.833  0.500  1.0
  Ga  Ga7  1  0.167  0.833  0.500  1.0
  Co  Co8  1  0.995  0.005  0.253  1.0
  Co  Co9  1  0.995  0.005  0.747  1.0
  Co  Co10  1  0.844  0.665  0.000  1.0
  Co  Co11  1  0.335  0.156  0.000  1.0
[/CIF]
.
The material structure described by HfCoGa is Hexagonal Laves-derived structured and crystallizes in the orthorhombic Amm2 space group. There are two inequivalent Hf sites. In the first Hf site, Hf(1) is bonded in a 16-coordinate geometry to one Hf(1), three equivalent Hf(2), three equivalent Co(1), four equivalent Co(2), one Ga(3), two equivalent Ga(1), and two equivalent Ga(2) atoms. In the second Hf site, Hf(2) is bonded in a 12-coordinate geometry to three equivalent Hf(1), two equivalent Co(2), three equivalent Co(1), one Ga(1), two equivalent Ga(3), and four equivalent Ga(2) atoms. There are two inequivalent Co sites. In the first Co site, Co(1) is bonded to three equivalent Hf(1), three equivalent Hf(2), two equivalent Co(2), one Ga(1), one Ga(3), and two equivalent Ga(2) atoms to form CoHf6Ga4Co2 cuboctahedra that share corners with two equivalent Ga(1)Hf6Co6 cuboctahedra, corners with two equivalent Ga(3)Hf6Ga4Co2 cuboctahedra, corners with four equivalent Co(2)Hf6Ga2Co4 cuboctahedra, corners with four equivalent Ga(2)Hf6Ga4Co2 cuboctahedra, edges with six equivalent Co(1)Hf6Ga4Co2 cuboctahedra, faces with two equivalent Co(1)Hf6Ga4Co2 cuboctahedra, faces with three equivalent Ga(1)Hf6Co6 cuboctahedra, faces with three equivalent Ga(3)Hf6Ga4Co2 cuboctahedra, faces with six equivalent Co(2)Hf6Ga2Co4 cuboctahedra, and faces with six equivalent Ga(2)Hf6Ga4Co2 cuboctahedra. In the second Co site, Co(2) is bonded to two equivalent Hf(2), four equivalent Hf(1), two equivalent Co(1), two equivalent Co(2), and two equivalent Ga(1) atoms to form CoHf6Ga2Co4 cuboctahedra that share corners with four equivalent Co(2)Hf6Ga2Co4 cuboctahedra, corners with four equivalent Co(1)Hf6Ga4Co2 cuboctahedra, corners with four equivalent Ga(3)Hf6Ga4Co2 cuboctahedra, corners with six equivalent Ga(2)Hf6Ga4Co2 cuboctahedra, edges with two equivalent Co(2)Hf6Ga2Co4 cuboctahedra, edges with four equivalent Ga(2)Hf6Ga4Co2 cuboctahedra, faces with two equivalent Ga(2)Hf6Ga4Co2 cuboctahedra, faces with two equivalent Ga(3)Hf6Ga4Co2 cuboctahedra, faces with four equivalent Co(2)Hf6Ga2Co4 cuboctahedra, faces with four equivalent Ga(1)Hf6Co6 cuboctahedra, and faces with six equivalent Co(1)Hf6Ga4Co2 cuboctahedra. There are three inequivalent Ga sites. In the first Ga site, Ga(1) is bonded to two equivalent Hf(2), four equivalent Hf(1), two equivalent Co(1), and four equivalent Co(2) atoms to form GaHf6Co6 cuboctahedra that share corners with two equivalent Ga(3)Hf6Ga4Co2 cuboctahedra, corners with four equivalent Co(1)Hf6Ga4Co2 cuboctahedra, corners with four equivalent Ga(1)Hf6Co6 cuboctahedra, corners with eight equivalent Ga(2)Hf6Ga4Co2 cuboctahedra, edges with two equivalent Ga(1)Hf6Co6 cuboctahedra, edges with four equivalent Ga(3)Hf6Ga4Co2 cuboctahedra, faces with four equivalent Ga(2)Hf6Ga4Co2 cuboctahedra, faces with six equivalent Co(1)Hf6Ga4Co2 cuboctahedra, and faces with eight equivalent Co(2)Hf6Ga2Co4 cuboctahedra. In the second Ga site, Ga(2) is bonded to two equivalent Hf(1), four equivalent Hf(2), two equivalent Co(1), two equivalent Ga(2), and two equivalent Ga(3) atoms to form GaHf6Ga4Co2 cuboctahedra that share corners with four equivalent Co(1)Hf6Ga4Co2 cuboctahedra, corners with four equivalent Ga(1)Hf6Co6 cuboctahedra, corners with four equivalent Ga(2)Hf6Ga4Co2 cuboctahedra, corners with six equivalent Co(2)Hf6Ga2Co4 cuboctahedra, edges with two equivalent Ga(2)Hf6Ga4Co2 cuboctahedra, edges with four equivalent Co(2)Hf6Ga2Co4 cuboctahedra, faces with two equivalent Co(2)Hf6Ga2Co4 cuboctahedra, faces with two equivalent Ga(1)Hf6Co6 cuboctahedra, faces with four equivalent Ga(2)Hf6Ga4Co2 cuboctahedra, faces with four equivalent Ga(3)Hf6Ga4Co2 cuboctahedra, and faces with six equivalent Co(1)Hf6Ga4Co2 cuboctahedra. In the third Ga site, Ga(3) is bonded to two equivalent Hf(1), four equivalent Hf(2), two equivalent Co(1), and four equivalent Ga(2) atoms to form GaHf6Ga4Co2 cuboctahedra that share corners with two equivalent Ga(1)Hf6Co6 cuboctahedra, corners with four equivalent Co(1)Hf6Ga4Co2 cuboctahedra, corners with four equivalent Ga(3)Hf6Ga4Co2 cuboctahedra, corners with eight equivalent Co(2)Hf6Ga2Co4 cuboctahedra, edges with two equivalent Ga(3)Hf6Ga4Co2 cuboctahedra, edges with four equivalent Ga(1)Hf6Co6 cuboctahedra, faces with four equivalent Co(2)Hf6Ga2Co4 cuboctahedra, faces with six equivalent Co(1)Hf6Ga4Co2 cuboctahedra, and faces with eight equivalent Ga(2)Hf6Ga4Co2 cuboctahedra. is represented by the CIF card [CIF]
data_HfGaCo
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.028
_cell_length_b   5.028
_cell_length_c   8.183
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   119.253
_symmetry_Int_Tables_number   1
_cell_volume   180.487
_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  0.666  0.181  1.0
  Hf  Hf1  1  0.662  0.338  0.289  1.0
  Hf  Hf2  1  0.662  0.338  0.711  1.0
  Hf  Hf3  1  0.334  0.666  0.819  1.0
  Ga  Ga4  1  0.840  0.160  0.000  1.0
  Ga  Ga5  1  0.167  0.335  0.500  1.0
  Ga  Ga6  1  0.665  0.833  0.500  1.0
  Ga  Ga7  1  0.167  0.833  0.500  1.0
  Co  Co8  1  0.995  0.005  0.253  1.0
  Co  Co9  1  0.995  0.005  0.747  1.0
  Co  Co10  1  0.844  0.665  0.000  1.0
  Co  Co11  1  0.335  0.156  0.000  1.0
[/CIF]
.