The material described by Mg6HfBiO8 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(2) and four equivalent O(3) atoms to form MgO6 octahedra that share corners with four equivalent Mg(1)O6 octahedra and edges with eight equivalent Mg(3)O5 trigonal bipyramids. The corner-sharing octahedra are not tilted. In the second Mg site, Mg(2) is bonded in a square co-planar geometry to four equivalent O(4) atoms. In the third Mg site, Mg(3) is bonded to one O(3), two equivalent O(1), and two equivalent O(2) atoms to form distorted MgO5 trigonal bipyramids that share corners with two equivalent Hf(1)O6 octahedra, corners with five equivalent Mg(3)O5 trigonal bipyramids, edges with two equivalent Mg(1)O6 octahedra, and edges with four equivalent Mg(3)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 71°. Hf(1) is bonded to two equivalent O(1) and four equivalent O(4) atoms to form HfO6 octahedra that share corners with four equivalent Hf(1)O6 octahedra and corners with eight equivalent Mg(3)O5 trigonal bipyramids. The corner-sharing octahedra are not tilted. Bi(1) is bonded in a square co-planar geometry to four equivalent O(3) atoms. There are four inequivalent O sites. In the first O site, O(1) is bonded in a 5-coordinate geometry to four equivalent Mg(3) and one Hf(1) atom. In the second O site, O(2) is bonded to one Mg(1) and four equivalent Mg(3) atoms to form OMg5 square pyramids that share corners with five equivalent O(2)Mg5 square pyramids and edges with four equivalent O(3)Mg4Bi2 octahedra. In the third O site, O(3) is bonded to two equivalent Mg(1), two equivalent Mg(3), and two equivalent Bi(1) atoms to form OMg4Bi2 octahedra that share corners with four equivalent O(3)Mg4Bi2 octahedra, edges with four equivalent O(3)Mg4Bi2 octahedra, and edges with four equivalent O(2)Mg5 square pyramids. The corner-sharing octahedra are not tilted. In the fourth O site, O(4) is bonded in a square co-planar geometry to two equivalent Mg(2) and two equivalent Hf(1) atoms. is represented by the CIF card [CIF]
data_HfMg6BiO8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   10.467
_cell_length_b   4.404
_cell_length_c   4.404
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   202.993
_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  0.500  0.000  0.000  1.0
  Mg  Mg1  1  0.000  0.500  0.500  1.0
  Mg  Mg2  1  0.500  0.500  0.500  1.0
  Mg  Mg3  1  0.231  0.000  0.500  1.0
  Mg  Mg4  1  0.769  0.000  0.500  1.0
  Mg  Mg5  1  0.231  0.500  0.000  1.0
  Mg  Mg6  1  0.769  0.500  0.000  1.0
  Bi  Bi7  1  0.000  0.000  0.000  1.0
  O  O8  1  0.304  0.000  0.000  1.0
  O  O9  1  0.696  0.000  0.000  1.0
  O  O10  1  0.213  0.500  0.500  1.0
  O  O11  1  0.787  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 material described by Mg6HfBiO8 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(2) and four equivalent O(3) atoms to form MgO6 octahedra that share corners with four equivalent Mg(1)O6 octahedra and edges with eight equivalent Mg(3)O5 trigonal bipyramids. The corner-sharing octahedra are not tilted. In the second Mg site, Mg(2) is bonded in a square co-planar geometry to four equivalent O(4) atoms. In the third Mg site, Mg(3) is bonded to one O(3), two equivalent O(1), and two equivalent O(2) atoms to form distorted MgO5 trigonal bipyramids that share corners with two equivalent Hf(1)O6 octahedra, corners with five equivalent Mg(3)O5 trigonal bipyramids, edges with two equivalent Mg(1)O6 octahedra, and edges with four equivalent Mg(3)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles are 71°. Hf(1) is bonded to two equivalent O(1) and four equivalent O(4) atoms to form HfO6 octahedra that share corners with four equivalent Hf(1)O6 octahedra and corners with eight equivalent Mg(3)O5 trigonal bipyramids. The corner-sharing octahedra are not tilted. Bi(1) is bonded in a square co-planar geometry to four equivalent O(3) atoms. There are four inequivalent O sites. In the first O site, O(1) is bonded in a 5-coordinate geometry to four equivalent Mg(3) and one Hf(1) atom. In the second O site, O(2) is bonded to one Mg(1) and four equivalent Mg(3) atoms to form OMg5 square pyramids that share corners with five equivalent O(2)Mg5 square pyramids and edges with four equivalent O(3)Mg4Bi2 octahedra. In the third O site, O(3) is bonded to two equivalent Mg(1), two equivalent Mg(3), and two equivalent Bi(1) atoms to form OMg4Bi2 octahedra that share corners with four equivalent O(3)Mg4Bi2 octahedra, edges with four equivalent O(3)Mg4Bi2 octahedra, and edges with four equivalent O(2)Mg5 square pyramids. The corner-sharing octahedra are not tilted. In the fourth O site, O(4) is bonded in a square co-planar geometry to two equivalent Mg(2) and two equivalent Hf(1) atoms. is represented by the CIF card [CIF]
data_HfMg6BiO8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   10.467
_cell_length_b   4.404
_cell_length_c   4.404
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   202.993
_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  0.500  0.000  0.000  1.0
  Mg  Mg1  1  0.000  0.500  0.500  1.0
  Mg  Mg2  1  0.500  0.500  0.500  1.0
  Mg  Mg3  1  0.231  0.000  0.500  1.0
  Mg  Mg4  1  0.769  0.000  0.500  1.0
  Mg  Mg5  1  0.231  0.500  0.000  1.0
  Mg  Mg6  1  0.769  0.500  0.000  1.0
  Bi  Bi7  1  0.000  0.000  0.000  1.0
  O  O8  1  0.304  0.000  0.000  1.0
  O  O9  1  0.696  0.000  0.000  1.0
  O  O10  1  0.213  0.500  0.500  1.0
  O  O11  1  0.787  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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