The material described by Mg14HfNb crystallizes in the hexagonal P-6m2 space group. There are six inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(4); four equivalent Mg(1); four Mg(3,3); and two equivalent Nb(1) atoms to form MgMg10Nb2 cuboctahedra that share corners with four equivalent Hf(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Nb2 cuboctahedra; corners with eight equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with two equivalent Nb(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Mg10Nb2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)HfMg10Nb cuboctahedra; faces with two equivalent Mg(2)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Nb(1)Mg12 cuboctahedra; faces with four equivalent Mg(1)Mg10Nb2 cuboctahedra; and faces with ten Mg(3,3,3)HfMg10Nb cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(4); four equivalent Mg(2); four Mg(3,3); and two equivalent Hf(1) atoms to form MgHf2Mg10 cuboctahedra that share corners with four equivalent Nb(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Hf2Mg10 cuboctahedra; corners with eight equivalent Mg(1)Mg10Nb2 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 Mg(3,3)HfMg10Nb cuboctahedra; faces with two equivalent Mg(1)Mg10Nb2 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 Mg(3,3,3)HfMg10Nb cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(1); two equivalent Mg(2); two equivalent Mg(4); four Mg(3,3); one Hf(1); and one Nb(1) atom to form distorted MgHfMg10Nb cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3,3)HfMg10Nb cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Hf(1)Mg12 cuboctahedra; edges with two equivalent Nb(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with four Mg(3,3)HfMg10Nb cuboctahedra; edges with four equivalent Mg(1)Mg10Nb2 cuboctahedra;  a faceface with one Hf(1)Mg12 cuboctahedra;  a faceface with one Nb(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five equivalent Mg(2)Hf2Mg10 cuboctahedra; faces with five equivalent Mg(1)Mg10Nb2 cuboctahedra; and faces with six Mg(3,3,3)HfMg10Nb cuboctahedra. In the fourth Mg site, Mg(3) is bonded to two equivalent Mg(1); two equivalent Mg(2); two equivalent Mg(4); four Mg(3,3); one Hf(1); and one Nb(1) atom to form distorted MgHfMg10Nb cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3,3)HfMg10Nb cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Hf(1)Mg12 cuboctahedra; edges with two equivalent Nb(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with four Mg(3,3)HfMg10Nb cuboctahedra; edges with four equivalent Mg(1)Mg10Nb2 cuboctahedra;  a faceface with one Hf(1)Mg12 cuboctahedra;  a faceface with one Nb(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five equivalent Mg(2)Hf2Mg10 cuboctahedra; faces with five equivalent Mg(1)Mg10Nb2 cuboctahedra; and faces with six Mg(3,3,3)HfMg10Nb cuboctahedra. In the fifth Mg site, Mg(3) is bonded to two equivalent Mg(1); two equivalent Mg(2); two equivalent Mg(4); four Mg(3,3); one Hf(1); and one Nb(1) atom to form distorted MgHfMg10Nb cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3,3)HfMg10Nb cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Hf(1)Mg12 cuboctahedra; edges with two equivalent Nb(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with four Mg(3,3)HfMg10Nb cuboctahedra; edges with four equivalent Mg(1)Mg10Nb2 cuboctahedra;  a faceface with one Hf(1)Mg12 cuboctahedra;  a faceface with one Nb(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five equivalent Mg(2)Hf2Mg10 cuboctahedra; faces with five equivalent Mg(1)Mg10Nb2 cuboctahedra; and faces with six Mg(3,3,3)HfMg10Nb cuboctahedra. In the sixth Mg site, Mg(4) is bonded to three equivalent Mg(1); three equivalent Mg(2); and six Mg(3,3,3) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(4)Mg12 cuboctahedra; corners with twelve Mg(3,3,3)HfMg10Nb cuboctahedra; edges with six equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with six Mg(3,3,3)HfMg10Nb cuboctahedra; edges with six equivalent Mg(1)Mg10Nb2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Mg(2)Hf2Mg10 cuboctahedra; faces with three equivalent Mg(1)Mg10Nb2 cuboctahedra; faces with three equivalent Hf(1)Mg12 cuboctahedra; faces with three equivalent Nb(1)Mg12 cuboctahedra; and faces with six Mg(3,3,3)HfMg10Nb cuboctahedra. Hf(1) is bonded to six equivalent Mg(2) and six Mg(3,3,3) atoms to form HfMg12 cuboctahedra that share corners with six equivalent Hf(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(1)Mg10Nb2 cuboctahedra; edges with six equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with twelve Mg(3,3,3)HfMg10Nb cuboctahedra; faces with two equivalent Nb(1)Mg12 cuboctahedra; faces with six equivalent Mg(2)Hf2Mg10 cuboctahedra; faces with six Mg(3,3,3)HfMg10Nb cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. Nb(1) is bonded to six equivalent Mg(1) and six Mg(3,3,3) atoms to form NbMg12 cuboctahedra that share corners with six equivalent Nb(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with six equivalent Mg(1)Mg10Nb2 cuboctahedra; edges with twelve Mg(3,3,3)HfMg10Nb cuboctahedra; faces with two equivalent Hf(1)Mg12 cuboctahedra; faces with six Mg(3,3,3)HfMg10Nb cuboctahedra; faces with six equivalent Mg(1)Mg10Nb2 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_HfMg14Nb
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.390
_cell_length_b   6.390
_cell_length_c   10.000
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   353.657
_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  0.168  0.834  0.125  1.0
  Mg  Mg2  1  0.170  0.835  0.625  1.0
  Mg  Mg3  1  0.666  0.332  0.125  1.0
  Mg  Mg4  1  0.665  0.330  0.625  1.0
  Mg  Mg5  1  0.666  0.834  0.125  1.0
  Mg  Mg6  1  0.665  0.835  0.625  1.0
  Mg  Mg7  1  0.329  0.171  0.371  1.0
  Mg  Mg8  1  0.329  0.171  0.879  1.0
  Mg  Mg9  1  0.329  0.657  0.371  1.0
  Mg  Mg10  1  0.329  0.657  0.879  1.0
  Mg  Mg11  1  0.843  0.171  0.371  1.0
  Mg  Mg12  1  0.843  0.171  0.879  1.0
  Mg  Mg13  1  0.833  0.667  0.376  1.0
  Mg  Mg14  1  0.833  0.667  0.874  1.0
  Nb  Nb15  1  0.167  0.333  0.125  1.0
[/CIF]
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The material described by Mg14HfNb crystallizes in the hexagonal P-6m2 space group. There are six inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(4); four equivalent Mg(1); four Mg(3,3); and two equivalent Nb(1) atoms to form MgMg10Nb2 cuboctahedra that share corners with four equivalent Hf(1)Mg12 cuboctahedra; corners with six equivalent Mg(1)Mg10Nb2 cuboctahedra; corners with eight equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with two equivalent Nb(1)Mg12 cuboctahedra; edges with four equivalent Mg(1)Mg10Nb2 cuboctahedra; edges with four equivalent Mg(4)Mg12 cuboctahedra; edges with eight Mg(3,3)HfMg10Nb cuboctahedra; faces with two equivalent Mg(2)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Nb(1)Mg12 cuboctahedra; faces with four equivalent Mg(1)Mg10Nb2 cuboctahedra; and faces with ten Mg(3,3,3)HfMg10Nb cuboctahedra. In the second Mg site, Mg(2) is bonded to two equivalent Mg(4); four equivalent Mg(2); four Mg(3,3); and two equivalent Hf(1) atoms to form MgHf2Mg10 cuboctahedra that share corners with four equivalent Nb(1)Mg12 cuboctahedra; corners with six equivalent Mg(2)Hf2Mg10 cuboctahedra; corners with eight equivalent Mg(1)Mg10Nb2 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 Mg(3,3)HfMg10Nb cuboctahedra; faces with two equivalent Mg(1)Mg10Nb2 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 Mg(3,3,3)HfMg10Nb cuboctahedra. In the third Mg site, Mg(3) is bonded to two equivalent Mg(1); two equivalent Mg(2); two equivalent Mg(4); four Mg(3,3); one Hf(1); and one Nb(1) atom to form distorted MgHfMg10Nb cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3,3)HfMg10Nb cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Hf(1)Mg12 cuboctahedra; edges with two equivalent Nb(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with four Mg(3,3)HfMg10Nb cuboctahedra; edges with four equivalent Mg(1)Mg10Nb2 cuboctahedra;  a faceface with one Hf(1)Mg12 cuboctahedra;  a faceface with one Nb(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five equivalent Mg(2)Hf2Mg10 cuboctahedra; faces with five equivalent Mg(1)Mg10Nb2 cuboctahedra; and faces with six Mg(3,3,3)HfMg10Nb cuboctahedra. In the fourth Mg site, Mg(3) is bonded to two equivalent Mg(1); two equivalent Mg(2); two equivalent Mg(4); four Mg(3,3); one Hf(1); and one Nb(1) atom to form distorted MgHfMg10Nb cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3,3)HfMg10Nb cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Hf(1)Mg12 cuboctahedra; edges with two equivalent Nb(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with four Mg(3,3)HfMg10Nb cuboctahedra; edges with four equivalent Mg(1)Mg10Nb2 cuboctahedra;  a faceface with one Hf(1)Mg12 cuboctahedra;  a faceface with one Nb(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five equivalent Mg(2)Hf2Mg10 cuboctahedra; faces with five equivalent Mg(1)Mg10Nb2 cuboctahedra; and faces with six Mg(3,3,3)HfMg10Nb cuboctahedra. In the fifth Mg site, Mg(3) is bonded to two equivalent Mg(1); two equivalent Mg(2); two equivalent Mg(4); four Mg(3,3); one Hf(1); and one Nb(1) atom to form distorted MgHfMg10Nb cuboctahedra that share corners with four equivalent Mg(4)Mg12 cuboctahedra; corners with fourteen Mg(3,3,3)HfMg10Nb cuboctahedra; edges with two equivalent Mg(4)Mg12 cuboctahedra; edges with two equivalent Hf(1)Mg12 cuboctahedra; edges with two equivalent Nb(1)Mg12 cuboctahedra; edges with four equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with four Mg(3,3)HfMg10Nb cuboctahedra; edges with four equivalent Mg(1)Mg10Nb2 cuboctahedra;  a faceface with one Hf(1)Mg12 cuboctahedra;  a faceface with one Nb(1)Mg12 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with five equivalent Mg(2)Hf2Mg10 cuboctahedra; faces with five equivalent Mg(1)Mg10Nb2 cuboctahedra; and faces with six Mg(3,3,3)HfMg10Nb cuboctahedra. In the sixth Mg site, Mg(4) is bonded to three equivalent Mg(1); three equivalent Mg(2); and six Mg(3,3,3) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(4)Mg12 cuboctahedra; corners with twelve Mg(3,3,3)HfMg10Nb cuboctahedra; edges with six equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with six Mg(3,3,3)HfMg10Nb cuboctahedra; edges with six equivalent Mg(1)Mg10Nb2 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three equivalent Mg(2)Hf2Mg10 cuboctahedra; faces with three equivalent Mg(1)Mg10Nb2 cuboctahedra; faces with three equivalent Hf(1)Mg12 cuboctahedra; faces with three equivalent Nb(1)Mg12 cuboctahedra; and faces with six Mg(3,3,3)HfMg10Nb cuboctahedra. Hf(1) is bonded to six equivalent Mg(2) and six Mg(3,3,3) atoms to form HfMg12 cuboctahedra that share corners with six equivalent Hf(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(1)Mg10Nb2 cuboctahedra; edges with six equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with twelve Mg(3,3,3)HfMg10Nb cuboctahedra; faces with two equivalent Nb(1)Mg12 cuboctahedra; faces with six equivalent Mg(2)Hf2Mg10 cuboctahedra; faces with six Mg(3,3,3)HfMg10Nb cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. Nb(1) is bonded to six equivalent Mg(1) and six Mg(3,3,3) atoms to form NbMg12 cuboctahedra that share corners with six equivalent Nb(1)Mg12 cuboctahedra; corners with twelve equivalent Mg(2)Hf2Mg10 cuboctahedra; edges with six equivalent Mg(1)Mg10Nb2 cuboctahedra; edges with twelve Mg(3,3,3)HfMg10Nb cuboctahedra; faces with two equivalent Hf(1)Mg12 cuboctahedra; faces with six Mg(3,3,3)HfMg10Nb cuboctahedra; faces with six equivalent Mg(1)Mg10Nb2 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_HfMg14Nb
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.390
_cell_length_b   6.390
_cell_length_c   10.000
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   353.657
_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  0.168  0.834  0.125  1.0
  Mg  Mg2  1  0.170  0.835  0.625  1.0
  Mg  Mg3  1  0.666  0.332  0.125  1.0
  Mg  Mg4  1  0.665  0.330  0.625  1.0
  Mg  Mg5  1  0.666  0.834  0.125  1.0
  Mg  Mg6  1  0.665  0.835  0.625  1.0
  Mg  Mg7  1  0.329  0.171  0.371  1.0
  Mg  Mg8  1  0.329  0.171  0.879  1.0
  Mg  Mg9  1  0.329  0.657  0.371  1.0
  Mg  Mg10  1  0.329  0.657  0.879  1.0
  Mg  Mg11  1  0.843  0.171  0.371  1.0
  Mg  Mg12  1  0.843  0.171  0.879  1.0
  Mg  Mg13  1  0.833  0.667  0.376  1.0
  Mg  Mg14  1  0.833  0.667  0.874  1.0
  Nb  Nb15  1  0.167  0.333  0.125  1.0
[/CIF]
.