The material structure described by Mg6HfZn 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 Zn(1) atoms to form MgHf2Mg8Zn2 cuboctahedra that share corners with four equivalent Hf(1)Mg10Zn2 cuboctahedra, corners with four equivalent Zn(1)Hf2Mg10 cuboctahedra, corners with ten equivalent Mg(1)Hf2Mg8Zn2 cuboctahedra, edges with two equivalent Mg(1)Hf2Mg8Zn2 cuboctahedra, edges with two equivalent Hf(1)Mg10Zn2 cuboctahedra, edges with two equivalent Zn(1)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(2)Hf2Mg8Zn2 cuboctahedra, edges with four equivalent Mg(3)Mg10Zn2 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(3)Mg10Zn2 cuboctahedra, faces with two equivalent Hf(1)Mg10Zn2 cuboctahedra, faces with two equivalent Zn(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Zn2 cuboctahedra, and faces with eight equivalent Mg(2)Hf2Mg8Zn2 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 Hf(1), and two equivalent Zn(1) atoms to form distorted MgHf2Mg8Zn2 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra, corners with four equivalent Mg(3)Mg10Zn2 cuboctahedra, corners with ten equivalent Mg(2)Hf2Mg8Zn2 cuboctahedra, edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with two equivalent Mg(2)Hf2Mg8Zn2 cuboctahedra, edges with two equivalent Mg(3)Mg10Zn2 cuboctahedra, edges with four equivalent Mg(1)Hf2Mg8Zn2 cuboctahedra, edges with four equivalent Hf(1)Mg10Zn2 cuboctahedra, edges with four equivalent Zn(1)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(3)Mg10Zn2 cuboctahedra, faces with two equivalent Hf(1)Mg10Zn2 cuboctahedra, faces with two equivalent Zn(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(2)Hf2Mg8Zn2 cuboctahedra, and faces with eight equivalent Mg(1)Hf2Mg8Zn2 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Zn(1) atoms to form distorted MgMg10Zn2 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra, corners with six equivalent Mg(3)Mg10Zn2 cuboctahedra, corners with eight equivalent Mg(2)Hf2Mg8Zn2 cuboctahedra, edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(2)Hf2Mg8Zn2 cuboctahedra, edges with four equivalent Zn(1)Hf2Mg10 cuboctahedra, edges with eight equivalent Mg(1)Hf2Mg8Zn2 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(3)Mg10Zn2 cuboctahedra, faces with two equivalent Zn(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Zn2 cuboctahedra, faces with four equivalent Mg(2)Hf2Mg8Zn2 cuboctahedra, and faces with six equivalent Hf(1)Mg10Zn2 cuboctahedra. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(3), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Hf(1) atoms to form MgHf2Mg10 cuboctahedra that share corners with four equivalent Mg(3)Mg10Zn2 cuboctahedra, corners with six equivalent Mg(4)Hf2Mg10 cuboctahedra, corners with eight equivalent Mg(2)Hf2Mg8Zn2 cuboctahedra, edges with two equivalent Mg(3)Mg10Zn2 cuboctahedra, edges with four equivalent Mg(2)Hf2Mg8Zn2 cuboctahedra, edges with four equivalent Hf(1)Mg10Zn2 cuboctahedra, edges with eight equivalent Mg(1)Hf2Mg8Zn2 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(3)Mg10Zn2 cuboctahedra, faces with two equivalent Hf(1)Mg10Zn2 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Zn2 cuboctahedra, faces with four equivalent Mg(2)Hf2Mg8Zn2 cuboctahedra, and faces with six equivalent Zn(1)Hf2Mg10 cuboctahedra. Hf(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Zn(1) atoms to form distorted HfMg10Zn2 cuboctahedra that share corners with four equivalent Zn(1)Hf2Mg10 cuboctahedra, corners with six equivalent Hf(1)Mg10Zn2 cuboctahedra, corners with eight equivalent Mg(1)Hf2Mg8Zn2 cuboctahedra, edges with two equivalent Zn(1)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(1)Hf2Mg8Zn2 cuboctahedra, edges with eight equivalent Mg(2)Hf2Mg8Zn2 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Hf(1)Mg10Zn2 cuboctahedra, faces with two equivalent Zn(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Zn2 cuboctahedra, faces with four equivalent Mg(2)Hf2Mg8Zn2 cuboctahedra, and faces with six equivalent Mg(3)Mg10Zn2 cuboctahedra. Zn(1) is bonded to two equivalent Mg(3), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Hf(1) atoms to form ZnHf2Mg10 cuboctahedra that share corners with four equivalent Hf(1)Mg10Zn2 cuboctahedra, corners with six equivalent Zn(1)Hf2Mg10 cuboctahedra, corners with eight equivalent Mg(1)Hf2Mg8Zn2 cuboctahedra, edges with two equivalent Hf(1)Mg10Zn2 cuboctahedra, edges with four equivalent Mg(1)Hf2Mg8Zn2 cuboctahedra, edges with four equivalent Mg(3)Mg10Zn2 cuboctahedra, edges with eight equivalent Mg(2)Hf2Mg8Zn2 cuboctahedra, faces with two equivalent Mg(3)Mg10Zn2 cuboctahedra, faces with two equivalent Hf(1)Mg10Zn2 cuboctahedra, faces with two equivalent Zn(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Zn2 cuboctahedra, faces with four equivalent Mg(2)Hf2Mg8Zn2 cuboctahedra, and faces with six equivalent Mg(4)Hf2Mg10 cuboctahedra. is represented by the CIF file [CIF]
data_HfMg6Zn
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   4.976
_cell_length_b   6.090
_cell_length_c   6.367
_cell_angle_alpha   118.571
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   169.450
_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  0.673  0.345  1.0
  Mg  Mg1  1  0.500  0.672  0.842  1.0
  Mg  Mg2  1  0.500  0.170  0.842  1.0
  Mg  Mg3  1  1.000  0.832  0.166  1.0
  Mg  Mg4  1  0.000  0.334  0.166  1.0
  Mg  Mg5  1  0.000  0.325  0.651  1.0
  Mg  Mg6  1  0.000  0.830  0.660  1.0
  Zn  Zn7  1  0.500  0.164  0.327  1.0
[/CIF]
.
The material structure described by Mg6HfZn 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 Zn(1) atoms to form MgHf2Mg8Zn2 cuboctahedra that share corners with four equivalent Hf(1)Mg10Zn2 cuboctahedra, corners with four equivalent Zn(1)Hf2Mg10 cuboctahedra, corners with ten equivalent Mg(1)Hf2Mg8Zn2 cuboctahedra, edges with two equivalent Mg(1)Hf2Mg8Zn2 cuboctahedra, edges with two equivalent Hf(1)Mg10Zn2 cuboctahedra, edges with two equivalent Zn(1)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(2)Hf2Mg8Zn2 cuboctahedra, edges with four equivalent Mg(3)Mg10Zn2 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(3)Mg10Zn2 cuboctahedra, faces with two equivalent Hf(1)Mg10Zn2 cuboctahedra, faces with two equivalent Zn(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Zn2 cuboctahedra, and faces with eight equivalent Mg(2)Hf2Mg8Zn2 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 Hf(1), and two equivalent Zn(1) atoms to form distorted MgHf2Mg8Zn2 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra, corners with four equivalent Mg(3)Mg10Zn2 cuboctahedra, corners with ten equivalent Mg(2)Hf2Mg8Zn2 cuboctahedra, edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with two equivalent Mg(2)Hf2Mg8Zn2 cuboctahedra, edges with two equivalent Mg(3)Mg10Zn2 cuboctahedra, edges with four equivalent Mg(1)Hf2Mg8Zn2 cuboctahedra, edges with four equivalent Hf(1)Mg10Zn2 cuboctahedra, edges with four equivalent Zn(1)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(3)Mg10Zn2 cuboctahedra, faces with two equivalent Hf(1)Mg10Zn2 cuboctahedra, faces with two equivalent Zn(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(2)Hf2Mg8Zn2 cuboctahedra, and faces with eight equivalent Mg(1)Hf2Mg8Zn2 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Zn(1) atoms to form distorted MgMg10Zn2 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra, corners with six equivalent Mg(3)Mg10Zn2 cuboctahedra, corners with eight equivalent Mg(2)Hf2Mg8Zn2 cuboctahedra, edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(2)Hf2Mg8Zn2 cuboctahedra, edges with four equivalent Zn(1)Hf2Mg10 cuboctahedra, edges with eight equivalent Mg(1)Hf2Mg8Zn2 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(3)Mg10Zn2 cuboctahedra, faces with two equivalent Zn(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Zn2 cuboctahedra, faces with four equivalent Mg(2)Hf2Mg8Zn2 cuboctahedra, and faces with six equivalent Hf(1)Mg10Zn2 cuboctahedra. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(3), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Hf(1) atoms to form MgHf2Mg10 cuboctahedra that share corners with four equivalent Mg(3)Mg10Zn2 cuboctahedra, corners with six equivalent Mg(4)Hf2Mg10 cuboctahedra, corners with eight equivalent Mg(2)Hf2Mg8Zn2 cuboctahedra, edges with two equivalent Mg(3)Mg10Zn2 cuboctahedra, edges with four equivalent Mg(2)Hf2Mg8Zn2 cuboctahedra, edges with four equivalent Hf(1)Mg10Zn2 cuboctahedra, edges with eight equivalent Mg(1)Hf2Mg8Zn2 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(3)Mg10Zn2 cuboctahedra, faces with two equivalent Hf(1)Mg10Zn2 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Zn2 cuboctahedra, faces with four equivalent Mg(2)Hf2Mg8Zn2 cuboctahedra, and faces with six equivalent Zn(1)Hf2Mg10 cuboctahedra. Hf(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Zn(1) atoms to form distorted HfMg10Zn2 cuboctahedra that share corners with four equivalent Zn(1)Hf2Mg10 cuboctahedra, corners with six equivalent Hf(1)Mg10Zn2 cuboctahedra, corners with eight equivalent Mg(1)Hf2Mg8Zn2 cuboctahedra, edges with two equivalent Zn(1)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(1)Hf2Mg8Zn2 cuboctahedra, edges with eight equivalent Mg(2)Hf2Mg8Zn2 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Hf(1)Mg10Zn2 cuboctahedra, faces with two equivalent Zn(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Zn2 cuboctahedra, faces with four equivalent Mg(2)Hf2Mg8Zn2 cuboctahedra, and faces with six equivalent Mg(3)Mg10Zn2 cuboctahedra. Zn(1) is bonded to two equivalent Mg(3), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Hf(1) atoms to form ZnHf2Mg10 cuboctahedra that share corners with four equivalent Hf(1)Mg10Zn2 cuboctahedra, corners with six equivalent Zn(1)Hf2Mg10 cuboctahedra, corners with eight equivalent Mg(1)Hf2Mg8Zn2 cuboctahedra, edges with two equivalent Hf(1)Mg10Zn2 cuboctahedra, edges with four equivalent Mg(1)Hf2Mg8Zn2 cuboctahedra, edges with four equivalent Mg(3)Mg10Zn2 cuboctahedra, edges with eight equivalent Mg(2)Hf2Mg8Zn2 cuboctahedra, faces with two equivalent Mg(3)Mg10Zn2 cuboctahedra, faces with two equivalent Hf(1)Mg10Zn2 cuboctahedra, faces with two equivalent Zn(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Zn2 cuboctahedra, faces with four equivalent Mg(2)Hf2Mg8Zn2 cuboctahedra, and faces with six equivalent Mg(4)Hf2Mg10 cuboctahedra. is represented by the CIF file [CIF]
data_HfMg6Zn
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   4.976
_cell_length_b   6.090
_cell_length_c   6.367
_cell_angle_alpha   118.571
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   169.450
_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  0.673  0.345  1.0
  Mg  Mg1  1  0.500  0.672  0.842  1.0
  Mg  Mg2  1  0.500  0.170  0.842  1.0
  Mg  Mg3  1  1.000  0.832  0.166  1.0
  Mg  Mg4  1  0.000  0.334  0.166  1.0
  Mg  Mg5  1  0.000  0.325  0.651  1.0
  Mg  Mg6  1  0.000  0.830  0.660  1.0
  Zn  Zn7  1  0.500  0.164  0.327  1.0
[/CIF]
.