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 9-coordinate geometry to one O(3), two equivalent O(10), two equivalent O(12), two equivalent O(5), and two equivalent O(8) atoms. In the second Ba site, Ba(2) is bonded in a 7-coordinate geometry to one O(2), one O(3), one O(4), two equivalent O(11), and two equivalent O(9) atoms. Mg(1) is bonded to one O(1), one O(2), one O(4), and two equivalent O(7) atoms to form MgO5 square pyramids that share corners with two equivalent Mg(1)O5 square pyramids, edges with two equivalent Nb(2)O6 octahedra, and edges with two equivalent Nb(4)O6 octahedra. There are four inequivalent Nb sites. In the first Nb site, Nb(1) is bonded in a 6-coordinate geometry to one O(10), one O(5), one O(6), one O(7), one O(8), and two equivalent O(1) atoms. In the second Nb site, Nb(2) is bonded to one O(5), one O(6), one O(7), one O(9), and two equivalent O(2) atoms to form distorted NbO6 octahedra that share corners with two equivalent Nb(2)O6 octahedra,  an edgeedge with one Nb(4)O6 octahedra, and edges with two equivalent Mg(1)O5 square pyramids. The corner-sharing octahedral tilt angles are 8°. In the third Nb site, Nb(3) is bonded to one O(10), one O(11), one O(12), one O(8), and two equivalent O(3) atoms to form distorted corner-sharing NbO6 octahedra. The corner-sharing octahedral tilt angles range from 21-39°. In the fourth Nb site, Nb(4) is bonded to one O(11), one O(12), one O(7), one O(9), and two equivalent O(4) atoms to form distorted NbO6 octahedra that share corners with two equivalent Nb(3)O6 octahedra, corners with two equivalent Nb(4)O6 octahedra,  an edgeedge with one Nb(2)O6 octahedra, and edges with two equivalent Mg(1)O5 square pyramids. The corner-sharing octahedral tilt angles range from 25-39°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a distorted T-shaped geometry to one Mg(1) and two equivalent Nb(1) atoms. In the second O site, O(2) is bonded in a distorted T-shaped geometry to one Ba(2), one Mg(1), and two equivalent Nb(2) atoms. In the third O site, O(3) is bonded in a 4-coordinate geometry to one Ba(1), one Ba(2), and two equivalent Nb(3) atoms. In the fourth O site, O(4) is bonded to one Ba(2), one Mg(1), and two equivalent Nb(4) atoms to form distorted OBaMgNb2 trigonal pyramids that share corners with four equivalent O(9)Ba2Nb2 tetrahedra and corners with two equivalent O(4)BaMgNb2 trigonal pyramids. In the fifth O site, O(5) is bonded in a 4-coordinate geometry to two equivalent Ba(1), one Nb(1), and one Nb(2) atom. In the sixth O site, O(6) is bonded in a bent 150 degrees geometry to one Nb(1) and one Nb(2) atom. In the seventh O site, O(7) is bonded in a 5-coordinate geometry to two equivalent Mg(1), one Nb(1), one Nb(2), and one Nb(4) atom. In the eighth O site, O(8) is bonded in a distorted water-like geometry to two equivalent Ba(1), one Nb(1), and one Nb(3) atom. In the ninth O site, O(9) is bonded to two equivalent Ba(2), one Nb(2), and one Nb(4) atom to form distorted OBa2Nb2 tetrahedra that share corners with two equivalent O(9)Ba2Nb2 tetrahedra and corners with four equivalent O(4)BaMgNb2 trigonal pyramids. In the tenth O site, O(10) is bonded in a 4-coordinate geometry to two equivalent Ba(1), one Nb(1), and one Nb(3) atom. In the eleventh O site, O(11) is bonded in a distorted rectangular see-saw-like geometry to two equivalent Ba(2), one Nb(3), and one Nb(4) atom. In the twelfth O site, O(12) is bonded in a 4-coordinate geometry to two equivalent Ba(1), one Nb(3), and one Nb(4) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_Ba2MgNb4O12
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   4.033
_cell_length_b   6.544
_cell_length_c   10.254
_cell_angle_alpha   83.986
_cell_angle_beta   90.001
_cell_angle_gamma   90.003
_symmetry_Int_Tables_number   1
_cell_volume   269.102
_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  0.988  0.001  1.0
  Ba  Ba1  1  1.000  0.580  0.579  1.0
  Mg  Mg2  1  0.000  0.193  0.390  1.0
  Nb  Nb3  1  0.500  0.393  0.172  1.0
  Nb  Nb4  1  0.500  0.876  0.343  1.0
  Nb  Nb5  1  0.500  0.565  0.865  1.0
  Nb  Nb6  1  0.500  0.104  0.637  1.0
  O  O7  1  0.000  0.351  0.203  1.0
  O  O8  1  1.000  0.893  0.351  1.0
  O  O9  1  1.000  0.616  0.843  1.0
  O  O10  1  0.000  0.146  0.596  1.0
  O  O11  1  0.500  0.062  0.182  1.0
  O  O12  1  0.500  0.596  0.310  1.0
  O  O13  1  0.500  0.203  0.416  1.0
  O  O14  1  0.500  0.654  0.051  1.0
  O  O15  1  0.500  0.833  0.540  1.0
  O  O16  1  0.500  0.307  0.977  1.0
  O  O17  1  0.500  0.377  0.714  1.0
  O  O18  1  0.500  0.920  0.793  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 9-coordinate geometry to one O(3), two equivalent O(10), two equivalent O(12), two equivalent O(5), and two equivalent O(8) atoms. In the second Ba site, Ba(2) is bonded in a 7-coordinate geometry to one O(2), one O(3), one O(4), two equivalent O(11), and two equivalent O(9) atoms. Mg(1) is bonded to one O(1), one O(2), one O(4), and two equivalent O(7) atoms to form MgO5 square pyramids that share corners with two equivalent Mg(1)O5 square pyramids, edges with two equivalent Nb(2)O6 octahedra, and edges with two equivalent Nb(4)O6 octahedra. There are four inequivalent Nb sites. In the first Nb site, Nb(1) is bonded in a 6-coordinate geometry to one O(10), one O(5), one O(6), one O(7), one O(8), and two equivalent O(1) atoms. In the second Nb site, Nb(2) is bonded to one O(5), one O(6), one O(7), one O(9), and two equivalent O(2) atoms to form distorted NbO6 octahedra that share corners with two equivalent Nb(2)O6 octahedra,  an edgeedge with one Nb(4)O6 octahedra, and edges with two equivalent Mg(1)O5 square pyramids. The corner-sharing octahedral tilt angles are 8°. In the third Nb site, Nb(3) is bonded to one O(10), one O(11), one O(12), one O(8), and two equivalent O(3) atoms to form distorted corner-sharing NbO6 octahedra. The corner-sharing octahedral tilt angles range from 21-39°. In the fourth Nb site, Nb(4) is bonded to one O(11), one O(12), one O(7), one O(9), and two equivalent O(4) atoms to form distorted NbO6 octahedra that share corners with two equivalent Nb(3)O6 octahedra, corners with two equivalent Nb(4)O6 octahedra,  an edgeedge with one Nb(2)O6 octahedra, and edges with two equivalent Mg(1)O5 square pyramids. The corner-sharing octahedral tilt angles range from 25-39°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a distorted T-shaped geometry to one Mg(1) and two equivalent Nb(1) atoms. In the second O site, O(2) is bonded in a distorted T-shaped geometry to one Ba(2), one Mg(1), and two equivalent Nb(2) atoms. In the third O site, O(3) is bonded in a 4-coordinate geometry to one Ba(1), one Ba(2), and two equivalent Nb(3) atoms. In the fourth O site, O(4) is bonded to one Ba(2), one Mg(1), and two equivalent Nb(4) atoms to form distorted OBaMgNb2 trigonal pyramids that share corners with four equivalent O(9)Ba2Nb2 tetrahedra and corners with two equivalent O(4)BaMgNb2 trigonal pyramids. In the fifth O site, O(5) is bonded in a 4-coordinate geometry to two equivalent Ba(1), one Nb(1), and one Nb(2) atom. In the sixth O site, O(6) is bonded in a bent 150 degrees geometry to one Nb(1) and one Nb(2) atom. In the seventh O site, O(7) is bonded in a 5-coordinate geometry to two equivalent Mg(1), one Nb(1), one Nb(2), and one Nb(4) atom. In the eighth O site, O(8) is bonded in a distorted water-like geometry to two equivalent Ba(1), one Nb(1), and one Nb(3) atom. In the ninth O site, O(9) is bonded to two equivalent Ba(2), one Nb(2), and one Nb(4) atom to form distorted OBa2Nb2 tetrahedra that share corners with two equivalent O(9)Ba2Nb2 tetrahedra and corners with four equivalent O(4)BaMgNb2 trigonal pyramids. In the tenth O site, O(10) is bonded in a 4-coordinate geometry to two equivalent Ba(1), one Nb(1), and one Nb(3) atom. In the eleventh O site, O(11) is bonded in a distorted rectangular see-saw-like geometry to two equivalent Ba(2), one Nb(3), and one Nb(4) atom. In the twelfth O site, O(12) is bonded in a 4-coordinate geometry to two equivalent Ba(1), one Nb(3), and one Nb(4) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_Ba2MgNb4O12
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   4.033
_cell_length_b   6.544
_cell_length_c   10.254
_cell_angle_alpha   83.986
_cell_angle_beta   90.001
_cell_angle_gamma   90.003
_symmetry_Int_Tables_number   1
_cell_volume   269.102
_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  0.988  0.001  1.0
  Ba  Ba1  1  1.000  0.580  0.579  1.0
  Mg  Mg2  1  0.000  0.193  0.390  1.0
  Nb  Nb3  1  0.500  0.393  0.172  1.0
  Nb  Nb4  1  0.500  0.876  0.343  1.0
  Nb  Nb5  1  0.500  0.565  0.865  1.0
  Nb  Nb6  1  0.500  0.104  0.637  1.0
  O  O7  1  0.000  0.351  0.203  1.0
  O  O8  1  1.000  0.893  0.351  1.0
  O  O9  1  1.000  0.616  0.843  1.0
  O  O10  1  0.000  0.146  0.596  1.0
  O  O11  1  0.500  0.062  0.182  1.0
  O  O12  1  0.500  0.596  0.310  1.0
  O  O13  1  0.500  0.203  0.416  1.0
  O  O14  1  0.500  0.654  0.051  1.0
  O  O15  1  0.500  0.833  0.540  1.0
  O  O16  1  0.500  0.307  0.977  1.0
  O  O17  1  0.500  0.377  0.714  1.0
  O  O18  1  0.500  0.920  0.793  1.0
[/CIF]
.