The material structure described by NaMg14HfO15 crystallizes in the orthorhombic Pmm2 space group. Na(1) is bonded to one O(2), two equivalent O(10), and two equivalent O(6) atoms to form NaO5 square pyramids that share corners with two equivalent Mg(1)O6 octahedra,  a cornercorner with one Mg(2)O5 square pyramid, corners with two equivalent Na(1)O5 square pyramids, corners with two equivalent Mg(9)O5 square pyramids, edges with two equivalent Mg(10)O6 octahedra, edges with two equivalent Mg(7)O6 octahedra, and edges with four equivalent Mg(3)O6 octahedra. The corner-sharing octahedra are not tilted. There are ten inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one O(1), one O(3), two equivalent O(10), and two equivalent O(7) atoms to form MgO6 octahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent Hf(1)O6 octahedra, corners with two equivalent Na(1)O5 square pyramids, edges with two equivalent Mg(10)O6 octahedra, edges with two equivalent Mg(6)O6 octahedra, edges with two equivalent Mg(8)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. In the second Mg site, Mg(2) is bonded to one O(2), two equivalent O(11), and two equivalent O(8) atoms to form MgO5 square pyramids that share corners with two equivalent Hf(1)O6 octahedra,  a cornercorner with one Na(1)O5 square pyramid, corners with two equivalent Mg(2)O5 square pyramids, corners with two equivalent Mg(9)O5 square pyramids, edges with two equivalent Mg(10)O6 octahedra, edges with two equivalent Mg(7)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedral tilt angles are 1°. 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(6)O6 octahedra,  an edgeedge with one Mg(7)O6 octahedra,  an edgeedge with one Mg(8)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Mg(10)O6 octahedra, edges with two equivalent Na(1)O5 square pyramids, and edges with two equivalent Mg(9)O5 square pyramids. The corner-sharing octahedral tilt angles range from 0-9°. 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(6)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 Hf(1)O6 octahedra, edges with two equivalent Mg(2)O5 square pyramids, and edges with two equivalent Mg(9)O5 square pyramids. The corner-sharing octahedral tilt angles range from 0-6°. In the fifth Mg site, Mg(5) is bonded in a square co-planar geometry to one O(6), one O(8), and two equivalent O(4) atoms. In the sixth Mg site, Mg(6) is bonded to one O(7), one O(9), two equivalent O(1), and two equivalent O(4) atoms to form MgO6 octahedra that share corners with two equivalent Mg(6)O6 octahedra, corners with two equivalent Mg(8)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, edges with two equivalent Mg(4)O6 octahedra, edges with two equivalent Hf(1)O6 octahedra, and edges with four equivalent Mg(9)O5 square pyramids. The corner-sharing octahedral tilt angles range from 0-5°. 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(7)O6 octahedra, corners with two equivalent Mg(8)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, edges with two equivalent Mg(4)O6 octahedra, edges with four equivalent Mg(10)O6 octahedra, edges with two equivalent Na(1)O5 square pyramids, and edges with two equivalent Mg(2)O5 square pyramids. The corner-sharing octahedral tilt angles range from 4-9°. 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 MgO6 octahedra that share corners with two equivalent Mg(6)O6 octahedra, corners with two equivalent Mg(7)O6 octahedra, corners with two equivalent Mg(8)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, edges with two equivalent Mg(4)O6 octahedra, edges with two equivalent Hf(1)O6 octahedra, and edges with four equivalent Mg(10)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-5°. 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,  a cornercorner with one Na(1)O5 square pyramid,  a cornercorner with one Mg(2)O5 square pyramid, corners with three equivalent Mg(9)O5 square pyramids,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Hf(1)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, edges with two equivalent Mg(4)O6 octahedra, and edges with two equivalent Mg(6)O6 octahedra. The corner-sharing octahedral tilt angles range from 4-10°. 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 Mg(1)O6 octahedra,  an edgeedge with one Hf(1)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, edges with two equivalent Mg(8)O6 octahedra,  an edgeedge with one Na(1)O5 square pyramid, and  an edgeedge with one Mg(2)O5 square pyramid. The corner-sharing octahedral tilt angles range from 4-11°. Hf(1) is bonded to one O(1), one O(3), two equivalent O(11), and two equivalent O(9) atoms to form HfO6 octahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent Hf(1)O6 octahedra, corners with two equivalent Mg(2)O5 square pyramids, edges with two equivalent Mg(10)O6 octahedra, edges with two equivalent Mg(6)O6 octahedra, edges with two equivalent Mg(8)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. There are eleven inequivalent O sites. In the first O site, O(1) is bonded to one Mg(1), two equivalent Mg(6), two equivalent Mg(9), and one Hf(1) atom to form OHfMg5 octahedra that share corners with two equivalent O(1)HfMg5 octahedra, corners with two equivalent O(3)HfMg5 octahedra, edges with two equivalent O(9)Hf2Mg4 octahedra, edges with two equivalent O(11)HfMg5 octahedra, edges with two equivalent O(7)Mg6 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 0-5°. 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(3)HfMg5 octahedra, corners with two equivalent O(2)NaMg5 octahedra, edges with two equivalent O(11)HfMg5 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 8-9°. In the third O site, O(3) is bonded to one Mg(1), two equivalent Mg(10), two equivalent Mg(8), and one Hf(1) atom to form OHfMg5 octahedra that share corners with two equivalent O(1)HfMg5 octahedra, corners with two equivalent O(3)HfMg5 octahedra, corners with two equivalent O(2)NaMg5 octahedra, edges with two equivalent O(9)Hf2Mg4 octahedra, edges with two equivalent O(11)HfMg5 octahedra, edges with two equivalent O(7)Mg6 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 0-8°. 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)Hf2Mg4 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(1)HfMg5 octahedra, edges with two equivalent O(11)HfMg5 octahedra, and edges with two equivalent O(10)NaMg5 octahedra. The corner-sharing octahedral tilt angles range from 3-6°. 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)Hf2Mg4 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)HfMg5 octahedra, edges with two equivalent O(3)HfMg5 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 3-7°. 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(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)Hf2Mg4 octahedra, corners with two equivalent O(7)Mg6 octahedra, corners with two equivalent O(6)Na2Mg4 octahedra, edges with two equivalent O(1)HfMg5 octahedra, edges with two equivalent O(3)HfMg5 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 octahedra are not tilted. 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)Hf2Mg4 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(2)NaMg5 octahedra, and edges with four equivalent O(11)HfMg5 octahedra. The corner-sharing octahedral tilt angles range from 0-1°. In the ninth O site, O(9) is bonded to one Mg(6), one Mg(8), two equivalent Mg(4), and two equivalent Hf(1) atoms to form OHf2Mg4 octahedra that share corners with two equivalent O(9)Hf2Mg4 octahedra, corners with two equivalent O(7)Mg6 octahedra, corners with two equivalent O(8)Mg6 octahedra, edges with two equivalent O(1)HfMg5 octahedra, edges with two equivalent O(3)HfMg5 octahedra, edges with two equivalent O(4)Mg6 octahedra, edges with two equivalent O(5)Mg6 octahedra, and edges with four equivalent O(11)HfMg5 octahedra. The corner-sharing octahedral tilt angles range from 0-1°. 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)HfMg5 octahedra, corners with four equivalent O(10)NaMg5 octahedra,  an edgeedge with one O(1)HfMg5 octahedra,  an edgeedge with one O(3)HfMg5 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 0-9°. 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 Hf(1) atom to form OHfMg5 octahedra that share corners with two equivalent O(10)NaMg5 octahedra, corners with four equivalent O(11)HfMg5 octahedra,  an edgeedge with one O(1)HfMg5 octahedra,  an edgeedge with one O(3)HfMg5 octahedra,  an edgeedge with one O(2)NaMg5 octahedra, edges with two equivalent O(9)Hf2Mg4 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 0-8°. is represented by the CIF file [CIF]
data_NaHfMg14O15
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.613
_cell_length_b   8.670
_cell_length_c   4.332
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   323.460
_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
  Hf  Hf1  1  0.501  0.500  0.000  1.0
  Mg  Mg2  1  1.000  0.500  0.000  1.0
  Mg  Mg3  1  0.499  0.000  0.000  1.0
  Mg  Mg4  1  0.000  0.245  0.500  1.0
  Mg  Mg5  1  0.000  0.755  0.500  1.0
  Mg  Mg6  1  0.500  0.240  0.500  1.0
  Mg  Mg7  1  0.500  0.760  0.500  1.0
  Mg  Mg8  1  0.246  0.000  0.500  1.0
  Mg  Mg9  1  0.240  0.500  0.500  1.0
  Mg  Mg10  1  0.756  0.000  0.500  1.0
  Mg  Mg11  1  0.760  0.500  0.500  1.0
  Mg  Mg12  1  0.242  0.245  0.000  1.0
  Mg  Mg13  1  0.242  0.755  0.000  1.0
  Mg  Mg14  1  0.759  0.241  0.000  1.0
  Mg  Mg15  1  0.759  0.759  0.000  1.0
  O  O16  1  0.251  0.500  0.000  1.0
  O  O17  1  0.736  0.000  0.000  1.0
  O  O18  1  0.749  0.500  0.000  1.0
  O  O19  1  0.253  0.255  0.500  1.0
  O  O20  1  0.253  0.745  0.500  1.0
  O  O21  1  0.748  0.252  0.500  1.0
  O  O22  1  0.748  0.748  0.500  1.0
  O  O23  1  0.001  0.000  0.500  1.0
  O  O24  1  1.000  0.500  0.500  1.0
  O  O25  1  0.502  0.000  0.500  1.0
  O  O26  1  0.500  0.500  0.500  1.0
  O  O27  1  1.000  0.265  0.000  1.0
  O  O28  1  1.000  0.735  0.000  1.0
  O  O29  1  0.502  0.252  0.000  1.0
  O  O30  1  0.502  0.748  0.000  1.0
[/CIF]
.
The material structure described by NaMg14HfO15 crystallizes in the orthorhombic Pmm2 space group. Na(1) is bonded to one O(2), two equivalent O(10), and two equivalent O(6) atoms to form NaO5 square pyramids that share corners with two equivalent Mg(1)O6 octahedra,  a cornercorner with one Mg(2)O5 square pyramid, corners with two equivalent Na(1)O5 square pyramids, corners with two equivalent Mg(9)O5 square pyramids, edges with two equivalent Mg(10)O6 octahedra, edges with two equivalent Mg(7)O6 octahedra, and edges with four equivalent Mg(3)O6 octahedra. The corner-sharing octahedra are not tilted. There are ten inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one O(1), one O(3), two equivalent O(10), and two equivalent O(7) atoms to form MgO6 octahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent Hf(1)O6 octahedra, corners with two equivalent Na(1)O5 square pyramids, edges with two equivalent Mg(10)O6 octahedra, edges with two equivalent Mg(6)O6 octahedra, edges with two equivalent Mg(8)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. In the second Mg site, Mg(2) is bonded to one O(2), two equivalent O(11), and two equivalent O(8) atoms to form MgO5 square pyramids that share corners with two equivalent Hf(1)O6 octahedra,  a cornercorner with one Na(1)O5 square pyramid, corners with two equivalent Mg(2)O5 square pyramids, corners with two equivalent Mg(9)O5 square pyramids, edges with two equivalent Mg(10)O6 octahedra, edges with two equivalent Mg(7)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedral tilt angles are 1°. 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(6)O6 octahedra,  an edgeedge with one Mg(7)O6 octahedra,  an edgeedge with one Mg(8)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Mg(10)O6 octahedra, edges with two equivalent Na(1)O5 square pyramids, and edges with two equivalent Mg(9)O5 square pyramids. The corner-sharing octahedral tilt angles range from 0-9°. 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(6)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 Hf(1)O6 octahedra, edges with two equivalent Mg(2)O5 square pyramids, and edges with two equivalent Mg(9)O5 square pyramids. The corner-sharing octahedral tilt angles range from 0-6°. In the fifth Mg site, Mg(5) is bonded in a square co-planar geometry to one O(6), one O(8), and two equivalent O(4) atoms. In the sixth Mg site, Mg(6) is bonded to one O(7), one O(9), two equivalent O(1), and two equivalent O(4) atoms to form MgO6 octahedra that share corners with two equivalent Mg(6)O6 octahedra, corners with two equivalent Mg(8)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, edges with two equivalent Mg(4)O6 octahedra, edges with two equivalent Hf(1)O6 octahedra, and edges with four equivalent Mg(9)O5 square pyramids. The corner-sharing octahedral tilt angles range from 0-5°. 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(7)O6 octahedra, corners with two equivalent Mg(8)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, edges with two equivalent Mg(4)O6 octahedra, edges with four equivalent Mg(10)O6 octahedra, edges with two equivalent Na(1)O5 square pyramids, and edges with two equivalent Mg(2)O5 square pyramids. The corner-sharing octahedral tilt angles range from 4-9°. 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 MgO6 octahedra that share corners with two equivalent Mg(6)O6 octahedra, corners with two equivalent Mg(7)O6 octahedra, corners with two equivalent Mg(8)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, edges with two equivalent Mg(4)O6 octahedra, edges with two equivalent Hf(1)O6 octahedra, and edges with four equivalent Mg(10)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-5°. 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,  a cornercorner with one Na(1)O5 square pyramid,  a cornercorner with one Mg(2)O5 square pyramid, corners with three equivalent Mg(9)O5 square pyramids,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Hf(1)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, edges with two equivalent Mg(4)O6 octahedra, and edges with two equivalent Mg(6)O6 octahedra. The corner-sharing octahedral tilt angles range from 4-10°. 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 Mg(1)O6 octahedra,  an edgeedge with one Hf(1)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, edges with two equivalent Mg(8)O6 octahedra,  an edgeedge with one Na(1)O5 square pyramid, and  an edgeedge with one Mg(2)O5 square pyramid. The corner-sharing octahedral tilt angles range from 4-11°. Hf(1) is bonded to one O(1), one O(3), two equivalent O(11), and two equivalent O(9) atoms to form HfO6 octahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent Hf(1)O6 octahedra, corners with two equivalent Mg(2)O5 square pyramids, edges with two equivalent Mg(10)O6 octahedra, edges with two equivalent Mg(6)O6 octahedra, edges with two equivalent Mg(8)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. There are eleven inequivalent O sites. In the first O site, O(1) is bonded to one Mg(1), two equivalent Mg(6), two equivalent Mg(9), and one Hf(1) atom to form OHfMg5 octahedra that share corners with two equivalent O(1)HfMg5 octahedra, corners with two equivalent O(3)HfMg5 octahedra, edges with two equivalent O(9)Hf2Mg4 octahedra, edges with two equivalent O(11)HfMg5 octahedra, edges with two equivalent O(7)Mg6 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 0-5°. 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(3)HfMg5 octahedra, corners with two equivalent O(2)NaMg5 octahedra, edges with two equivalent O(11)HfMg5 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 8-9°. In the third O site, O(3) is bonded to one Mg(1), two equivalent Mg(10), two equivalent Mg(8), and one Hf(1) atom to form OHfMg5 octahedra that share corners with two equivalent O(1)HfMg5 octahedra, corners with two equivalent O(3)HfMg5 octahedra, corners with two equivalent O(2)NaMg5 octahedra, edges with two equivalent O(9)Hf2Mg4 octahedra, edges with two equivalent O(11)HfMg5 octahedra, edges with two equivalent O(7)Mg6 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 0-8°. 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)Hf2Mg4 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(1)HfMg5 octahedra, edges with two equivalent O(11)HfMg5 octahedra, and edges with two equivalent O(10)NaMg5 octahedra. The corner-sharing octahedral tilt angles range from 3-6°. 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)Hf2Mg4 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)HfMg5 octahedra, edges with two equivalent O(3)HfMg5 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 3-7°. 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(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)Hf2Mg4 octahedra, corners with two equivalent O(7)Mg6 octahedra, corners with two equivalent O(6)Na2Mg4 octahedra, edges with two equivalent O(1)HfMg5 octahedra, edges with two equivalent O(3)HfMg5 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 octahedra are not tilted. 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)Hf2Mg4 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(2)NaMg5 octahedra, and edges with four equivalent O(11)HfMg5 octahedra. The corner-sharing octahedral tilt angles range from 0-1°. In the ninth O site, O(9) is bonded to one Mg(6), one Mg(8), two equivalent Mg(4), and two equivalent Hf(1) atoms to form OHf2Mg4 octahedra that share corners with two equivalent O(9)Hf2Mg4 octahedra, corners with two equivalent O(7)Mg6 octahedra, corners with two equivalent O(8)Mg6 octahedra, edges with two equivalent O(1)HfMg5 octahedra, edges with two equivalent O(3)HfMg5 octahedra, edges with two equivalent O(4)Mg6 octahedra, edges with two equivalent O(5)Mg6 octahedra, and edges with four equivalent O(11)HfMg5 octahedra. The corner-sharing octahedral tilt angles range from 0-1°. 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)HfMg5 octahedra, corners with four equivalent O(10)NaMg5 octahedra,  an edgeedge with one O(1)HfMg5 octahedra,  an edgeedge with one O(3)HfMg5 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 0-9°. 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 Hf(1) atom to form OHfMg5 octahedra that share corners with two equivalent O(10)NaMg5 octahedra, corners with four equivalent O(11)HfMg5 octahedra,  an edgeedge with one O(1)HfMg5 octahedra,  an edgeedge with one O(3)HfMg5 octahedra,  an edgeedge with one O(2)NaMg5 octahedra, edges with two equivalent O(9)Hf2Mg4 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 0-8°. is represented by the CIF file [CIF]
data_NaHfMg14O15
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.613
_cell_length_b   8.670
_cell_length_c   4.332
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   323.460
_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
  Hf  Hf1  1  0.501  0.500  0.000  1.0
  Mg  Mg2  1  1.000  0.500  0.000  1.0
  Mg  Mg3  1  0.499  0.000  0.000  1.0
  Mg  Mg4  1  0.000  0.245  0.500  1.0
  Mg  Mg5  1  0.000  0.755  0.500  1.0
  Mg  Mg6  1  0.500  0.240  0.500  1.0
  Mg  Mg7  1  0.500  0.760  0.500  1.0
  Mg  Mg8  1  0.246  0.000  0.500  1.0
  Mg  Mg9  1  0.240  0.500  0.500  1.0
  Mg  Mg10  1  0.756  0.000  0.500  1.0
  Mg  Mg11  1  0.760  0.500  0.500  1.0
  Mg  Mg12  1  0.242  0.245  0.000  1.0
  Mg  Mg13  1  0.242  0.755  0.000  1.0
  Mg  Mg14  1  0.759  0.241  0.000  1.0
  Mg  Mg15  1  0.759  0.759  0.000  1.0
  O  O16  1  0.251  0.500  0.000  1.0
  O  O17  1  0.736  0.000  0.000  1.0
  O  O18  1  0.749  0.500  0.000  1.0
  O  O19  1  0.253  0.255  0.500  1.0
  O  O20  1  0.253  0.745  0.500  1.0
  O  O21  1  0.748  0.252  0.500  1.0
  O  O22  1  0.748  0.748  0.500  1.0
  O  O23  1  0.001  0.000  0.500  1.0
  O  O24  1  1.000  0.500  0.500  1.0
  O  O25  1  0.502  0.000  0.500  1.0
  O  O26  1  0.500  0.500  0.500  1.0
  O  O27  1  1.000  0.265  0.000  1.0
  O  O28  1  1.000  0.735  0.000  1.0
  O  O29  1  0.502  0.252  0.000  1.0
  O  O30  1  0.502  0.748  0.000  1.0
[/CIF]
.