The compound described by Mg14HfZn crystallizes in the hexagonal P-6m2 space group. There are five inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Zn(1) atoms to form MgMg10Zn2 cuboctahedra that share corners with four equivalent Hf(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Zn2 cuboctahedra; corners with eight Mg(2,2)Hf2Mg10 cuboctahedra; edges with two equivalent Zn(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Mg10Zn2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)HfMg10Zn cuboctahedra; faces with two equivalent Mg(2)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Zn(1)Mg12 cuboctahedra; faces with four equivalent Mg(1)Mg10Zn2 cuboctahedra; and faces with ten equivalent Mg(3)HfMg10Zn cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(4); four Mg(2,2); four equivalent Mg(3); and two equivalent Hf(1) atoms to form MgHf2Mg10 cuboctahedra that share corners with four equivalent Zn(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Hf2Mg10 cuboctahedra; corners with eight equivalent Mg(1)Mg10Zn2 cuboctahedra; edges with two equivalent Hf(1)Mg12 cuboctahedra; edges with four Mg(2,2)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)HfMg10Zn cuboctahedra; faces with two equivalent Mg(1)Mg10Zn2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Hf(1)Mg12 cuboctahedra; faces with four Mg(2,2)Hf2Mg10 cuboctahedra; and faces with ten equivalent Mg(3)HfMg10Zn cuboctahedra. In the third Mg site, Mg(2) is bonded to two equivalent Mg(4), four equivalent Mg(2), four equivalent Mg(3), and two equivalent Hf(1) atoms to form MgHf2Mg10 cuboctahedra that share corners with four equivalent Zn(1)Mg12 cuboctahedra, corners with six equivalent Mg(2)Hf2Mg10 cuboctahedra, corners with eight equivalent Mg(1)Mg10Zn2 cuboctahedra, edges with two equivalent Hf(1)Mg12 cuboctahedra, edges with four equivalent Mg(2)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with eight equivalent Mg(3)HfMg10Zn cuboctahedra, faces with two equivalent Mg(1)Mg10Zn2 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Hf(1)Mg12 cuboctahedra, faces with four equivalent Mg(2)Hf2Mg10 cuboctahedra, and faces with ten equivalent Mg(3)HfMg10Zn cuboctahedra. In the fourth Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), four equivalent Mg(3), one Hf(1), and one Zn(1) atom to form distorted MgHfMg10Zn cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen equivalent Mg(3)HfMg10Zn cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Hf(1)Mg12 cuboctahedra; edges with two equivalent Zn(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(3)HfMg10Zn cuboctahedra; edges with four equivalent Mg(1)Mg10Zn2 cuboctahedra;  a faceface with one Hf(1)Mg12 cuboctahedra;  a faceface with one Zn(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(2,2)Hf2Mg10 cuboctahedra; faces with five equivalent Mg(1)Mg10Zn2 cuboctahedra; and faces with six equivalent Mg(3)HfMg10Zn cuboctahedra. In the fifth Mg site, Mg(4) is bonded to three equivalent Mg(1); three Mg(2,2); and six equivalent Mg(3) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(4)Mg12 cuboctahedra; corners with twelve equivalent Mg(3)HfMg10Zn cuboctahedra; edges with six Mg(2,2)Hf2Mg10 cuboctahedra; edges with six equivalent Mg(3)HfMg10Zn cuboctahedra; edges with six equivalent Mg(1)Mg10Zn2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three Mg(2,2)Hf2Mg10 cuboctahedra; faces with three equivalent Mg(1)Mg10Zn2 cuboctahedra; faces with three equivalent Hf(1)Mg12 cuboctahedra; faces with three equivalent Zn(1)Mg12 cuboctahedra; and faces with six equivalent Mg(3)HfMg10Zn cuboctahedra. Hf(1) is bonded to six Mg(2,2) and six equivalent Mg(3) atoms to form HfMg12 cuboctahedra that share corners with six equivalent Hf(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(1)Mg10Zn2 cuboctahedra; edges with six Mg(2,2)Hf2Mg10 cuboctahedra; edges with twelve equivalent Mg(3)HfMg10Zn cuboctahedra; faces with two equivalent Zn(1)Mg12 cuboctahedra; faces with six Mg(2,2)Hf2Mg10 cuboctahedra; faces with six equivalent Mg(3)HfMg10Zn cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. Zn(1) is bonded to six equivalent Mg(1) and six equivalent Mg(3) atoms to form ZnMg12 cuboctahedra that share corners with six equivalent Zn(1)Mg12 cuboctahedra; corners with twelve Mg(2,2)Hf2Mg10 cuboctahedra; edges with six equivalent Mg(1)Mg10Zn2 cuboctahedra; edges with twelve equivalent Mg(3)HfMg10Zn cuboctahedra; faces with two equivalent Hf(1)Mg12 cuboctahedra; faces with six equivalent Mg(3)HfMg10Zn cuboctahedra; faces with six equivalent Mg(1)Mg10Zn2 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_HfMg14Zn
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.363
_cell_length_b   6.363
_cell_length_c   10.081
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   353.442
_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  0.167  0.333  0.625  1.0
  Mg  Mg1  1  0.165  0.832  0.125  1.0
  Mg  Mg2  1  0.173  0.837  0.625  1.0
  Mg  Mg3  1  0.668  0.335  0.125  1.0
  Mg  Mg4  1  0.663  0.327  0.625  1.0
  Mg  Mg5  1  0.668  0.832  0.125  1.0
  Mg  Mg6  1  0.663  0.837  0.625  1.0
  Mg  Mg7  1  0.328  0.172  0.372  1.0
  Mg  Mg8  1  0.328  0.172  0.878  1.0
  Mg  Mg9  1  0.328  0.657  0.372  1.0
  Mg  Mg10  1  0.328  0.657  0.878  1.0
  Mg  Mg11  1  0.843  0.172  0.372  1.0
  Mg  Mg12  1  0.843  0.172  0.878  1.0
  Mg  Mg13  1  0.833  0.667  0.379  1.0
  Mg  Mg14  1  0.833  0.667  0.871  1.0
  Zn  Zn15  1  0.167  0.333  0.125  1.0
[/CIF]
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The compound described by Mg14HfZn crystallizes in the hexagonal P-6m2 space group. There are five inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Zn(1) atoms to form MgMg10Zn2 cuboctahedra that share corners with four equivalent Hf(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Zn2 cuboctahedra; corners with eight Mg(2,2)Hf2Mg10 cuboctahedra; edges with two equivalent Zn(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Mg10Zn2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)HfMg10Zn cuboctahedra; faces with two equivalent Mg(2)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Zn(1)Mg12 cuboctahedra; faces with four equivalent Mg(1)Mg10Zn2 cuboctahedra; and faces with ten equivalent Mg(3)HfMg10Zn cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(4); four Mg(2,2); four equivalent Mg(3); and two equivalent Hf(1) atoms to form MgHf2Mg10 cuboctahedra that share corners with four equivalent Zn(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Hf2Mg10 cuboctahedra; corners with eight equivalent Mg(1)Mg10Zn2 cuboctahedra; edges with two equivalent Hf(1)Mg12 cuboctahedra; edges with four Mg(2,2)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight equivalent Mg(3)HfMg10Zn cuboctahedra; faces with two equivalent Mg(1)Mg10Zn2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Hf(1)Mg12 cuboctahedra; faces with four Mg(2,2)Hf2Mg10 cuboctahedra; and faces with ten equivalent Mg(3)HfMg10Zn cuboctahedra. In the third Mg site, Mg(2) is bonded to two equivalent Mg(4), four equivalent Mg(2), four equivalent Mg(3), and two equivalent Hf(1) atoms to form MgHf2Mg10 cuboctahedra that share corners with four equivalent Zn(1)Mg12 cuboctahedra, corners with six equivalent Mg(2)Hf2Mg10 cuboctahedra, corners with eight equivalent Mg(1)Mg10Zn2 cuboctahedra, edges with two equivalent Hf(1)Mg12 cuboctahedra, edges with four equivalent Mg(2)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(4)Mg12 cuboctahedra, edges with eight equivalent Mg(3)HfMg10Zn cuboctahedra, faces with two equivalent Mg(1)Mg10Zn2 cuboctahedra, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Hf(1)Mg12 cuboctahedra, faces with four equivalent Mg(2)Hf2Mg10 cuboctahedra, and faces with ten equivalent Mg(3)HfMg10Zn cuboctahedra. In the fourth Mg site, Mg(3) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(4), four equivalent Mg(3), one Hf(1), and one Zn(1) atom to form distorted MgHfMg10Zn cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen equivalent Mg(3)HfMg10Zn cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Hf(1)Mg12 cuboctahedra; edges with two equivalent Zn(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with four equivalent Mg(3)HfMg10Zn cuboctahedra; edges with four equivalent Mg(1)Mg10Zn2 cuboctahedra;  a faceface with one Hf(1)Mg12 cuboctahedra;  a faceface with one Zn(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five Mg(2,2)Hf2Mg10 cuboctahedra; faces with five equivalent Mg(1)Mg10Zn2 cuboctahedra; and faces with six equivalent Mg(3)HfMg10Zn cuboctahedra. In the fifth Mg site, Mg(4) is bonded to three equivalent Mg(1); three Mg(2,2); and six equivalent Mg(3) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(4)Mg12 cuboctahedra; corners with twelve equivalent Mg(3)HfMg10Zn cuboctahedra; edges with six Mg(2,2)Hf2Mg10 cuboctahedra; edges with six equivalent Mg(3)HfMg10Zn cuboctahedra; edges with six equivalent Mg(1)Mg10Zn2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three Mg(2,2)Hf2Mg10 cuboctahedra; faces with three equivalent Mg(1)Mg10Zn2 cuboctahedra; faces with three equivalent Hf(1)Mg12 cuboctahedra; faces with three equivalent Zn(1)Mg12 cuboctahedra; and faces with six equivalent Mg(3)HfMg10Zn cuboctahedra. Hf(1) is bonded to six Mg(2,2) and six equivalent Mg(3) atoms to form HfMg12 cuboctahedra that share corners with six equivalent Hf(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(1)Mg10Zn2 cuboctahedra; edges with six Mg(2,2)Hf2Mg10 cuboctahedra; edges with twelve equivalent Mg(3)HfMg10Zn cuboctahedra; faces with two equivalent Zn(1)Mg12 cuboctahedra; faces with six Mg(2,2)Hf2Mg10 cuboctahedra; faces with six equivalent Mg(3)HfMg10Zn cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. Zn(1) is bonded to six equivalent Mg(1) and six equivalent Mg(3) atoms to form ZnMg12 cuboctahedra that share corners with six equivalent Zn(1)Mg12 cuboctahedra; corners with twelve Mg(2,2)Hf2Mg10 cuboctahedra; edges with six equivalent Mg(1)Mg10Zn2 cuboctahedra; edges with twelve equivalent Mg(3)HfMg10Zn cuboctahedra; faces with two equivalent Hf(1)Mg12 cuboctahedra; faces with six equivalent Mg(3)HfMg10Zn cuboctahedra; faces with six equivalent Mg(1)Mg10Zn2 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_HfMg14Zn
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.363
_cell_length_b   6.363
_cell_length_c   10.081
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   353.442
_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  0.167  0.333  0.625  1.0
  Mg  Mg1  1  0.165  0.832  0.125  1.0
  Mg  Mg2  1  0.173  0.837  0.625  1.0
  Mg  Mg3  1  0.668  0.335  0.125  1.0
  Mg  Mg4  1  0.663  0.327  0.625  1.0
  Mg  Mg5  1  0.668  0.832  0.125  1.0
  Mg  Mg6  1  0.663  0.837  0.625  1.0
  Mg  Mg7  1  0.328  0.172  0.372  1.0
  Mg  Mg8  1  0.328  0.172  0.878  1.0
  Mg  Mg9  1  0.328  0.657  0.372  1.0
  Mg  Mg10  1  0.328  0.657  0.878  1.0
  Mg  Mg11  1  0.843  0.172  0.372  1.0
  Mg  Mg12  1  0.843  0.172  0.878  1.0
  Mg  Mg13  1  0.833  0.667  0.379  1.0
  Mg  Mg14  1  0.833  0.667  0.871  1.0
  Zn  Zn15  1  0.167  0.333  0.125  1.0
[/CIF]
.