The crystal structure described by Mg6CeHfO8 is Caswellsilverite-derived structured and crystallizes in the tetragonal P4/mmm space group. There are three inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent O(1) and four equivalent O(4) atoms to form MgO6 octahedra that share corners with two equivalent Ce(1)O6 octahedra, corners with four equivalent Mg(1)O6 octahedra, edges with four equivalent Mg(2)O6 octahedra, and edges with eight equivalent Mg(3)O6 octahedra. The corner-sharing octahedra are not tilted. In the second Mg site, Mg(2) is bonded to two equivalent O(2) and four equivalent O(4) atoms to form MgO6 octahedra that share corners with two equivalent Hf(1)O6 octahedra, corners with four equivalent Mg(2)O6 octahedra, edges with four equivalent Mg(1)O6 octahedra, and edges with eight equivalent Mg(3)O6 octahedra. The corner-sharing octahedra are not tilted. In the third Mg site, Mg(3) is bonded to one O(3), one O(4), two equivalent O(1), and two equivalent O(2) atoms to form MgO6 octahedra that share corners with six equivalent Mg(3)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Mg(2)O6 octahedra, edges with two equivalent Ce(1)O6 octahedra, edges with two equivalent Hf(1)O6 octahedra, and edges with four equivalent Mg(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-3°. Ce(1) is bonded to two equivalent O(1) and four equivalent O(3) atoms to form CeO6 octahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with four equivalent Ce(1)O6 octahedra, edges with four equivalent Hf(1)O6 octahedra, and edges with eight equivalent Mg(3)O6 octahedra. The corner-sharing octahedra are not tilted. Hf(1) is bonded to two equivalent O(2) and four equivalent O(3) atoms to form HfO6 octahedra that share corners with two equivalent Mg(2)O6 octahedra, corners with four equivalent Hf(1)O6 octahedra, edges with four equivalent Ce(1)O6 octahedra, and edges with eight equivalent Mg(3)O6 octahedra. The corner-sharing octahedra are not tilted. There are four inequivalent O sites. In the first O site, O(1) is bonded to one Mg(1), four equivalent Mg(3), and one Ce(1) atom to form OCeMg5 octahedra that share corners with six equivalent O(1)CeMg5 octahedra, edges with four equivalent O(3)Ce2Hf2Mg2 octahedra, edges with four equivalent O(2)HfMg5 octahedra, and edges with four equivalent O(4)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 0-1°. In the second O site, O(2) is bonded to one Mg(2), four equivalent Mg(3), and one Hf(1) atom to form OHfMg5 octahedra that share corners with six equivalent O(2)HfMg5 octahedra, edges with four equivalent O(3)Ce2Hf2Mg2 octahedra, edges with four equivalent O(1)CeMg5 octahedra, and edges with four equivalent O(4)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 0-3°. In the third O site, O(3) is bonded to two equivalent Mg(3), two equivalent Ce(1), and two equivalent Hf(1) atoms to form OCe2Hf2Mg2 octahedra that share corners with two equivalent O(4)Mg6 octahedra, corners with four equivalent O(3)Ce2Hf2Mg2 octahedra, edges with four equivalent O(3)Ce2Hf2Mg2 octahedra, edges with four equivalent O(1)CeMg5 octahedra, and edges with four equivalent O(2)HfMg5 octahedra. The corner-sharing octahedra are not tilted. In the fourth O site, O(4) is bonded to two equivalent Mg(1), two equivalent Mg(2), and two equivalent Mg(3) atoms to form OMg6 octahedra that share corners with two equivalent O(3)Ce2Hf2Mg2 octahedra, corners with four equivalent O(4)Mg6 octahedra, edges with four equivalent O(1)CeMg5 octahedra, edges with four equivalent O(2)HfMg5 octahedra, and edges with four equivalent O(4)Mg6 octahedra. The corner-sharing octahedra are not tilted. is represented by the CIF file [CIF]
data_CeHfMg6O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   9.057
_cell_length_b   4.486
_cell_length_c   4.486
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   182.274
_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  0.000  0.000  0.000  1.0
  Hf  Hf1  1  0.000  0.500  0.500  1.0
  Mg  Mg2  1  0.500  0.000  0.000  1.0
  Mg  Mg3  1  0.500  0.500  0.500  1.0
  Mg  Mg4  1  0.270  0.000  0.500  1.0
  Mg  Mg5  1  0.730  0.000  0.500  1.0
  Mg  Mg6  1  0.270  0.500  0.000  1.0
  Mg  Mg7  1  0.730  0.500  0.000  1.0
  O  O8  1  0.273  0.000  0.000  1.0
  O  O9  1  0.727  0.000  0.000  1.0
  O  O10  1  0.264  0.500  0.500  1.0
  O  O11  1  0.736  0.500  0.500  1.0
  O  O12  1  0.000  0.000  0.500  1.0
  O  O13  1  0.500  0.000  0.500  1.0
  O  O14  1  0.000  0.500  0.000  1.0
  O  O15  1  0.500  0.500  0.000  1.0
[/CIF]
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The crystal structure described by Mg6CeHfO8 is Caswellsilverite-derived structured and crystallizes in the tetragonal P4/mmm space group. There are three inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent O(1) and four equivalent O(4) atoms to form MgO6 octahedra that share corners with two equivalent Ce(1)O6 octahedra, corners with four equivalent Mg(1)O6 octahedra, edges with four equivalent Mg(2)O6 octahedra, and edges with eight equivalent Mg(3)O6 octahedra. The corner-sharing octahedra are not tilted. In the second Mg site, Mg(2) is bonded to two equivalent O(2) and four equivalent O(4) atoms to form MgO6 octahedra that share corners with two equivalent Hf(1)O6 octahedra, corners with four equivalent Mg(2)O6 octahedra, edges with four equivalent Mg(1)O6 octahedra, and edges with eight equivalent Mg(3)O6 octahedra. The corner-sharing octahedra are not tilted. In the third Mg site, Mg(3) is bonded to one O(3), one O(4), two equivalent O(1), and two equivalent O(2) atoms to form MgO6 octahedra that share corners with six equivalent Mg(3)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Mg(2)O6 octahedra, edges with two equivalent Ce(1)O6 octahedra, edges with two equivalent Hf(1)O6 octahedra, and edges with four equivalent Mg(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-3°. Ce(1) is bonded to two equivalent O(1) and four equivalent O(3) atoms to form CeO6 octahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with four equivalent Ce(1)O6 octahedra, edges with four equivalent Hf(1)O6 octahedra, and edges with eight equivalent Mg(3)O6 octahedra. The corner-sharing octahedra are not tilted. Hf(1) is bonded to two equivalent O(2) and four equivalent O(3) atoms to form HfO6 octahedra that share corners with two equivalent Mg(2)O6 octahedra, corners with four equivalent Hf(1)O6 octahedra, edges with four equivalent Ce(1)O6 octahedra, and edges with eight equivalent Mg(3)O6 octahedra. The corner-sharing octahedra are not tilted. There are four inequivalent O sites. In the first O site, O(1) is bonded to one Mg(1), four equivalent Mg(3), and one Ce(1) atom to form OCeMg5 octahedra that share corners with six equivalent O(1)CeMg5 octahedra, edges with four equivalent O(3)Ce2Hf2Mg2 octahedra, edges with four equivalent O(2)HfMg5 octahedra, and edges with four equivalent O(4)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 0-1°. In the second O site, O(2) is bonded to one Mg(2), four equivalent Mg(3), and one Hf(1) atom to form OHfMg5 octahedra that share corners with six equivalent O(2)HfMg5 octahedra, edges with four equivalent O(3)Ce2Hf2Mg2 octahedra, edges with four equivalent O(1)CeMg5 octahedra, and edges with four equivalent O(4)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 0-3°. In the third O site, O(3) is bonded to two equivalent Mg(3), two equivalent Ce(1), and two equivalent Hf(1) atoms to form OCe2Hf2Mg2 octahedra that share corners with two equivalent O(4)Mg6 octahedra, corners with four equivalent O(3)Ce2Hf2Mg2 octahedra, edges with four equivalent O(3)Ce2Hf2Mg2 octahedra, edges with four equivalent O(1)CeMg5 octahedra, and edges with four equivalent O(2)HfMg5 octahedra. The corner-sharing octahedra are not tilted. In the fourth O site, O(4) is bonded to two equivalent Mg(1), two equivalent Mg(2), and two equivalent Mg(3) atoms to form OMg6 octahedra that share corners with two equivalent O(3)Ce2Hf2Mg2 octahedra, corners with four equivalent O(4)Mg6 octahedra, edges with four equivalent O(1)CeMg5 octahedra, edges with four equivalent O(2)HfMg5 octahedra, and edges with four equivalent O(4)Mg6 octahedra. The corner-sharing octahedra are not tilted. is represented by the CIF file [CIF]
data_CeHfMg6O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   9.057
_cell_length_b   4.486
_cell_length_c   4.486
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   182.274
_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  0.000  0.000  0.000  1.0
  Hf  Hf1  1  0.000  0.500  0.500  1.0
  Mg  Mg2  1  0.500  0.000  0.000  1.0
  Mg  Mg3  1  0.500  0.500  0.500  1.0
  Mg  Mg4  1  0.270  0.000  0.500  1.0
  Mg  Mg5  1  0.730  0.000  0.500  1.0
  Mg  Mg6  1  0.270  0.500  0.000  1.0
  Mg  Mg7  1  0.730  0.500  0.000  1.0
  O  O8  1  0.273  0.000  0.000  1.0
  O  O9  1  0.727  0.000  0.000  1.0
  O  O10  1  0.264  0.500  0.500  1.0
  O  O11  1  0.736  0.500  0.500  1.0
  O  O12  1  0.000  0.000  0.500  1.0
  O  O13  1  0.500  0.000  0.500  1.0
  O  O14  1  0.000  0.500  0.000  1.0
  O  O15  1  0.500  0.500  0.000  1.0
[/CIF]
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