The crystal structure described by Mg6HfSn 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 Sn(1) atoms to form distorted MgHf2Mg8Sn2 cuboctahedra that share corners with four equivalent Hf(1)Mg10Sn2 cuboctahedra, corners with four equivalent Sn(1)Hf2Mg10 cuboctahedra, corners with ten equivalent Mg(1)Hf2Mg8Sn2 cuboctahedra, edges with two equivalent Mg(1)Hf2Mg8Sn2 cuboctahedra, edges with two equivalent Hf(1)Mg10Sn2 cuboctahedra, edges with two equivalent Sn(1)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(2)Hf2Mg8Sn2 cuboctahedra, edges with four equivalent Mg(3)Mg10Sn2 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(3)Mg10Sn2 cuboctahedra, faces with two equivalent Hf(1)Mg10Sn2 cuboctahedra, faces with two equivalent Sn(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Sn2 cuboctahedra, and faces with eight equivalent Mg(2)Hf2Mg8Sn2 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 Sn(1) atoms to form distorted MgHf2Mg8Sn2 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra, corners with four equivalent Mg(3)Mg10Sn2 cuboctahedra, corners with ten equivalent Mg(2)Hf2Mg8Sn2 cuboctahedra, edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with two equivalent Mg(2)Hf2Mg8Sn2 cuboctahedra, edges with two equivalent Mg(3)Mg10Sn2 cuboctahedra, edges with four equivalent Mg(1)Hf2Mg8Sn2 cuboctahedra, edges with four equivalent Hf(1)Mg10Sn2 cuboctahedra, edges with four equivalent Sn(1)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(3)Mg10Sn2 cuboctahedra, faces with two equivalent Hf(1)Mg10Sn2 cuboctahedra, faces with two equivalent Sn(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(2)Hf2Mg8Sn2 cuboctahedra, and faces with eight equivalent Mg(1)Hf2Mg8Sn2 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 Sn(1) atoms to form distorted MgMg10Sn2 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra, corners with six equivalent Mg(3)Mg10Sn2 cuboctahedra, corners with eight equivalent Mg(2)Hf2Mg8Sn2 cuboctahedra, edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(2)Hf2Mg8Sn2 cuboctahedra, edges with four equivalent Sn(1)Hf2Mg10 cuboctahedra, edges with eight equivalent Mg(1)Hf2Mg8Sn2 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(3)Mg10Sn2 cuboctahedra, faces with two equivalent Sn(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Sn2 cuboctahedra, faces with four equivalent Mg(2)Hf2Mg8Sn2 cuboctahedra, and faces with six equivalent Hf(1)Mg10Sn2 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)Mg10Sn2 cuboctahedra, corners with six equivalent Mg(4)Hf2Mg10 cuboctahedra, corners with eight equivalent Mg(2)Hf2Mg8Sn2 cuboctahedra, edges with two equivalent Mg(3)Mg10Sn2 cuboctahedra, edges with four equivalent Mg(2)Hf2Mg8Sn2 cuboctahedra, edges with four equivalent Hf(1)Mg10Sn2 cuboctahedra, edges with eight equivalent Mg(1)Hf2Mg8Sn2 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(3)Mg10Sn2 cuboctahedra, faces with two equivalent Hf(1)Mg10Sn2 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Sn2 cuboctahedra, faces with four equivalent Mg(2)Hf2Mg8Sn2 cuboctahedra, and faces with six equivalent Sn(1)Hf2Mg10 cuboctahedra. Hf(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Sn(1) atoms to form distorted HfMg10Sn2 cuboctahedra that share corners with four equivalent Sn(1)Hf2Mg10 cuboctahedra, corners with six equivalent Hf(1)Mg10Sn2 cuboctahedra, corners with eight equivalent Mg(1)Hf2Mg8Sn2 cuboctahedra, edges with two equivalent Sn(1)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(1)Hf2Mg8Sn2 cuboctahedra, edges with eight equivalent Mg(2)Hf2Mg8Sn2 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Hf(1)Mg10Sn2 cuboctahedra, faces with two equivalent Sn(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Sn2 cuboctahedra, faces with four equivalent Mg(2)Hf2Mg8Sn2 cuboctahedra, and faces with six equivalent Mg(3)Mg10Sn2 cuboctahedra. Sn(1) is bonded to two equivalent Mg(3), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Hf(1) atoms to form SnHf2Mg10 cuboctahedra that share corners with four equivalent Hf(1)Mg10Sn2 cuboctahedra, corners with six equivalent Sn(1)Hf2Mg10 cuboctahedra, corners with eight equivalent Mg(1)Hf2Mg8Sn2 cuboctahedra, edges with two equivalent Hf(1)Mg10Sn2 cuboctahedra, edges with four equivalent Mg(1)Hf2Mg8Sn2 cuboctahedra, edges with four equivalent Mg(3)Mg10Sn2 cuboctahedra, edges with eight equivalent Mg(2)Hf2Mg8Sn2 cuboctahedra, faces with two equivalent Mg(3)Mg10Sn2 cuboctahedra, faces with two equivalent Hf(1)Mg10Sn2 cuboctahedra, faces with two equivalent Sn(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Sn2 cuboctahedra, faces with four equivalent Mg(2)Hf2Mg8Sn2 cuboctahedra, and faces with six equivalent Mg(4)Hf2Mg10 cuboctahedra. is represented by the CIF file [CIF]
data_HfMg6Sn
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.198
_cell_length_b   6.128
_cell_length_c   6.397
_cell_angle_alpha   118.616
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   178.847
_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  0.670  0.340  1.0
  Mg  Mg1  1  0.500  0.669  0.835  1.0
  Mg  Mg2  1  0.500  0.166  0.835  1.0
  Mg  Mg3  1  0.000  0.824  0.162  1.0
  Mg  Mg4  1  0.000  0.338  0.162  1.0
  Mg  Mg5  1  0.000  0.335  0.669  1.0
  Mg  Mg6  1  0.000  0.831  0.661  1.0
  Sn  Sn7  1  0.500  0.167  0.334  1.0
[/CIF]
.
The crystal structure described by Mg6HfSn 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 Sn(1) atoms to form distorted MgHf2Mg8Sn2 cuboctahedra that share corners with four equivalent Hf(1)Mg10Sn2 cuboctahedra, corners with four equivalent Sn(1)Hf2Mg10 cuboctahedra, corners with ten equivalent Mg(1)Hf2Mg8Sn2 cuboctahedra, edges with two equivalent Mg(1)Hf2Mg8Sn2 cuboctahedra, edges with two equivalent Hf(1)Mg10Sn2 cuboctahedra, edges with two equivalent Sn(1)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(2)Hf2Mg8Sn2 cuboctahedra, edges with four equivalent Mg(3)Mg10Sn2 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(3)Mg10Sn2 cuboctahedra, faces with two equivalent Hf(1)Mg10Sn2 cuboctahedra, faces with two equivalent Sn(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Sn2 cuboctahedra, and faces with eight equivalent Mg(2)Hf2Mg8Sn2 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 Sn(1) atoms to form distorted MgHf2Mg8Sn2 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra, corners with four equivalent Mg(3)Mg10Sn2 cuboctahedra, corners with ten equivalent Mg(2)Hf2Mg8Sn2 cuboctahedra, edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with two equivalent Mg(2)Hf2Mg8Sn2 cuboctahedra, edges with two equivalent Mg(3)Mg10Sn2 cuboctahedra, edges with four equivalent Mg(1)Hf2Mg8Sn2 cuboctahedra, edges with four equivalent Hf(1)Mg10Sn2 cuboctahedra, edges with four equivalent Sn(1)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(3)Mg10Sn2 cuboctahedra, faces with two equivalent Hf(1)Mg10Sn2 cuboctahedra, faces with two equivalent Sn(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(2)Hf2Mg8Sn2 cuboctahedra, and faces with eight equivalent Mg(1)Hf2Mg8Sn2 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 Sn(1) atoms to form distorted MgMg10Sn2 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra, corners with six equivalent Mg(3)Mg10Sn2 cuboctahedra, corners with eight equivalent Mg(2)Hf2Mg8Sn2 cuboctahedra, edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(2)Hf2Mg8Sn2 cuboctahedra, edges with four equivalent Sn(1)Hf2Mg10 cuboctahedra, edges with eight equivalent Mg(1)Hf2Mg8Sn2 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(3)Mg10Sn2 cuboctahedra, faces with two equivalent Sn(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Sn2 cuboctahedra, faces with four equivalent Mg(2)Hf2Mg8Sn2 cuboctahedra, and faces with six equivalent Hf(1)Mg10Sn2 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)Mg10Sn2 cuboctahedra, corners with six equivalent Mg(4)Hf2Mg10 cuboctahedra, corners with eight equivalent Mg(2)Hf2Mg8Sn2 cuboctahedra, edges with two equivalent Mg(3)Mg10Sn2 cuboctahedra, edges with four equivalent Mg(2)Hf2Mg8Sn2 cuboctahedra, edges with four equivalent Hf(1)Mg10Sn2 cuboctahedra, edges with eight equivalent Mg(1)Hf2Mg8Sn2 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(3)Mg10Sn2 cuboctahedra, faces with two equivalent Hf(1)Mg10Sn2 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Sn2 cuboctahedra, faces with four equivalent Mg(2)Hf2Mg8Sn2 cuboctahedra, and faces with six equivalent Sn(1)Hf2Mg10 cuboctahedra. Hf(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Sn(1) atoms to form distorted HfMg10Sn2 cuboctahedra that share corners with four equivalent Sn(1)Hf2Mg10 cuboctahedra, corners with six equivalent Hf(1)Mg10Sn2 cuboctahedra, corners with eight equivalent Mg(1)Hf2Mg8Sn2 cuboctahedra, edges with two equivalent Sn(1)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(1)Hf2Mg8Sn2 cuboctahedra, edges with eight equivalent Mg(2)Hf2Mg8Sn2 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Hf(1)Mg10Sn2 cuboctahedra, faces with two equivalent Sn(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Sn2 cuboctahedra, faces with four equivalent Mg(2)Hf2Mg8Sn2 cuboctahedra, and faces with six equivalent Mg(3)Mg10Sn2 cuboctahedra. Sn(1) is bonded to two equivalent Mg(3), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Hf(1) atoms to form SnHf2Mg10 cuboctahedra that share corners with four equivalent Hf(1)Mg10Sn2 cuboctahedra, corners with six equivalent Sn(1)Hf2Mg10 cuboctahedra, corners with eight equivalent Mg(1)Hf2Mg8Sn2 cuboctahedra, edges with two equivalent Hf(1)Mg10Sn2 cuboctahedra, edges with four equivalent Mg(1)Hf2Mg8Sn2 cuboctahedra, edges with four equivalent Mg(3)Mg10Sn2 cuboctahedra, edges with eight equivalent Mg(2)Hf2Mg8Sn2 cuboctahedra, faces with two equivalent Mg(3)Mg10Sn2 cuboctahedra, faces with two equivalent Hf(1)Mg10Sn2 cuboctahedra, faces with two equivalent Sn(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(1)Hf2Mg8Sn2 cuboctahedra, faces with four equivalent Mg(2)Hf2Mg8Sn2 cuboctahedra, and faces with six equivalent Mg(4)Hf2Mg10 cuboctahedra. is represented by the CIF file [CIF]
data_HfMg6Sn
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.198
_cell_length_b   6.128
_cell_length_c   6.397
_cell_angle_alpha   118.616
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   178.847
_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  0.670  0.340  1.0
  Mg  Mg1  1  0.500  0.669  0.835  1.0
  Mg  Mg2  1  0.500  0.166  0.835  1.0
  Mg  Mg3  1  0.000  0.824  0.162  1.0
  Mg  Mg4  1  0.000  0.338  0.162  1.0
  Mg  Mg5  1  0.000  0.335  0.669  1.0
  Mg  Mg6  1  0.000  0.831  0.661  1.0
  Sn  Sn7  1  0.500  0.167  0.334  1.0
[/CIF]
.