The structure described by Mg6LaHf crystallizes in the orthorhombic Amm2 space group. There are five 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 La(1), and two equivalent Hf(1) atoms to form MgLa2Hf2Mg8 cuboctahedra that share corners with four equivalent La(1)Hf2Mg10 cuboctahedra; corners with four equivalent Hf(1)La2Mg10 cuboctahedra; corners with ten equivalent Mg(1)La2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(1)La2Hf2Mg8 cuboctahedra; edges with two equivalent La(1)Hf2Mg10 cuboctahedra; edges with two equivalent Hf(1)La2Mg10 cuboctahedra; edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(2)La2Hf2Mg8 cuboctahedra; edges with four equivalent Mg(3)La2Mg10 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(3)La2Mg10 cuboctahedra; faces with two equivalent La(1)Hf2Mg10 cuboctahedra; faces with two equivalent Hf(1)La2Mg10 cuboctahedra; faces with four equivalent Mg(1)La2Hf2Mg8 cuboctahedra; and faces with eight Mg(2,2)La2Hf2Mg8 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent La(1), and two equivalent Hf(1) atoms to form distorted MgLa2Hf2Mg8 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra; corners with four equivalent Mg(3)La2Mg10 cuboctahedra; corners with ten Mg(2,2)La2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(2)La2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(3)La2Mg10 cuboctahedra; edges with four equivalent Mg(1)La2Hf2Mg8 cuboctahedra; edges with four equivalent La(1)Hf2Mg10 cuboctahedra; edges with four equivalent Hf(1)La2Mg10 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(3)La2Mg10 cuboctahedra; faces with two equivalent La(1)Hf2Mg10 cuboctahedra; faces with two equivalent Hf(1)La2Mg10 cuboctahedra; faces with four equivalent Mg(2)La2Hf2Mg8 cuboctahedra; and faces with eight equivalent Mg(1)La2Hf2Mg8 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(4); four equivalent Mg(1); four Mg(2,2); and two equivalent La(1) atoms to form distorted MgLa2Mg10 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra; corners with six equivalent Mg(3)La2Mg10 cuboctahedra; corners with eight Mg(2,2)La2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with four Mg(2,2)La2Hf2Mg8 cuboctahedra; edges with four equivalent La(1)Hf2Mg10 cuboctahedra; edges with eight equivalent Mg(1)La2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(3)La2Mg10 cuboctahedra; faces with two equivalent La(1)Hf2Mg10 cuboctahedra; faces with four equivalent Mg(1)La2Hf2Mg8 cuboctahedra; faces with four Mg(2,2)La2Hf2Mg8 cuboctahedra; and faces with six equivalent Hf(1)La2Mg10 cuboctahedra. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(3); four equivalent Mg(1); four Mg(2,2); and two equivalent Hf(1) atoms to form MgHf2Mg10 cuboctahedra that share corners with four equivalent Mg(3)La2Mg10 cuboctahedra; corners with six equivalent Mg(4)Hf2Mg10 cuboctahedra; corners with eight Mg(2,2)La2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(3)La2Mg10 cuboctahedra; edges with four Mg(2,2)La2Hf2Mg8 cuboctahedra; edges with four equivalent Hf(1)La2Mg10 cuboctahedra; edges with eight equivalent Mg(1)La2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(3)La2Mg10 cuboctahedra; faces with two equivalent Hf(1)La2Mg10 cuboctahedra; faces with four equivalent Mg(1)La2Hf2Mg8 cuboctahedra; faces with four Mg(2,2)La2Hf2Mg8 cuboctahedra; and faces with six equivalent La(1)Hf2Mg10 cuboctahedra. In the fifth Mg site, Mg(2) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent La(1), and two equivalent Hf(1) atoms to form distorted MgLa2Hf2Mg8 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra; corners with four equivalent Mg(3)La2Mg10 cuboctahedra; corners with ten Mg(2,2)La2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(2)La2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(3)La2Mg10 cuboctahedra; edges with four equivalent Mg(1)La2Hf2Mg8 cuboctahedra; edges with four equivalent La(1)Hf2Mg10 cuboctahedra; edges with four equivalent Hf(1)La2Mg10 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(3)La2Mg10 cuboctahedra; faces with two equivalent La(1)Hf2Mg10 cuboctahedra; faces with two equivalent Hf(1)La2Mg10 cuboctahedra; faces with four Mg(2,2)La2Hf2Mg8 cuboctahedra; and faces with eight equivalent Mg(1)La2Hf2Mg8 cuboctahedra. La(1) is bonded to two equivalent Mg(3), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Hf(1) atoms to form LaHf2Mg10 cuboctahedra that share corners with four equivalent Hf(1)La2Mg10 cuboctahedra; corners with six equivalent La(1)Hf2Mg10 cuboctahedra; corners with eight equivalent Mg(1)La2Hf2Mg8 cuboctahedra; edges with two equivalent Hf(1)La2Mg10 cuboctahedra; edges with four equivalent Mg(1)La2Hf2Mg8 cuboctahedra; edges with four equivalent Mg(3)La2Mg10 cuboctahedra; edges with eight Mg(2,2)La2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(3)La2Mg10 cuboctahedra; faces with two equivalent La(1)Hf2Mg10 cuboctahedra; faces with two equivalent Hf(1)La2Mg10 cuboctahedra; faces with four equivalent Mg(1)La2Hf2Mg8 cuboctahedra; faces with four equivalent Mg(2)La2Hf2Mg8 cuboctahedra; and faces with six equivalent Mg(4)Hf2Mg10 cuboctahedra. Hf(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(2), and two equivalent La(1) atoms to form HfLa2Mg10 cuboctahedra that share corners with four equivalent La(1)Hf2Mg10 cuboctahedra; corners with six equivalent Hf(1)La2Mg10 cuboctahedra; corners with eight equivalent Mg(1)La2Hf2Mg8 cuboctahedra; edges with two equivalent La(1)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(1)La2Hf2Mg8 cuboctahedra; edges with eight Mg(2,2)La2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent La(1)Hf2Mg10 cuboctahedra; faces with two equivalent Hf(1)La2Mg10 cuboctahedra; faces with four equivalent Mg(1)La2Hf2Mg8 cuboctahedra; faces with four equivalent Mg(2)La2Hf2Mg8 cuboctahedra; and faces with six equivalent Mg(3)La2Mg10 cuboctahedra. is represented by the CIF card [CIF]
data_LaHfMg6
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.239
_cell_length_b   6.618
_cell_length_c   6.620
_cell_angle_alpha   119.986
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   198.795
_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  0.500  0.662  0.324  1.0
  La  La1  1  0.500  0.165  0.329  1.0
  Mg  Mg2  1  0.500  0.666  0.834  1.0
  Mg  Mg3  1  0.500  0.168  0.834  1.0
  Mg  Mg4  1  0.000  0.821  0.168  1.0
  Mg  Mg5  1  0.000  0.347  0.168  1.0
  Mg  Mg6  1  0.000  0.341  0.681  1.0
  Mg  Mg7  1  0.000  0.831  0.661  1.0
[/CIF]
.
The structure described by Mg6LaHf crystallizes in the orthorhombic Amm2 space group. There are five 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 La(1), and two equivalent Hf(1) atoms to form MgLa2Hf2Mg8 cuboctahedra that share corners with four equivalent La(1)Hf2Mg10 cuboctahedra; corners with four equivalent Hf(1)La2Mg10 cuboctahedra; corners with ten equivalent Mg(1)La2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(1)La2Hf2Mg8 cuboctahedra; edges with two equivalent La(1)Hf2Mg10 cuboctahedra; edges with two equivalent Hf(1)La2Mg10 cuboctahedra; edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(2)La2Hf2Mg8 cuboctahedra; edges with four equivalent Mg(3)La2Mg10 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(3)La2Mg10 cuboctahedra; faces with two equivalent La(1)Hf2Mg10 cuboctahedra; faces with two equivalent Hf(1)La2Mg10 cuboctahedra; faces with four equivalent Mg(1)La2Hf2Mg8 cuboctahedra; and faces with eight Mg(2,2)La2Hf2Mg8 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent La(1), and two equivalent Hf(1) atoms to form distorted MgLa2Hf2Mg8 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra; corners with four equivalent Mg(3)La2Mg10 cuboctahedra; corners with ten Mg(2,2)La2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(2)La2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(3)La2Mg10 cuboctahedra; edges with four equivalent Mg(1)La2Hf2Mg8 cuboctahedra; edges with four equivalent La(1)Hf2Mg10 cuboctahedra; edges with four equivalent Hf(1)La2Mg10 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(3)La2Mg10 cuboctahedra; faces with two equivalent La(1)Hf2Mg10 cuboctahedra; faces with two equivalent Hf(1)La2Mg10 cuboctahedra; faces with four equivalent Mg(2)La2Hf2Mg8 cuboctahedra; and faces with eight equivalent Mg(1)La2Hf2Mg8 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(4); four equivalent Mg(1); four Mg(2,2); and two equivalent La(1) atoms to form distorted MgLa2Mg10 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra; corners with six equivalent Mg(3)La2Mg10 cuboctahedra; corners with eight Mg(2,2)La2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with four Mg(2,2)La2Hf2Mg8 cuboctahedra; edges with four equivalent La(1)Hf2Mg10 cuboctahedra; edges with eight equivalent Mg(1)La2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(3)La2Mg10 cuboctahedra; faces with two equivalent La(1)Hf2Mg10 cuboctahedra; faces with four equivalent Mg(1)La2Hf2Mg8 cuboctahedra; faces with four Mg(2,2)La2Hf2Mg8 cuboctahedra; and faces with six equivalent Hf(1)La2Mg10 cuboctahedra. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(3); four equivalent Mg(1); four Mg(2,2); and two equivalent Hf(1) atoms to form MgHf2Mg10 cuboctahedra that share corners with four equivalent Mg(3)La2Mg10 cuboctahedra; corners with six equivalent Mg(4)Hf2Mg10 cuboctahedra; corners with eight Mg(2,2)La2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(3)La2Mg10 cuboctahedra; edges with four Mg(2,2)La2Hf2Mg8 cuboctahedra; edges with four equivalent Hf(1)La2Mg10 cuboctahedra; edges with eight equivalent Mg(1)La2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(3)La2Mg10 cuboctahedra; faces with two equivalent Hf(1)La2Mg10 cuboctahedra; faces with four equivalent Mg(1)La2Hf2Mg8 cuboctahedra; faces with four Mg(2,2)La2Hf2Mg8 cuboctahedra; and faces with six equivalent La(1)Hf2Mg10 cuboctahedra. In the fifth Mg site, Mg(2) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent La(1), and two equivalent Hf(1) atoms to form distorted MgLa2Hf2Mg8 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra; corners with four equivalent Mg(3)La2Mg10 cuboctahedra; corners with ten Mg(2,2)La2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(2)La2Hf2Mg8 cuboctahedra; edges with two equivalent Mg(3)La2Mg10 cuboctahedra; edges with four equivalent Mg(1)La2Hf2Mg8 cuboctahedra; edges with four equivalent La(1)Hf2Mg10 cuboctahedra; edges with four equivalent Hf(1)La2Mg10 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(3)La2Mg10 cuboctahedra; faces with two equivalent La(1)Hf2Mg10 cuboctahedra; faces with two equivalent Hf(1)La2Mg10 cuboctahedra; faces with four Mg(2,2)La2Hf2Mg8 cuboctahedra; and faces with eight equivalent Mg(1)La2Hf2Mg8 cuboctahedra. La(1) is bonded to two equivalent Mg(3), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Hf(1) atoms to form LaHf2Mg10 cuboctahedra that share corners with four equivalent Hf(1)La2Mg10 cuboctahedra; corners with six equivalent La(1)Hf2Mg10 cuboctahedra; corners with eight equivalent Mg(1)La2Hf2Mg8 cuboctahedra; edges with two equivalent Hf(1)La2Mg10 cuboctahedra; edges with four equivalent Mg(1)La2Hf2Mg8 cuboctahedra; edges with four equivalent Mg(3)La2Mg10 cuboctahedra; edges with eight Mg(2,2)La2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(3)La2Mg10 cuboctahedra; faces with two equivalent La(1)Hf2Mg10 cuboctahedra; faces with two equivalent Hf(1)La2Mg10 cuboctahedra; faces with four equivalent Mg(1)La2Hf2Mg8 cuboctahedra; faces with four equivalent Mg(2)La2Hf2Mg8 cuboctahedra; and faces with six equivalent Mg(4)Hf2Mg10 cuboctahedra. Hf(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(2), and two equivalent La(1) atoms to form HfLa2Mg10 cuboctahedra that share corners with four equivalent La(1)Hf2Mg10 cuboctahedra; corners with six equivalent Hf(1)La2Mg10 cuboctahedra; corners with eight equivalent Mg(1)La2Hf2Mg8 cuboctahedra; edges with two equivalent La(1)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(1)La2Hf2Mg8 cuboctahedra; edges with eight Mg(2,2)La2Hf2Mg8 cuboctahedra; faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra; faces with two equivalent La(1)Hf2Mg10 cuboctahedra; faces with two equivalent Hf(1)La2Mg10 cuboctahedra; faces with four equivalent Mg(1)La2Hf2Mg8 cuboctahedra; faces with four equivalent Mg(2)La2Hf2Mg8 cuboctahedra; and faces with six equivalent Mg(3)La2Mg10 cuboctahedra. is represented by the CIF card [CIF]
data_LaHfMg6
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.239
_cell_length_b   6.618
_cell_length_c   6.620
_cell_angle_alpha   119.986
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   198.795
_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  0.500  0.662  0.324  1.0
  La  La1  1  0.500  0.165  0.329  1.0
  Mg  Mg2  1  0.500  0.666  0.834  1.0
  Mg  Mg3  1  0.500  0.168  0.834  1.0
  Mg  Mg4  1  0.000  0.821  0.168  1.0
  Mg  Mg5  1  0.000  0.347  0.168  1.0
  Mg  Mg6  1  0.000  0.341  0.681  1.0
  Mg  Mg7  1  0.000  0.831  0.661  1.0
[/CIF]
.