The compound described by Mg14HfBO15 crystallizes in the orthorhombic Pmm2 space group. There are ten inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one B(1), one O(2), two equivalent O(11), and two equivalent O(8) atoms to form distorted MgBO5 octahedra that share corners with two equivalent Mg(1)BO5 octahedra, corners with two equivalent Mg(2)O6 octahedra, edges with two equivalent Mg(5)B2O4 octahedra, edges with two equivalent Mg(9)BO5 octahedra, 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 range from 1-2°. In the second Mg site, Mg(2) is bonded to one O(1), one O(3), two equivalent O(11), and two equivalent O(9) atoms to form MgO6 octahedra that share corners with two equivalent Mg(1)BO5 octahedra, corners with two equivalent Mg(2)O6 octahedra, corners with two equivalent Hf(1)O6 octahedra, edges with two equivalent Mg(9)BO5 octahedra, edges with two equivalent Mg(10)O6 octahedra, edges with two equivalent Mg(6)O6 octahedra, edges with two equivalent Mg(8)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-1°. 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 distorted 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)B2O4 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(9)BO5 octahedra, edges with two equivalent Mg(10)O6 octahedra, and edges with two equivalent Hf(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 1-25°. 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)B2O4 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)BO5 octahedra, edges with two equivalent Mg(9)BO5 octahedra, edges with two equivalent Mg(10)O6 octahedra, and edges with two equivalent Mg(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 3-18°. In the fifth Mg site, Mg(5) is bonded to two equivalent B(1), one O(6), one O(8), and two equivalent O(4) atoms to form MgB2O4 octahedra that share corners with two equivalent Mg(5)B2O4 octahedra, corners with two equivalent Mg(6)O6 octahedra, corners with two equivalent Mg(7)O6 octahedra, edges with two equivalent Mg(1)BO5 octahedra, edges with two equivalent Mg(3)O6 octahedra, edges with two equivalent Mg(4)O6 octahedra, and edges with four equivalent Mg(9)BO5 octahedra. The corner-sharing octahedral tilt angles range from 0-15°. 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(5)B2O4 octahedra, corners with two equivalent Mg(6)O6 octahedra, corners with two equivalent Mg(8)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, edges with two equivalent Hf(1)O6 octahedra, and edges with four equivalent Mg(9)BO5 octahedra. The corner-sharing octahedral tilt angles range from 0-8°. 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)B2O4 octahedra, corners with two equivalent Mg(7)O6 octahedra, corners with two equivalent Mg(8)O6 octahedra, edges with two equivalent Mg(1)BO5 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 0-13°. 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(2)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 B(1), one O(1), one O(10), one O(11), and two equivalent O(4) atoms to form MgBO5 octahedra that share corners with two equivalent Mg(10)O6 octahedra, corners with four equivalent Mg(9)BO5 octahedra,  an edgeedge with one Mg(1)BO5 octahedra,  an edgeedge with one Mg(2)O6 octahedra,  an edgeedge with one Hf(1)O6 octahedra, edges with two equivalent Mg(5)B2O4 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 3-16°. 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 two equivalent Mg(9)BO5 octahedra, corners with four equivalent Mg(10)O6 octahedra,  an edgeedge with one Mg(1)BO5 octahedra,  an edgeedge with one Mg(2)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, and edges with two equivalent Mg(8)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-16°. Hf(1) is bonded to one O(1), one O(3), two equivalent O(10), and two equivalent O(7) atoms to form HfO6 octahedra that share corners with two equivalent Mg(2)O6 octahedra, corners with two equivalent Hf(1)O6 octahedra, edges with two equivalent Mg(9)BO5 octahedra, edges with two equivalent Mg(10)O6 octahedra, edges with two equivalent Mg(6)O6 octahedra, edges with two equivalent Mg(8)O6 octahedra, and edges with four equivalent Mg(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-1°. B(1) is bonded to one Mg(1), two equivalent Mg(5), and two equivalent Mg(9) atoms to form BMg5 square pyramids that share corners with two equivalent O(1)HfMg5 octahedra,  a cornercorner with one O(2)Mg5 square pyramid, corners with two equivalent B(1)Mg5 square pyramids, corners with two equivalent O(10)HfMg4 trigonal bipyramids, edges with two equivalent O(11)Mg6 octahedra, edges with two equivalent O(8)Mg6 octahedra, and edges with four equivalent O(4)Mg6 octahedra. The corner-sharing octahedral tilt angles are 9°. There are eleven inequivalent O sites. In the first O site, O(1) is bonded to one Mg(2), 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, corners with two equivalent B(1)Mg5 square pyramids, edges with two equivalent O(7)Hf2Mg4 octahedra, edges with two equivalent O(11)Mg6 octahedra, edges with two equivalent O(9)Mg6 octahedra, edges with four equivalent O(4)Mg6 octahedra, and edges with two equivalent O(10)HfMg4 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 0-8°. In the second O site, O(2) is bonded to one Mg(1), two equivalent Mg(10), and two equivalent Mg(7) atoms to form OMg5 square pyramids that share corners with two equivalent O(3)HfMg5 octahedra,  a cornercorner with one B(1)Mg5 square pyramid, corners with two equivalent O(2)Mg5 square pyramids, corners with two equivalent O(10)HfMg4 trigonal bipyramids, edges with two equivalent O(11)Mg6 octahedra, edges with two equivalent O(8)Mg6 octahedra, and edges with four equivalent O(5)Mg6 octahedra. The corner-sharing octahedral tilt angles are 5°. In the third O site, O(3) is bonded to one Mg(2), 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)Mg5 square pyramids, edges with two equivalent O(7)Hf2Mg4 octahedra, edges with two equivalent O(11)Mg6 octahedra, edges with two equivalent O(9)Mg6 octahedra, edges with four equivalent O(5)Mg6 octahedra, and edges with two equivalent O(10)HfMg4 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 0-5°. 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(7)Hf2Mg4 octahedra,  an edgeedge with one O(8)Mg6 octahedra,  an edgeedge with one O(9)Mg6 octahedra, edges with two equivalent O(1)HfMg5 octahedra, edges with two equivalent O(11)Mg6 octahedra, edges with two equivalent B(1)Mg5 square pyramids, and edges with two equivalent O(10)HfMg4 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 2-18°. 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(7)Hf2Mg4 octahedra,  an edgeedge with one O(8)Mg6 octahedra,  an edgeedge with one O(9)Mg6 octahedra, edges with two equivalent O(3)HfMg5 octahedra, edges with two equivalent O(11)Mg6 octahedra, edges with two equivalent O(2)Mg5 square pyramids, and edges with two equivalent O(10)HfMg4 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 3-18°. In the sixth O site, O(6) is bonded in a square co-planar geometry to one Mg(5), one Mg(7), and two equivalent Mg(3) atoms. In the seventh O site, O(7) is bonded to one Mg(6), one Mg(8), two equivalent Mg(3), and two equivalent Hf(1) atoms to form OHf2Mg4 octahedra that share corners with two equivalent O(7)Hf2Mg4 octahedra, corners with two equivalent O(9)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(10)HfMg4 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 0-1°. In the eighth O site, O(8) is bonded to one Mg(5), one Mg(7), two equivalent Mg(1), and two equivalent Mg(4) atoms to form OMg6 octahedra that share corners with two equivalent O(8)Mg6 octahedra, corners with two equivalent O(9)Mg6 octahedra, edges with two equivalent O(4)Mg6 octahedra, edges with two equivalent O(5)Mg6 octahedra, edges with four equivalent O(11)Mg6 octahedra, edges with two equivalent B(1)Mg5 square pyramids, and edges with two equivalent O(2)Mg5 square pyramids. The corner-sharing octahedral tilt angles range from 0-2°. In the ninth O site, O(9) is bonded to one Mg(6), one Mg(8), two equivalent Mg(2), and two equivalent Mg(4) atoms to form OMg6 octahedra that share corners with two equivalent O(7)Hf2Mg4 octahedra, corners with two equivalent O(8)Mg6 octahedra, corners with two equivalent O(9)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)Mg6 octahedra. The corner-sharing octahedra are not tilted. In the tenth O site, O(10) is bonded to one Mg(10), one Mg(9), two equivalent Mg(3), and one Hf(1) atom to form OHfMg4 trigonal bipyramids that share corners with two equivalent O(11)Mg6 octahedra,  a cornercorner with one B(1)Mg5 square pyramid,  a cornercorner with one O(2)Mg5 square pyramid, corners with three equivalent O(10)HfMg4 trigonal bipyramids,  an edgeedge with one O(1)HfMg5 octahedra,  an edgeedge with one O(3)HfMg5 octahedra, edges with two equivalent O(7)Hf2Mg4 octahedra, edges with two equivalent O(4)Mg6 octahedra, and edges with two equivalent O(5)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 6-18°. In the eleventh O site, O(11) is bonded to one Mg(1), one Mg(10), one Mg(2), one Mg(9), and two equivalent Mg(4) atoms to form OMg6 octahedra that share corners with four equivalent O(11)Mg6 octahedra, corners with two equivalent O(10)HfMg4 trigonal bipyramids,  an edgeedge with one O(1)HfMg5 octahedra,  an edgeedge with one O(3)HfMg5 octahedra, edges with two equivalent O(4)Mg6 octahedra, edges with two equivalent O(5)Mg6 octahedra, edges with two equivalent O(8)Mg6 octahedra, edges with two equivalent O(9)Mg6 octahedra,  an edgeedge with one B(1)Mg5 square pyramid, and  an edgeedge with one O(2)Mg5 square pyramid. The corner-sharing octahedral tilt angles range from 1-5°. is represented by the CIF card [CIF]
data_HfMg14BO15
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.508
_cell_length_b   8.969
_cell_length_c   4.273
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   326.090
_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  0.990  0.500  0.000  1.0
  Mg  Mg1  1  0.489  0.000  0.000  1.0
  Mg  Mg2  1  0.499  0.500  0.000  1.0
  Mg  Mg3  1  0.999  0.222  0.500  1.0
  Mg  Mg4  1  0.999  0.778  0.500  1.0
  Mg  Mg5  1  0.493  0.247  0.500  1.0
  Mg  Mg6  1  0.493  0.753  0.500  1.0
  Mg  Mg7  1  0.239  0.000  0.500  1.0
  Mg  Mg8  1  0.257  0.500  0.500  1.0
  Mg  Mg9  1  0.752  0.000  0.500  1.0
  Mg  Mg10  1  0.735  0.500  0.500  1.0
  Mg  Mg11  1  0.245  0.253  0.000  1.0
  Mg  Mg12  1  0.245  0.747  0.000  1.0
  Mg  Mg13  1  0.745  0.228  0.000  1.0
  Mg  Mg14  1  0.745  0.772  0.000  1.0
  B  B15  1  0.207  0.000  0.000  1.0
  O  O16  1  0.239  0.500  0.000  1.0
  O  O17  1  0.723  0.000  0.000  1.0
  O  O18  1  0.745  0.500  0.000  1.0
  O  O19  1  0.243  0.272  0.500  1.0
  O  O20  1  0.243  0.728  0.500  1.0
  O  O21  1  0.746  0.246  0.500  1.0
  O  O22  1  0.746  0.754  0.500  1.0
  O  O23  1  0.997  0.000  0.500  1.0
  O  O24  1  0.986  0.500  0.500  1.0
  O  O25  1  0.485  0.000  0.500  1.0
  O  O26  1  0.499  0.500  0.500  1.0
  O  O27  1  0.987  0.273  0.000  1.0
  O  O28  1  0.987  0.727  0.000  1.0
  O  O29  1  0.496  0.258  0.000  1.0
  O  O30  1  0.496  0.742  0.000  1.0
[/CIF]
.
The compound described by Mg14HfBO15 crystallizes in the orthorhombic Pmm2 space group. There are ten inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one B(1), one O(2), two equivalent O(11), and two equivalent O(8) atoms to form distorted MgBO5 octahedra that share corners with two equivalent Mg(1)BO5 octahedra, corners with two equivalent Mg(2)O6 octahedra, edges with two equivalent Mg(5)B2O4 octahedra, edges with two equivalent Mg(9)BO5 octahedra, 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 range from 1-2°. In the second Mg site, Mg(2) is bonded to one O(1), one O(3), two equivalent O(11), and two equivalent O(9) atoms to form MgO6 octahedra that share corners with two equivalent Mg(1)BO5 octahedra, corners with two equivalent Mg(2)O6 octahedra, corners with two equivalent Hf(1)O6 octahedra, edges with two equivalent Mg(9)BO5 octahedra, edges with two equivalent Mg(10)O6 octahedra, edges with two equivalent Mg(6)O6 octahedra, edges with two equivalent Mg(8)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-1°. 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 distorted 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)B2O4 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(9)BO5 octahedra, edges with two equivalent Mg(10)O6 octahedra, and edges with two equivalent Hf(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 1-25°. 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)B2O4 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)BO5 octahedra, edges with two equivalent Mg(9)BO5 octahedra, edges with two equivalent Mg(10)O6 octahedra, and edges with two equivalent Mg(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 3-18°. In the fifth Mg site, Mg(5) is bonded to two equivalent B(1), one O(6), one O(8), and two equivalent O(4) atoms to form MgB2O4 octahedra that share corners with two equivalent Mg(5)B2O4 octahedra, corners with two equivalent Mg(6)O6 octahedra, corners with two equivalent Mg(7)O6 octahedra, edges with two equivalent Mg(1)BO5 octahedra, edges with two equivalent Mg(3)O6 octahedra, edges with two equivalent Mg(4)O6 octahedra, and edges with four equivalent Mg(9)BO5 octahedra. The corner-sharing octahedral tilt angles range from 0-15°. 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(5)B2O4 octahedra, corners with two equivalent Mg(6)O6 octahedra, corners with two equivalent Mg(8)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, edges with two equivalent Hf(1)O6 octahedra, and edges with four equivalent Mg(9)BO5 octahedra. The corner-sharing octahedral tilt angles range from 0-8°. 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)B2O4 octahedra, corners with two equivalent Mg(7)O6 octahedra, corners with two equivalent Mg(8)O6 octahedra, edges with two equivalent Mg(1)BO5 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 0-13°. 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(2)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 B(1), one O(1), one O(10), one O(11), and two equivalent O(4) atoms to form MgBO5 octahedra that share corners with two equivalent Mg(10)O6 octahedra, corners with four equivalent Mg(9)BO5 octahedra,  an edgeedge with one Mg(1)BO5 octahedra,  an edgeedge with one Mg(2)O6 octahedra,  an edgeedge with one Hf(1)O6 octahedra, edges with two equivalent Mg(5)B2O4 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 3-16°. 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 two equivalent Mg(9)BO5 octahedra, corners with four equivalent Mg(10)O6 octahedra,  an edgeedge with one Mg(1)BO5 octahedra,  an edgeedge with one Mg(2)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, and edges with two equivalent Mg(8)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-16°. Hf(1) is bonded to one O(1), one O(3), two equivalent O(10), and two equivalent O(7) atoms to form HfO6 octahedra that share corners with two equivalent Mg(2)O6 octahedra, corners with two equivalent Hf(1)O6 octahedra, edges with two equivalent Mg(9)BO5 octahedra, edges with two equivalent Mg(10)O6 octahedra, edges with two equivalent Mg(6)O6 octahedra, edges with two equivalent Mg(8)O6 octahedra, and edges with four equivalent Mg(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-1°. B(1) is bonded to one Mg(1), two equivalent Mg(5), and two equivalent Mg(9) atoms to form BMg5 square pyramids that share corners with two equivalent O(1)HfMg5 octahedra,  a cornercorner with one O(2)Mg5 square pyramid, corners with two equivalent B(1)Mg5 square pyramids, corners with two equivalent O(10)HfMg4 trigonal bipyramids, edges with two equivalent O(11)Mg6 octahedra, edges with two equivalent O(8)Mg6 octahedra, and edges with four equivalent O(4)Mg6 octahedra. The corner-sharing octahedral tilt angles are 9°. There are eleven inequivalent O sites. In the first O site, O(1) is bonded to one Mg(2), 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, corners with two equivalent B(1)Mg5 square pyramids, edges with two equivalent O(7)Hf2Mg4 octahedra, edges with two equivalent O(11)Mg6 octahedra, edges with two equivalent O(9)Mg6 octahedra, edges with four equivalent O(4)Mg6 octahedra, and edges with two equivalent O(10)HfMg4 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 0-8°. In the second O site, O(2) is bonded to one Mg(1), two equivalent Mg(10), and two equivalent Mg(7) atoms to form OMg5 square pyramids that share corners with two equivalent O(3)HfMg5 octahedra,  a cornercorner with one B(1)Mg5 square pyramid, corners with two equivalent O(2)Mg5 square pyramids, corners with two equivalent O(10)HfMg4 trigonal bipyramids, edges with two equivalent O(11)Mg6 octahedra, edges with two equivalent O(8)Mg6 octahedra, and edges with four equivalent O(5)Mg6 octahedra. The corner-sharing octahedral tilt angles are 5°. In the third O site, O(3) is bonded to one Mg(2), 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)Mg5 square pyramids, edges with two equivalent O(7)Hf2Mg4 octahedra, edges with two equivalent O(11)Mg6 octahedra, edges with two equivalent O(9)Mg6 octahedra, edges with four equivalent O(5)Mg6 octahedra, and edges with two equivalent O(10)HfMg4 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 0-5°. 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(7)Hf2Mg4 octahedra,  an edgeedge with one O(8)Mg6 octahedra,  an edgeedge with one O(9)Mg6 octahedra, edges with two equivalent O(1)HfMg5 octahedra, edges with two equivalent O(11)Mg6 octahedra, edges with two equivalent B(1)Mg5 square pyramids, and edges with two equivalent O(10)HfMg4 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 2-18°. 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(7)Hf2Mg4 octahedra,  an edgeedge with one O(8)Mg6 octahedra,  an edgeedge with one O(9)Mg6 octahedra, edges with two equivalent O(3)HfMg5 octahedra, edges with two equivalent O(11)Mg6 octahedra, edges with two equivalent O(2)Mg5 square pyramids, and edges with two equivalent O(10)HfMg4 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 3-18°. In the sixth O site, O(6) is bonded in a square co-planar geometry to one Mg(5), one Mg(7), and two equivalent Mg(3) atoms. In the seventh O site, O(7) is bonded to one Mg(6), one Mg(8), two equivalent Mg(3), and two equivalent Hf(1) atoms to form OHf2Mg4 octahedra that share corners with two equivalent O(7)Hf2Mg4 octahedra, corners with two equivalent O(9)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(10)HfMg4 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 0-1°. In the eighth O site, O(8) is bonded to one Mg(5), one Mg(7), two equivalent Mg(1), and two equivalent Mg(4) atoms to form OMg6 octahedra that share corners with two equivalent O(8)Mg6 octahedra, corners with two equivalent O(9)Mg6 octahedra, edges with two equivalent O(4)Mg6 octahedra, edges with two equivalent O(5)Mg6 octahedra, edges with four equivalent O(11)Mg6 octahedra, edges with two equivalent B(1)Mg5 square pyramids, and edges with two equivalent O(2)Mg5 square pyramids. The corner-sharing octahedral tilt angles range from 0-2°. In the ninth O site, O(9) is bonded to one Mg(6), one Mg(8), two equivalent Mg(2), and two equivalent Mg(4) atoms to form OMg6 octahedra that share corners with two equivalent O(7)Hf2Mg4 octahedra, corners with two equivalent O(8)Mg6 octahedra, corners with two equivalent O(9)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)Mg6 octahedra. The corner-sharing octahedra are not tilted. In the tenth O site, O(10) is bonded to one Mg(10), one Mg(9), two equivalent Mg(3), and one Hf(1) atom to form OHfMg4 trigonal bipyramids that share corners with two equivalent O(11)Mg6 octahedra,  a cornercorner with one B(1)Mg5 square pyramid,  a cornercorner with one O(2)Mg5 square pyramid, corners with three equivalent O(10)HfMg4 trigonal bipyramids,  an edgeedge with one O(1)HfMg5 octahedra,  an edgeedge with one O(3)HfMg5 octahedra, edges with two equivalent O(7)Hf2Mg4 octahedra, edges with two equivalent O(4)Mg6 octahedra, and edges with two equivalent O(5)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 6-18°. In the eleventh O site, O(11) is bonded to one Mg(1), one Mg(10), one Mg(2), one Mg(9), and two equivalent Mg(4) atoms to form OMg6 octahedra that share corners with four equivalent O(11)Mg6 octahedra, corners with two equivalent O(10)HfMg4 trigonal bipyramids,  an edgeedge with one O(1)HfMg5 octahedra,  an edgeedge with one O(3)HfMg5 octahedra, edges with two equivalent O(4)Mg6 octahedra, edges with two equivalent O(5)Mg6 octahedra, edges with two equivalent O(8)Mg6 octahedra, edges with two equivalent O(9)Mg6 octahedra,  an edgeedge with one B(1)Mg5 square pyramid, and  an edgeedge with one O(2)Mg5 square pyramid. The corner-sharing octahedral tilt angles range from 1-5°. is represented by the CIF card [CIF]
data_HfMg14BO15
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.508
_cell_length_b   8.969
_cell_length_c   4.273
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   326.090
_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  0.990  0.500  0.000  1.0
  Mg  Mg1  1  0.489  0.000  0.000  1.0
  Mg  Mg2  1  0.499  0.500  0.000  1.0
  Mg  Mg3  1  0.999  0.222  0.500  1.0
  Mg  Mg4  1  0.999  0.778  0.500  1.0
  Mg  Mg5  1  0.493  0.247  0.500  1.0
  Mg  Mg6  1  0.493  0.753  0.500  1.0
  Mg  Mg7  1  0.239  0.000  0.500  1.0
  Mg  Mg8  1  0.257  0.500  0.500  1.0
  Mg  Mg9  1  0.752  0.000  0.500  1.0
  Mg  Mg10  1  0.735  0.500  0.500  1.0
  Mg  Mg11  1  0.245  0.253  0.000  1.0
  Mg  Mg12  1  0.245  0.747  0.000  1.0
  Mg  Mg13  1  0.745  0.228  0.000  1.0
  Mg  Mg14  1  0.745  0.772  0.000  1.0
  B  B15  1  0.207  0.000  0.000  1.0
  O  O16  1  0.239  0.500  0.000  1.0
  O  O17  1  0.723  0.000  0.000  1.0
  O  O18  1  0.745  0.500  0.000  1.0
  O  O19  1  0.243  0.272  0.500  1.0
  O  O20  1  0.243  0.728  0.500  1.0
  O  O21  1  0.746  0.246  0.500  1.0
  O  O22  1  0.746  0.754  0.500  1.0
  O  O23  1  0.997  0.000  0.500  1.0
  O  O24  1  0.986  0.500  0.500  1.0
  O  O25  1  0.485  0.000  0.500  1.0
  O  O26  1  0.499  0.500  0.500  1.0
  O  O27  1  0.987  0.273  0.000  1.0
  O  O28  1  0.987  0.727  0.000  1.0
  O  O29  1  0.496  0.258  0.000  1.0
  O  O30  1  0.496  0.742  0.000  1.0
[/CIF]
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