The structure described by Ba2MgNb4O12 crystallizes in the monoclinic Pm space group. There are two inequivalent Ba sites. In the first Ba site, Ba(1) is bonded in a 10-coordinate geometry to one O(4), one O(7), two equivalent O(10), two equivalent O(11), two equivalent O(5), and two equivalent O(9) atoms. In the second Ba site, Ba(2) is bonded in a 8-coordinate geometry to one O(4), one O(7), two equivalent O(3), two equivalent O(8), and two equivalent O(9) atoms. Mg(1) is bonded in a see-saw-like geometry to one O(1), one O(6), and two equivalent O(2) atoms. There are four inequivalent Nb sites. In the first Nb site, Nb(1) is bonded to one O(10), one O(3), one O(8), one O(9), and two equivalent O(4) atoms to form a mixture of edge and corner-sharing NbO6 octahedra. The corner-sharing octahedral tilt angles range from 3-34°. In the second Nb site, Nb(2) is bonded to one O(12), one O(2), one O(5), one O(8), and two equivalent O(1) atoms to form a mixture of edge and corner-sharing NbO6 octahedra. The corner-sharing octahedral tilt angles range from 9-34°. In the third Nb site, Nb(3) is bonded to one O(11), one O(12), one O(2), one O(5), and two equivalent O(6) atoms to form a mixture of edge and corner-sharing NbO6 octahedra. The corner-sharing octahedral tilt angles range from 8-52°. In the fourth Nb site, Nb(4) is bonded to one O(10), one O(11), one O(3), one O(9), and two equivalent O(7) atoms to form a mixture of edge and corner-sharing NbO6 octahedra. The corner-sharing octahedral tilt angles range from 3-52°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a T-shaped geometry to one Mg(1) and two equivalent Nb(2) atoms. In the second O site, O(2) is bonded in a rectangular see-saw-like geometry to two equivalent Mg(1), one Nb(2), and one Nb(3) atom. In the third O site, O(3) is bonded in a distorted rectangular see-saw-like geometry to two equivalent Ba(2), one Nb(1), and one Nb(4) atom. In the fourth O site, O(4) is bonded in a distorted linear geometry to one Ba(1), one Ba(2), and two equivalent Nb(1) atoms. In the fifth O site, O(5) is bonded to two equivalent Ba(1), one Nb(2), and one Nb(3) atom to form a mixture of distorted edge and corner-sharing OBa2Nb2 tetrahedra. In the sixth O site, O(6) is bonded in a T-shaped geometry to one Mg(1) and two equivalent Nb(3) atoms. In the seventh O site, O(7) is bonded in a distorted linear geometry to one Ba(1), one Ba(2), and two equivalent Nb(4) atoms. In the eighth O site, O(8) is bonded in a distorted rectangular see-saw-like geometry to two equivalent Ba(2), one Nb(1), and one Nb(2) atom. In the ninth O site, O(9) is bonded in a distorted linear geometry to two equivalent Ba(1), two equivalent Ba(2), one Nb(1), and one Nb(4) atom. In the tenth O site, O(10) is bonded to two equivalent Ba(1), one Nb(1), and one Nb(4) atom to form a mixture of distorted edge and corner-sharing OBa2Nb2 tetrahedra. In the eleventh O site, O(11) is bonded in a distorted bent 120 degrees geometry to two equivalent Ba(1), one Nb(3), and one Nb(4) atom. In the twelfth O site, O(12) is bonded in a linear geometry to one Nb(2) and one Nb(3) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_Ba2MgNb4O12
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   4.064
_cell_length_b   6.406
_cell_length_c   10.749
_cell_angle_alpha   88.443
_cell_angle_beta   89.998
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   279.769
_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  0.000  0.295  0.785  1.0
  Ba  Ba1  1  1.000  0.578  0.170  1.0
  Mg  Mg2  1  0.000  0.962  0.408  1.0
  Nb  Nb3  1  0.500  0.161  0.084  1.0
  Nb  Nb4  1  0.500  0.291  0.437  1.0
  Nb  Nb5  1  0.500  0.827  0.592  1.0
  Nb  Nb6  1  0.500  0.751  0.922  1.0
  O  O7  1  0.000  0.270  0.428  1.0
  O  O8  1  0.500  0.953  0.397  1.0
  O  O9  1  0.500  0.856  0.111  1.0
  O  O10  1  1.000  0.176  0.085  1.0
  O  O11  1  0.500  0.146  0.612  1.0
  O  O12  1  0.000  0.842  0.583  1.0
  O  O13  1  1.000  0.735  0.924  1.0
  O  O14  1  0.500  0.318  0.247  1.0
  O  O15  1  0.500  0.458  0.998  1.0
  O  O16  1  0.500  0.063  0.895  1.0
  O  O17  1  0.500  0.655  0.746  1.0
  O  O18  1  0.500  0.571  0.487  1.0
[/CIF]
.
The structure described by Ba2MgNb4O12 crystallizes in the monoclinic Pm space group. There are two inequivalent Ba sites. In the first Ba site, Ba(1) is bonded in a 10-coordinate geometry to one O(4), one O(7), two equivalent O(10), two equivalent O(11), two equivalent O(5), and two equivalent O(9) atoms. In the second Ba site, Ba(2) is bonded in a 8-coordinate geometry to one O(4), one O(7), two equivalent O(3), two equivalent O(8), and two equivalent O(9) atoms. Mg(1) is bonded in a see-saw-like geometry to one O(1), one O(6), and two equivalent O(2) atoms. There are four inequivalent Nb sites. In the first Nb site, Nb(1) is bonded to one O(10), one O(3), one O(8), one O(9), and two equivalent O(4) atoms to form a mixture of edge and corner-sharing NbO6 octahedra. The corner-sharing octahedral tilt angles range from 3-34°. In the second Nb site, Nb(2) is bonded to one O(12), one O(2), one O(5), one O(8), and two equivalent O(1) atoms to form a mixture of edge and corner-sharing NbO6 octahedra. The corner-sharing octahedral tilt angles range from 9-34°. In the third Nb site, Nb(3) is bonded to one O(11), one O(12), one O(2), one O(5), and two equivalent O(6) atoms to form a mixture of edge and corner-sharing NbO6 octahedra. The corner-sharing octahedral tilt angles range from 8-52°. In the fourth Nb site, Nb(4) is bonded to one O(10), one O(11), one O(3), one O(9), and two equivalent O(7) atoms to form a mixture of edge and corner-sharing NbO6 octahedra. The corner-sharing octahedral tilt angles range from 3-52°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a T-shaped geometry to one Mg(1) and two equivalent Nb(2) atoms. In the second O site, O(2) is bonded in a rectangular see-saw-like geometry to two equivalent Mg(1), one Nb(2), and one Nb(3) atom. In the third O site, O(3) is bonded in a distorted rectangular see-saw-like geometry to two equivalent Ba(2), one Nb(1), and one Nb(4) atom. In the fourth O site, O(4) is bonded in a distorted linear geometry to one Ba(1), one Ba(2), and two equivalent Nb(1) atoms. In the fifth O site, O(5) is bonded to two equivalent Ba(1), one Nb(2), and one Nb(3) atom to form a mixture of distorted edge and corner-sharing OBa2Nb2 tetrahedra. In the sixth O site, O(6) is bonded in a T-shaped geometry to one Mg(1) and two equivalent Nb(3) atoms. In the seventh O site, O(7) is bonded in a distorted linear geometry to one Ba(1), one Ba(2), and two equivalent Nb(4) atoms. In the eighth O site, O(8) is bonded in a distorted rectangular see-saw-like geometry to two equivalent Ba(2), one Nb(1), and one Nb(2) atom. In the ninth O site, O(9) is bonded in a distorted linear geometry to two equivalent Ba(1), two equivalent Ba(2), one Nb(1), and one Nb(4) atom. In the tenth O site, O(10) is bonded to two equivalent Ba(1), one Nb(1), and one Nb(4) atom to form a mixture of distorted edge and corner-sharing OBa2Nb2 tetrahedra. In the eleventh O site, O(11) is bonded in a distorted bent 120 degrees geometry to two equivalent Ba(1), one Nb(3), and one Nb(4) atom. In the twelfth O site, O(12) is bonded in a linear geometry to one Nb(2) and one Nb(3) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_Ba2MgNb4O12
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   4.064
_cell_length_b   6.406
_cell_length_c   10.749
_cell_angle_alpha   88.443
_cell_angle_beta   89.998
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   279.769
_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  0.000  0.295  0.785  1.0
  Ba  Ba1  1  1.000  0.578  0.170  1.0
  Mg  Mg2  1  0.000  0.962  0.408  1.0
  Nb  Nb3  1  0.500  0.161  0.084  1.0
  Nb  Nb4  1  0.500  0.291  0.437  1.0
  Nb  Nb5  1  0.500  0.827  0.592  1.0
  Nb  Nb6  1  0.500  0.751  0.922  1.0
  O  O7  1  0.000  0.270  0.428  1.0
  O  O8  1  0.500  0.953  0.397  1.0
  O  O9  1  0.500  0.856  0.111  1.0
  O  O10  1  1.000  0.176  0.085  1.0
  O  O11  1  0.500  0.146  0.612  1.0
  O  O12  1  0.000  0.842  0.583  1.0
  O  O13  1  1.000  0.735  0.924  1.0
  O  O14  1  0.500  0.318  0.247  1.0
  O  O15  1  0.500  0.458  0.998  1.0
  O  O16  1  0.500  0.063  0.895  1.0
  O  O17  1  0.500  0.655  0.746  1.0
  O  O18  1  0.500  0.571  0.487  1.0
[/CIF]
.