The crystal structure described by NaMg14BO15 crystallizes in the orthorhombic Pmm2 space group. Na(1) is bonded to one O(1), one O(2), two equivalent O(10), and two equivalent O(6) atoms to form NaO6 octahedra that share corners with two equivalent Na(1)O6 octahedra, corners with two equivalent Mg(2)O6 octahedra, edges with two equivalent Mg(10)O6 octahedra, edges with two equivalent Mg(5)O6 octahedra, edges with two equivalent Mg(7)O6 octahedra, edges with four equivalent Mg(3)O6 octahedra, and edges with two equivalent Mg(9)O5 square pyramids. The corner-sharing octahedra are not tilted. There are ten inequivalent Mg sites. In the first Mg site, Mg(1) is bonded in a distorted rectangular see-saw-like geometry to two equivalent O(10) and two equivalent O(7) atoms. In the second Mg site, Mg(2) is bonded to one O(1), one O(2), two equivalent O(11), and two equivalent O(8) atoms to form MgO6 octahedra that share corners with two equivalent Na(1)O6 octahedra, corners with two equivalent Mg(2)O6 octahedra, edges with two equivalent Mg(10)O6 octahedra, edges with two equivalent Mg(5)O6 octahedra, edges with two equivalent Mg(7)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, and edges with two equivalent Mg(9)O5 square pyramids. The corner-sharing octahedra are not tilted. In the third Mg site, Mg(3) is bonded to one O(4), one O(5), one O(6), one O(7), and two equivalent O(10) atoms to form MgO6 octahedra that share corners with two equivalent Mg(4)O6 octahedra, corners with four equivalent Mg(3)O6 octahedra,  an edgeedge with one Mg(5)O6 octahedra,  an edgeedge with one Mg(7)O6 octahedra,  an edgeedge with one Mg(8)O6 octahedra, edges with two equivalent Na(1)O6 octahedra, edges with two equivalent Mg(10)O6 octahedra, and edges with two equivalent Mg(9)O5 square pyramids. The corner-sharing octahedral tilt angles range from 1-11°. In the fourth Mg site, Mg(4) is bonded to one O(4), one O(5), one O(8), one O(9), and two equivalent O(11) atoms to form MgO6 octahedra that share corners with two equivalent Mg(3)O6 octahedra, corners with four equivalent Mg(4)O6 octahedra,  an edgeedge with one Mg(5)O6 octahedra,  an edgeedge with one Mg(7)O6 octahedra,  an edgeedge with one Mg(8)O6 octahedra, edges with two equivalent Mg(10)O6 octahedra, edges with two equivalent Mg(2)O6 octahedra, and edges with two equivalent Mg(9)O5 square pyramids. The corner-sharing octahedral tilt angles range from 0-3°. In the fifth Mg site, Mg(5) is bonded to one O(6), one O(8), two equivalent O(1), and two equivalent O(4) atoms to form MgO6 octahedra that share corners with two equivalent Mg(5)O6 octahedra, corners with two equivalent Mg(7)O6 octahedra, edges with two equivalent Na(1)O6 octahedra, edges with two equivalent Mg(2)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, edges with two equivalent Mg(4)O6 octahedra, and edges with four equivalent Mg(9)O5 square pyramids. The corner-sharing octahedral tilt angles range from 0-7°. In the sixth Mg site, Mg(6) is bonded in a square co-planar geometry to one O(7), one O(9), and two equivalent O(4) atoms. In the seventh Mg site, Mg(7) is bonded to one O(6), one O(8), two equivalent O(2), and two equivalent O(5) atoms to form MgO6 octahedra that share corners with two equivalent Mg(5)O6 octahedra, corners with two equivalent Mg(7)O6 octahedra, corners with two equivalent Mg(8)O6 octahedra, edges with two equivalent Na(1)O6 octahedra, edges with two equivalent Mg(2)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, edges with two equivalent Mg(4)O6 octahedra, and edges with four equivalent Mg(10)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-7°. In the eighth Mg site, Mg(8) is bonded to one O(7), one O(9), two equivalent O(3), and two equivalent O(5) atoms to form a mixture of corner and edge-sharing MgO6 octahedra. The corner-sharing octahedral tilt angles range from 1-24°. In the ninth Mg site, Mg(9) is bonded to one O(1), one O(10), one O(11), and two equivalent O(4) atoms to form MgO5 square pyramids that share corners with two equivalent Mg(10)O6 octahedra, corners with three equivalent Mg(9)O5 square pyramids,  an edgeedge with one Na(1)O6 octahedra,  an edgeedge with one Mg(2)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, edges with two equivalent Mg(4)O6 octahedra, and edges with two equivalent Mg(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 5-15°. In the tenth Mg site, Mg(10) is bonded to one O(10), one O(11), one O(2), one O(3), and two equivalent O(5) atoms to form MgO6 octahedra that share corners with four equivalent Mg(10)O6 octahedra, corners with two equivalent Mg(9)O5 square pyramids,  an edgeedge with one Na(1)O6 octahedra,  an edgeedge with one Mg(2)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, edges with two equivalent Mg(4)O6 octahedra, edges with two equivalent Mg(7)O6 octahedra, and edges with two equivalent Mg(8)O6 octahedra. The corner-sharing octahedral tilt angles range from 4-25°. B(1) is bonded in a distorted single-bond geometry to one O(3), two equivalent O(11), and two equivalent O(9) atoms. There are eleven inequivalent O sites. In the first O site, O(1) is bonded to one Na(1), one Mg(2), two equivalent Mg(5), and two equivalent Mg(9) atoms to form ONaMg5 octahedra that share corners with two equivalent O(1)NaMg5 octahedra, corners with two equivalent O(2)NaMg5 octahedra, edges with two equivalent O(11)Mg5B octahedra, edges with two equivalent O(8)Mg6 octahedra, edges with two equivalent O(6)Na2Mg4 octahedra, edges with two equivalent O(10)NaMg5 octahedra, and edges with four equivalent O(4)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 0-7°. In the second O site, O(2) is bonded to one Na(1), one Mg(2), two equivalent Mg(10), and two equivalent Mg(7) atoms to form ONaMg5 octahedra that share corners with two equivalent O(1)NaMg5 octahedra, corners with two equivalent O(2)NaMg5 octahedra, edges with two equivalent O(11)Mg5B octahedra, edges with two equivalent O(8)Mg6 octahedra, edges with two equivalent O(6)Na2Mg4 octahedra, edges with two equivalent O(10)NaMg5 octahedra, and edges with four equivalent O(5)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 0-7°. In the third O site, O(3) is bonded in a 1-coordinate geometry to two equivalent Mg(10), two equivalent Mg(8), and one B(1) atom. In the fourth O site, O(4) is bonded to one Mg(3), one Mg(4), one Mg(5), one Mg(6), and two equivalent Mg(9) atoms to form OMg6 octahedra that share corners with two equivalent O(5)Mg6 octahedra, corners with four equivalent O(4)Mg6 octahedra,  an edgeedge with one O(9)Mg4B2 octahedra,  an edgeedge with one O(7)Mg6 octahedra,  an edgeedge with one O(8)Mg6 octahedra,  an edgeedge with one O(6)Na2Mg4 octahedra, edges with two equivalent O(11)Mg5B octahedra, edges with two equivalent O(1)NaMg5 octahedra, and edges with two equivalent O(10)NaMg5 octahedra. The corner-sharing octahedral tilt angles range from 1-8°. In the fifth O site, O(5) is bonded to one Mg(3), one Mg(4), one Mg(7), one Mg(8), and two equivalent Mg(10) atoms to form OMg6 octahedra that share corners with two equivalent O(4)Mg6 octahedra, corners with four equivalent O(5)Mg6 octahedra,  an edgeedge with one O(9)Mg4B2 octahedra,  an edgeedge with one O(7)Mg6 octahedra,  an edgeedge with one O(8)Mg6 octahedra,  an edgeedge with one O(6)Na2Mg4 octahedra, edges with two equivalent O(11)Mg5B octahedra, edges with two equivalent O(10)NaMg5 octahedra, and edges with two equivalent O(2)NaMg5 octahedra. The corner-sharing octahedral tilt angles range from 2-7°. In the sixth O site, O(6) is bonded to two equivalent Na(1), one Mg(5), one Mg(7), and two equivalent Mg(3) atoms to form ONa2Mg4 octahedra that share corners with two equivalent O(7)Mg6 octahedra, corners with two equivalent O(8)Mg6 octahedra, corners with two equivalent O(6)Na2Mg4 octahedra, edges with two equivalent O(4)Mg6 octahedra, edges with two equivalent O(5)Mg6 octahedra, edges with two equivalent O(1)NaMg5 octahedra, edges with two equivalent O(2)NaMg5 octahedra, and edges with four equivalent O(10)NaMg5 octahedra. The corner-sharing octahedral tilt angles range from 0-1°. In the seventh O site, O(7) is bonded to one Mg(6), one Mg(8), two equivalent Mg(1), and two equivalent Mg(3) atoms to form OMg6 octahedra that share corners with two equivalent O(9)Mg4B2 octahedra, corners with two equivalent O(7)Mg6 octahedra, corners with two equivalent O(6)Na2Mg4 octahedra, edges with two equivalent O(4)Mg6 octahedra, edges with two equivalent O(5)Mg6 octahedra, and edges with four equivalent O(10)NaMg5 octahedra. The corner-sharing octahedral tilt angles range from 0-3°. In the eighth O site, O(8) is bonded to one Mg(5), one Mg(7), two equivalent Mg(2), and two equivalent Mg(4) atoms to form OMg6 octahedra that share corners with two equivalent O(9)Mg4B2 octahedra, corners with two equivalent O(8)Mg6 octahedra, corners with two equivalent O(6)Na2Mg4 octahedra, edges with two equivalent O(4)Mg6 octahedra, edges with two equivalent O(5)Mg6 octahedra, edges with two equivalent O(1)NaMg5 octahedra, edges with two equivalent O(2)NaMg5 octahedra, and edges with four equivalent O(11)Mg5B octahedra. The corner-sharing octahedra are not tilted. In the ninth O site, O(9) is bonded to one Mg(6), one Mg(8), two equivalent Mg(4), and two equivalent B(1) atoms to form OMg4B2 octahedra that share corners with two equivalent O(9)Mg4B2 octahedra, corners with two equivalent O(7)Mg6 octahedra, corners with two equivalent O(8)Mg6 octahedra, edges with two equivalent O(4)Mg6 octahedra, edges with two equivalent O(5)Mg6 octahedra, and edges with four equivalent O(11)Mg5B octahedra. The corner-sharing octahedral tilt angles range from 0-7°. In the tenth O site, O(10) is bonded to one Na(1), one Mg(1), one Mg(10), one Mg(9), and two equivalent Mg(3) atoms to form ONaMg5 octahedra that share corners with two equivalent O(11)Mg5B octahedra, corners with four equivalent O(10)NaMg5 octahedra,  an edgeedge with one O(1)NaMg5 octahedra,  an edgeedge with one O(2)NaMg5 octahedra, edges with two equivalent O(4)Mg6 octahedra, edges with two equivalent O(5)Mg6 octahedra, edges with two equivalent O(7)Mg6 octahedra, and edges with two equivalent O(6)Na2Mg4 octahedra. The corner-sharing octahedral tilt angles range from 1-11°. In the eleventh O site, O(11) is bonded to one Mg(10), one Mg(2), one Mg(9), two equivalent Mg(4), and one B(1) atom to form OMg5B octahedra that share corners with two equivalent O(10)NaMg5 octahedra, corners with four equivalent O(11)Mg5B octahedra,  an edgeedge with one O(1)NaMg5 octahedra,  an edgeedge with one O(2)NaMg5 octahedra, edges with two equivalent O(9)Mg4B2 octahedra, edges with two equivalent O(4)Mg6 octahedra, edges with two equivalent O(5)Mg6 octahedra, and edges with two equivalent O(8)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 0-10°. is represented by the Crystallographic Information File (CIF) [CIF]
data_NaMg14BO15
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.407
_cell_length_b   8.616
_cell_length_c   4.285
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   310.390
_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  0.002  0.000  0.000  1.0
  Mg  Mg1  1  0.004  0.500  0.000  1.0
  Mg  Mg2  1  0.502  0.000  0.000  1.0
  Mg  Mg3  1  0.001  0.247  0.500  1.0
  Mg  Mg4  1  0.001  0.753  0.500  1.0
  Mg  Mg5  1  0.502  0.252  0.500  1.0
  Mg  Mg6  1  0.502  0.748  0.500  1.0
  Mg  Mg7  1  0.249  0.000  0.500  1.0
  Mg  Mg8  1  0.265  0.500  0.500  1.0
  Mg  Mg9  1  0.755  0.000  0.500  1.0
  Mg  Mg10  1  0.742  0.500  0.500  1.0
  Mg  Mg11  1  0.256  0.241  0.000  1.0
  Mg  Mg12  1  0.256  0.759  0.000  1.0
  Mg  Mg13  1  0.748  0.239  0.000  1.0
  Mg  Mg14  1  0.748  0.761  0.000  1.0
  B  B15  1  0.518  0.500  0.000  1.0
  O  O16  1  0.264  0.000  0.000  1.0
  O  O17  1  0.739  0.000  0.000  1.0
  O  O18  1  0.688  0.500  0.000  1.0
  O  O19  1  0.252  0.257  0.500  1.0
  O  O20  1  0.252  0.743  0.500  1.0
  O  O21  1  0.751  0.254  0.500  1.0
  O  O22  1  0.751  0.746  0.500  1.0
  O  O23  1  0.002  0.000  0.500  1.0
  O  O24  1  0.997  0.500  0.500  1.0
  O  O25  1  0.501  0.000  0.500  1.0
  O  O26  1  0.502  0.500  0.500  1.0
  O  O27  1  1.000  0.272  0.000  1.0
  O  O28  1  1.000  0.728  0.000  1.0
  O  O29  1  0.502  0.250  0.000  1.0
  O  O30  1  0.502  0.750  0.000  1.0
[/CIF]
.
The crystal structure described by NaMg14BO15 crystallizes in the orthorhombic Pmm2 space group. Na(1) is bonded to one O(1), one O(2), two equivalent O(10), and two equivalent O(6) atoms to form NaO6 octahedra that share corners with two equivalent Na(1)O6 octahedra, corners with two equivalent Mg(2)O6 octahedra, edges with two equivalent Mg(10)O6 octahedra, edges with two equivalent Mg(5)O6 octahedra, edges with two equivalent Mg(7)O6 octahedra, edges with four equivalent Mg(3)O6 octahedra, and edges with two equivalent Mg(9)O5 square pyramids. The corner-sharing octahedra are not tilted. There are ten inequivalent Mg sites. In the first Mg site, Mg(1) is bonded in a distorted rectangular see-saw-like geometry to two equivalent O(10) and two equivalent O(7) atoms. In the second Mg site, Mg(2) is bonded to one O(1), one O(2), two equivalent O(11), and two equivalent O(8) atoms to form MgO6 octahedra that share corners with two equivalent Na(1)O6 octahedra, corners with two equivalent Mg(2)O6 octahedra, edges with two equivalent Mg(10)O6 octahedra, edges with two equivalent Mg(5)O6 octahedra, edges with two equivalent Mg(7)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, and edges with two equivalent Mg(9)O5 square pyramids. The corner-sharing octahedra are not tilted. In the third Mg site, Mg(3) is bonded to one O(4), one O(5), one O(6), one O(7), and two equivalent O(10) atoms to form MgO6 octahedra that share corners with two equivalent Mg(4)O6 octahedra, corners with four equivalent Mg(3)O6 octahedra,  an edgeedge with one Mg(5)O6 octahedra,  an edgeedge with one Mg(7)O6 octahedra,  an edgeedge with one Mg(8)O6 octahedra, edges with two equivalent Na(1)O6 octahedra, edges with two equivalent Mg(10)O6 octahedra, and edges with two equivalent Mg(9)O5 square pyramids. The corner-sharing octahedral tilt angles range from 1-11°. In the fourth Mg site, Mg(4) is bonded to one O(4), one O(5), one O(8), one O(9), and two equivalent O(11) atoms to form MgO6 octahedra that share corners with two equivalent Mg(3)O6 octahedra, corners with four equivalent Mg(4)O6 octahedra,  an edgeedge with one Mg(5)O6 octahedra,  an edgeedge with one Mg(7)O6 octahedra,  an edgeedge with one Mg(8)O6 octahedra, edges with two equivalent Mg(10)O6 octahedra, edges with two equivalent Mg(2)O6 octahedra, and edges with two equivalent Mg(9)O5 square pyramids. The corner-sharing octahedral tilt angles range from 0-3°. In the fifth Mg site, Mg(5) is bonded to one O(6), one O(8), two equivalent O(1), and two equivalent O(4) atoms to form MgO6 octahedra that share corners with two equivalent Mg(5)O6 octahedra, corners with two equivalent Mg(7)O6 octahedra, edges with two equivalent Na(1)O6 octahedra, edges with two equivalent Mg(2)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, edges with two equivalent Mg(4)O6 octahedra, and edges with four equivalent Mg(9)O5 square pyramids. The corner-sharing octahedral tilt angles range from 0-7°. In the sixth Mg site, Mg(6) is bonded in a square co-planar geometry to one O(7), one O(9), and two equivalent O(4) atoms. In the seventh Mg site, Mg(7) is bonded to one O(6), one O(8), two equivalent O(2), and two equivalent O(5) atoms to form MgO6 octahedra that share corners with two equivalent Mg(5)O6 octahedra, corners with two equivalent Mg(7)O6 octahedra, corners with two equivalent Mg(8)O6 octahedra, edges with two equivalent Na(1)O6 octahedra, edges with two equivalent Mg(2)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, edges with two equivalent Mg(4)O6 octahedra, and edges with four equivalent Mg(10)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-7°. In the eighth Mg site, Mg(8) is bonded to one O(7), one O(9), two equivalent O(3), and two equivalent O(5) atoms to form a mixture of corner and edge-sharing MgO6 octahedra. The corner-sharing octahedral tilt angles range from 1-24°. In the ninth Mg site, Mg(9) is bonded to one O(1), one O(10), one O(11), and two equivalent O(4) atoms to form MgO5 square pyramids that share corners with two equivalent Mg(10)O6 octahedra, corners with three equivalent Mg(9)O5 square pyramids,  an edgeedge with one Na(1)O6 octahedra,  an edgeedge with one Mg(2)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, edges with two equivalent Mg(4)O6 octahedra, and edges with two equivalent Mg(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 5-15°. In the tenth Mg site, Mg(10) is bonded to one O(10), one O(11), one O(2), one O(3), and two equivalent O(5) atoms to form MgO6 octahedra that share corners with four equivalent Mg(10)O6 octahedra, corners with two equivalent Mg(9)O5 square pyramids,  an edgeedge with one Na(1)O6 octahedra,  an edgeedge with one Mg(2)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, edges with two equivalent Mg(4)O6 octahedra, edges with two equivalent Mg(7)O6 octahedra, and edges with two equivalent Mg(8)O6 octahedra. The corner-sharing octahedral tilt angles range from 4-25°. B(1) is bonded in a distorted single-bond geometry to one O(3), two equivalent O(11), and two equivalent O(9) atoms. There are eleven inequivalent O sites. In the first O site, O(1) is bonded to one Na(1), one Mg(2), two equivalent Mg(5), and two equivalent Mg(9) atoms to form ONaMg5 octahedra that share corners with two equivalent O(1)NaMg5 octahedra, corners with two equivalent O(2)NaMg5 octahedra, edges with two equivalent O(11)Mg5B octahedra, edges with two equivalent O(8)Mg6 octahedra, edges with two equivalent O(6)Na2Mg4 octahedra, edges with two equivalent O(10)NaMg5 octahedra, and edges with four equivalent O(4)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 0-7°. In the second O site, O(2) is bonded to one Na(1), one Mg(2), two equivalent Mg(10), and two equivalent Mg(7) atoms to form ONaMg5 octahedra that share corners with two equivalent O(1)NaMg5 octahedra, corners with two equivalent O(2)NaMg5 octahedra, edges with two equivalent O(11)Mg5B octahedra, edges with two equivalent O(8)Mg6 octahedra, edges with two equivalent O(6)Na2Mg4 octahedra, edges with two equivalent O(10)NaMg5 octahedra, and edges with four equivalent O(5)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 0-7°. In the third O site, O(3) is bonded in a 1-coordinate geometry to two equivalent Mg(10), two equivalent Mg(8), and one B(1) atom. In the fourth O site, O(4) is bonded to one Mg(3), one Mg(4), one Mg(5), one Mg(6), and two equivalent Mg(9) atoms to form OMg6 octahedra that share corners with two equivalent O(5)Mg6 octahedra, corners with four equivalent O(4)Mg6 octahedra,  an edgeedge with one O(9)Mg4B2 octahedra,  an edgeedge with one O(7)Mg6 octahedra,  an edgeedge with one O(8)Mg6 octahedra,  an edgeedge with one O(6)Na2Mg4 octahedra, edges with two equivalent O(11)Mg5B octahedra, edges with two equivalent O(1)NaMg5 octahedra, and edges with two equivalent O(10)NaMg5 octahedra. The corner-sharing octahedral tilt angles range from 1-8°. In the fifth O site, O(5) is bonded to one Mg(3), one Mg(4), one Mg(7), one Mg(8), and two equivalent Mg(10) atoms to form OMg6 octahedra that share corners with two equivalent O(4)Mg6 octahedra, corners with four equivalent O(5)Mg6 octahedra,  an edgeedge with one O(9)Mg4B2 octahedra,  an edgeedge with one O(7)Mg6 octahedra,  an edgeedge with one O(8)Mg6 octahedra,  an edgeedge with one O(6)Na2Mg4 octahedra, edges with two equivalent O(11)Mg5B octahedra, edges with two equivalent O(10)NaMg5 octahedra, and edges with two equivalent O(2)NaMg5 octahedra. The corner-sharing octahedral tilt angles range from 2-7°. In the sixth O site, O(6) is bonded to two equivalent Na(1), one Mg(5), one Mg(7), and two equivalent Mg(3) atoms to form ONa2Mg4 octahedra that share corners with two equivalent O(7)Mg6 octahedra, corners with two equivalent O(8)Mg6 octahedra, corners with two equivalent O(6)Na2Mg4 octahedra, edges with two equivalent O(4)Mg6 octahedra, edges with two equivalent O(5)Mg6 octahedra, edges with two equivalent O(1)NaMg5 octahedra, edges with two equivalent O(2)NaMg5 octahedra, and edges with four equivalent O(10)NaMg5 octahedra. The corner-sharing octahedral tilt angles range from 0-1°. In the seventh O site, O(7) is bonded to one Mg(6), one Mg(8), two equivalent Mg(1), and two equivalent Mg(3) atoms to form OMg6 octahedra that share corners with two equivalent O(9)Mg4B2 octahedra, corners with two equivalent O(7)Mg6 octahedra, corners with two equivalent O(6)Na2Mg4 octahedra, edges with two equivalent O(4)Mg6 octahedra, edges with two equivalent O(5)Mg6 octahedra, and edges with four equivalent O(10)NaMg5 octahedra. The corner-sharing octahedral tilt angles range from 0-3°. In the eighth O site, O(8) is bonded to one Mg(5), one Mg(7), two equivalent Mg(2), and two equivalent Mg(4) atoms to form OMg6 octahedra that share corners with two equivalent O(9)Mg4B2 octahedra, corners with two equivalent O(8)Mg6 octahedra, corners with two equivalent O(6)Na2Mg4 octahedra, edges with two equivalent O(4)Mg6 octahedra, edges with two equivalent O(5)Mg6 octahedra, edges with two equivalent O(1)NaMg5 octahedra, edges with two equivalent O(2)NaMg5 octahedra, and edges with four equivalent O(11)Mg5B octahedra. The corner-sharing octahedra are not tilted. In the ninth O site, O(9) is bonded to one Mg(6), one Mg(8), two equivalent Mg(4), and two equivalent B(1) atoms to form OMg4B2 octahedra that share corners with two equivalent O(9)Mg4B2 octahedra, corners with two equivalent O(7)Mg6 octahedra, corners with two equivalent O(8)Mg6 octahedra, edges with two equivalent O(4)Mg6 octahedra, edges with two equivalent O(5)Mg6 octahedra, and edges with four equivalent O(11)Mg5B octahedra. The corner-sharing octahedral tilt angles range from 0-7°. In the tenth O site, O(10) is bonded to one Na(1), one Mg(1), one Mg(10), one Mg(9), and two equivalent Mg(3) atoms to form ONaMg5 octahedra that share corners with two equivalent O(11)Mg5B octahedra, corners with four equivalent O(10)NaMg5 octahedra,  an edgeedge with one O(1)NaMg5 octahedra,  an edgeedge with one O(2)NaMg5 octahedra, edges with two equivalent O(4)Mg6 octahedra, edges with two equivalent O(5)Mg6 octahedra, edges with two equivalent O(7)Mg6 octahedra, and edges with two equivalent O(6)Na2Mg4 octahedra. The corner-sharing octahedral tilt angles range from 1-11°. In the eleventh O site, O(11) is bonded to one Mg(10), one Mg(2), one Mg(9), two equivalent Mg(4), and one B(1) atom to form OMg5B octahedra that share corners with two equivalent O(10)NaMg5 octahedra, corners with four equivalent O(11)Mg5B octahedra,  an edgeedge with one O(1)NaMg5 octahedra,  an edgeedge with one O(2)NaMg5 octahedra, edges with two equivalent O(9)Mg4B2 octahedra, edges with two equivalent O(4)Mg6 octahedra, edges with two equivalent O(5)Mg6 octahedra, and edges with two equivalent O(8)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 0-10°. is represented by the Crystallographic Information File (CIF) [CIF]
data_NaMg14BO15
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.407
_cell_length_b   8.616
_cell_length_c   4.285
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   310.390
_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  0.002  0.000  0.000  1.0
  Mg  Mg1  1  0.004  0.500  0.000  1.0
  Mg  Mg2  1  0.502  0.000  0.000  1.0
  Mg  Mg3  1  0.001  0.247  0.500  1.0
  Mg  Mg4  1  0.001  0.753  0.500  1.0
  Mg  Mg5  1  0.502  0.252  0.500  1.0
  Mg  Mg6  1  0.502  0.748  0.500  1.0
  Mg  Mg7  1  0.249  0.000  0.500  1.0
  Mg  Mg8  1  0.265  0.500  0.500  1.0
  Mg  Mg9  1  0.755  0.000  0.500  1.0
  Mg  Mg10  1  0.742  0.500  0.500  1.0
  Mg  Mg11  1  0.256  0.241  0.000  1.0
  Mg  Mg12  1  0.256  0.759  0.000  1.0
  Mg  Mg13  1  0.748  0.239  0.000  1.0
  Mg  Mg14  1  0.748  0.761  0.000  1.0
  B  B15  1  0.518  0.500  0.000  1.0
  O  O16  1  0.264  0.000  0.000  1.0
  O  O17  1  0.739  0.000  0.000  1.0
  O  O18  1  0.688  0.500  0.000  1.0
  O  O19  1  0.252  0.257  0.500  1.0
  O  O20  1  0.252  0.743  0.500  1.0
  O  O21  1  0.751  0.254  0.500  1.0
  O  O22  1  0.751  0.746  0.500  1.0
  O  O23  1  0.002  0.000  0.500  1.0
  O  O24  1  0.997  0.500  0.500  1.0
  O  O25  1  0.501  0.000  0.500  1.0
  O  O26  1  0.502  0.500  0.500  1.0
  O  O27  1  1.000  0.272  0.000  1.0
  O  O28  1  1.000  0.728  0.000  1.0
  O  O29  1  0.502  0.250  0.000  1.0
  O  O30  1  0.502  0.750  0.000  1.0
[/CIF]
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