The compound described by Mg14HfB crystallizes in the hexagonal P-6m2 space group. There are six inequivalent Mg sites. In the first Mg site, Mg(1) is bonded in a 10-coordinate geometry to two equivalent Mg(4) and four Mg(3,3) atoms. In the second Mg site, Mg(2) is bonded to two equivalent Mg(4); four Mg(2,2); four Mg(3,3); and two equivalent Hf(1) atoms to form MgHf2Mg10 cuboctahedra that share corners with six equivalent Mg(2)Hf2Mg10 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; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Hf(1)Mg12 cuboctahedra; and faces with four Mg(2,2)Hf2Mg10 cuboctahedra. In the third 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 six equivalent Mg(2)Hf2Mg10 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, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Hf(1)Mg12 cuboctahedra, and faces with four equivalent Mg(2)Hf2Mg10 cuboctahedra. In the fourth Mg site, Mg(3) is bonded in a 12-coordinate geometry to two equivalent Mg(1); two equivalent Mg(2); two equivalent Mg(4); four Mg(3,3); one Hf(1); and one B(1) atom. In the fifth Mg site, Mg(3) is bonded in a 12-coordinate geometry to two equivalent Mg(1); two Mg(2,2); two equivalent Mg(4); four equivalent Mg(3); one Hf(1); and one B(1) atom. In the sixth Mg site, Mg(4) is bonded to three equivalent Mg(1); three Mg(2,2); and six Mg(3,3) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(4)Mg12 cuboctahedra; edges with six Mg(2,2)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three Mg(2,2)Hf2Mg10 cuboctahedra; and faces with three equivalent Hf(1)Mg12 cuboctahedra. Hf(1) is bonded to six Mg(2,2) and six Mg(3,3) atoms to form HfMg12 cuboctahedra that share corners with six equivalent Hf(1)Mg12 cuboctahedra; edges with six Mg(2,2)Hf2Mg10 cuboctahedra; faces with six Mg(2,2)Hf2Mg10 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. B(1) is bonded in a 6-coordinate geometry to six Mg(3,3) atoms. is represented by the Crystallographic Information File (CIF) [CIF]
data_HfMg14B
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.263
_cell_length_b   6.263
_cell_length_c   9.971
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   338.710
_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  0.161  0.831  0.125  1.0
  Mg  Mg2  1  0.176  0.838  0.625  1.0
  Mg  Mg3  1  0.669  0.339  0.125  1.0
  Mg  Mg4  1  0.662  0.324  0.625  1.0
  Mg  Mg5  1  0.669  0.831  0.125  1.0
  Mg  Mg6  1  0.662  0.838  0.625  1.0
  Mg  Mg7  1  0.325  0.175  0.365  1.0
  Mg  Mg8  1  0.325  0.175  0.885  1.0
  Mg  Mg9  1  0.325  0.650  0.365  1.0
  Mg  Mg10  1  0.325  0.650  0.885  1.0
  Mg  Mg11  1  0.850  0.175  0.365  1.0
  Mg  Mg12  1  0.850  0.175  0.885  1.0
  Mg  Mg13  1  0.833  0.667  0.384  1.0
  Mg  Mg14  1  0.833  0.667  0.866  1.0
  B  B15  1  0.167  0.333  0.125  1.0
[/CIF]
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The compound described by Mg14HfB crystallizes in the hexagonal P-6m2 space group. There are six inequivalent Mg sites. In the first Mg site, Mg(1) is bonded in a 10-coordinate geometry to two equivalent Mg(4) and four Mg(3,3) atoms. In the second Mg site, Mg(2) is bonded to two equivalent Mg(4); four Mg(2,2); four Mg(3,3); and two equivalent Hf(1) atoms to form MgHf2Mg10 cuboctahedra that share corners with six equivalent Mg(2)Hf2Mg10 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; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with two equivalent Hf(1)Mg12 cuboctahedra; and faces with four Mg(2,2)Hf2Mg10 cuboctahedra. In the third 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 six equivalent Mg(2)Hf2Mg10 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, faces with two equivalent Mg(4)Mg12 cuboctahedra, faces with two equivalent Hf(1)Mg12 cuboctahedra, and faces with four equivalent Mg(2)Hf2Mg10 cuboctahedra. In the fourth Mg site, Mg(3) is bonded in a 12-coordinate geometry to two equivalent Mg(1); two equivalent Mg(2); two equivalent Mg(4); four Mg(3,3); one Hf(1); and one B(1) atom. In the fifth Mg site, Mg(3) is bonded in a 12-coordinate geometry to two equivalent Mg(1); two Mg(2,2); two equivalent Mg(4); four equivalent Mg(3); one Hf(1); and one B(1) atom. In the sixth Mg site, Mg(4) is bonded to three equivalent Mg(1); three Mg(2,2); and six Mg(3,3) atoms to form MgMg12 cuboctahedra that share corners with six equivalent Mg(4)Mg12 cuboctahedra; edges with six Mg(2,2)Hf2Mg10 cuboctahedra; faces with two equivalent Mg(4)Mg12 cuboctahedra; faces with three Mg(2,2)Hf2Mg10 cuboctahedra; and faces with three equivalent Hf(1)Mg12 cuboctahedra. Hf(1) is bonded to six Mg(2,2) and six Mg(3,3) atoms to form HfMg12 cuboctahedra that share corners with six equivalent Hf(1)Mg12 cuboctahedra; edges with six Mg(2,2)Hf2Mg10 cuboctahedra; faces with six Mg(2,2)Hf2Mg10 cuboctahedra; and faces with six equivalent Mg(4)Mg12 cuboctahedra. B(1) is bonded in a 6-coordinate geometry to six Mg(3,3) atoms. is represented by the Crystallographic Information File (CIF) [CIF]
data_HfMg14B
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.263
_cell_length_b   6.263
_cell_length_c   9.971
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   338.710
_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  0.161  0.831  0.125  1.0
  Mg  Mg2  1  0.176  0.838  0.625  1.0
  Mg  Mg3  1  0.669  0.339  0.125  1.0
  Mg  Mg4  1  0.662  0.324  0.625  1.0
  Mg  Mg5  1  0.669  0.831  0.125  1.0
  Mg  Mg6  1  0.662  0.838  0.625  1.0
  Mg  Mg7  1  0.325  0.175  0.365  1.0
  Mg  Mg8  1  0.325  0.175  0.885  1.0
  Mg  Mg9  1  0.325  0.650  0.365  1.0
  Mg  Mg10  1  0.325  0.650  0.885  1.0
  Mg  Mg11  1  0.850  0.175  0.365  1.0
  Mg  Mg12  1  0.850  0.175  0.885  1.0
  Mg  Mg13  1  0.833  0.667  0.384  1.0
  Mg  Mg14  1  0.833  0.667  0.866  1.0
  B  B15  1  0.167  0.333  0.125  1.0
[/CIF]
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