The crystal structure described by Ba3MgTi2O7 crystallizes in the monoclinic Cm space group. There are two inequivalent Ba sites. In the first Ba site, Ba(1) is bonded to one O(3), two equivalent O(2), and three equivalent O(1) atoms to form a mixture of distorted corner and edge-sharing BaO6 octahedra. The corner-sharing octahedral tilt angles range from 69-70°. In the second Ba site, Ba(2) is bonded in a 4-coordinate geometry to two equivalent O(2) and two equivalent O(4) atoms. Mg(1) is bonded in a rectangular see-saw-like geometry to two equivalent O(3) and two equivalent O(4) atoms. Ti(1) is bonded in a 5-coordinate geometry to one O(1), one O(2), one O(4), and two equivalent O(3) atoms. There are four inequivalent O sites. In the first O site, O(1) is bonded to three equivalent Ba(1) and one Ti(1) atom to form distorted OBa3Ti tetrahedra that share  a cornercorner with one O(4)Ba2Mg2Ti2 octahedra, corners with five equivalent O(2)Ba3Ti tetrahedra, corners with six equivalent O(1)Ba3Ti tetrahedra, and  an edgeedge with one O(2)Ba3Ti tetrahedra. The corner-sharing octahedral tilt angles are 27°. In the second O site, O(2) is bonded to one Ba(2), two equivalent Ba(1), and one Ti(1) atom to form distorted OBa3Ti tetrahedra that share  a cornercorner with one O(4)Ba2Mg2Ti2 octahedra, corners with three equivalent O(2)Ba3Ti tetrahedra, corners with five equivalent O(1)Ba3Ti tetrahedra,  an edgeedge with one O(4)Ba2Mg2Ti2 octahedra, and  an edgeedge with one O(1)Ba3Ti tetrahedra. The corner-sharing octahedral tilt angles are 69°. In the third O site, O(3) is bonded in a 4-coordinate geometry to one Ba(1), one Mg(1), and two equivalent Ti(1) atoms. In the fourth O site, O(4) is bonded to two equivalent Ba(2), two equivalent Mg(1), and two equivalent Ti(1) atoms to form distorted OBa2Mg2Ti2 octahedra that share corners with four equivalent O(4)Ba2Mg2Ti2 octahedra, corners with two equivalent O(1)Ba3Ti tetrahedra, corners with two equivalent O(2)Ba3Ti tetrahedra, and edges with two equivalent O(2)Ba3Ti tetrahedra. The corner-sharing octahedral tilt angles range from 2-9°. is represented by the CIF file [CIF]
data_Ba3MgTi2O7
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.860
_cell_length_b   10.636
_cell_length_c   7.155
_cell_angle_alpha   96.903
_cell_angle_beta   34.115
_cell_angle_gamma   105.838
_symmetry_Int_Tables_number   1
_cell_volume   235.947
_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  0.992  0.631  0.969  1.0
  Ba  Ba1  1  0.907  1.000  0.305  1.0
  Ba  Ba2  1  0.730  0.369  0.600  1.0
  Mg  Mg3  1  0.913  0.000  0.794  1.0
  Ti  Ti4  1  0.155  0.771  0.419  1.0
  Ti  Ti5  1  0.614  0.230  0.190  1.0
  O  O6  1  0.160  0.610  0.483  1.0
  O  O7  1  0.857  0.752  0.397  1.0
  O  O8  1  0.188  0.193  0.681  1.0
  O  O9  1  0.353  0.249  0.149  1.0
  O  O10  1  0.802  0.807  0.874  1.0
  O  O11  1  0.387  0.000  0.292  1.0
  O  O12  1  0.940  0.390  0.092  1.0
[/CIF]
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The crystal structure described by Ba3MgTi2O7 crystallizes in the monoclinic Cm space group. There are two inequivalent Ba sites. In the first Ba site, Ba(1) is bonded to one O(3), two equivalent O(2), and three equivalent O(1) atoms to form a mixture of distorted corner and edge-sharing BaO6 octahedra. The corner-sharing octahedral tilt angles range from 69-70°. In the second Ba site, Ba(2) is bonded in a 4-coordinate geometry to two equivalent O(2) and two equivalent O(4) atoms. Mg(1) is bonded in a rectangular see-saw-like geometry to two equivalent O(3) and two equivalent O(4) atoms. Ti(1) is bonded in a 5-coordinate geometry to one O(1), one O(2), one O(4), and two equivalent O(3) atoms. There are four inequivalent O sites. In the first O site, O(1) is bonded to three equivalent Ba(1) and one Ti(1) atom to form distorted OBa3Ti tetrahedra that share  a cornercorner with one O(4)Ba2Mg2Ti2 octahedra, corners with five equivalent O(2)Ba3Ti tetrahedra, corners with six equivalent O(1)Ba3Ti tetrahedra, and  an edgeedge with one O(2)Ba3Ti tetrahedra. The corner-sharing octahedral tilt angles are 27°. In the second O site, O(2) is bonded to one Ba(2), two equivalent Ba(1), and one Ti(1) atom to form distorted OBa3Ti tetrahedra that share  a cornercorner with one O(4)Ba2Mg2Ti2 octahedra, corners with three equivalent O(2)Ba3Ti tetrahedra, corners with five equivalent O(1)Ba3Ti tetrahedra,  an edgeedge with one O(4)Ba2Mg2Ti2 octahedra, and  an edgeedge with one O(1)Ba3Ti tetrahedra. The corner-sharing octahedral tilt angles are 69°. In the third O site, O(3) is bonded in a 4-coordinate geometry to one Ba(1), one Mg(1), and two equivalent Ti(1) atoms. In the fourth O site, O(4) is bonded to two equivalent Ba(2), two equivalent Mg(1), and two equivalent Ti(1) atoms to form distorted OBa2Mg2Ti2 octahedra that share corners with four equivalent O(4)Ba2Mg2Ti2 octahedra, corners with two equivalent O(1)Ba3Ti tetrahedra, corners with two equivalent O(2)Ba3Ti tetrahedra, and edges with two equivalent O(2)Ba3Ti tetrahedra. The corner-sharing octahedral tilt angles range from 2-9°. is represented by the CIF file [CIF]
data_Ba3MgTi2O7
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.860
_cell_length_b   10.636
_cell_length_c   7.155
_cell_angle_alpha   96.903
_cell_angle_beta   34.115
_cell_angle_gamma   105.838
_symmetry_Int_Tables_number   1
_cell_volume   235.947
_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  0.992  0.631  0.969  1.0
  Ba  Ba1  1  0.907  1.000  0.305  1.0
  Ba  Ba2  1  0.730  0.369  0.600  1.0
  Mg  Mg3  1  0.913  0.000  0.794  1.0
  Ti  Ti4  1  0.155  0.771  0.419  1.0
  Ti  Ti5  1  0.614  0.230  0.190  1.0
  O  O6  1  0.160  0.610  0.483  1.0
  O  O7  1  0.857  0.752  0.397  1.0
  O  O8  1  0.188  0.193  0.681  1.0
  O  O9  1  0.353  0.249  0.149  1.0
  O  O10  1  0.802  0.807  0.874  1.0
  O  O11  1  0.387  0.000  0.292  1.0
  O  O12  1  0.940  0.390  0.092  1.0
[/CIF]
.