The material structure described by Mg6HfCd 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 Cd(1) atoms to form distorted MgHf2Mg8Cd2 cuboctahedra that share corners with four equivalent Mg(2)Mg10Cd2 cuboctahedra, corners with four equivalent Cd(1)Hf2Mg10 cuboctahedra, corners with ten equivalent Mg(1)Hf2Mg8Cd2 cuboctahedra, edges with two equivalent Mg(1)Hf2Mg8Cd2 cuboctahedra, edges with two equivalent Mg(2)Mg10Cd2 cuboctahedra, edges with two equivalent Cd(1)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(3)Hf2Mg8Cd2 cuboctahedra, edges with four equivalent Hf(1)Mg10Cd2 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(2)Mg10Cd2 cuboctahedra, faces with two equivalent Hf(1)Mg10Cd2 cuboctahedra, faces with two equivalent Cd(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Cd2 cuboctahedra, and faces with eight equivalent Mg(3)Hf2Mg8Cd2 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 Cd(1) atoms to form distorted MgMg10Cd2 cuboctahedra that share corners with four equivalent Cd(1)Hf2Mg10 cuboctahedra, corners with six equivalent Mg(2)Mg10Cd2 cuboctahedra, corners with eight equivalent Mg(1)Hf2Mg8Cd2 cuboctahedra, edges with two equivalent Cd(1)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(1)Hf2Mg8Cd2 cuboctahedra, edges with eight equivalent Mg(3)Hf2Mg8Cd2 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(2)Mg10Cd2 cuboctahedra, faces with two equivalent Cd(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Cd2 cuboctahedra, faces with four equivalent Mg(3)Hf2Mg8Cd2 cuboctahedra, and faces with six equivalent Hf(1)Mg10Cd2 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 Cd(1) atoms to form distorted MgHf2Mg8Cd2 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra, corners with four equivalent Hf(1)Mg10Cd2 cuboctahedra, corners with ten equivalent Mg(3)Hf2Mg8Cd2 cuboctahedra, edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with two equivalent Mg(3)Hf2Mg8Cd2 cuboctahedra, edges with two equivalent Hf(1)Mg10Cd2 cuboctahedra, edges with four equivalent Mg(1)Hf2Mg8Cd2 cuboctahedra, edges with four equivalent Mg(2)Mg10Cd2 cuboctahedra, edges with four equivalent Cd(1)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(2)Mg10Cd2 cuboctahedra, faces with two equivalent Hf(1)Mg10Cd2 cuboctahedra, faces with two equivalent Cd(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(3)Hf2Mg8Cd2 cuboctahedra, and faces with eight equivalent Mg(1)Hf2Mg8Cd2 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 four equivalent Hf(1)Mg10Cd2 cuboctahedra, corners with six equivalent Mg(4)Hf2Mg10 cuboctahedra, corners with eight equivalent Mg(3)Hf2Mg8Cd2 cuboctahedra, edges with two equivalent Hf(1)Mg10Cd2 cuboctahedra, edges with four equivalent Mg(3)Hf2Mg8Cd2 cuboctahedra, edges with four equivalent Mg(2)Mg10Cd2 cuboctahedra, edges with eight equivalent Mg(1)Hf2Mg8Cd2 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(2)Mg10Cd2 cuboctahedra, faces with two equivalent Hf(1)Mg10Cd2 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Cd2 cuboctahedra, faces with four equivalent Mg(3)Hf2Mg8Cd2 cuboctahedra, and faces with six equivalent Cd(1)Hf2Mg10 cuboctahedra. Hf(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Cd(1) atoms to form distorted HfMg10Cd2 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra, corners with six equivalent Hf(1)Mg10Cd2 cuboctahedra, corners with eight equivalent Mg(3)Hf2Mg8Cd2 cuboctahedra, edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(3)Hf2Mg8Cd2 cuboctahedra, edges with four equivalent Cd(1)Hf2Mg10 cuboctahedra, edges with eight equivalent Mg(1)Hf2Mg8Cd2 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Hf(1)Mg10Cd2 cuboctahedra, faces with two equivalent Cd(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Cd2 cuboctahedra, faces with four equivalent Mg(3)Hf2Mg8Cd2 cuboctahedra, and faces with six equivalent Mg(2)Mg10Cd2 cuboctahedra. Cd(1) is bonded to two equivalent Mg(2), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Hf(1) atoms to form CdHf2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Mg10Cd2 cuboctahedra, corners with six equivalent Cd(1)Hf2Mg10 cuboctahedra, corners with eight equivalent Mg(1)Hf2Mg8Cd2 cuboctahedra, edges with two equivalent Mg(2)Mg10Cd2 cuboctahedra, edges with four equivalent Mg(1)Hf2Mg8Cd2 cuboctahedra, edges with four equivalent Hf(1)Mg10Cd2 cuboctahedra, edges with eight equivalent Mg(3)Hf2Mg8Cd2 cuboctahedra, faces with two equivalent Mg(2)Mg10Cd2 cuboctahedra, faces with two equivalent Hf(1)Mg10Cd2 cuboctahedra, faces with two equivalent Cd(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Cd2 cuboctahedra, faces with four equivalent Mg(3)Hf2Mg8Cd2 cuboctahedra, and faces with six equivalent Mg(4)Hf2Mg10 cuboctahedra. is represented by the CIF card [CIF]
data_HfMg6Cd
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.033
_cell_length_b   6.368
_cell_length_c   6.385
_cell_angle_alpha   119.913
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   177.364
_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
  Cd  Cd0  1  0.000  0.827  0.655  1.0
  Hf  Hf1  1  0.500  0.669  0.339  1.0
  Mg  Mg2  1  0.000  0.831  0.167  1.0
  Mg  Mg3  1  0.000  0.336  0.167  1.0
  Mg  Mg4  1  0.000  0.333  0.665  1.0
  Mg  Mg5  1  0.500  0.670  0.838  1.0
  Mg  Mg6  1  0.500  0.167  0.838  1.0
  Mg  Mg7  1  0.500  0.166  0.331  1.0
[/CIF]
.
The material structure described by Mg6HfCd 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 Cd(1) atoms to form distorted MgHf2Mg8Cd2 cuboctahedra that share corners with four equivalent Mg(2)Mg10Cd2 cuboctahedra, corners with four equivalent Cd(1)Hf2Mg10 cuboctahedra, corners with ten equivalent Mg(1)Hf2Mg8Cd2 cuboctahedra, edges with two equivalent Mg(1)Hf2Mg8Cd2 cuboctahedra, edges with two equivalent Mg(2)Mg10Cd2 cuboctahedra, edges with two equivalent Cd(1)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(3)Hf2Mg8Cd2 cuboctahedra, edges with four equivalent Hf(1)Mg10Cd2 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(2)Mg10Cd2 cuboctahedra, faces with two equivalent Hf(1)Mg10Cd2 cuboctahedra, faces with two equivalent Cd(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Cd2 cuboctahedra, and faces with eight equivalent Mg(3)Hf2Mg8Cd2 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 Cd(1) atoms to form distorted MgMg10Cd2 cuboctahedra that share corners with four equivalent Cd(1)Hf2Mg10 cuboctahedra, corners with six equivalent Mg(2)Mg10Cd2 cuboctahedra, corners with eight equivalent Mg(1)Hf2Mg8Cd2 cuboctahedra, edges with two equivalent Cd(1)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(1)Hf2Mg8Cd2 cuboctahedra, edges with eight equivalent Mg(3)Hf2Mg8Cd2 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(2)Mg10Cd2 cuboctahedra, faces with two equivalent Cd(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Cd2 cuboctahedra, faces with four equivalent Mg(3)Hf2Mg8Cd2 cuboctahedra, and faces with six equivalent Hf(1)Mg10Cd2 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 Cd(1) atoms to form distorted MgHf2Mg8Cd2 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra, corners with four equivalent Hf(1)Mg10Cd2 cuboctahedra, corners with ten equivalent Mg(3)Hf2Mg8Cd2 cuboctahedra, edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with two equivalent Mg(3)Hf2Mg8Cd2 cuboctahedra, edges with two equivalent Hf(1)Mg10Cd2 cuboctahedra, edges with four equivalent Mg(1)Hf2Mg8Cd2 cuboctahedra, edges with four equivalent Mg(2)Mg10Cd2 cuboctahedra, edges with four equivalent Cd(1)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(2)Mg10Cd2 cuboctahedra, faces with two equivalent Hf(1)Mg10Cd2 cuboctahedra, faces with two equivalent Cd(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(3)Hf2Mg8Cd2 cuboctahedra, and faces with eight equivalent Mg(1)Hf2Mg8Cd2 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 four equivalent Hf(1)Mg10Cd2 cuboctahedra, corners with six equivalent Mg(4)Hf2Mg10 cuboctahedra, corners with eight equivalent Mg(3)Hf2Mg8Cd2 cuboctahedra, edges with two equivalent Hf(1)Mg10Cd2 cuboctahedra, edges with four equivalent Mg(3)Hf2Mg8Cd2 cuboctahedra, edges with four equivalent Mg(2)Mg10Cd2 cuboctahedra, edges with eight equivalent Mg(1)Hf2Mg8Cd2 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(2)Mg10Cd2 cuboctahedra, faces with two equivalent Hf(1)Mg10Cd2 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Cd2 cuboctahedra, faces with four equivalent Mg(3)Hf2Mg8Cd2 cuboctahedra, and faces with six equivalent Cd(1)Hf2Mg10 cuboctahedra. Hf(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Cd(1) atoms to form distorted HfMg10Cd2 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra, corners with six equivalent Hf(1)Mg10Cd2 cuboctahedra, corners with eight equivalent Mg(3)Hf2Mg8Cd2 cuboctahedra, edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(3)Hf2Mg8Cd2 cuboctahedra, edges with four equivalent Cd(1)Hf2Mg10 cuboctahedra, edges with eight equivalent Mg(1)Hf2Mg8Cd2 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Hf(1)Mg10Cd2 cuboctahedra, faces with two equivalent Cd(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Cd2 cuboctahedra, faces with four equivalent Mg(3)Hf2Mg8Cd2 cuboctahedra, and faces with six equivalent Mg(2)Mg10Cd2 cuboctahedra. Cd(1) is bonded to two equivalent Mg(2), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Hf(1) atoms to form CdHf2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Mg10Cd2 cuboctahedra, corners with six equivalent Cd(1)Hf2Mg10 cuboctahedra, corners with eight equivalent Mg(1)Hf2Mg8Cd2 cuboctahedra, edges with two equivalent Mg(2)Mg10Cd2 cuboctahedra, edges with four equivalent Mg(1)Hf2Mg8Cd2 cuboctahedra, edges with four equivalent Hf(1)Mg10Cd2 cuboctahedra, edges with eight equivalent Mg(3)Hf2Mg8Cd2 cuboctahedra, faces with two equivalent Mg(2)Mg10Cd2 cuboctahedra, faces with two equivalent Hf(1)Mg10Cd2 cuboctahedra, faces with two equivalent Cd(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Cd2 cuboctahedra, faces with four equivalent Mg(3)Hf2Mg8Cd2 cuboctahedra, and faces with six equivalent Mg(4)Hf2Mg10 cuboctahedra. is represented by the CIF card [CIF]
data_HfMg6Cd
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.033
_cell_length_b   6.368
_cell_length_c   6.385
_cell_angle_alpha   119.913
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   177.364
_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
  Cd  Cd0  1  0.000  0.827  0.655  1.0
  Hf  Hf1  1  0.500  0.669  0.339  1.0
  Mg  Mg2  1  0.000  0.831  0.167  1.0
  Mg  Mg3  1  0.000  0.336  0.167  1.0
  Mg  Mg4  1  0.000  0.333  0.665  1.0
  Mg  Mg5  1  0.500  0.670  0.838  1.0
  Mg  Mg6  1  0.500  0.167  0.838  1.0
  Mg  Mg7  1  0.500  0.166  0.331  1.0
[/CIF]
.