The compound described by Mg14HfW crystallizes in the orthorhombic Amm2 space group. There are seven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(2), two equivalent Mg(6), four equivalent Mg(4), and four equivalent Mg(5) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(1)Mg12 cuboctahedra, corners with eight equivalent Mg(3)Hf2Mg8W2 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with two equivalent W(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(4)Mg12 cuboctahedra, and faces with six equivalent Mg(7)HfMg11 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(1), two equivalent Mg(7), four equivalent Mg(4), and four equivalent Mg(5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent W(1)Hf2Mg10 cuboctahedra, corners with six equivalent Mg(2)Mg12 cuboctahedra, corners with eight equivalent Mg(3)Hf2Mg8W2 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with four equivalent Mg(7)HfMg11 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(7)HfMg11 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, and faces with four equivalent Mg(4)Mg12 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(3), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), two equivalent Hf(1), and two equivalent W(1) atoms to form distorted MgHf2Mg8W2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra, corners with four equivalent Mg(2)Mg12 cuboctahedra, corners with four equivalent Mg(4)Mg12 cuboctahedra, corners with six equivalent Mg(3)Hf2Mg8W2 cuboctahedra, edges with two equivalent Mg(3)Hf2Mg8W2 cuboctahedra, edges with two equivalent W(1)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(7)HfMg11 cuboctahedra, faces with two equivalent Mg(3)Hf2Mg8W2 cuboctahedra, faces with two equivalent Mg(7)HfMg11 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, and faces with two equivalent W(1)Hf2Mg10 cuboctahedra. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), two equivalent Mg(5), two equivalent Mg(6), and two equivalent Mg(7) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Mg(3)Hf2Mg8W2 cuboctahedra, corners with four equivalent W(1)Hf2Mg10 cuboctahedra, corners with six equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with two equivalent Mg(4)Mg12 cuboctahedra, edges with four equivalent Mg(7)HfMg11 cuboctahedra, faces with two equivalent Mg(3)Hf2Mg8W2 cuboctahedra, faces with two equivalent Mg(7)HfMg11 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, and faces with two equivalent Mg(4)Mg12 cuboctahedra. In the fifth Mg site, Mg(5) is bonded in a distorted single-bond geometry to one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(7), and one W(1) atom. In the sixth Mg site, Mg(6) is bonded in a distorted single-bond geometry to one Mg(1), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(7), and one W(1) atom. In the seventh Mg site, Mg(7) is bonded to one Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(6), four equivalent Mg(5), and one Hf(1) atom to form MgHfMg11 cuboctahedra that share corners with six equivalent Mg(7)HfMg11 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with four equivalent Mg(3)Hf2Mg8W2 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra,  a faceface with one Mg(2)Mg12 cuboctahedra, faces with two equivalent Mg(3)Hf2Mg8W2 cuboctahedra, faces with two equivalent Mg(7)HfMg11 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with three equivalent Mg(1)Mg12 cuboctahedra, and faces with three equivalent W(1)Hf2Mg10 cuboctahedra. Hf(1) is bonded in a distorted linear geometry to two equivalent Mg(7), four equivalent Mg(3), and two equivalent W(1) atoms. W(1) is bonded to two equivalent Mg(6), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Hf(1) atoms to form WHf2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra, corners with six equivalent W(1)Hf2Mg10 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with four equivalent Mg(3)Hf2Mg8W2 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with four equivalent Mg(3)Hf2Mg8W2 cuboctahedra, and faces with six equivalent Mg(7)HfMg11 cuboctahedra. is represented by the CIF card [CIF]
data_HfMg14W
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.359
_cell_length_b   6.082
_cell_length_c   10.145
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   118.570
_symmetry_Int_Tables_number   1
_cell_volume   344.619
_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  0.154  0.827  0.125  1.0
  Mg  Mg1  1  0.162  0.331  0.625  1.0
  Mg  Mg2  1  0.167  0.834  0.625  1.0
  Mg  Mg3  1  0.656  0.331  0.125  1.0
  Mg  Mg4  1  0.663  0.329  0.625  1.0
  Mg  Mg5  1  0.656  0.824  0.125  1.0
  Mg  Mg6  1  0.663  0.833  0.625  1.0
  Mg  Mg7  1  0.333  0.171  0.367  1.0
  Mg  Mg8  1  0.333  0.171  0.883  1.0
  Mg  Mg9  1  0.333  0.661  0.367  1.0
  Mg  Mg10  1  0.333  0.661  0.883  1.0
  Mg  Mg11  1  0.852  0.176  0.362  1.0
  Mg  Mg12  1  0.852  0.176  0.888  1.0
  Mg  Mg13  1  0.844  0.672  0.377  1.0
  Mg  Mg14  1  0.844  0.672  0.873  1.0
  W  W15  1  0.158  0.329  0.125  1.0
[/CIF]
.
The compound described by Mg14HfW crystallizes in the orthorhombic Amm2 space group. There are seven inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(2), two equivalent Mg(6), four equivalent Mg(4), and four equivalent Mg(5) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(1)Mg12 cuboctahedra, corners with eight equivalent Mg(3)Hf2Mg8W2 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, faces with two equivalent W(1)Hf2Mg10 cuboctahedra, faces with four equivalent Mg(4)Mg12 cuboctahedra, and faces with six equivalent Mg(7)HfMg11 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(1), two equivalent Mg(7), four equivalent Mg(4), and four equivalent Mg(5) atoms to form MgMg12 cuboctahedra that share corners with four equivalent W(1)Hf2Mg10 cuboctahedra, corners with six equivalent Mg(2)Mg12 cuboctahedra, corners with eight equivalent Mg(3)Hf2Mg8W2 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with four equivalent Mg(7)HfMg11 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Mg(7)HfMg11 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, and faces with four equivalent Mg(4)Mg12 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(3), two equivalent Mg(5), two equivalent Mg(6), two equivalent Mg(7), two equivalent Hf(1), and two equivalent W(1) atoms to form distorted MgHf2Mg8W2 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra, corners with four equivalent Mg(2)Mg12 cuboctahedra, corners with four equivalent Mg(4)Mg12 cuboctahedra, corners with six equivalent Mg(3)Hf2Mg8W2 cuboctahedra, edges with two equivalent Mg(3)Hf2Mg8W2 cuboctahedra, edges with two equivalent W(1)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(7)HfMg11 cuboctahedra, faces with two equivalent Mg(3)Hf2Mg8W2 cuboctahedra, faces with two equivalent Mg(7)HfMg11 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, and faces with two equivalent W(1)Hf2Mg10 cuboctahedra. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), two equivalent Mg(5), two equivalent Mg(6), and two equivalent Mg(7) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Mg(3)Hf2Mg8W2 cuboctahedra, corners with four equivalent W(1)Hf2Mg10 cuboctahedra, corners with six equivalent Mg(4)Mg12 cuboctahedra, edges with two equivalent Mg(1)Mg12 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with two equivalent Mg(4)Mg12 cuboctahedra, edges with four equivalent Mg(7)HfMg11 cuboctahedra, faces with two equivalent Mg(3)Hf2Mg8W2 cuboctahedra, faces with two equivalent Mg(7)HfMg11 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with two equivalent Mg(2)Mg12 cuboctahedra, and faces with two equivalent Mg(4)Mg12 cuboctahedra. In the fifth Mg site, Mg(5) is bonded in a distorted single-bond geometry to one Mg(1), one Mg(2), one Mg(3), one Mg(4), two equivalent Mg(7), and one W(1) atom. In the sixth Mg site, Mg(6) is bonded in a distorted single-bond geometry to one Mg(1), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(7), and one W(1) atom. In the seventh Mg site, Mg(7) is bonded to one Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Mg(6), four equivalent Mg(5), and one Hf(1) atom to form MgHfMg11 cuboctahedra that share corners with six equivalent Mg(7)HfMg11 cuboctahedra, edges with two equivalent Mg(2)Mg12 cuboctahedra, edges with four equivalent Mg(3)Hf2Mg8W2 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra,  a faceface with one Mg(2)Mg12 cuboctahedra, faces with two equivalent Mg(3)Hf2Mg8W2 cuboctahedra, faces with two equivalent Mg(7)HfMg11 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with three equivalent Mg(1)Mg12 cuboctahedra, and faces with three equivalent W(1)Hf2Mg10 cuboctahedra. Hf(1) is bonded in a distorted linear geometry to two equivalent Mg(7), four equivalent Mg(3), and two equivalent W(1) atoms. W(1) is bonded to two equivalent Mg(6), four equivalent Mg(3), four equivalent Mg(5), and two equivalent Hf(1) atoms to form WHf2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Mg12 cuboctahedra, corners with six equivalent W(1)Hf2Mg10 cuboctahedra, corners with eight equivalent Mg(4)Mg12 cuboctahedra, edges with four equivalent Mg(3)Hf2Mg8W2 cuboctahedra, faces with two equivalent Mg(1)Mg12 cuboctahedra, faces with four equivalent Mg(3)Hf2Mg8W2 cuboctahedra, and faces with six equivalent Mg(7)HfMg11 cuboctahedra. is represented by the CIF card [CIF]
data_HfMg14W
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.359
_cell_length_b   6.082
_cell_length_c   10.145
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   118.570
_symmetry_Int_Tables_number   1
_cell_volume   344.619
_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  0.154  0.827  0.125  1.0
  Mg  Mg1  1  0.162  0.331  0.625  1.0
  Mg  Mg2  1  0.167  0.834  0.625  1.0
  Mg  Mg3  1  0.656  0.331  0.125  1.0
  Mg  Mg4  1  0.663  0.329  0.625  1.0
  Mg  Mg5  1  0.656  0.824  0.125  1.0
  Mg  Mg6  1  0.663  0.833  0.625  1.0
  Mg  Mg7  1  0.333  0.171  0.367  1.0
  Mg  Mg8  1  0.333  0.171  0.883  1.0
  Mg  Mg9  1  0.333  0.661  0.367  1.0
  Mg  Mg10  1  0.333  0.661  0.883  1.0
  Mg  Mg11  1  0.852  0.176  0.362  1.0
  Mg  Mg12  1  0.852  0.176  0.888  1.0
  Mg  Mg13  1  0.844  0.672  0.377  1.0
  Mg  Mg14  1  0.844  0.672  0.873  1.0
  W  W15  1  0.158  0.329  0.125  1.0
[/CIF]
.