The structure described by NaMg6BO7 crystallizes in the tetragonal P4mm space group. Na(1) is bonded to one O(1) and four equivalent O(4) atoms to form NaO5 square pyramids that share  a cornercorner with one Mg(1)O5 square pyramid, corners with four equivalent Na(1)O5 square pyramids, and edges with four equivalent Mg(4)O6 octahedra. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one O(1) and four equivalent O(5) atoms to form MgO5 square pyramids that share  a cornercorner with one Na(1)O5 square pyramid, corners with four equivalent Mg(1)O5 square pyramids, edges with four equivalent Mg(4)O6 octahedra, and edges with four equivalent Mg(2)O5 square pyramids. In the second Mg site, Mg(2) is bonded to one O(2) and four equivalent O(5) atoms to form distorted MgO5 square pyramids that share corners with four equivalent Mg(4)O6 octahedra, corners with four equivalent Mg(2)O5 square pyramids, and edges with four equivalent Mg(1)O5 square pyramids. The corner-sharing octahedral tilt angles are 82°. In the third Mg site, Mg(3) is bonded in a 4-coordinate geometry to one O(4), one O(5), and two equivalent O(2) atoms. 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 four equivalent Mg(4)O6 octahedra, corners with two equivalent Mg(2)O5 square pyramids, edges with four equivalent Mg(4)O6 octahedra, edges with two equivalent Na(1)O5 square pyramids, and edges with two equivalent Mg(1)O5 square pyramids. The corner-sharing octahedral tilt angles range from 9-18°. B(1) is bonded in a distorted single-bond geometry to one O(3) and four equivalent O(4) atoms. There are five inequivalent O sites. In the first O site, O(1) is bonded to one Na(1), one Mg(1), and four equivalent Mg(4) atoms to form ONaMg5 octahedra that share corners with four equivalent O(1)NaMg5 octahedra, edges with four equivalent O(5)Mg6 octahedra, and edges with four equivalent O(4)Na2Mg2B2 octahedra. The corner-sharing octahedral tilt angles are 9°. In the second O site, O(2) is bonded to one Mg(2) and four equivalent Mg(3) atoms to form OMg5 square pyramids that share corners with four equivalent O(4)Na2Mg2B2 octahedra, corners with four equivalent O(2)Mg5 square pyramids, and edges with four equivalent O(5)Mg6 octahedra. The corner-sharing octahedral tilt angles are 81°. In the third O site, O(3) is bonded in a 5-coordinate geometry to four equivalent Mg(4) and one B(1) atom. In the fourth O site, O(4) is bonded to two equivalent Na(1), one Mg(3), one Mg(4), and two equivalent B(1) atoms to form ONa2Mg2B2 octahedra that share corners with two equivalent O(5)Mg6 octahedra, corners with four equivalent O(4)Na2Mg2B2 octahedra, corners with two equivalent O(2)Mg5 square pyramids, edges with two equivalent O(1)NaMg5 octahedra, and edges with four equivalent O(4)Na2Mg2B2 octahedra. The corner-sharing octahedral tilt angles range from 0-20°. 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 two equivalent O(4)Na2Mg2B2 octahedra, corners with four equivalent O(5)Mg6 octahedra, edges with two equivalent O(1)NaMg5 octahedra, edges with four equivalent O(5)Mg6 octahedra, and edges with two equivalent O(2)Mg5 square pyramids. The corner-sharing octahedral tilt angles range from 0-16°. is represented by the Crystallographic Information File (CIF) [CIF]
data_NaMg6BO7
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.908
_cell_length_b   4.231
_cell_length_c   4.231
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   159.493
_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  0.994  0.000  0.000  1.0
  Mg  Mg1  1  0.515  0.000  0.000  1.0
  Mg  Mg2  1  0.485  0.500  0.500  1.0
  Mg  Mg3  1  0.225  0.000  0.500  1.0
  Mg  Mg4  1  0.761  0.000  0.500  1.0
  Mg  Mg5  1  0.225  0.500  0.000  1.0
  Mg  Mg6  1  0.761  0.500  0.000  1.0
  B  B7  1  0.954  0.500  0.500  1.0
  O  O8  1  0.742  0.000  0.000  1.0
  O  O9  1  0.262  0.500  0.500  1.0
  O  O10  1  0.798  0.500  0.500  1.0
  O  O11  1  0.996  0.000  0.500  1.0
  O  O12  1  0.518  0.000  0.500  1.0
  O  O13  1  0.996  0.500  0.000  1.0
  O  O14  1  0.518  0.500  0.000  1.0
[/CIF]
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The structure described by NaMg6BO7 crystallizes in the tetragonal P4mm space group. Na(1) is bonded to one O(1) and four equivalent O(4) atoms to form NaO5 square pyramids that share  a cornercorner with one Mg(1)O5 square pyramid, corners with four equivalent Na(1)O5 square pyramids, and edges with four equivalent Mg(4)O6 octahedra. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one O(1) and four equivalent O(5) atoms to form MgO5 square pyramids that share  a cornercorner with one Na(1)O5 square pyramid, corners with four equivalent Mg(1)O5 square pyramids, edges with four equivalent Mg(4)O6 octahedra, and edges with four equivalent Mg(2)O5 square pyramids. In the second Mg site, Mg(2) is bonded to one O(2) and four equivalent O(5) atoms to form distorted MgO5 square pyramids that share corners with four equivalent Mg(4)O6 octahedra, corners with four equivalent Mg(2)O5 square pyramids, and edges with four equivalent Mg(1)O5 square pyramids. The corner-sharing octahedral tilt angles are 82°. In the third Mg site, Mg(3) is bonded in a 4-coordinate geometry to one O(4), one O(5), and two equivalent O(2) atoms. 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 four equivalent Mg(4)O6 octahedra, corners with two equivalent Mg(2)O5 square pyramids, edges with four equivalent Mg(4)O6 octahedra, edges with two equivalent Na(1)O5 square pyramids, and edges with two equivalent Mg(1)O5 square pyramids. The corner-sharing octahedral tilt angles range from 9-18°. B(1) is bonded in a distorted single-bond geometry to one O(3) and four equivalent O(4) atoms. There are five inequivalent O sites. In the first O site, O(1) is bonded to one Na(1), one Mg(1), and four equivalent Mg(4) atoms to form ONaMg5 octahedra that share corners with four equivalent O(1)NaMg5 octahedra, edges with four equivalent O(5)Mg6 octahedra, and edges with four equivalent O(4)Na2Mg2B2 octahedra. The corner-sharing octahedral tilt angles are 9°. In the second O site, O(2) is bonded to one Mg(2) and four equivalent Mg(3) atoms to form OMg5 square pyramids that share corners with four equivalent O(4)Na2Mg2B2 octahedra, corners with four equivalent O(2)Mg5 square pyramids, and edges with four equivalent O(5)Mg6 octahedra. The corner-sharing octahedral tilt angles are 81°. In the third O site, O(3) is bonded in a 5-coordinate geometry to four equivalent Mg(4) and one B(1) atom. In the fourth O site, O(4) is bonded to two equivalent Na(1), one Mg(3), one Mg(4), and two equivalent B(1) atoms to form ONa2Mg2B2 octahedra that share corners with two equivalent O(5)Mg6 octahedra, corners with four equivalent O(4)Na2Mg2B2 octahedra, corners with two equivalent O(2)Mg5 square pyramids, edges with two equivalent O(1)NaMg5 octahedra, and edges with four equivalent O(4)Na2Mg2B2 octahedra. The corner-sharing octahedral tilt angles range from 0-20°. 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 two equivalent O(4)Na2Mg2B2 octahedra, corners with four equivalent O(5)Mg6 octahedra, edges with two equivalent O(1)NaMg5 octahedra, edges with four equivalent O(5)Mg6 octahedra, and edges with two equivalent O(2)Mg5 square pyramids. The corner-sharing octahedral tilt angles range from 0-16°. is represented by the Crystallographic Information File (CIF) [CIF]
data_NaMg6BO7
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.908
_cell_length_b   4.231
_cell_length_c   4.231
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   159.493
_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  0.994  0.000  0.000  1.0
  Mg  Mg1  1  0.515  0.000  0.000  1.0
  Mg  Mg2  1  0.485  0.500  0.500  1.0
  Mg  Mg3  1  0.225  0.000  0.500  1.0
  Mg  Mg4  1  0.761  0.000  0.500  1.0
  Mg  Mg5  1  0.225  0.500  0.000  1.0
  Mg  Mg6  1  0.761  0.500  0.000  1.0
  B  B7  1  0.954  0.500  0.500  1.0
  O  O8  1  0.742  0.000  0.000  1.0
  O  O9  1  0.262  0.500  0.500  1.0
  O  O10  1  0.798  0.500  0.500  1.0
  O  O11  1  0.996  0.000  0.500  1.0
  O  O12  1  0.518  0.000  0.500  1.0
  O  O13  1  0.996  0.500  0.000  1.0
  O  O14  1  0.518  0.500  0.000  1.0
[/CIF]
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