The material 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 O(3) and four equivalent O(4) atoms to form MgO5 square pyramids that share  a cornercorner with one Mg(2)O5 square pyramid, corners with four equivalent Mg(1)O5 square pyramids, and edges with four equivalent Mg(4)O6 octahedra. In the second Mg site, Mg(2) is bonded to one O(3) and four equivalent O(5) atoms to form MgO5 square pyramids that share  a cornercorner with one Mg(1)O5 square pyramid, corners with four equivalent Mg(2)O5 square pyramids, edges with four equivalent Mg(4)O6 octahedra, and edges with four equivalent Hf(1)O6 octahedra. In the third Mg site, Mg(3) is bonded in a distorted trigonal planar geometry to one O(4) and two equivalent O(1) atoms. In the fourth Mg site, Mg(4) is bonded to one O(4), one O(5), two equivalent O(2), and two equivalent O(3) atoms to form distorted MgO6 octahedra that share corners with four equivalent Mg(4)O6 octahedra, edges with two equivalent Hf(1)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, edges with two equivalent Mg(1)O5 square pyramids, and edges with two equivalent Mg(2)O5 square pyramids. The corner-sharing octahedral tilt angles range from 10-28°. Hf(1) is bonded to one O(1), one O(2), and four equivalent O(5) atoms to form HfO6 octahedra that share corners with four equivalent Hf(1)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, and edges with four equivalent Mg(2)O5 square pyramids. The corner-sharing octahedral tilt angles are 15°. B(1) is bonded in a 4-coordinate geometry to four equivalent O(4) atoms. There are five 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 four equivalent Mg(4) and one Hf(1) atom to form distorted OHfMg4 trigonal bipyramids that share corners with four equivalent O(4)Mg4B2 octahedra, corners with four equivalent O(2)HfMg4 trigonal bipyramids, edges with four equivalent O(3)Mg6 octahedra, and edges with four equivalent O(5)Hf2Mg3 square pyramids. The corner-sharing octahedral tilt angles are 76°. In the third O site, O(3) is bonded to one Mg(1), one Mg(2), and four equivalent Mg(4) atoms to form OMg6 octahedra that share corners with four equivalent O(3)Mg6 octahedra, edges with four equivalent O(4)Mg4B2 octahedra, edges with four equivalent O(5)Hf2Mg3 square pyramids, and edges with four equivalent O(2)HfMg4 trigonal bipyramids. The corner-sharing octahedral tilt angles are 10°. In the fourth O site, O(4) is bonded to one Mg(3), one Mg(4), two equivalent Mg(1), and two equivalent B(1) atoms to form OMg4B2 octahedra that share corners with four equivalent O(4)Mg4B2 octahedra,  a cornercorner with one O(5)Hf2Mg3 square pyramid, corners with two equivalent O(2)HfMg4 trigonal bipyramids, edges with two equivalent O(3)Mg6 octahedra, and edges with four equivalent O(4)Mg4B2 octahedra. The corner-sharing octahedral tilt angles range from 4-28°. In the fifth O site, O(5) is bonded to one Mg(4), two equivalent Mg(2), and two equivalent Hf(1) atoms to form OHf2Mg3 square pyramids that share  a cornercorner with one O(4)Mg4B2 octahedra, corners with four equivalent O(5)Hf2Mg3 square pyramids, edges with two equivalent O(3)Mg6 octahedra, edges with four equivalent O(5)Hf2Mg3 square pyramids, and edges with two equivalent O(2)HfMg4 trigonal bipyramids. The corner-sharing octahedra are not tilted. is represented by the CIF file [CIF]
data_HfMg6BO7
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   10.250
_cell_length_b   4.176
_cell_length_c   4.176
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   178.778
_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  0.502  0.000  0.000  1.0
  Mg  Mg1  1  0.976  0.500  0.500  1.0
  Mg  Mg2  1  0.553  0.500  0.500  1.0
  Mg  Mg3  1  0.192  0.000  0.500  1.0
  Mg  Mg4  1  0.770  0.000  0.500  1.0
  Mg  Mg5  1  0.192  0.500  0.000  1.0
  Mg  Mg6  1  0.770  0.500  0.000  1.0
  B  B7  1  0.019  0.000  0.000  1.0
  O  O8  1  0.310  0.000  0.000  1.0
  O  O9  1  0.719  0.000  0.000  1.0
  O  O10  1  0.752  0.500  0.500  1.0
  O  O11  1  0.969  0.000  0.500  1.0
  O  O12  1  0.530  0.000  0.500  1.0
  O  O13  1  0.969  0.500  0.000  1.0
  O  O14  1  0.530  0.500  0.000  1.0
[/CIF]
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The material 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 O(3) and four equivalent O(4) atoms to form MgO5 square pyramids that share  a cornercorner with one Mg(2)O5 square pyramid, corners with four equivalent Mg(1)O5 square pyramids, and edges with four equivalent Mg(4)O6 octahedra. In the second Mg site, Mg(2) is bonded to one O(3) and four equivalent O(5) atoms to form MgO5 square pyramids that share  a cornercorner with one Mg(1)O5 square pyramid, corners with four equivalent Mg(2)O5 square pyramids, edges with four equivalent Mg(4)O6 octahedra, and edges with four equivalent Hf(1)O6 octahedra. In the third Mg site, Mg(3) is bonded in a distorted trigonal planar geometry to one O(4) and two equivalent O(1) atoms. In the fourth Mg site, Mg(4) is bonded to one O(4), one O(5), two equivalent O(2), and two equivalent O(3) atoms to form distorted MgO6 octahedra that share corners with four equivalent Mg(4)O6 octahedra, edges with two equivalent Hf(1)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, edges with two equivalent Mg(1)O5 square pyramids, and edges with two equivalent Mg(2)O5 square pyramids. The corner-sharing octahedral tilt angles range from 10-28°. Hf(1) is bonded to one O(1), one O(2), and four equivalent O(5) atoms to form HfO6 octahedra that share corners with four equivalent Hf(1)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, and edges with four equivalent Mg(2)O5 square pyramids. The corner-sharing octahedral tilt angles are 15°. B(1) is bonded in a 4-coordinate geometry to four equivalent O(4) atoms. There are five 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 four equivalent Mg(4) and one Hf(1) atom to form distorted OHfMg4 trigonal bipyramids that share corners with four equivalent O(4)Mg4B2 octahedra, corners with four equivalent O(2)HfMg4 trigonal bipyramids, edges with four equivalent O(3)Mg6 octahedra, and edges with four equivalent O(5)Hf2Mg3 square pyramids. The corner-sharing octahedral tilt angles are 76°. In the third O site, O(3) is bonded to one Mg(1), one Mg(2), and four equivalent Mg(4) atoms to form OMg6 octahedra that share corners with four equivalent O(3)Mg6 octahedra, edges with four equivalent O(4)Mg4B2 octahedra, edges with four equivalent O(5)Hf2Mg3 square pyramids, and edges with four equivalent O(2)HfMg4 trigonal bipyramids. The corner-sharing octahedral tilt angles are 10°. In the fourth O site, O(4) is bonded to one Mg(3), one Mg(4), two equivalent Mg(1), and two equivalent B(1) atoms to form OMg4B2 octahedra that share corners with four equivalent O(4)Mg4B2 octahedra,  a cornercorner with one O(5)Hf2Mg3 square pyramid, corners with two equivalent O(2)HfMg4 trigonal bipyramids, edges with two equivalent O(3)Mg6 octahedra, and edges with four equivalent O(4)Mg4B2 octahedra. The corner-sharing octahedral tilt angles range from 4-28°. In the fifth O site, O(5) is bonded to one Mg(4), two equivalent Mg(2), and two equivalent Hf(1) atoms to form OHf2Mg3 square pyramids that share  a cornercorner with one O(4)Mg4B2 octahedra, corners with four equivalent O(5)Hf2Mg3 square pyramids, edges with two equivalent O(3)Mg6 octahedra, edges with four equivalent O(5)Hf2Mg3 square pyramids, and edges with two equivalent O(2)HfMg4 trigonal bipyramids. The corner-sharing octahedra are not tilted. is represented by the CIF file [CIF]
data_HfMg6BO7
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   10.250
_cell_length_b   4.176
_cell_length_c   4.176
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   178.778
_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  0.502  0.000  0.000  1.0
  Mg  Mg1  1  0.976  0.500  0.500  1.0
  Mg  Mg2  1  0.553  0.500  0.500  1.0
  Mg  Mg3  1  0.192  0.000  0.500  1.0
  Mg  Mg4  1  0.770  0.000  0.500  1.0
  Mg  Mg5  1  0.192  0.500  0.000  1.0
  Mg  Mg6  1  0.770  0.500  0.000  1.0
  B  B7  1  0.019  0.000  0.000  1.0
  O  O8  1  0.310  0.000  0.000  1.0
  O  O9  1  0.719  0.000  0.000  1.0
  O  O10  1  0.752  0.500  0.500  1.0
  O  O11  1  0.969  0.000  0.500  1.0
  O  O12  1  0.530  0.000  0.500  1.0
  O  O13  1  0.969  0.500  0.000  1.0
  O  O14  1  0.530  0.500  0.000  1.0
[/CIF]
.