The compound described by BaMg6Hf crystallizes in the tetragonal P4/mmm space group. Ba(1) is bonded to four equivalent Mg(1) and eight equivalent Mg(2) atoms to form BaMg12 cuboctahedra that share corners with four equivalent Ba(1)Mg12 cuboctahedra, corners with eight equivalent Hf(1)Mg12 cuboctahedra, edges with eight equivalent Mg(1)Ba2Hf2Mg8 cuboctahedra, faces with two equivalent Ba(1)Mg12 cuboctahedra, faces with four equivalent Mg(1)Ba2Hf2Mg8 cuboctahedra, and faces with four equivalent Hf(1)Mg12 cuboctahedra. There are two inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Ba(1), eight equivalent Mg(2), and two equivalent Hf(1) atoms to form distorted MgBa2Hf2Mg8 cuboctahedra that share corners with twelve equivalent Mg(1)Ba2Hf2Mg8 cuboctahedra, edges with four equivalent Ba(1)Mg12 cuboctahedra, edges with four equivalent Hf(1)Mg12 cuboctahedra, faces with two equivalent Ba(1)Mg12 cuboctahedra, faces with two equivalent Hf(1)Mg12 cuboctahedra, and faces with six equivalent Mg(1)Ba2Hf2Mg8 cuboctahedra. In the second Mg site, Mg(2) is bonded in a 10-coordinate geometry to two equivalent Ba(1), two equivalent Mg(2), four equivalent Mg(1), and two equivalent Hf(1) atoms. Hf(1) is bonded to four equivalent Mg(1) and eight equivalent Mg(2) atoms to form HfMg12 cuboctahedra that share corners with four equivalent Hf(1)Mg12 cuboctahedra, corners with eight equivalent Ba(1)Mg12 cuboctahedra, edges with eight equivalent Mg(1)Ba2Hf2Mg8 cuboctahedra, faces with two equivalent Hf(1)Mg12 cuboctahedra, faces with four equivalent Ba(1)Mg12 cuboctahedra, and faces with four equivalent Mg(1)Ba2Hf2Mg8 cuboctahedra. is represented by the CIF file [CIF]
data_BaHfMg6
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.701
_cell_length_b   6.701
_cell_length_c   4.767
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   214.007
_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
  Ba  Ba0  1  0.500  0.500  0.500  1.0
  Hf  Hf1  1  0.000  0.000  0.500  1.0
  Mg  Mg2  1  0.500  0.000  0.500  1.0
  Mg  Mg3  1  0.000  0.500  0.500  1.0
  Mg  Mg4  1  0.221  0.779  0.000  1.0
  Mg  Mg5  1  0.779  0.221  0.000  1.0
  Mg  Mg6  1  0.221  0.221  0.000  1.0
  Mg  Mg7  1  0.779  0.779  0.000  1.0
[/CIF]
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The compound described by BaMg6Hf crystallizes in the tetragonal P4/mmm space group. Ba(1) is bonded to four equivalent Mg(1) and eight equivalent Mg(2) atoms to form BaMg12 cuboctahedra that share corners with four equivalent Ba(1)Mg12 cuboctahedra, corners with eight equivalent Hf(1)Mg12 cuboctahedra, edges with eight equivalent Mg(1)Ba2Hf2Mg8 cuboctahedra, faces with two equivalent Ba(1)Mg12 cuboctahedra, faces with four equivalent Mg(1)Ba2Hf2Mg8 cuboctahedra, and faces with four equivalent Hf(1)Mg12 cuboctahedra. There are two inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Ba(1), eight equivalent Mg(2), and two equivalent Hf(1) atoms to form distorted MgBa2Hf2Mg8 cuboctahedra that share corners with twelve equivalent Mg(1)Ba2Hf2Mg8 cuboctahedra, edges with four equivalent Ba(1)Mg12 cuboctahedra, edges with four equivalent Hf(1)Mg12 cuboctahedra, faces with two equivalent Ba(1)Mg12 cuboctahedra, faces with two equivalent Hf(1)Mg12 cuboctahedra, and faces with six equivalent Mg(1)Ba2Hf2Mg8 cuboctahedra. In the second Mg site, Mg(2) is bonded in a 10-coordinate geometry to two equivalent Ba(1), two equivalent Mg(2), four equivalent Mg(1), and two equivalent Hf(1) atoms. Hf(1) is bonded to four equivalent Mg(1) and eight equivalent Mg(2) atoms to form HfMg12 cuboctahedra that share corners with four equivalent Hf(1)Mg12 cuboctahedra, corners with eight equivalent Ba(1)Mg12 cuboctahedra, edges with eight equivalent Mg(1)Ba2Hf2Mg8 cuboctahedra, faces with two equivalent Hf(1)Mg12 cuboctahedra, faces with four equivalent Ba(1)Mg12 cuboctahedra, and faces with four equivalent Mg(1)Ba2Hf2Mg8 cuboctahedra. is represented by the CIF file [CIF]
data_BaHfMg6
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.701
_cell_length_b   6.701
_cell_length_c   4.767
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   214.007
_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
  Ba  Ba0  1  0.500  0.500  0.500  1.0
  Hf  Hf1  1  0.000  0.000  0.500  1.0
  Mg  Mg2  1  0.500  0.000  0.500  1.0
  Mg  Mg3  1  0.000  0.500  0.500  1.0
  Mg  Mg4  1  0.221  0.779  0.000  1.0
  Mg  Mg5  1  0.779  0.221  0.000  1.0
  Mg  Mg6  1  0.221  0.221  0.000  1.0
  Mg  Mg7  1  0.779  0.779  0.000  1.0
[/CIF]
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