The structure described by BaMg14FeO16 is Caswellsilverite-derived structured and crystallizes in the tetragonal P4/mmm space group. Ba(1) is bonded to two equivalent O(6) and four equivalent O(2) atoms to form BaO6 octahedra that share corners with two equivalent Ba(1)O6 octahedra, corners with four equivalent Mg(1)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, and edges with eight equivalent Mg(3)O6 octahedra. The corner-sharing octahedra are not tilted. There are four 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 Ba(1)O6 octahedra, corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent Fe(1)O6 octahedra, edges with four equivalent Mg(2)O6 octahedra, edges with four equivalent Mg(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 MgO6 octahedra that share corners with two equivalent Mg(3)O6 octahedra, corners with four equivalent Mg(2)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Mg(2)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-4°. In the third 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 Ba(1)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Mg(2)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-7°. In the fourth 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 Ba(1)O6 octahedra,  an edgeedge with one Fe(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 2-10°. Fe(1) is bonded to two equivalent O(4) and four equivalent O(1) atoms to form FeO6 octahedra that share corners with two equivalent Fe(1)O6 octahedra, corners with four equivalent Mg(1)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, and edges with eight equivalent Mg(2)O6 octahedra. The corner-sharing octahedra are not tilted. There are six inequivalent O sites. In the first O site, O(1) is bonded to one Mg(1), two equivalent Mg(2), two equivalent Mg(4), and one Fe(1) atom to form OMg5Fe octahedra that share corners with two equivalent O(2)BaMg5 octahedra, corners with four equivalent O(1)Mg5Fe octahedra, edges with two equivalent O(2)BaMg5 octahedra, edges with two equivalent O(4)Mg4Fe2 octahedra, edges with two equivalent O(1)Mg5Fe 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 0-4°. In the second O site, O(2) is bonded to one Ba(1), one Mg(1), two equivalent Mg(3), and two equivalent Mg(4) atoms to form OBaMg5 octahedra that share corners with two equivalent O(1)Mg5Fe octahedra, corners with four equivalent O(2)BaMg5 octahedra, edges with two equivalent O(6)Ba2Mg4 octahedra, edges with two equivalent O(2)BaMg5 octahedra, edges with two equivalent O(1)Mg5Fe 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 0-7°. 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(6)Ba2Mg4 octahedra,  an edgeedge with one O(4)Mg4Fe2 octahedra, edges with two equivalent O(5)Mg6 octahedra, edges with four equivalent O(2)BaMg5 octahedra, and edges with four equivalent O(1)Mg5Fe octahedra. The corner-sharing octahedral tilt angles range from 1-6°. In the fourth O site, O(4) is bonded to four equivalent Mg(2) and two equivalent Fe(1) atoms to form OMg4Fe2 octahedra that share corners with two equivalent O(4)Mg4Fe2 octahedra, corners with four equivalent O(5)Mg6 octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with eight equivalent O(1)Mg5Fe octahedra. The corner-sharing octahedra are not tilted. In the fifth O site, O(5) is bonded to two equivalent Mg(1), two equivalent Mg(2), and two equivalent Mg(3) atoms to form OMg6 octahedra that share corners with two equivalent O(6)Ba2Mg4 octahedra, corners with two equivalent O(4)Mg4Fe2 octahedra, corners with two equivalent O(5)Mg6 octahedra, edges with four equivalent O(2)BaMg5 octahedra, edges with four equivalent O(1)Mg5Fe octahedra, and edges with four equivalent O(3)Mg6 octahedra. The corner-sharing octahedra are not tilted. In the sixth O site, O(6) is bonded to two equivalent Ba(1) and four equivalent Mg(3) atoms to form OBa2Mg4 octahedra that share corners with two equivalent O(6)Ba2Mg4 octahedra, corners with four equivalent O(5)Mg6 octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with eight equivalent O(2)BaMg5 octahedra. The corner-sharing octahedra are not tilted. is represented by the CIF file [CIF]
data_BaMg14FeO16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.745
_cell_length_b   8.745
_cell_length_c   4.508
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   344.709
_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
  Ba  Ba0  1  0.500  0.500  0.000  1.0
  Mg  Mg1  1  0.000  0.500  0.000  1.0
  Mg  Mg2  1  0.500  0.000  0.000  1.0
  Mg  Mg3  1  0.000  0.247  0.500  1.0
  Mg  Mg4  1  0.000  0.753  0.500  1.0
  Mg  Mg5  1  0.500  0.235  0.500  1.0
  Mg  Mg6  1  0.500  0.765  0.500  1.0
  Mg  Mg7  1  0.247  0.000  0.500  1.0
  Mg  Mg8  1  0.235  0.500  0.500  1.0
  Mg  Mg9  1  0.753  0.000  0.500  1.0
  Mg  Mg10  1  0.765  0.500  0.500  1.0
  Mg  Mg11  1  0.242  0.242  0.000  1.0
  Mg  Mg12  1  0.242  0.758  0.000  1.0
  Mg  Mg13  1  0.758  0.242  0.000  1.0
  Mg  Mg14  1  0.758  0.758  0.000  1.0
  Fe  Fe15  1  0.000  0.000  0.000  1.0
  O  O16  1  0.247  0.000  0.000  1.0
  O  O17  1  0.219  0.500  0.000  1.0
  O  O18  1  0.753  0.000  0.000  1.0
  O  O19  1  0.781  0.500  0.000  1.0
  O  O20  1  0.249  0.249  0.500  1.0
  O  O21  1  0.249  0.751  0.500  1.0
  O  O22  1  0.751  0.249  0.500  1.0
  O  O23  1  0.751  0.751  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  0.247  0.000  1.0
  O  O29  1  0.000  0.753  0.000  1.0
  O  O30  1  0.500  0.219  0.000  1.0
  O  O31  1  0.500  0.781  0.000  1.0
[/CIF]
.
The structure described by BaMg14FeO16 is Caswellsilverite-derived structured and crystallizes in the tetragonal P4/mmm space group. Ba(1) is bonded to two equivalent O(6) and four equivalent O(2) atoms to form BaO6 octahedra that share corners with two equivalent Ba(1)O6 octahedra, corners with four equivalent Mg(1)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, and edges with eight equivalent Mg(3)O6 octahedra. The corner-sharing octahedra are not tilted. There are four 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 Ba(1)O6 octahedra, corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent Fe(1)O6 octahedra, edges with four equivalent Mg(2)O6 octahedra, edges with four equivalent Mg(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 MgO6 octahedra that share corners with two equivalent Mg(3)O6 octahedra, corners with four equivalent Mg(2)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Mg(2)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, edges with two equivalent Fe(1)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-4°. In the third 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 Ba(1)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Mg(2)O6 octahedra, edges with two equivalent Mg(3)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-7°. In the fourth 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 Ba(1)O6 octahedra,  an edgeedge with one Fe(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 2-10°. Fe(1) is bonded to two equivalent O(4) and four equivalent O(1) atoms to form FeO6 octahedra that share corners with two equivalent Fe(1)O6 octahedra, corners with four equivalent Mg(1)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, and edges with eight equivalent Mg(2)O6 octahedra. The corner-sharing octahedra are not tilted. There are six inequivalent O sites. In the first O site, O(1) is bonded to one Mg(1), two equivalent Mg(2), two equivalent Mg(4), and one Fe(1) atom to form OMg5Fe octahedra that share corners with two equivalent O(2)BaMg5 octahedra, corners with four equivalent O(1)Mg5Fe octahedra, edges with two equivalent O(2)BaMg5 octahedra, edges with two equivalent O(4)Mg4Fe2 octahedra, edges with two equivalent O(1)Mg5Fe 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 0-4°. In the second O site, O(2) is bonded to one Ba(1), one Mg(1), two equivalent Mg(3), and two equivalent Mg(4) atoms to form OBaMg5 octahedra that share corners with two equivalent O(1)Mg5Fe octahedra, corners with four equivalent O(2)BaMg5 octahedra, edges with two equivalent O(6)Ba2Mg4 octahedra, edges with two equivalent O(2)BaMg5 octahedra, edges with two equivalent O(1)Mg5Fe 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 0-7°. 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(6)Ba2Mg4 octahedra,  an edgeedge with one O(4)Mg4Fe2 octahedra, edges with two equivalent O(5)Mg6 octahedra, edges with four equivalent O(2)BaMg5 octahedra, and edges with four equivalent O(1)Mg5Fe octahedra. The corner-sharing octahedral tilt angles range from 1-6°. In the fourth O site, O(4) is bonded to four equivalent Mg(2) and two equivalent Fe(1) atoms to form OMg4Fe2 octahedra that share corners with two equivalent O(4)Mg4Fe2 octahedra, corners with four equivalent O(5)Mg6 octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with eight equivalent O(1)Mg5Fe octahedra. The corner-sharing octahedra are not tilted. In the fifth O site, O(5) is bonded to two equivalent Mg(1), two equivalent Mg(2), and two equivalent Mg(3) atoms to form OMg6 octahedra that share corners with two equivalent O(6)Ba2Mg4 octahedra, corners with two equivalent O(4)Mg4Fe2 octahedra, corners with two equivalent O(5)Mg6 octahedra, edges with four equivalent O(2)BaMg5 octahedra, edges with four equivalent O(1)Mg5Fe octahedra, and edges with four equivalent O(3)Mg6 octahedra. The corner-sharing octahedra are not tilted. In the sixth O site, O(6) is bonded to two equivalent Ba(1) and four equivalent Mg(3) atoms to form OBa2Mg4 octahedra that share corners with two equivalent O(6)Ba2Mg4 octahedra, corners with four equivalent O(5)Mg6 octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with eight equivalent O(2)BaMg5 octahedra. The corner-sharing octahedra are not tilted. is represented by the CIF file [CIF]
data_BaMg14FeO16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.745
_cell_length_b   8.745
_cell_length_c   4.508
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   344.709
_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
  Ba  Ba0  1  0.500  0.500  0.000  1.0
  Mg  Mg1  1  0.000  0.500  0.000  1.0
  Mg  Mg2  1  0.500  0.000  0.000  1.0
  Mg  Mg3  1  0.000  0.247  0.500  1.0
  Mg  Mg4  1  0.000  0.753  0.500  1.0
  Mg  Mg5  1  0.500  0.235  0.500  1.0
  Mg  Mg6  1  0.500  0.765  0.500  1.0
  Mg  Mg7  1  0.247  0.000  0.500  1.0
  Mg  Mg8  1  0.235  0.500  0.500  1.0
  Mg  Mg9  1  0.753  0.000  0.500  1.0
  Mg  Mg10  1  0.765  0.500  0.500  1.0
  Mg  Mg11  1  0.242  0.242  0.000  1.0
  Mg  Mg12  1  0.242  0.758  0.000  1.0
  Mg  Mg13  1  0.758  0.242  0.000  1.0
  Mg  Mg14  1  0.758  0.758  0.000  1.0
  Fe  Fe15  1  0.000  0.000  0.000  1.0
  O  O16  1  0.247  0.000  0.000  1.0
  O  O17  1  0.219  0.500  0.000  1.0
  O  O18  1  0.753  0.000  0.000  1.0
  O  O19  1  0.781  0.500  0.000  1.0
  O  O20  1  0.249  0.249  0.500  1.0
  O  O21  1  0.249  0.751  0.500  1.0
  O  O22  1  0.751  0.249  0.500  1.0
  O  O23  1  0.751  0.751  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  0.247  0.000  1.0
  O  O29  1  0.000  0.753  0.000  1.0
  O  O30  1  0.500  0.219  0.000  1.0
  O  O31  1  0.500  0.781  0.000  1.0
[/CIF]
.