The material described by Mg6HfGa crystallizes in the orthorhombic Amm2 space group. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Hf(1), and two equivalent Ga(1) atoms to form distorted MgHf2Mg8Ga2 cuboctahedra that share corners with four equivalent Mg(2)Mg10Ga2 cuboctahedra, corners with four equivalent Ga(1)Hf2Mg10 cuboctahedra, corners with ten equivalent Mg(1)Hf2Mg8Ga2 cuboctahedra, edges with two equivalent Mg(1)Hf2Mg8Ga2 cuboctahedra, edges with two equivalent Mg(2)Mg10Ga2 cuboctahedra, edges with two equivalent Ga(1)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(3)Hf2Mg8Ga2 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(2)Mg10Ga2 cuboctahedra, faces with two equivalent Ga(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Ga2 cuboctahedra, and faces with eight equivalent Mg(3)Hf2Mg8Ga2 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Ga(1) atoms to form distorted MgMg10Ga2 cuboctahedra that share corners with four equivalent Ga(1)Hf2Mg10 cuboctahedra, corners with six equivalent Mg(2)Mg10Ga2 cuboctahedra, corners with eight equivalent Mg(1)Hf2Mg8Ga2 cuboctahedra, edges with two equivalent Ga(1)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(1)Hf2Mg8Ga2 cuboctahedra, edges with eight equivalent Mg(3)Hf2Mg8Ga2 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(2)Mg10Ga2 cuboctahedra, faces with two equivalent Ga(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Ga2 cuboctahedra, and faces with four equivalent Mg(3)Hf2Mg8Ga2 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Hf(1), and two equivalent Ga(1) atoms to form distorted MgHf2Mg8Ga2 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra, corners with ten equivalent Mg(3)Hf2Mg8Ga2 cuboctahedra, edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with two equivalent Mg(3)Hf2Mg8Ga2 cuboctahedra, edges with four equivalent Mg(1)Hf2Mg8Ga2 cuboctahedra, edges with four equivalent Mg(2)Mg10Ga2 cuboctahedra, edges with four equivalent Ga(1)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(2)Mg10Ga2 cuboctahedra, faces with two equivalent Ga(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(3)Hf2Mg8Ga2 cuboctahedra, and faces with eight equivalent Mg(1)Hf2Mg8Ga2 cuboctahedra. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(2), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Hf(1) atoms to form MgHf2Mg10 cuboctahedra that share corners with six equivalent Mg(4)Hf2Mg10 cuboctahedra, corners with eight equivalent Mg(3)Hf2Mg8Ga2 cuboctahedra, edges with four equivalent Mg(3)Hf2Mg8Ga2 cuboctahedra, edges with four equivalent Mg(2)Mg10Ga2 cuboctahedra, edges with eight equivalent Mg(1)Hf2Mg8Ga2 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(2)Mg10Ga2 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Ga2 cuboctahedra, faces with four equivalent Mg(3)Hf2Mg8Ga2 cuboctahedra, and faces with six equivalent Ga(1)Hf2Mg10 cuboctahedra. Hf(1) is bonded in a distorted bent 120 degrees geometry to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Ga(1) atoms. Ga(1) is bonded to two equivalent Mg(2), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Hf(1) atoms to form distorted GaHf2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Mg10Ga2 cuboctahedra, corners with six equivalent Ga(1)Hf2Mg10 cuboctahedra, corners with eight equivalent Mg(1)Hf2Mg8Ga2 cuboctahedra, edges with two equivalent Mg(2)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(1)Hf2Mg8Ga2 cuboctahedra, edges with eight equivalent Mg(3)Hf2Mg8Ga2 cuboctahedra, faces with two equivalent Mg(2)Mg10Ga2 cuboctahedra, faces with two equivalent Ga(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Ga2 cuboctahedra, faces with four equivalent Mg(3)Hf2Mg8Ga2 cuboctahedra, and faces with six equivalent Mg(4)Hf2Mg10 cuboctahedra. is represented by the CIF card [CIF]
data_HfMg6Ga
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   4.904
_cell_length_b   6.340
_cell_length_c   6.340
_cell_angle_alpha   119.493
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   171.565
_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
  Ga  Ga0  1  0.000  0.179  0.821  1.0
  Hf  Hf1  1  0.500  0.324  0.676  1.0
  Mg  Mg2  1  1.000  0.665  0.833  1.0
  Mg  Mg3  1  0.000  0.167  0.335  1.0
  Mg  Mg4  1  0.000  0.667  0.333  1.0
  Mg  Mg5  1  0.500  0.834  0.671  1.0
  Mg  Mg6  1  0.500  0.329  0.166  1.0
  Mg  Mg7  1  0.500  0.834  0.166  1.0
[/CIF]
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The material described by Mg6HfGa crystallizes in the orthorhombic Amm2 space group. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Hf(1), and two equivalent Ga(1) atoms to form distorted MgHf2Mg8Ga2 cuboctahedra that share corners with four equivalent Mg(2)Mg10Ga2 cuboctahedra, corners with four equivalent Ga(1)Hf2Mg10 cuboctahedra, corners with ten equivalent Mg(1)Hf2Mg8Ga2 cuboctahedra, edges with two equivalent Mg(1)Hf2Mg8Ga2 cuboctahedra, edges with two equivalent Mg(2)Mg10Ga2 cuboctahedra, edges with two equivalent Ga(1)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(3)Hf2Mg8Ga2 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(2)Mg10Ga2 cuboctahedra, faces with two equivalent Ga(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Ga2 cuboctahedra, and faces with eight equivalent Mg(3)Hf2Mg8Ga2 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Ga(1) atoms to form distorted MgMg10Ga2 cuboctahedra that share corners with four equivalent Ga(1)Hf2Mg10 cuboctahedra, corners with six equivalent Mg(2)Mg10Ga2 cuboctahedra, corners with eight equivalent Mg(1)Hf2Mg8Ga2 cuboctahedra, edges with two equivalent Ga(1)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(1)Hf2Mg8Ga2 cuboctahedra, edges with eight equivalent Mg(3)Hf2Mg8Ga2 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(2)Mg10Ga2 cuboctahedra, faces with two equivalent Ga(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Ga2 cuboctahedra, and faces with four equivalent Mg(3)Hf2Mg8Ga2 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Hf(1), and two equivalent Ga(1) atoms to form distorted MgHf2Mg8Ga2 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra, corners with ten equivalent Mg(3)Hf2Mg8Ga2 cuboctahedra, edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with two equivalent Mg(3)Hf2Mg8Ga2 cuboctahedra, edges with four equivalent Mg(1)Hf2Mg8Ga2 cuboctahedra, edges with four equivalent Mg(2)Mg10Ga2 cuboctahedra, edges with four equivalent Ga(1)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(2)Mg10Ga2 cuboctahedra, faces with two equivalent Ga(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(3)Hf2Mg8Ga2 cuboctahedra, and faces with eight equivalent Mg(1)Hf2Mg8Ga2 cuboctahedra. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(2), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Hf(1) atoms to form MgHf2Mg10 cuboctahedra that share corners with six equivalent Mg(4)Hf2Mg10 cuboctahedra, corners with eight equivalent Mg(3)Hf2Mg8Ga2 cuboctahedra, edges with four equivalent Mg(3)Hf2Mg8Ga2 cuboctahedra, edges with four equivalent Mg(2)Mg10Ga2 cuboctahedra, edges with eight equivalent Mg(1)Hf2Mg8Ga2 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(2)Mg10Ga2 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Ga2 cuboctahedra, faces with four equivalent Mg(3)Hf2Mg8Ga2 cuboctahedra, and faces with six equivalent Ga(1)Hf2Mg10 cuboctahedra. Hf(1) is bonded in a distorted bent 120 degrees geometry to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Ga(1) atoms. Ga(1) is bonded to two equivalent Mg(2), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Hf(1) atoms to form distorted GaHf2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Mg10Ga2 cuboctahedra, corners with six equivalent Ga(1)Hf2Mg10 cuboctahedra, corners with eight equivalent Mg(1)Hf2Mg8Ga2 cuboctahedra, edges with two equivalent Mg(2)Mg10Ga2 cuboctahedra, edges with four equivalent Mg(1)Hf2Mg8Ga2 cuboctahedra, edges with eight equivalent Mg(3)Hf2Mg8Ga2 cuboctahedra, faces with two equivalent Mg(2)Mg10Ga2 cuboctahedra, faces with two equivalent Ga(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Ga2 cuboctahedra, faces with four equivalent Mg(3)Hf2Mg8Ga2 cuboctahedra, and faces with six equivalent Mg(4)Hf2Mg10 cuboctahedra. is represented by the CIF card [CIF]
data_HfMg6Ga
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   4.904
_cell_length_b   6.340
_cell_length_c   6.340
_cell_angle_alpha   119.493
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   171.565
_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
  Ga  Ga0  1  0.000  0.179  0.821  1.0
  Hf  Hf1  1  0.500  0.324  0.676  1.0
  Mg  Mg2  1  1.000  0.665  0.833  1.0
  Mg  Mg3  1  0.000  0.167  0.335  1.0
  Mg  Mg4  1  0.000  0.667  0.333  1.0
  Mg  Mg5  1  0.500  0.834  0.671  1.0
  Mg  Mg6  1  0.500  0.329  0.166  1.0
  Mg  Mg7  1  0.500  0.834  0.166  1.0
[/CIF]
.