The structure described by Mg6HfBO7 crystallizes in the tetragonal P4mm space group. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one B(1), one O(1), and four equivalent O(5) atoms to form distorted MgBO5 square pyramids that share corners with four equivalent Mg(1)BO5 square pyramids, edges with four equivalent Mg(3)B2O4 octahedra, edges with four equivalent Mg(2)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. In the second Mg site, Mg(2) is bonded to one O(2), one O(3), and four equivalent O(5) 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(3)B2O4 octahedra, edges with four equivalent Mg(4)O6 octahedra, and edges with four equivalent Mg(1)BO5 square pyramids. The corner-sharing octahedral tilt angles range from 0-1°. In the third Mg site, Mg(3) is bonded to two equivalent B(1), one O(4), one O(5), and two equivalent O(2) atoms to form MgB2O4 octahedra that share corners with two equivalent Mg(4)O6 octahedra, corners with four equivalent Mg(3)B2O4 octahedra, edges with two equivalent Mg(2)O6 octahedra, edges with two equivalent Hf(1)O6 octahedra, edges with four equivalent Mg(3)B2O4 octahedra, and edges with two equivalent Mg(1)BO5 square pyramids. The corner-sharing octahedral tilt angles range from 0-18°. In the fourth Mg site, Mg(4) is bonded to one O(4), one O(5), two equivalent O(1), and two equivalent O(3) atoms to form MgO6 octahedra that share corners with two equivalent Mg(3)B2O4 octahedra, corners with four equivalent Mg(4)O6 octahedra, edges with two equivalent Mg(2)O6 octahedra, edges with two equivalent Hf(1)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, and edges with two equivalent Mg(1)BO5 square pyramids. The corner-sharing octahedral tilt angles range from 0-10°. Hf(1) is bonded to one O(2), one O(3), and four equivalent O(4) 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 Mg(3)B2O4 octahedra, and edges with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-5°. B(1) is bonded to one Mg(1) and four equivalent Mg(3) atoms to form distorted BMg5 square pyramids that share  a cornercorner with one O(1)Mg5 square pyramid, corners with four equivalent B(1)Mg5 square pyramids, edges with four equivalent O(2)HfMg5 octahedra, and edges with four equivalent O(5)Mg6 octahedra. There are five inequivalent O sites. In the first O site, O(1) is bonded to one Mg(1) and four equivalent Mg(4) atoms to form OMg5 square pyramids that share  a cornercorner with one B(1)Mg5 square pyramid, corners with four equivalent O(1)Mg5 square pyramids, edges with four equivalent O(3)HfMg5 octahedra, and edges with four equivalent O(5)Mg6 octahedra. 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 two equivalent O(3)HfMg5 octahedra, corners with four equivalent O(2)HfMg5 octahedra, edges with four equivalent O(5)Mg6 octahedra, and edges with four equivalent B(1)Mg5 square pyramids. The corner-sharing octahedral tilt angles range from 0-8°. In the third O site, O(3) is bonded to one Mg(2), four equivalent Mg(4), and one Hf(1) atom to form OHfMg5 octahedra that share corners with two equivalent O(2)HfMg5 octahedra, corners with four equivalent O(3)HfMg5 octahedra, edges with four equivalent O(5)Mg6 octahedra, and edges with four equivalent O(1)Mg5 square pyramids. The corner-sharing octahedral tilt angles range from 0-3°. In the fourth O site, O(4) is bonded in a square co-planar geometry to one Mg(3), one Mg(4), and two equivalent Hf(1) atoms. In the fifth O site, O(5) is bonded to one Mg(3), one Mg(4), two equivalent Mg(1), and two equivalent Mg(2) atoms to form OMg6 octahedra that share corners with four equivalent O(5)Mg6 octahedra, edges with two equivalent O(2)HfMg5 octahedra, edges with two equivalent O(3)HfMg5 octahedra, edges with four equivalent O(5)Mg6 octahedra, edges with two equivalent B(1)Mg5 square pyramids, and edges with two equivalent O(1)Mg5 square pyramids. The corner-sharing octahedral tilt angles range from 1-3°. is represented by the Crystallographic Information File (CIF) [CIF]
data_HfMg6BO7
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.821
_cell_length_b   4.322
_cell_length_c   4.322
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   164.789
_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  0.988  0.500  0.500  1.0
  Mg  Mg1  1  0.491  0.000  0.000  1.0
  Mg  Mg2  1  0.489  0.500  0.500  1.0
  Mg  Mg3  1  0.245  0.000  0.500  1.0
  Mg  Mg4  1  0.737  0.000  0.500  1.0
  Mg  Mg5  1  0.245  0.500  0.000  1.0
  Mg  Mg6  1  0.737  0.500  0.000  1.0
  B  B7  1  0.207  0.000  0.000  1.0
  O  O8  1  0.715  0.000  0.000  1.0
  O  O9  1  0.229  0.500  0.500  1.0
  O  O10  1  0.744  0.500  0.500  1.0
  O  O11  1  0.976  0.000  0.500  1.0
  O  O12  1  0.486  0.000  0.500  1.0
  O  O13  1  0.976  0.500  0.000  1.0
  O  O14  1  0.486  0.500  0.000  1.0
[/CIF]
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The structure described by Mg6HfBO7 crystallizes in the tetragonal P4mm space group. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one B(1), one O(1), and four equivalent O(5) atoms to form distorted MgBO5 square pyramids that share corners with four equivalent Mg(1)BO5 square pyramids, edges with four equivalent Mg(3)B2O4 octahedra, edges with four equivalent Mg(2)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. In the second Mg site, Mg(2) is bonded to one O(2), one O(3), and four equivalent O(5) 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(3)B2O4 octahedra, edges with four equivalent Mg(4)O6 octahedra, and edges with four equivalent Mg(1)BO5 square pyramids. The corner-sharing octahedral tilt angles range from 0-1°. In the third Mg site, Mg(3) is bonded to two equivalent B(1), one O(4), one O(5), and two equivalent O(2) atoms to form MgB2O4 octahedra that share corners with two equivalent Mg(4)O6 octahedra, corners with four equivalent Mg(3)B2O4 octahedra, edges with two equivalent Mg(2)O6 octahedra, edges with two equivalent Hf(1)O6 octahedra, edges with four equivalent Mg(3)B2O4 octahedra, and edges with two equivalent Mg(1)BO5 square pyramids. The corner-sharing octahedral tilt angles range from 0-18°. In the fourth Mg site, Mg(4) is bonded to one O(4), one O(5), two equivalent O(1), and two equivalent O(3) atoms to form MgO6 octahedra that share corners with two equivalent Mg(3)B2O4 octahedra, corners with four equivalent Mg(4)O6 octahedra, edges with two equivalent Mg(2)O6 octahedra, edges with two equivalent Hf(1)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, and edges with two equivalent Mg(1)BO5 square pyramids. The corner-sharing octahedral tilt angles range from 0-10°. Hf(1) is bonded to one O(2), one O(3), and four equivalent O(4) 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 Mg(3)B2O4 octahedra, and edges with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-5°. B(1) is bonded to one Mg(1) and four equivalent Mg(3) atoms to form distorted BMg5 square pyramids that share  a cornercorner with one O(1)Mg5 square pyramid, corners with four equivalent B(1)Mg5 square pyramids, edges with four equivalent O(2)HfMg5 octahedra, and edges with four equivalent O(5)Mg6 octahedra. There are five inequivalent O sites. In the first O site, O(1) is bonded to one Mg(1) and four equivalent Mg(4) atoms to form OMg5 square pyramids that share  a cornercorner with one B(1)Mg5 square pyramid, corners with four equivalent O(1)Mg5 square pyramids, edges with four equivalent O(3)HfMg5 octahedra, and edges with four equivalent O(5)Mg6 octahedra. 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 two equivalent O(3)HfMg5 octahedra, corners with four equivalent O(2)HfMg5 octahedra, edges with four equivalent O(5)Mg6 octahedra, and edges with four equivalent B(1)Mg5 square pyramids. The corner-sharing octahedral tilt angles range from 0-8°. In the third O site, O(3) is bonded to one Mg(2), four equivalent Mg(4), and one Hf(1) atom to form OHfMg5 octahedra that share corners with two equivalent O(2)HfMg5 octahedra, corners with four equivalent O(3)HfMg5 octahedra, edges with four equivalent O(5)Mg6 octahedra, and edges with four equivalent O(1)Mg5 square pyramids. The corner-sharing octahedral tilt angles range from 0-3°. In the fourth O site, O(4) is bonded in a square co-planar geometry to one Mg(3), one Mg(4), and two equivalent Hf(1) atoms. In the fifth O site, O(5) is bonded to one Mg(3), one Mg(4), two equivalent Mg(1), and two equivalent Mg(2) atoms to form OMg6 octahedra that share corners with four equivalent O(5)Mg6 octahedra, edges with two equivalent O(2)HfMg5 octahedra, edges with two equivalent O(3)HfMg5 octahedra, edges with four equivalent O(5)Mg6 octahedra, edges with two equivalent B(1)Mg5 square pyramids, and edges with two equivalent O(1)Mg5 square pyramids. The corner-sharing octahedral tilt angles range from 1-3°. is represented by the Crystallographic Information File (CIF) [CIF]
data_HfMg6BO7
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.821
_cell_length_b   4.322
_cell_length_c   4.322
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   164.789
_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  0.988  0.500  0.500  1.0
  Mg  Mg1  1  0.491  0.000  0.000  1.0
  Mg  Mg2  1  0.489  0.500  0.500  1.0
  Mg  Mg3  1  0.245  0.000  0.500  1.0
  Mg  Mg4  1  0.737  0.000  0.500  1.0
  Mg  Mg5  1  0.245  0.500  0.000  1.0
  Mg  Mg6  1  0.737  0.500  0.000  1.0
  B  B7  1  0.207  0.000  0.000  1.0
  O  O8  1  0.715  0.000  0.000  1.0
  O  O9  1  0.229  0.500  0.500  1.0
  O  O10  1  0.744  0.500  0.500  1.0
  O  O11  1  0.976  0.000  0.500  1.0
  O  O12  1  0.486  0.000  0.500  1.0
  O  O13  1  0.976  0.500  0.000  1.0
  O  O14  1  0.486  0.500  0.000  1.0
[/CIF]
.