The material described by Mg14GaBO16 crystallizes in the tetragonal P4/mmm space group. There are six inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(5) atoms to form MgO6 octahedra that share corners with two equivalent Mg(1)O6 octahedra; corners with two equivalent Ga(1)O6 octahedra; edges with four Mg(2,2)O6 octahedra; edges with four Mg(3,3)O6 octahedra; and edges with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedra are not tilted. In the second Mg site, Mg(2) is bonded to one O(4), one O(5), two equivalent O(1), and two equivalent O(3) atoms to form a mixture of corner and edge-sharing MgO6 octahedra. The corner-sharing octahedral tilt angles range from 0-11°. In the third Mg site, Mg(2) is bonded to one O(4), one O(5), two equivalent O(1), and two equivalent O(3) atoms to form a mixture of corner and edge-sharing MgO6 octahedra. The corner-sharing octahedral tilt angles range from 0-11°. In the fourth Mg site, Mg(3) is bonded to one O(5), one O(6), two equivalent O(2), and two equivalent O(3) atoms to form MgO6 octahedra that share corners with two equivalent Mg(2)O6 octahedra; corners with four equivalent Mg(3)O6 octahedra; edges with two equivalent Mg(1)O6 octahedra; edges with two Mg(2,2)O6 octahedra; edges with two Mg(3,3)O6 octahedra; edges with two equivalent Ga(1)O6 octahedra; and edges with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-8°. In the fifth Mg site, Mg(3) is bonded to one O(5), one O(6), two equivalent O(2), and two equivalent O(3) atoms to form MgO6 octahedra that share corners with two equivalent Mg(2)O6 octahedra; corners with four Mg(3,3)O6 octahedra; edges with two equivalent Mg(1)O6 octahedra; edges with two Mg(2,2)O6 octahedra; edges with two equivalent Mg(3)O6 octahedra; edges with two equivalent Ga(1)O6 octahedra; and edges with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-8°. In the sixth Mg site, Mg(4) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(3) atoms to form MgO6 octahedra that share corners with six equivalent Mg(4)O6 octahedra,  an edgeedge with one Ga(1)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with four equivalent Mg(2)O6 octahedra, and edges with four equivalent Mg(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 5-12°. Ga(1) is bonded to two equivalent O(6) and four equivalent O(2) atoms to form GaO6 octahedra that share corners with two equivalent Ga(1)O6 octahedra; corners with four equivalent Mg(1)O6 octahedra; edges with four equivalent Mg(4)O6 octahedra; and edges with eight Mg(3,3)O6 octahedra. The corner-sharing octahedra are not tilted. B(1) is bonded in a distorted linear geometry to two equivalent O(4) atoms. There are six inequivalent O sites. In the first O site, O(1) is bonded to one Mg(1), two equivalent Mg(2), and two equivalent Mg(4) atoms to form distorted OMg5 square pyramids that share corners with two equivalent O(4)Mg4B2 octahedra, corners with two equivalent O(2)Mg5Ga octahedra, corners with five equivalent O(1)Mg5 square pyramids, edges with two equivalent O(2)Mg5Ga octahedra, edges with two equivalent O(5)Mg6 octahedra, and edges with four equivalent O(3)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 11-84°. In the second O site, O(2) is bonded to one Mg(1), two equivalent Mg(3), two equivalent Mg(4), and one Ga(1) atom to form OMg5Ga octahedra that share corners with four equivalent O(2)Mg5Ga octahedra, corners with two equivalent O(1)Mg5 square pyramids, edges with two equivalent O(6)Mg4Ga2 octahedra, edges with two equivalent O(2)Mg5Ga octahedra, edges with two equivalent O(5)Mg6 octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with two equivalent O(1)Mg5 square pyramids. The corner-sharing octahedral tilt angles range from 0-8°. In the third O site, O(3) is bonded to two equivalent Mg(2), two equivalent Mg(3), and two equivalent Mg(4) atoms to form OMg6 octahedra that share corners with six equivalent O(3)Mg6 octahedra,  an edgeedge with one O(4)Mg4B2 octahedra,  an edgeedge with one O(6)Mg4Ga2 octahedra, edges with two equivalent O(5)Mg6 octahedra, edges with four equivalent O(2)Mg5Ga octahedra, and edges with four equivalent O(1)Mg5 square pyramids. The corner-sharing octahedral tilt angles range from 2-5°. In the fourth O site, O(4) is bonded to four Mg(2,2) and two equivalent B(1) atoms to form OMg4B2 octahedra that share corners with two equivalent O(4)Mg4B2 octahedra, corners with four equivalent O(5)Mg6 octahedra, corners with eight equivalent O(1)Mg5 square pyramids, and edges with four equivalent O(3)Mg6 octahedra. The corner-sharing octahedra are not tilted. In the fifth O site, O(5) is bonded to two equivalent Mg(1); two Mg(2,2); and two Mg(3,3) atoms to form OMg6 octahedra that share corners with two equivalent O(4)Mg4B2 octahedra, corners with two equivalent O(6)Mg4Ga2 octahedra, corners with two equivalent O(5)Mg6 octahedra, edges with four equivalent O(2)Mg5Ga octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with four equivalent O(1)Mg5 square pyramids. The corner-sharing octahedra are not tilted. In the sixth O site, O(6) is bonded to four Mg(3,3) and two equivalent Ga(1) atoms to form OMg4Ga2 octahedra that share corners with two equivalent O(6)Mg4Ga2 octahedra, corners with four equivalent O(5)Mg6 octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with eight equivalent O(2)Mg5Ga octahedra. The corner-sharing octahedra are not tilted. is represented by the Crystallographic Information File (CIF) [CIF]
data_Mg14GaBO16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.568
_cell_length_b   8.568
_cell_length_c   4.260
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   312.723
_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
  Mg  Mg0  1  0.000  0.500  0.000  1.0
  Mg  Mg1  1  0.500  0.000  0.000  1.0
  Mg  Mg2  1  0.000  0.244  0.500  1.0
  Mg  Mg3  1  0.000  0.756  0.500  1.0
  Mg  Mg4  1  0.500  0.246  0.500  1.0
  Mg  Mg5  1  0.500  0.754  0.500  1.0
  Mg  Mg6  1  0.244  0.000  0.500  1.0
  Mg  Mg7  1  0.246  0.500  0.500  1.0
  Mg  Mg8  1  0.756  0.000  0.500  1.0
  Mg  Mg9  1  0.754  0.500  0.500  1.0
  Mg  Mg10  1  0.243  0.243  0.000  1.0
  Mg  Mg11  1  0.243  0.757  0.000  1.0
  Mg  Mg12  1  0.757  0.243  0.000  1.0
  Mg  Mg13  1  0.757  0.757  0.000  1.0
  Ga  Ga14  1  0.500  0.500  0.000  1.0
  B  B15  1  0.000  0.000  0.000  1.0
  O  O16  1  0.268  0.000  0.000  1.0
  O  O17  1  0.263  0.500  0.000  1.0
  O  O18  1  0.732  0.000  0.000  1.0
  O  O19  1  0.737  0.500  0.000  1.0
  O  O20  1  0.250  0.250  0.500  1.0
  O  O21  1  0.250  0.750  0.500  1.0
  O  O22  1  0.750  0.250  0.500  1.0
  O  O23  1  0.750  0.750  0.500  1.0
  O  O24  1  0.000  0.000  0.500  1.0
  O  O25  1  0.000  0.500  0.500  1.0
  O  O26  1  0.500  0.000  0.500  1.0
  O  O27  1  0.500  0.500  0.500  1.0
  O  O28  1  0.000  0.268  0.000  1.0
  O  O29  1  0.000  0.732  0.000  1.0
  O  O30  1  0.500  0.263  0.000  1.0
  O  O31  1  0.500  0.737  0.000  1.0
[/CIF]
.
The material described by Mg14GaBO16 crystallizes in the tetragonal P4/mmm space group. There are six inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(5) atoms to form MgO6 octahedra that share corners with two equivalent Mg(1)O6 octahedra; corners with two equivalent Ga(1)O6 octahedra; edges with four Mg(2,2)O6 octahedra; edges with four Mg(3,3)O6 octahedra; and edges with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedra are not tilted. In the second Mg site, Mg(2) is bonded to one O(4), one O(5), two equivalent O(1), and two equivalent O(3) atoms to form a mixture of corner and edge-sharing MgO6 octahedra. The corner-sharing octahedral tilt angles range from 0-11°. In the third Mg site, Mg(2) is bonded to one O(4), one O(5), two equivalent O(1), and two equivalent O(3) atoms to form a mixture of corner and edge-sharing MgO6 octahedra. The corner-sharing octahedral tilt angles range from 0-11°. In the fourth Mg site, Mg(3) is bonded to one O(5), one O(6), two equivalent O(2), and two equivalent O(3) atoms to form MgO6 octahedra that share corners with two equivalent Mg(2)O6 octahedra; corners with four equivalent Mg(3)O6 octahedra; edges with two equivalent Mg(1)O6 octahedra; edges with two Mg(2,2)O6 octahedra; edges with two Mg(3,3)O6 octahedra; edges with two equivalent Ga(1)O6 octahedra; and edges with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-8°. In the fifth Mg site, Mg(3) is bonded to one O(5), one O(6), two equivalent O(2), and two equivalent O(3) atoms to form MgO6 octahedra that share corners with two equivalent Mg(2)O6 octahedra; corners with four Mg(3,3)O6 octahedra; edges with two equivalent Mg(1)O6 octahedra; edges with two Mg(2,2)O6 octahedra; edges with two equivalent Mg(3)O6 octahedra; edges with two equivalent Ga(1)O6 octahedra; and edges with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-8°. In the sixth Mg site, Mg(4) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(3) atoms to form MgO6 octahedra that share corners with six equivalent Mg(4)O6 octahedra,  an edgeedge with one Ga(1)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with four equivalent Mg(2)O6 octahedra, and edges with four equivalent Mg(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 5-12°. Ga(1) is bonded to two equivalent O(6) and four equivalent O(2) atoms to form GaO6 octahedra that share corners with two equivalent Ga(1)O6 octahedra; corners with four equivalent Mg(1)O6 octahedra; edges with four equivalent Mg(4)O6 octahedra; and edges with eight Mg(3,3)O6 octahedra. The corner-sharing octahedra are not tilted. B(1) is bonded in a distorted linear geometry to two equivalent O(4) atoms. There are six inequivalent O sites. In the first O site, O(1) is bonded to one Mg(1), two equivalent Mg(2), and two equivalent Mg(4) atoms to form distorted OMg5 square pyramids that share corners with two equivalent O(4)Mg4B2 octahedra, corners with two equivalent O(2)Mg5Ga octahedra, corners with five equivalent O(1)Mg5 square pyramids, edges with two equivalent O(2)Mg5Ga octahedra, edges with two equivalent O(5)Mg6 octahedra, and edges with four equivalent O(3)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 11-84°. In the second O site, O(2) is bonded to one Mg(1), two equivalent Mg(3), two equivalent Mg(4), and one Ga(1) atom to form OMg5Ga octahedra that share corners with four equivalent O(2)Mg5Ga octahedra, corners with two equivalent O(1)Mg5 square pyramids, edges with two equivalent O(6)Mg4Ga2 octahedra, edges with two equivalent O(2)Mg5Ga octahedra, edges with two equivalent O(5)Mg6 octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with two equivalent O(1)Mg5 square pyramids. The corner-sharing octahedral tilt angles range from 0-8°. In the third O site, O(3) is bonded to two equivalent Mg(2), two equivalent Mg(3), and two equivalent Mg(4) atoms to form OMg6 octahedra that share corners with six equivalent O(3)Mg6 octahedra,  an edgeedge with one O(4)Mg4B2 octahedra,  an edgeedge with one O(6)Mg4Ga2 octahedra, edges with two equivalent O(5)Mg6 octahedra, edges with four equivalent O(2)Mg5Ga octahedra, and edges with four equivalent O(1)Mg5 square pyramids. The corner-sharing octahedral tilt angles range from 2-5°. In the fourth O site, O(4) is bonded to four Mg(2,2) and two equivalent B(1) atoms to form OMg4B2 octahedra that share corners with two equivalent O(4)Mg4B2 octahedra, corners with four equivalent O(5)Mg6 octahedra, corners with eight equivalent O(1)Mg5 square pyramids, and edges with four equivalent O(3)Mg6 octahedra. The corner-sharing octahedra are not tilted. In the fifth O site, O(5) is bonded to two equivalent Mg(1); two Mg(2,2); and two Mg(3,3) atoms to form OMg6 octahedra that share corners with two equivalent O(4)Mg4B2 octahedra, corners with two equivalent O(6)Mg4Ga2 octahedra, corners with two equivalent O(5)Mg6 octahedra, edges with four equivalent O(2)Mg5Ga octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with four equivalent O(1)Mg5 square pyramids. The corner-sharing octahedra are not tilted. In the sixth O site, O(6) is bonded to four Mg(3,3) and two equivalent Ga(1) atoms to form OMg4Ga2 octahedra that share corners with two equivalent O(6)Mg4Ga2 octahedra, corners with four equivalent O(5)Mg6 octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with eight equivalent O(2)Mg5Ga octahedra. The corner-sharing octahedra are not tilted. is represented by the Crystallographic Information File (CIF) [CIF]
data_Mg14GaBO16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.568
_cell_length_b   8.568
_cell_length_c   4.260
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   312.723
_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
  Mg  Mg0  1  0.000  0.500  0.000  1.0
  Mg  Mg1  1  0.500  0.000  0.000  1.0
  Mg  Mg2  1  0.000  0.244  0.500  1.0
  Mg  Mg3  1  0.000  0.756  0.500  1.0
  Mg  Mg4  1  0.500  0.246  0.500  1.0
  Mg  Mg5  1  0.500  0.754  0.500  1.0
  Mg  Mg6  1  0.244  0.000  0.500  1.0
  Mg  Mg7  1  0.246  0.500  0.500  1.0
  Mg  Mg8  1  0.756  0.000  0.500  1.0
  Mg  Mg9  1  0.754  0.500  0.500  1.0
  Mg  Mg10  1  0.243  0.243  0.000  1.0
  Mg  Mg11  1  0.243  0.757  0.000  1.0
  Mg  Mg12  1  0.757  0.243  0.000  1.0
  Mg  Mg13  1  0.757  0.757  0.000  1.0
  Ga  Ga14  1  0.500  0.500  0.000  1.0
  B  B15  1  0.000  0.000  0.000  1.0
  O  O16  1  0.268  0.000  0.000  1.0
  O  O17  1  0.263  0.500  0.000  1.0
  O  O18  1  0.732  0.000  0.000  1.0
  O  O19  1  0.737  0.500  0.000  1.0
  O  O20  1  0.250  0.250  0.500  1.0
  O  O21  1  0.250  0.750  0.500  1.0
  O  O22  1  0.750  0.250  0.500  1.0
  O  O23  1  0.750  0.750  0.500  1.0
  O  O24  1  0.000  0.000  0.500  1.0
  O  O25  1  0.000  0.500  0.500  1.0
  O  O26  1  0.500  0.000  0.500  1.0
  O  O27  1  0.500  0.500  0.500  1.0
  O  O28  1  0.000  0.268  0.000  1.0
  O  O29  1  0.000  0.732  0.000  1.0
  O  O30  1  0.500  0.263  0.000  1.0
  O  O31  1  0.500  0.737  0.000  1.0
[/CIF]
.