The material described by Mg15Hf is Magnesium-derived structured and crystallizes in the hexagonal P-6m2 space group. There are eight inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to six Mg(3,3) and six Mg(4,4) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(1)Mg12 cuboctahedra; corners with twelve Mg(2,2)Hf2Mg10 cuboctahedra; edges with six Mg(3,3)Mg12 cuboctahedra; edges with twelve Mg(4,4)HfMg11 cuboctahedra; faces with two equivalent Hf(1)Mg12 cuboctahedra; faces with six Mg(4,4)HfMg11 cuboctahedra; faces with six Mg(3,3)Mg12 cuboctahedra; and faces with six equivalent Mg(5)Mg12 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(5); four Mg(2,2); four equivalent Mg(4); and two equivalent Hf(1) atoms to form MgHf2Mg10 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Hf2Mg10 cuboctahedra; corners with eight Mg(3,3)Mg12 cuboctahedra; edges with two equivalent Hf(1)Mg12 cuboctahedra; edges with four Mg(2,2)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight equivalent Mg(4)HfMg11 cuboctahedra; faces with two equivalent Mg(3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with two equivalent Hf(1)Mg12 cuboctahedra; faces with four Mg(2,2)Hf2Mg10 cuboctahedra; and faces with ten Mg(4,4)HfMg11 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(1); two equivalent Mg(5); four Mg(3,3); and four equivalent Mg(4) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Hf(1)Mg12 cuboctahedra; corners with six equivalent Mg(3)Mg12 cuboctahedra; corners with eight Mg(2,2)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four Mg(3,3)Mg12 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight equivalent Mg(4)HfMg11 cuboctahedra; faces with two equivalent Mg(2)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with four Mg(3,3)Mg12 cuboctahedra; and faces with ten Mg(4,4)HfMg11 cuboctahedra. In the fourth Mg site, Mg(2) is bonded to two equivalent Mg(5); four equivalent Mg(2); four Mg(4,4); and two equivalent Hf(1) atoms to form MgHf2Mg10 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Hf2Mg10 cuboctahedra; corners with eight equivalent Mg(3)Mg12 cuboctahedra; edges with two equivalent Hf(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight Mg(4,4)HfMg11 cuboctahedra; faces with two equivalent Mg(3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with two equivalent Hf(1)Mg12 cuboctahedra; faces with four equivalent Mg(2)Hf2Mg10 cuboctahedra; and faces with ten Mg(4,4)HfMg11 cuboctahedra. In the fifth Mg site, Mg(3) is bonded to two equivalent Mg(1); two equivalent Mg(5); four equivalent Mg(3); and four Mg(4,4) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Hf(1)Mg12 cuboctahedra; corners with six equivalent Mg(3)Mg12 cuboctahedra; corners with eight equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Mg(3)Mg12 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight Mg(4,4)HfMg11 cuboctahedra; faces with two equivalent Mg(2)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with four equivalent Mg(3)Mg12 cuboctahedra; and faces with ten Mg(4,4)HfMg11 cuboctahedra. In the sixth Mg site, Mg(4) is bonded to one Mg(1); two equivalent Mg(2); two equivalent Mg(3); two equivalent Mg(5); four Mg(4,4); and one Hf(1) atom to form MgHfMg11 cuboctahedra that share corners with four equivalent Mg(5)Mg12 cuboctahedra; corners with fourteen Mg(4,4)HfMg11 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(5)Mg12 cuboctahedra; edges with two equivalent Hf(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with four Mg(4,4)HfMg11 cuboctahedra; edges with four equivalent Mg(3)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Hf(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with five Mg(2,2)Hf2Mg10 cuboctahedra; faces with five Mg(3,3)Mg12 cuboctahedra; and faces with six Mg(4,4)HfMg11 cuboctahedra. In the seventh Mg site, Mg(4) is bonded to one Mg(1); two Mg(2,2); two Mg(3,3); two equivalent Mg(5); four equivalent Mg(4); and one Hf(1) atom to form MgHfMg11 cuboctahedra that share corners with four equivalent Mg(5)Mg12 cuboctahedra; corners with fourteen Mg(4,4)HfMg11 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(5)Mg12 cuboctahedra; edges with two equivalent Hf(1)Mg12 cuboctahedra; edges with four Mg(2,2)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(4)HfMg11 cuboctahedra; edges with four Mg(3,3)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Hf(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with five Mg(2,2)Hf2Mg10 cuboctahedra; faces with five Mg(3,3)Mg12 cuboctahedra; and faces with six Mg(4,4)HfMg11 cuboctahedra. In the eighth Mg site, Mg(5) is bonded to three Mg(2,2); three Mg(3,3); and six Mg(4,4) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(5)Mg12 cuboctahedra; corners with twelve Mg(4,4)HfMg11 cuboctahedra; edges with six Mg(2,2)Hf2Mg10 cuboctahedra; edges with six Mg(4,4)HfMg11 cuboctahedra; edges with six Mg(3,3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with three Mg(2,2)Hf2Mg10 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; faces with three Mg(3,3)Mg12 cuboctahedra; faces with three equivalent Hf(1)Mg12 cuboctahedra; and faces with six Mg(4,4)HfMg11 cuboctahedra. Hf(1) is bonded to six Mg(2,2) and six Mg(4,4) atoms to form HfMg12 cuboctahedra that share corners with six equivalent Hf(1)Mg12 cuboctahedra; corners with twelve Mg(3,3)Mg12 cuboctahedra; edges with six Mg(2,2)Hf2Mg10 cuboctahedra; edges with twelve Mg(4,4)HfMg11 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with six Mg(2,2)Hf2Mg10 cuboctahedra; faces with six Mg(4,4)HfMg11 cuboctahedra; and faces with six equivalent Mg(5)Mg12 cuboctahedra. is represented by the CIF card [CIF]
data_HfMg15
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.413
_cell_length_b   6.413
_cell_length_c   10.176
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   362.449
_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  0.667  0.333  0.000  1.0
  Mg  Mg1  1  0.667  0.333  0.500  1.0
  Mg  Mg2  1  0.168  0.337  0.000  1.0
  Mg  Mg3  1  0.167  0.333  0.500  1.0
  Mg  Mg4  1  0.168  0.832  0.000  1.0
  Mg  Mg5  1  0.167  0.833  0.500  1.0
  Mg  Mg6  1  0.663  0.832  0.000  1.0
  Mg  Mg7  1  0.667  0.833  0.500  1.0
  Mg  Mg8  1  0.996  0.498  0.248  1.0
  Mg  Mg9  1  0.996  0.498  0.752  1.0
  Mg  Mg10  1  0.502  0.498  0.248  1.0
  Mg  Mg11  1  0.502  0.498  0.752  1.0
  Mg  Mg12  1  0.502  0.004  0.248  1.0
  Mg  Mg13  1  0.502  0.004  0.752  1.0
  Mg  Mg14  1  0.000  0.000  0.249  1.0
  Mg  Mg15  1  0.000  0.000  0.751  1.0
[/CIF]
.
The material described by Mg15Hf is Magnesium-derived structured and crystallizes in the hexagonal P-6m2 space group. There are eight inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to six Mg(3,3) and six Mg(4,4) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(1)Mg12 cuboctahedra; corners with twelve Mg(2,2)Hf2Mg10 cuboctahedra; edges with six Mg(3,3)Mg12 cuboctahedra; edges with twelve Mg(4,4)HfMg11 cuboctahedra; faces with two equivalent Hf(1)Mg12 cuboctahedra; faces with six Mg(4,4)HfMg11 cuboctahedra; faces with six Mg(3,3)Mg12 cuboctahedra; and faces with six equivalent Mg(5)Mg12 cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(5); four Mg(2,2); four equivalent Mg(4); and two equivalent Hf(1) atoms to form MgHf2Mg10 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Hf2Mg10 cuboctahedra; corners with eight Mg(3,3)Mg12 cuboctahedra; edges with two equivalent Hf(1)Mg12 cuboctahedra; edges with four Mg(2,2)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight equivalent Mg(4)HfMg11 cuboctahedra; faces with two equivalent Mg(3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with two equivalent Hf(1)Mg12 cuboctahedra; faces with four Mg(2,2)Hf2Mg10 cuboctahedra; and faces with ten Mg(4,4)HfMg11 cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(1); two equivalent Mg(5); four Mg(3,3); and four equivalent Mg(4) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Hf(1)Mg12 cuboctahedra; corners with six equivalent Mg(3)Mg12 cuboctahedra; corners with eight Mg(2,2)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four Mg(3,3)Mg12 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight equivalent Mg(4)HfMg11 cuboctahedra; faces with two equivalent Mg(2)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with four Mg(3,3)Mg12 cuboctahedra; and faces with ten Mg(4,4)HfMg11 cuboctahedra. In the fourth Mg site, Mg(2) is bonded to two equivalent Mg(5); four equivalent Mg(2); four Mg(4,4); and two equivalent Hf(1) atoms to form MgHf2Mg10 cuboctahedra that share corners with four equivalent Mg(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Hf2Mg10 cuboctahedra; corners with eight equivalent Mg(3)Mg12 cuboctahedra; edges with two equivalent Hf(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight Mg(4,4)HfMg11 cuboctahedra; faces with two equivalent Mg(3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with two equivalent Hf(1)Mg12 cuboctahedra; faces with four equivalent Mg(2)Hf2Mg10 cuboctahedra; and faces with ten Mg(4,4)HfMg11 cuboctahedra. In the fifth Mg site, Mg(3) is bonded to two equivalent Mg(1); two equivalent Mg(5); four equivalent Mg(3); and four Mg(4,4) atoms to form MgMg12 cuboctahedra that share corners with four equivalent Hf(1)Mg12 cuboctahedra; corners with six equivalent Mg(3)Mg12 cuboctahedra; corners with eight equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with four equivalent Mg(3)Mg12 cuboctahedra; edges with four equivalent Mg(5)Mg12 cuboctahedra; edges with eight Mg(4,4)HfMg11 cuboctahedra; faces with two equivalent Mg(2)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with four equivalent Mg(3)Mg12 cuboctahedra; and faces with ten Mg(4,4)HfMg11 cuboctahedra. In the sixth Mg site, Mg(4) is bonded to one Mg(1); two equivalent Mg(2); two equivalent Mg(3); two equivalent Mg(5); four Mg(4,4); and one Hf(1) atom to form MgHfMg11 cuboctahedra that share corners with four equivalent Mg(5)Mg12 cuboctahedra; corners with fourteen Mg(4,4)HfMg11 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(5)Mg12 cuboctahedra; edges with two equivalent Hf(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with four Mg(4,4)HfMg11 cuboctahedra; edges with four equivalent Mg(3)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Hf(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with five Mg(2,2)Hf2Mg10 cuboctahedra; faces with five Mg(3,3)Mg12 cuboctahedra; and faces with six Mg(4,4)HfMg11 cuboctahedra. In the seventh Mg site, Mg(4) is bonded to one Mg(1); two Mg(2,2); two Mg(3,3); two equivalent Mg(5); four equivalent Mg(4); and one Hf(1) atom to form MgHfMg11 cuboctahedra that share corners with four equivalent Mg(5)Mg12 cuboctahedra; corners with fourteen Mg(4,4)HfMg11 cuboctahedra; edges with two equivalent Mg(1)Mg12 cuboctahedra; edges with two equivalent Mg(5)Mg12 cuboctahedra; edges with two equivalent Hf(1)Mg12 cuboctahedra; edges with four Mg(2,2)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(4)HfMg11 cuboctahedra; edges with four Mg(3,3)Mg12 cuboctahedra;  a faceface with one Mg(1)Mg12 cuboctahedra;  a faceface with one Hf(1)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with five Mg(2,2)Hf2Mg10 cuboctahedra; faces with five Mg(3,3)Mg12 cuboctahedra; and faces with six Mg(4,4)HfMg11 cuboctahedra. In the eighth Mg site, Mg(5) is bonded to three Mg(2,2); three Mg(3,3); and six Mg(4,4) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(5)Mg12 cuboctahedra; corners with twelve Mg(4,4)HfMg11 cuboctahedra; edges with six Mg(2,2)Hf2Mg10 cuboctahedra; edges with six Mg(4,4)HfMg11 cuboctahedra; edges with six Mg(3,3)Mg12 cuboctahedra; faces with two equivalent Mg(5)Mg12 cuboctahedra; faces with three Mg(2,2)Hf2Mg10 cuboctahedra; faces with three equivalent Mg(1)Mg12 cuboctahedra; faces with three Mg(3,3)Mg12 cuboctahedra; faces with three equivalent Hf(1)Mg12 cuboctahedra; and faces with six Mg(4,4)HfMg11 cuboctahedra. Hf(1) is bonded to six Mg(2,2) and six Mg(4,4) atoms to form HfMg12 cuboctahedra that share corners with six equivalent Hf(1)Mg12 cuboctahedra; corners with twelve Mg(3,3)Mg12 cuboctahedra; edges with six Mg(2,2)Hf2Mg10 cuboctahedra; edges with twelve Mg(4,4)HfMg11 cuboctahedra; faces with two equivalent Mg(1)Mg12 cuboctahedra; faces with six Mg(2,2)Hf2Mg10 cuboctahedra; faces with six Mg(4,4)HfMg11 cuboctahedra; and faces with six equivalent Mg(5)Mg12 cuboctahedra. is represented by the CIF card [CIF]
data_HfMg15
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.413
_cell_length_b   6.413
_cell_length_c   10.176
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   362.449
_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  0.667  0.333  0.000  1.0
  Mg  Mg1  1  0.667  0.333  0.500  1.0
  Mg  Mg2  1  0.168  0.337  0.000  1.0
  Mg  Mg3  1  0.167  0.333  0.500  1.0
  Mg  Mg4  1  0.168  0.832  0.000  1.0
  Mg  Mg5  1  0.167  0.833  0.500  1.0
  Mg  Mg6  1  0.663  0.832  0.000  1.0
  Mg  Mg7  1  0.667  0.833  0.500  1.0
  Mg  Mg8  1  0.996  0.498  0.248  1.0
  Mg  Mg9  1  0.996  0.498  0.752  1.0
  Mg  Mg10  1  0.502  0.498  0.248  1.0
  Mg  Mg11  1  0.502  0.498  0.752  1.0
  Mg  Mg12  1  0.502  0.004  0.248  1.0
  Mg  Mg13  1  0.502  0.004  0.752  1.0
  Mg  Mg14  1  0.000  0.000  0.249  1.0
  Mg  Mg15  1  0.000  0.000  0.751  1.0
[/CIF]
.