The structure described by MgTi3Nb3O12 crystallizes in the triclinic P1 space group. Mg(1) is bonded to one O(10), one O(12), one O(3), one O(4), one O(6), and one O(7) atom to form MgO6 octahedra that share  a cornercorner with one Ti(1)O6 octahedra, corners with two equivalent Nb(2)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra,  an edgeedge with one Nb(3)O6 octahedra, edges with two equivalent Nb(1)O6 octahedra, and  a faceface with one Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 47-55°. There are three inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(1), one O(10), one O(3), one O(4), one O(6), and one O(8) atom to form TiO6 octahedra that share  a cornercorner with one Mg(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra, corners with three equivalent Nb(1)O6 octahedra, corners with three equivalent Nb(3)O6 octahedra,  an edgeedge with one Nb(2)O6 octahedra, and  a faceface with one Mg(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 32-58°. In the second Ti site, Ti(2) is bonded to one O(11), one O(12), one O(2), one O(4), one O(8), and one O(9) atom to form TiO6 octahedra that share corners with two equivalent Ti(1)O6 octahedra, corners with three equivalent Nb(2)O6 octahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Nb(1)O6 octahedra, and  an edgeedge with one Nb(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 38-58°. In the third Ti site, Ti(3) is bonded in a 5-coordinate geometry to one O(11), one O(4), one O(5), one O(6), and one O(7) atom. There are three inequivalent Nb sites. In the first Nb site, Nb(1) is bonded to one O(1), one O(10), one O(11), one O(12), one O(3), and one O(7) atom to form NbO6 octahedra that share corners with two equivalent Nb(2)O6 octahedra, corners with three equivalent Ti(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra,  an edgeedge with one Nb(3)O6 octahedra, and edges with two equivalent Mg(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 32-66°. In the second Nb site, Nb(2) is bonded to one O(2), one O(3), one O(5), one O(7), one O(8), and one O(9) atom to form NbO6 octahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent Nb(1)O6 octahedra, corners with three equivalent Ti(2)O6 octahedra, corners with three equivalent Nb(3)O6 octahedra, and  an edgeedge with one Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 38-66°. In the third Nb site, Nb(3) is bonded to one O(1), one O(10), one O(2), one O(5), one O(6), and one O(9) atom to form NbO6 octahedra that share corners with three equivalent Ti(1)O6 octahedra, corners with three equivalent Nb(2)O6 octahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra, and  an edgeedge with one Nb(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 41-64°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a 3-coordinate geometry to one Ti(1), one Nb(1), and one Nb(3) atom. In the second O site, O(2) is bonded in a distorted T-shaped geometry to one Ti(2), one Nb(2), and one Nb(3) atom. In the third O site, O(3) is bonded in a distorted see-saw-like geometry to one Mg(1), one Ti(1), one Nb(1), and one Nb(2) atom. In the fourth O site, O(4) is bonded to one Mg(1), one Ti(1), one Ti(2), and one Ti(3) atom to form distorted OMgTi3 trigonal pyramids that share  a cornercorner with one O(6)MgTi2Nb trigonal pyramid, corners with two equivalent O(7)MgTiNb2 trigonal pyramids, and  an edgeedge with one O(6)MgTi2Nb trigonal pyramid. In the fifth O site, O(5) is bonded in a distorted trigonal planar geometry to one Ti(3), one Nb(2), and one Nb(3) atom. In the sixth O site, O(6) is bonded to one Mg(1), one Ti(1), one Ti(3), and one Nb(3) atom to form distorted OMgTi2Nb trigonal pyramids that share  a cornercorner with one O(4)MgTi3 trigonal pyramid,  an edgeedge with one O(4)MgTi3 trigonal pyramid, and  an edgeedge with one O(7)MgTiNb2 trigonal pyramid. In the seventh O site, O(7) is bonded to one Mg(1), one Ti(3), one Nb(1), and one Nb(2) atom to form distorted OMgTiNb2 trigonal pyramids that share corners with two equivalent O(4)MgTi3 trigonal pyramids and  an edgeedge with one O(6)MgTi2Nb trigonal pyramid. In the eighth O site, O(8) is bonded in a distorted trigonal planar geometry to one Ti(1), one Ti(2), and one Nb(2) atom. In the ninth O site, O(9) is bonded in a distorted T-shaped geometry to one Ti(2), one Nb(2), and one Nb(3) atom. In the tenth O site, O(10) is bonded in a rectangular see-saw-like geometry to one Mg(1), one Ti(1), one Nb(1), and one Nb(3) atom. In the eleventh O site, O(11) is bonded in a distorted trigonal planar geometry to one Ti(2), one Ti(3), and one Nb(1) atom. In the twelfth O site, O(12) is bonded in a distorted trigonal non-coplanar geometry to one Mg(1), one Ti(2), and one Nb(1) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_MgTi3Nb3O12
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   7.456
_cell_length_b   5.665
_cell_length_c   5.887
_cell_angle_alpha   77.157
_cell_angle_beta   69.040
_cell_angle_gamma   71.436
_symmetry_Int_Tables_number   1
_cell_volume   218.456
_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  0.858  0.652  0.159  1.0
  Ti  Ti1  1  0.650  0.295  0.345  1.0
  Ti  Ti2  1  0.197  0.324  0.311  1.0
  Ti  Ti3  1  0.003  0.075  0.940  1.0
  Nb  Nb4  1  0.814  0.679  0.680  1.0
  Nb  Nb5  1  0.350  0.669  0.666  1.0
  Nb  Nb6  1  0.505  0.975  0.984  1.0
  O  O7  1  0.669  0.051  0.614  1.0
  O  O8  1  0.351  0.380  0.966  1.0
  O  O9  1  0.660  0.562  0.512  1.0
  O  O10  1  0.964  0.265  0.192  1.0
  O  O11  1  0.276  0.924  0.913  1.0
  O  O12  1  0.723  0.046  0.111  1.0
  O  O13  1  0.024  0.754  0.804  1.0
  O  O14  1  0.363  0.416  0.453  1.0
  O  O15  1  0.333  0.958  0.381  1.0
  O  O16  1  0.655  0.590  0.049  1.0
  O  O17  1  0.995  0.300  0.674  1.0
  O  O18  1  0.027  0.668  0.332  1.0
[/CIF]
.
The structure described by MgTi3Nb3O12 crystallizes in the triclinic P1 space group. Mg(1) is bonded to one O(10), one O(12), one O(3), one O(4), one O(6), and one O(7) atom to form MgO6 octahedra that share  a cornercorner with one Ti(1)O6 octahedra, corners with two equivalent Nb(2)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra,  an edgeedge with one Nb(3)O6 octahedra, edges with two equivalent Nb(1)O6 octahedra, and  a faceface with one Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 47-55°. There are three inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(1), one O(10), one O(3), one O(4), one O(6), and one O(8) atom to form TiO6 octahedra that share  a cornercorner with one Mg(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra, corners with three equivalent Nb(1)O6 octahedra, corners with three equivalent Nb(3)O6 octahedra,  an edgeedge with one Nb(2)O6 octahedra, and  a faceface with one Mg(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 32-58°. In the second Ti site, Ti(2) is bonded to one O(11), one O(12), one O(2), one O(4), one O(8), and one O(9) atom to form TiO6 octahedra that share corners with two equivalent Ti(1)O6 octahedra, corners with three equivalent Nb(2)O6 octahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Nb(1)O6 octahedra, and  an edgeedge with one Nb(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 38-58°. In the third Ti site, Ti(3) is bonded in a 5-coordinate geometry to one O(11), one O(4), one O(5), one O(6), and one O(7) atom. There are three inequivalent Nb sites. In the first Nb site, Nb(1) is bonded to one O(1), one O(10), one O(11), one O(12), one O(3), and one O(7) atom to form NbO6 octahedra that share corners with two equivalent Nb(2)O6 octahedra, corners with three equivalent Ti(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra,  an edgeedge with one Nb(3)O6 octahedra, and edges with two equivalent Mg(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 32-66°. In the second Nb site, Nb(2) is bonded to one O(2), one O(3), one O(5), one O(7), one O(8), and one O(9) atom to form NbO6 octahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent Nb(1)O6 octahedra, corners with three equivalent Ti(2)O6 octahedra, corners with three equivalent Nb(3)O6 octahedra, and  an edgeedge with one Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 38-66°. In the third Nb site, Nb(3) is bonded to one O(1), one O(10), one O(2), one O(5), one O(6), and one O(9) atom to form NbO6 octahedra that share corners with three equivalent Ti(1)O6 octahedra, corners with three equivalent Nb(2)O6 octahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra, and  an edgeedge with one Nb(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 41-64°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a 3-coordinate geometry to one Ti(1), one Nb(1), and one Nb(3) atom. In the second O site, O(2) is bonded in a distorted T-shaped geometry to one Ti(2), one Nb(2), and one Nb(3) atom. In the third O site, O(3) is bonded in a distorted see-saw-like geometry to one Mg(1), one Ti(1), one Nb(1), and one Nb(2) atom. In the fourth O site, O(4) is bonded to one Mg(1), one Ti(1), one Ti(2), and one Ti(3) atom to form distorted OMgTi3 trigonal pyramids that share  a cornercorner with one O(6)MgTi2Nb trigonal pyramid, corners with two equivalent O(7)MgTiNb2 trigonal pyramids, and  an edgeedge with one O(6)MgTi2Nb trigonal pyramid. In the fifth O site, O(5) is bonded in a distorted trigonal planar geometry to one Ti(3), one Nb(2), and one Nb(3) atom. In the sixth O site, O(6) is bonded to one Mg(1), one Ti(1), one Ti(3), and one Nb(3) atom to form distorted OMgTi2Nb trigonal pyramids that share  a cornercorner with one O(4)MgTi3 trigonal pyramid,  an edgeedge with one O(4)MgTi3 trigonal pyramid, and  an edgeedge with one O(7)MgTiNb2 trigonal pyramid. In the seventh O site, O(7) is bonded to one Mg(1), one Ti(3), one Nb(1), and one Nb(2) atom to form distorted OMgTiNb2 trigonal pyramids that share corners with two equivalent O(4)MgTi3 trigonal pyramids and  an edgeedge with one O(6)MgTi2Nb trigonal pyramid. In the eighth O site, O(8) is bonded in a distorted trigonal planar geometry to one Ti(1), one Ti(2), and one Nb(2) atom. In the ninth O site, O(9) is bonded in a distorted T-shaped geometry to one Ti(2), one Nb(2), and one Nb(3) atom. In the tenth O site, O(10) is bonded in a rectangular see-saw-like geometry to one Mg(1), one Ti(1), one Nb(1), and one Nb(3) atom. In the eleventh O site, O(11) is bonded in a distorted trigonal planar geometry to one Ti(2), one Ti(3), and one Nb(1) atom. In the twelfth O site, O(12) is bonded in a distorted trigonal non-coplanar geometry to one Mg(1), one Ti(2), and one Nb(1) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_MgTi3Nb3O12
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   7.456
_cell_length_b   5.665
_cell_length_c   5.887
_cell_angle_alpha   77.157
_cell_angle_beta   69.040
_cell_angle_gamma   71.436
_symmetry_Int_Tables_number   1
_cell_volume   218.456
_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  0.858  0.652  0.159  1.0
  Ti  Ti1  1  0.650  0.295  0.345  1.0
  Ti  Ti2  1  0.197  0.324  0.311  1.0
  Ti  Ti3  1  0.003  0.075  0.940  1.0
  Nb  Nb4  1  0.814  0.679  0.680  1.0
  Nb  Nb5  1  0.350  0.669  0.666  1.0
  Nb  Nb6  1  0.505  0.975  0.984  1.0
  O  O7  1  0.669  0.051  0.614  1.0
  O  O8  1  0.351  0.380  0.966  1.0
  O  O9  1  0.660  0.562  0.512  1.0
  O  O10  1  0.964  0.265  0.192  1.0
  O  O11  1  0.276  0.924  0.913  1.0
  O  O12  1  0.723  0.046  0.111  1.0
  O  O13  1  0.024  0.754  0.804  1.0
  O  O14  1  0.363  0.416  0.453  1.0
  O  O15  1  0.333  0.958  0.381  1.0
  O  O16  1  0.655  0.590  0.049  1.0
  O  O17  1  0.995  0.300  0.674  1.0
  O  O18  1  0.027  0.668  0.332  1.0
[/CIF]
.