The compound described by NaMg6HfO7 crystallizes in the tetragonal P4mm space group. Na(1) is bonded to one O(1), one O(2), and four equivalent O(4) atoms to form NaO6 octahedra that share corners with two equivalent Hf(1)O6 octahedra, corners with four equivalent Na(1)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, and edges with four equivalent Mg(1)O5 square pyramids. The corner-sharing octahedral tilt angles range from 0-1°. 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, edges with four equivalent Na(1)O6 octahedra, 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 square co-planar geometry to one O(4), one O(5), 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 MgO6 octahedra that share corners with four equivalent Mg(4)O6 octahedra, edges with two equivalent Na(1)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 7-15°. 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 two equivalent Na(1)O6 octahedra, 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 range from 0-8°. There are five inequivalent O sites. In the first O site, O(1) is bonded to one Na(1), four equivalent Mg(3), and one Hf(1) atom to form distorted ONaHfMg4 octahedra that share corners with two equivalent O(2)NaHfMg4 octahedra, corners with four equivalent O(1)NaHfMg4 octahedra, edges with four equivalent O(5)Hf2Mg4 octahedra, and edges with four equivalent O(4)Na2Mg4 octahedra. The corner-sharing octahedral tilt angles range from 0-20°. In the second O site, O(2) is bonded to one Na(1), four equivalent Mg(4), and one Hf(1) atom to form ONaHfMg4 octahedra that share corners with two equivalent O(1)NaHfMg4 octahedra, corners with four equivalent O(2)NaHfMg4 octahedra, edges with four equivalent O(5)Hf2Mg4 octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with four equivalent O(4)Na2Mg4 octahedra. The corner-sharing octahedral tilt angles range from 0-15°. 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(5)Hf2Mg4 octahedra, edges with four equivalent O(4)Na2Mg4 octahedra, and edges with four equivalent O(2)NaHfMg4 octahedra. The corner-sharing octahedral tilt angles are 7°. In the fourth O site, O(4) is bonded to two equivalent Na(1), one Mg(3), one Mg(4), and two equivalent Mg(1) atoms to form ONa2Mg4 octahedra that share corners with two equivalent O(5)Hf2Mg4 octahedra, corners with four equivalent O(4)Na2Mg4 octahedra, edges with two equivalent O(3)Mg6 octahedra, edges with two equivalent O(1)NaHfMg4 octahedra, edges with two equivalent O(2)NaHfMg4 octahedra, and edges with four equivalent O(4)Na2Mg4 octahedra. The corner-sharing octahedral tilt angles range from 0-2°. In the fifth O site, O(5) is bonded to one Mg(3), one Mg(4), two equivalent Mg(2), and two equivalent Hf(1) atoms to form OHf2Mg4 octahedra that share corners with two equivalent O(4)Na2Mg4 octahedra, corners with four equivalent O(5)Hf2Mg4 octahedra, edges with two equivalent O(3)Mg6 octahedra, edges with two equivalent O(1)NaHfMg4 octahedra, edges with two equivalent O(2)NaHfMg4 octahedra, and edges with four equivalent O(5)Hf2Mg4 octahedra. The corner-sharing octahedral tilt angles range from 0-8°. is represented by the CIF file [CIF]
data_NaHfMg6O7
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.925
_cell_length_b   4.395
_cell_length_c   4.395
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   172.394
_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
  Na  Na0  1  0.997  0.000  0.000  1.0
  Hf  Hf1  1  0.500  0.000  0.000  1.0
  Mg  Mg2  1  0.989  0.500  0.500  1.0
  Mg  Mg3  1  0.511  0.500  0.500  1.0
  Mg  Mg4  1  0.224  0.000  0.500  1.0
  Mg  Mg5  1  0.765  0.000  0.500  1.0
  Mg  Mg6  1  0.224  0.500  0.000  1.0
  Mg  Mg7  1  0.765  0.500  0.000  1.0
  O  O8  1  0.267  0.000  0.000  1.0
  O  O9  1  0.734  0.000  0.000  1.0
  O  O10  1  0.751  0.500  0.500  1.0
  O  O11  1  0.994  0.000  0.500  1.0
  O  O12  1  0.517  0.000  0.500  1.0
  O  O13  1  0.994  0.500  0.000  1.0
  O  O14  1  0.517  0.500  0.000  1.0
[/CIF]
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The compound described by NaMg6HfO7 crystallizes in the tetragonal P4mm space group. Na(1) is bonded to one O(1), one O(2), and four equivalent O(4) atoms to form NaO6 octahedra that share corners with two equivalent Hf(1)O6 octahedra, corners with four equivalent Na(1)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, and edges with four equivalent Mg(1)O5 square pyramids. The corner-sharing octahedral tilt angles range from 0-1°. 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, edges with four equivalent Na(1)O6 octahedra, 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 square co-planar geometry to one O(4), one O(5), 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 MgO6 octahedra that share corners with four equivalent Mg(4)O6 octahedra, edges with two equivalent Na(1)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 7-15°. 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 two equivalent Na(1)O6 octahedra, 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 range from 0-8°. There are five inequivalent O sites. In the first O site, O(1) is bonded to one Na(1), four equivalent Mg(3), and one Hf(1) atom to form distorted ONaHfMg4 octahedra that share corners with two equivalent O(2)NaHfMg4 octahedra, corners with four equivalent O(1)NaHfMg4 octahedra, edges with four equivalent O(5)Hf2Mg4 octahedra, and edges with four equivalent O(4)Na2Mg4 octahedra. The corner-sharing octahedral tilt angles range from 0-20°. In the second O site, O(2) is bonded to one Na(1), four equivalent Mg(4), and one Hf(1) atom to form ONaHfMg4 octahedra that share corners with two equivalent O(1)NaHfMg4 octahedra, corners with four equivalent O(2)NaHfMg4 octahedra, edges with four equivalent O(5)Hf2Mg4 octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with four equivalent O(4)Na2Mg4 octahedra. The corner-sharing octahedral tilt angles range from 0-15°. 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(5)Hf2Mg4 octahedra, edges with four equivalent O(4)Na2Mg4 octahedra, and edges with four equivalent O(2)NaHfMg4 octahedra. The corner-sharing octahedral tilt angles are 7°. In the fourth O site, O(4) is bonded to two equivalent Na(1), one Mg(3), one Mg(4), and two equivalent Mg(1) atoms to form ONa2Mg4 octahedra that share corners with two equivalent O(5)Hf2Mg4 octahedra, corners with four equivalent O(4)Na2Mg4 octahedra, edges with two equivalent O(3)Mg6 octahedra, edges with two equivalent O(1)NaHfMg4 octahedra, edges with two equivalent O(2)NaHfMg4 octahedra, and edges with four equivalent O(4)Na2Mg4 octahedra. The corner-sharing octahedral tilt angles range from 0-2°. In the fifth O site, O(5) is bonded to one Mg(3), one Mg(4), two equivalent Mg(2), and two equivalent Hf(1) atoms to form OHf2Mg4 octahedra that share corners with two equivalent O(4)Na2Mg4 octahedra, corners with four equivalent O(5)Hf2Mg4 octahedra, edges with two equivalent O(3)Mg6 octahedra, edges with two equivalent O(1)NaHfMg4 octahedra, edges with two equivalent O(2)NaHfMg4 octahedra, and edges with four equivalent O(5)Hf2Mg4 octahedra. The corner-sharing octahedral tilt angles range from 0-8°. is represented by the CIF file [CIF]
data_NaHfMg6O7
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.925
_cell_length_b   4.395
_cell_length_c   4.395
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   172.394
_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
  Na  Na0  1  0.997  0.000  0.000  1.0
  Hf  Hf1  1  0.500  0.000  0.000  1.0
  Mg  Mg2  1  0.989  0.500  0.500  1.0
  Mg  Mg3  1  0.511  0.500  0.500  1.0
  Mg  Mg4  1  0.224  0.000  0.500  1.0
  Mg  Mg5  1  0.765  0.000  0.500  1.0
  Mg  Mg6  1  0.224  0.500  0.000  1.0
  Mg  Mg7  1  0.765  0.500  0.000  1.0
  O  O8  1  0.267  0.000  0.000  1.0
  O  O9  1  0.734  0.000  0.000  1.0
  O  O10  1  0.751  0.500  0.500  1.0
  O  O11  1  0.994  0.000  0.500  1.0
  O  O12  1  0.517  0.000  0.500  1.0
  O  O13  1  0.994  0.500  0.000  1.0
  O  O14  1  0.517  0.500  0.000  1.0
[/CIF]
.