The material described by Mg6CeHf crystallizes in the orthorhombic Amm2 space group. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Ce(1), and two equivalent Hf(1) atoms to form MgCe2Hf2Mg8 cuboctahedra that share corners with four equivalent Ce(1)Hf2Mg10 cuboctahedra, corners with four equivalent Hf(1)Ce2Mg10 cuboctahedra, corners with ten equivalent Mg(1)Ce2Hf2Mg8 cuboctahedra, edges with two equivalent Mg(1)Ce2Hf2Mg8 cuboctahedra, edges with two equivalent Ce(1)Hf2Mg10 cuboctahedra, edges with two equivalent Hf(1)Ce2Mg10 cuboctahedra, edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Ce(1)Hf2Mg10 cuboctahedra, faces with two equivalent Hf(1)Ce2Mg10 cuboctahedra, and faces with four equivalent Mg(1)Ce2Hf2Mg8 cuboctahedra. In the second Mg site, Mg(2) is bonded in a 12-coordinate geometry to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Ce(1), and two equivalent Hf(1) atoms. In the third Mg site, Mg(3) is bonded in a 12-coordinate geometry to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Ce(1) atoms. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(3), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Hf(1) atoms to form distorted MgHf2Mg10 cuboctahedra that share corners with six equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with four equivalent Hf(1)Ce2Mg10 cuboctahedra, edges with eight equivalent Mg(1)Ce2Hf2Mg8 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Hf(1)Ce2Mg10 cuboctahedra, faces with four equivalent Mg(1)Ce2Hf2Mg8 cuboctahedra, and faces with six equivalent Ce(1)Hf2Mg10 cuboctahedra. Ce(1) is bonded to two equivalent Mg(3), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Hf(1) atoms to form CeHf2Mg10 cuboctahedra that share corners with four equivalent Hf(1)Ce2Mg10 cuboctahedra, corners with six equivalent Ce(1)Hf2Mg10 cuboctahedra, corners with eight equivalent Mg(1)Ce2Hf2Mg8 cuboctahedra, edges with two equivalent Hf(1)Ce2Mg10 cuboctahedra, edges with four equivalent Mg(1)Ce2Hf2Mg8 cuboctahedra, faces with two equivalent Ce(1)Hf2Mg10 cuboctahedra, faces with two equivalent Hf(1)Ce2Mg10 cuboctahedra, faces with four equivalent Mg(1)Ce2Hf2Mg8 cuboctahedra, and faces with six equivalent Mg(4)Hf2Mg10 cuboctahedra. Hf(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Ce(1) atoms to form distorted HfCe2Mg10 cuboctahedra that share corners with four equivalent Ce(1)Hf2Mg10 cuboctahedra, corners with six equivalent Hf(1)Ce2Mg10 cuboctahedra, corners with eight equivalent Mg(1)Ce2Hf2Mg8 cuboctahedra, edges with two equivalent Ce(1)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(1)Ce2Hf2Mg8 cuboctahedra, edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Ce(1)Hf2Mg10 cuboctahedra, faces with two equivalent Hf(1)Ce2Mg10 cuboctahedra, and faces with four equivalent Mg(1)Ce2Hf2Mg8 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_CeHfMg6
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.204
_cell_length_b   6.115
_cell_length_c   6.733
_cell_angle_alpha   117.007
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   190.882
_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
  Ce  Ce0  1  0.500  0.175  0.350  1.0
  Hf  Hf1  1  0.500  0.668  0.336  1.0
  Mg  Mg2  1  0.500  0.674  0.846  1.0
  Mg  Mg3  1  0.500  0.172  0.846  1.0
  Mg  Mg4  1  1.000  0.822  0.155  1.0
  Mg  Mg5  1  0.000  0.333  0.155  1.0
  Mg  Mg6  1  0.000  0.337  0.674  1.0
  Mg  Mg7  1  0.000  0.819  0.638  1.0
[/CIF]
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The material described by Mg6CeHf crystallizes in the orthorhombic Amm2 space group. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Ce(1), and two equivalent Hf(1) atoms to form MgCe2Hf2Mg8 cuboctahedra that share corners with four equivalent Ce(1)Hf2Mg10 cuboctahedra, corners with four equivalent Hf(1)Ce2Mg10 cuboctahedra, corners with ten equivalent Mg(1)Ce2Hf2Mg8 cuboctahedra, edges with two equivalent Mg(1)Ce2Hf2Mg8 cuboctahedra, edges with two equivalent Ce(1)Hf2Mg10 cuboctahedra, edges with two equivalent Hf(1)Ce2Mg10 cuboctahedra, edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Ce(1)Hf2Mg10 cuboctahedra, faces with two equivalent Hf(1)Ce2Mg10 cuboctahedra, and faces with four equivalent Mg(1)Ce2Hf2Mg8 cuboctahedra. In the second Mg site, Mg(2) is bonded in a 12-coordinate geometry to two equivalent Mg(1), two equivalent Mg(2), two equivalent Mg(3), two equivalent Mg(4), two equivalent Ce(1), and two equivalent Hf(1) atoms. In the third Mg site, Mg(3) is bonded in a 12-coordinate geometry to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Ce(1) atoms. In the fourth Mg site, Mg(4) is bonded to two equivalent Mg(3), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Hf(1) atoms to form distorted MgHf2Mg10 cuboctahedra that share corners with six equivalent Mg(4)Hf2Mg10 cuboctahedra, edges with four equivalent Hf(1)Ce2Mg10 cuboctahedra, edges with eight equivalent Mg(1)Ce2Hf2Mg8 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Hf(1)Ce2Mg10 cuboctahedra, faces with four equivalent Mg(1)Ce2Hf2Mg8 cuboctahedra, and faces with six equivalent Ce(1)Hf2Mg10 cuboctahedra. Ce(1) is bonded to two equivalent Mg(3), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Hf(1) atoms to form CeHf2Mg10 cuboctahedra that share corners with four equivalent Hf(1)Ce2Mg10 cuboctahedra, corners with six equivalent Ce(1)Hf2Mg10 cuboctahedra, corners with eight equivalent Mg(1)Ce2Hf2Mg8 cuboctahedra, edges with two equivalent Hf(1)Ce2Mg10 cuboctahedra, edges with four equivalent Mg(1)Ce2Hf2Mg8 cuboctahedra, faces with two equivalent Ce(1)Hf2Mg10 cuboctahedra, faces with two equivalent Hf(1)Ce2Mg10 cuboctahedra, faces with four equivalent Mg(1)Ce2Hf2Mg8 cuboctahedra, and faces with six equivalent Mg(4)Hf2Mg10 cuboctahedra. Hf(1) is bonded to two equivalent Mg(4), four equivalent Mg(1), four equivalent Mg(2), and two equivalent Ce(1) atoms to form distorted HfCe2Mg10 cuboctahedra that share corners with four equivalent Ce(1)Hf2Mg10 cuboctahedra, corners with six equivalent Hf(1)Ce2Mg10 cuboctahedra, corners with eight equivalent Mg(1)Ce2Hf2Mg8 cuboctahedra, edges with two equivalent Ce(1)Hf2Mg10 cuboctahedra, edges with four equivalent Mg(1)Ce2Hf2Mg8 cuboctahedra, edges with four equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Mg(4)Hf2Mg10 cuboctahedra, faces with two equivalent Ce(1)Hf2Mg10 cuboctahedra, faces with two equivalent Hf(1)Ce2Mg10 cuboctahedra, and faces with four equivalent Mg(1)Ce2Hf2Mg8 cuboctahedra. is represented by the Crystallographic Information File (CIF) [CIF]
data_CeHfMg6
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.204
_cell_length_b   6.115
_cell_length_c   6.733
_cell_angle_alpha   117.007
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   190.882
_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
  Ce  Ce0  1  0.500  0.175  0.350  1.0
  Hf  Hf1  1  0.500  0.668  0.336  1.0
  Mg  Mg2  1  0.500  0.674  0.846  1.0
  Mg  Mg3  1  0.500  0.172  0.846  1.0
  Mg  Mg4  1  1.000  0.822  0.155  1.0
  Mg  Mg5  1  0.000  0.333  0.155  1.0
  Mg  Mg6  1  0.000  0.337  0.674  1.0
  Mg  Mg7  1  0.000  0.819  0.638  1.0
[/CIF]
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