The crystal structure described by Mg6HfCO8 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 corner-sharing MgO6 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 Mg(1)O6 octahedra, corners with four equivalent Mg(2)O6 octahedra, and edges with four equivalent Hf(1)O6 octahedra. The corner-sharing octahedra are not tilted. In the third Mg site, Mg(3) is bonded in a 6-coordinate geometry to one O(3), one O(4), two equivalent O(1), and two equivalent O(2) atoms. 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 edges with four equivalent Mg(2)O6 octahedra. The corner-sharing octahedra are not tilted. C(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 to four equivalent Mg(3) and one Hf(1) atom to form distorted OHfMg4 trigonal bipyramids that share corners with five equivalent O(1)HfMg4 trigonal bipyramids, edges with four equivalent O(4)Hf2Mg4 octahedra, and edges with four equivalent O(2)Mg6 octahedra. In the second O site, O(2) is bonded to one Mg(1), one Mg(2), and four equivalent Mg(3) atoms to form OMg6 octahedra that share corners with six equivalent O(2)Mg6 octahedra, edges with four equivalent O(4)Hf2Mg4 octahedra, and edges with four equivalent O(1)HfMg4 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 0-12°. In the third O site, O(3) is bonded in a distorted square co-planar geometry to two equivalent Mg(1), two equivalent Mg(3), and two equivalent C(1) atoms. In the fourth O site, O(4) is bonded to two equivalent Mg(2), two equivalent Mg(3), and two equivalent Hf(1) atoms to form distorted OHf2Mg4 octahedra that share corners with four equivalent O(4)Hf2Mg4 octahedra, edges with four equivalent O(4)Hf2Mg4 octahedra, edges with four equivalent O(2)Mg6 octahedra, and edges with four equivalent O(1)HfMg4 trigonal bipyramids. The corner-sharing octahedra are not tilted. is represented by the CIF card [CIF]
data_HfMg6CO8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   9.360
_cell_length_b   4.251
_cell_length_c   4.251
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   169.109
_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  0.219  0.000  0.500  1.0
  Mg  Mg4  1  0.781  0.000  0.500  1.0
  Mg  Mg5  1  0.219  0.500  0.000  1.0
  Mg  Mg6  1  0.781  0.500  0.000  1.0
  C  C7  1  0.000  0.000  0.000  1.0
  O  O8  1  0.282  0.000  0.000  1.0
  O  O9  1  0.718  0.000  0.000  1.0
  O  O10  1  0.243  0.500  0.500  1.0
  O  O11  1  0.757  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 Mg6HfCO8 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 corner-sharing MgO6 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 Mg(1)O6 octahedra, corners with four equivalent Mg(2)O6 octahedra, and edges with four equivalent Hf(1)O6 octahedra. The corner-sharing octahedra are not tilted. In the third Mg site, Mg(3) is bonded in a 6-coordinate geometry to one O(3), one O(4), two equivalent O(1), and two equivalent O(2) atoms. 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 edges with four equivalent Mg(2)O6 octahedra. The corner-sharing octahedra are not tilted. C(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 to four equivalent Mg(3) and one Hf(1) atom to form distorted OHfMg4 trigonal bipyramids that share corners with five equivalent O(1)HfMg4 trigonal bipyramids, edges with four equivalent O(4)Hf2Mg4 octahedra, and edges with four equivalent O(2)Mg6 octahedra. In the second O site, O(2) is bonded to one Mg(1), one Mg(2), and four equivalent Mg(3) atoms to form OMg6 octahedra that share corners with six equivalent O(2)Mg6 octahedra, edges with four equivalent O(4)Hf2Mg4 octahedra, and edges with four equivalent O(1)HfMg4 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 0-12°. In the third O site, O(3) is bonded in a distorted square co-planar geometry to two equivalent Mg(1), two equivalent Mg(3), and two equivalent C(1) atoms. In the fourth O site, O(4) is bonded to two equivalent Mg(2), two equivalent Mg(3), and two equivalent Hf(1) atoms to form distorted OHf2Mg4 octahedra that share corners with four equivalent O(4)Hf2Mg4 octahedra, edges with four equivalent O(4)Hf2Mg4 octahedra, edges with four equivalent O(2)Mg6 octahedra, and edges with four equivalent O(1)HfMg4 trigonal bipyramids. The corner-sharing octahedra are not tilted. is represented by the CIF card [CIF]
data_HfMg6CO8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   9.360
_cell_length_b   4.251
_cell_length_c   4.251
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   169.109
_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  0.219  0.000  0.500  1.0
  Mg  Mg4  1  0.781  0.000  0.500  1.0
  Mg  Mg5  1  0.219  0.500  0.000  1.0
  Mg  Mg6  1  0.781  0.500  0.000  1.0
  C  C7  1  0.000  0.000  0.000  1.0
  O  O8  1  0.282  0.000  0.000  1.0
  O  O9  1  0.718  0.000  0.000  1.0
  O  O10  1  0.243  0.500  0.500  1.0
  O  O11  1  0.757  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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