The compound described by BaMg6Hf crystallizes in the orthorhombic Amm2 space group. Ba(1) is bonded to two equivalent Mg(2), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Hf(1) atoms to form BaHf2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Ba2Mg10 cuboctahedra, corners with six equivalent Ba(1)Hf2Mg10 cuboctahedra, edges with two equivalent Mg(2)Ba2Mg10 cuboctahedra, edges with four equivalent Hf(1)Ba2Mg10 cuboctahedra, faces with two equivalent Ba(1)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(2)Ba2Mg10 cuboctahedra, faces with two equivalent Hf(1)Ba2Mg10 cuboctahedra, and faces with six equivalent Mg(4)Hf2Mg10 cuboctahedra. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded in a 11-coordinate geometry to two equivalent Ba(1), one Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), and two equivalent Hf(1) atoms. In the second Mg site, Mg(2) is bonded to two equivalent Ba(1), two equivalent Mg(4), four equivalent Mg(1), and four equivalent Mg(3) atoms to form distorted MgBa2Mg10 cuboctahedra that share corners with four equivalent Ba(1)Hf2Mg10 cuboctahedra, corners with six equivalent Mg(2)Ba2Mg10 cuboctahedra, edges with two equivalent Ba(1)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Ba(1)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(2)Ba2Mg10 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, and faces with six equivalent Hf(1)Ba2Mg10 cuboctahedra. In the third Mg site, Mg(3) is bonded in a 12-coordinate geometry to two equivalent Ba(1), two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), and two equivalent Hf(1) atoms. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(2), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Hf(1) atoms to form MgHf2Mg10 cuboctahedra that share corners with four equivalent Hf(1)Ba2Mg10 cuboctahedra, corners with six equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with two equivalent Hf(1)Ba2Mg10 cuboctahedra, edges with four equivalent Mg(2)Ba2Mg10 cuboctahedra, faces with two equivalent Mg(2)Ba2Mg10 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Hf(1)Ba2Mg10 cuboctahedra, and faces with six equivalent Ba(1)Hf2Mg10 cuboctahedra. Hf(1) is bonded to two equivalent Ba(1), two equivalent Mg(4), four equivalent Mg(1), and four equivalent Mg(3) atoms to form distorted HfBa2Mg10 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra, corners with six equivalent Hf(1)Ba2Mg10 cuboctahedra, edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with four equivalent Ba(1)Hf2Mg10 cuboctahedra, faces with two equivalent Ba(1)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Hf(1)Ba2Mg10 cuboctahedra, and faces with six equivalent Mg(2)Ba2Mg10 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_BaHfMg6
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.736
_cell_length_b   6.736
_cell_length_c   5.368
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.056
_symmetry_Int_Tables_number   1
_cell_volume   210.827
_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  0.167  0.833  0.000  1.0
  Hf  Hf1  1  0.346  0.654  0.500  1.0
  Mg  Mg2  1  0.180  0.351  0.000  1.0
  Mg  Mg3  1  0.649  0.820  0.000  1.0
  Mg  Mg4  1  0.666  0.334  0.000  1.0
  Mg  Mg5  1  0.341  0.184  0.500  1.0
  Mg  Mg6  1  0.816  0.659  0.500  1.0
  Mg  Mg7  1  0.836  0.164  0.500  1.0
[/CIF]
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The compound described by BaMg6Hf crystallizes in the orthorhombic Amm2 space group. Ba(1) is bonded to two equivalent Mg(2), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Hf(1) atoms to form BaHf2Mg10 cuboctahedra that share corners with four equivalent Mg(2)Ba2Mg10 cuboctahedra, corners with six equivalent Ba(1)Hf2Mg10 cuboctahedra, edges with two equivalent Mg(2)Ba2Mg10 cuboctahedra, edges with four equivalent Hf(1)Ba2Mg10 cuboctahedra, faces with two equivalent Ba(1)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(2)Ba2Mg10 cuboctahedra, faces with two equivalent Hf(1)Ba2Mg10 cuboctahedra, and faces with six equivalent Mg(4)Hf2Mg10 cuboctahedra. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded in a 11-coordinate geometry to two equivalent Ba(1), one Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), and two equivalent Hf(1) atoms. In the second Mg site, Mg(2) is bonded to two equivalent Ba(1), two equivalent Mg(4), four equivalent Mg(1), and four equivalent Mg(3) atoms to form distorted MgBa2Mg10 cuboctahedra that share corners with four equivalent Ba(1)Hf2Mg10 cuboctahedra, corners with six equivalent Mg(2)Ba2Mg10 cuboctahedra, edges with two equivalent Ba(1)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Ba(1)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(2)Ba2Mg10 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, and faces with six equivalent Hf(1)Ba2Mg10 cuboctahedra. In the third Mg site, Mg(3) is bonded in a 12-coordinate geometry to two equivalent Ba(1), two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), and two equivalent Hf(1) atoms. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(2), four equivalent Mg(1), four equivalent Mg(3), and two equivalent Hf(1) atoms to form MgHf2Mg10 cuboctahedra that share corners with four equivalent Hf(1)Ba2Mg10 cuboctahedra, corners with six equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with two equivalent Hf(1)Ba2Mg10 cuboctahedra, edges with four equivalent Mg(2)Ba2Mg10 cuboctahedra, faces with two equivalent Mg(2)Ba2Mg10 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Hf(1)Ba2Mg10 cuboctahedra, and faces with six equivalent Ba(1)Hf2Mg10 cuboctahedra. Hf(1) is bonded to two equivalent Ba(1), two equivalent Mg(4), four equivalent Mg(1), and four equivalent Mg(3) atoms to form distorted HfBa2Mg10 cuboctahedra that share corners with four equivalent Mg(4)Hf2Mg10 cuboctahedra, corners with six equivalent Hf(1)Ba2Mg10 cuboctahedra, edges with two equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with four equivalent Ba(1)Hf2Mg10 cuboctahedra, faces with two equivalent Ba(1)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Hf(1)Ba2Mg10 cuboctahedra, and faces with six equivalent Mg(2)Ba2Mg10 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_BaHfMg6
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.736
_cell_length_b   6.736
_cell_length_c   5.368
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.056
_symmetry_Int_Tables_number   1
_cell_volume   210.827
_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  0.167  0.833  0.000  1.0
  Hf  Hf1  1  0.346  0.654  0.500  1.0
  Mg  Mg2  1  0.180  0.351  0.000  1.0
  Mg  Mg3  1  0.649  0.820  0.000  1.0
  Mg  Mg4  1  0.666  0.334  0.000  1.0
  Mg  Mg5  1  0.341  0.184  0.500  1.0
  Mg  Mg6  1  0.816  0.659  0.500  1.0
  Mg  Mg7  1  0.836  0.164  0.500  1.0
[/CIF]
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