The material structure described by Mg3Ti9O20 crystallizes in the monoclinic Cm space group. There are two inequivalent Mg sites. In the first Mg site, Mg(1) is bonded in a 6-coordinate geometry to one O(1), one O(10), one O(6), one O(7), and two equivalent O(2) atoms. In the second Mg site, Mg(2) is bonded to one O(11), one O(3), two equivalent O(4), and two equivalent O(8) atoms to form distorted MgO6 octahedra that share corners with two equivalent Ti(2)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, edges with two equivalent Ti(3)O6 octahedra, and edges with two equivalent Ti(4)O6 octahedra. The corner-sharing octahedral tilt angles are 27°. There are five inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(1), one O(10), one O(2), one O(5), one O(7), and one O(9) atom to form a mixture of distorted corner and edge-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 30-48°. In the second Ti site, Ti(2) is bonded to one O(1), one O(3), one O(4), one O(5), one O(6), and one O(8) atom to form distorted TiO6 octahedra that share  a cornercorner with one Mg(2)O6 octahedra,  a cornercorner with one Ti(2)O6 octahedra, corners with two equivalent Ti(3)O6 octahedra,  an edgeedge with one Mg(2)O6 octahedra,  an edgeedge with one Ti(1)O6 octahedra, and edges with two equivalent Ti(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 27-51°. In the third Ti site, Ti(3) is bonded to one O(10), one O(11), one O(4), one O(5), one O(7), and one O(9) atom to form distorted TiO6 octahedra that share  a cornercorner with one Ti(3)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra,  an edgeedge with one Mg(2)O6 octahedra,  an edgeedge with one Ti(4)O6 octahedra, and edges with two equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 30-49°. In the fourth Ti site, Ti(4) is bonded to one O(1), one O(10), one O(2), one O(4), one O(6), and one O(8) atom to form distorted TiO6 octahedra that share corners with three equivalent Ti(1)O6 octahedra,  an edgeedge with one Mg(2)O6 octahedra,  an edgeedge with one Ti(3)O6 octahedra, and edges with two equivalent Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 30-48°. In the fifth Ti site, Ti(5) is bonded in a 6-coordinate geometry to one O(11), one O(3), two equivalent O(5), and two equivalent O(9) atoms. There are eleven inequivalent O sites. In the first O site, O(8) is bonded in a distorted T-shaped geometry to one Mg(2), one Ti(2), and one Ti(4) atom. In the second O site, O(9) is bonded in a distorted T-shaped geometry to one Ti(1), one Ti(3), and one Ti(5) atom. In the third O site, O(10) is bonded to one Mg(1), one Ti(1), one Ti(3), and one Ti(4) atom to form OMgTi3 trigonal pyramids that share  a cornercorner with one O(11)MgTi3 trigonal pyramid, corners with three equivalent O(1)MgTi3 trigonal pyramids,  an edgeedge with one O(4)MgTi3 trigonal pyramid,  an edgeedge with one O(5)Ti4 trigonal pyramid, and edges with two equivalent O(2)Mg2Ti2 trigonal pyramids. In the fourth O site, O(11) is bonded to one Mg(2), one Ti(5), and two equivalent Ti(3) atoms to form distorted OMgTi3 trigonal pyramids that share corners with two equivalent O(10)MgTi3 trigonal pyramids, corners with two equivalent O(3)MgTi3 trigonal pyramids, edges with two equivalent O(4)MgTi3 trigonal pyramids, and edges with two equivalent O(5)Ti4 trigonal pyramids. In the fifth O site, O(1) is bonded to one Mg(1), one Ti(1), one Ti(2), and one Ti(4) atom to form OMgTi3 trigonal pyramids that share  a cornercorner with one O(3)MgTi3 trigonal pyramid, corners with three equivalent O(10)MgTi3 trigonal pyramids,  an edgeedge with one O(4)MgTi3 trigonal pyramid,  an edgeedge with one O(5)Ti4 trigonal pyramid, and edges with two equivalent O(2)Mg2Ti2 trigonal pyramids. In the sixth O site, O(2) is bonded to two equivalent Mg(1), one Ti(1), and one Ti(4) atom to form distorted OMg2Ti2 trigonal pyramids that share  a cornercorner with one O(4)MgTi3 trigonal pyramid,  a cornercorner with one O(5)Ti4 trigonal pyramid, corners with two equivalent O(2)Mg2Ti2 trigonal pyramids, edges with two equivalent O(1)MgTi3 trigonal pyramids, and edges with two equivalent O(10)MgTi3 trigonal pyramids. In the seventh O site, O(3) is bonded to one Mg(2), one Ti(5), and two equivalent Ti(2) atoms to form distorted OMgTi3 trigonal pyramids that share corners with two equivalent O(1)MgTi3 trigonal pyramids, corners with two equivalent O(11)MgTi3 trigonal pyramids, edges with two equivalent O(4)MgTi3 trigonal pyramids, and edges with two equivalent O(5)Ti4 trigonal pyramids. In the eighth O site, O(4) is bonded to one Mg(2), one Ti(2), one Ti(3), and one Ti(4) atom to form distorted OMgTi3 trigonal pyramids that share  a cornercorner with one O(2)Mg2Ti2 trigonal pyramid,  a cornercorner with one O(4)MgTi3 trigonal pyramid, corners with two equivalent O(5)Ti4 trigonal pyramids,  an edgeedge with one O(1)MgTi3 trigonal pyramid,  an edgeedge with one O(10)MgTi3 trigonal pyramid,  an edgeedge with one O(11)MgTi3 trigonal pyramid, and  an edgeedge with one O(3)MgTi3 trigonal pyramid. In the ninth O site, O(5) is bonded to one Ti(1), one Ti(2), one Ti(3), and one Ti(5) atom to form distorted OTi4 trigonal pyramids that share  a cornercorner with one O(2)Mg2Ti2 trigonal pyramid,  a cornercorner with one O(5)Ti4 trigonal pyramid, corners with two equivalent O(4)MgTi3 trigonal pyramids,  an edgeedge with one O(1)MgTi3 trigonal pyramid,  an edgeedge with one O(10)MgTi3 trigonal pyramid,  an edgeedge with one O(11)MgTi3 trigonal pyramid, and  an edgeedge with one O(3)MgTi3 trigonal pyramid. In the tenth O site, O(6) is bonded in a distorted T-shaped geometry to one Mg(1), one Ti(2), and one Ti(4) atom. In the eleventh O site, O(7) is bonded in a distorted trigonal non-coplanar geometry to one Mg(1), one Ti(1), and one Ti(3) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_Mg3Ti9O20
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   10.688
_cell_length_b   10.688
_cell_length_c   5.215
_cell_angle_alpha   82.703
_cell_angle_beta   82.699
_cell_angle_gamma   138.736
_symmetry_Int_Tables_number   1
_cell_volume   366.457
_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  0.223  0.725  0.609  1.0
  Mg  Mg1  1  0.725  0.223  0.609  1.0
  Mg  Mg2  1  0.280  0.280  0.388  1.0
  Ti  Ti3  1  0.965  0.647  0.275  1.0
  Ti  Ti4  1  0.534  0.347  0.733  1.0
  Ti  Ti5  1  0.347  0.534  0.733  1.0
  Ti  Ti6  1  0.852  0.039  0.728  1.0
  Ti  Ti7  1  0.467  0.152  0.268  1.0
  Ti  Ti8  1  0.647  0.965  0.275  1.0
  Ti  Ti9  1  0.152  0.467  0.268  1.0
  Ti  Ti10  1  0.779  0.779  0.390  1.0
  Ti  Ti11  1  0.039  0.852  0.728  1.0
  O  O12  1  0.375  0.688  0.374  1.0
  O  O13  1  0.015  0.516  0.440  1.0
  O  O14  1  0.496  0.496  0.549  1.0
  O  O15  1  0.310  0.129  0.627  1.0
  O  O16  1  0.129  0.310  0.627  1.0
  O  O17  1  0.811  0.628  0.623  1.0
  O  O18  1  0.580  0.215  0.907  1.0
  O  O19  1  0.718  0.079  0.910  1.0
  O  O20  1  0.215  0.580  0.907  1.0
  O  O21  1  0.079  0.718  0.910  1.0
  O  O22  1  0.285  0.422  0.091  1.0
  O  O23  1  0.785  0.916  0.098  1.0
  O  O24  1  0.916  0.785  0.098  1.0
  O  O25  1  0.422  0.285  0.091  1.0
  O  O26  1  0.688  0.375  0.374  1.0
  O  O27  1  0.188  0.876  0.378  1.0
  O  O28  1  0.876  0.188  0.378  1.0
  O  O29  1  0.516  0.015  0.440  1.0
  O  O30  1  0.981  0.981  0.554  1.0
  O  O31  1  0.628  0.811  0.623  1.0
[/CIF]
.
The material structure described by Mg3Ti9O20 crystallizes in the monoclinic Cm space group. There are two inequivalent Mg sites. In the first Mg site, Mg(1) is bonded in a 6-coordinate geometry to one O(1), one O(10), one O(6), one O(7), and two equivalent O(2) atoms. In the second Mg site, Mg(2) is bonded to one O(11), one O(3), two equivalent O(4), and two equivalent O(8) atoms to form distorted MgO6 octahedra that share corners with two equivalent Ti(2)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, edges with two equivalent Ti(3)O6 octahedra, and edges with two equivalent Ti(4)O6 octahedra. The corner-sharing octahedral tilt angles are 27°. There are five inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(1), one O(10), one O(2), one O(5), one O(7), and one O(9) atom to form a mixture of distorted corner and edge-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 30-48°. In the second Ti site, Ti(2) is bonded to one O(1), one O(3), one O(4), one O(5), one O(6), and one O(8) atom to form distorted TiO6 octahedra that share  a cornercorner with one Mg(2)O6 octahedra,  a cornercorner with one Ti(2)O6 octahedra, corners with two equivalent Ti(3)O6 octahedra,  an edgeedge with one Mg(2)O6 octahedra,  an edgeedge with one Ti(1)O6 octahedra, and edges with two equivalent Ti(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 27-51°. In the third Ti site, Ti(3) is bonded to one O(10), one O(11), one O(4), one O(5), one O(7), and one O(9) atom to form distorted TiO6 octahedra that share  a cornercorner with one Ti(3)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra,  an edgeedge with one Mg(2)O6 octahedra,  an edgeedge with one Ti(4)O6 octahedra, and edges with two equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 30-49°. In the fourth Ti site, Ti(4) is bonded to one O(1), one O(10), one O(2), one O(4), one O(6), and one O(8) atom to form distorted TiO6 octahedra that share corners with three equivalent Ti(1)O6 octahedra,  an edgeedge with one Mg(2)O6 octahedra,  an edgeedge with one Ti(3)O6 octahedra, and edges with two equivalent Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 30-48°. In the fifth Ti site, Ti(5) is bonded in a 6-coordinate geometry to one O(11), one O(3), two equivalent O(5), and two equivalent O(9) atoms. There are eleven inequivalent O sites. In the first O site, O(8) is bonded in a distorted T-shaped geometry to one Mg(2), one Ti(2), and one Ti(4) atom. In the second O site, O(9) is bonded in a distorted T-shaped geometry to one Ti(1), one Ti(3), and one Ti(5) atom. In the third O site, O(10) is bonded to one Mg(1), one Ti(1), one Ti(3), and one Ti(4) atom to form OMgTi3 trigonal pyramids that share  a cornercorner with one O(11)MgTi3 trigonal pyramid, corners with three equivalent O(1)MgTi3 trigonal pyramids,  an edgeedge with one O(4)MgTi3 trigonal pyramid,  an edgeedge with one O(5)Ti4 trigonal pyramid, and edges with two equivalent O(2)Mg2Ti2 trigonal pyramids. In the fourth O site, O(11) is bonded to one Mg(2), one Ti(5), and two equivalent Ti(3) atoms to form distorted OMgTi3 trigonal pyramids that share corners with two equivalent O(10)MgTi3 trigonal pyramids, corners with two equivalent O(3)MgTi3 trigonal pyramids, edges with two equivalent O(4)MgTi3 trigonal pyramids, and edges with two equivalent O(5)Ti4 trigonal pyramids. In the fifth O site, O(1) is bonded to one Mg(1), one Ti(1), one Ti(2), and one Ti(4) atom to form OMgTi3 trigonal pyramids that share  a cornercorner with one O(3)MgTi3 trigonal pyramid, corners with three equivalent O(10)MgTi3 trigonal pyramids,  an edgeedge with one O(4)MgTi3 trigonal pyramid,  an edgeedge with one O(5)Ti4 trigonal pyramid, and edges with two equivalent O(2)Mg2Ti2 trigonal pyramids. In the sixth O site, O(2) is bonded to two equivalent Mg(1), one Ti(1), and one Ti(4) atom to form distorted OMg2Ti2 trigonal pyramids that share  a cornercorner with one O(4)MgTi3 trigonal pyramid,  a cornercorner with one O(5)Ti4 trigonal pyramid, corners with two equivalent O(2)Mg2Ti2 trigonal pyramids, edges with two equivalent O(1)MgTi3 trigonal pyramids, and edges with two equivalent O(10)MgTi3 trigonal pyramids. In the seventh O site, O(3) is bonded to one Mg(2), one Ti(5), and two equivalent Ti(2) atoms to form distorted OMgTi3 trigonal pyramids that share corners with two equivalent O(1)MgTi3 trigonal pyramids, corners with two equivalent O(11)MgTi3 trigonal pyramids, edges with two equivalent O(4)MgTi3 trigonal pyramids, and edges with two equivalent O(5)Ti4 trigonal pyramids. In the eighth O site, O(4) is bonded to one Mg(2), one Ti(2), one Ti(3), and one Ti(4) atom to form distorted OMgTi3 trigonal pyramids that share  a cornercorner with one O(2)Mg2Ti2 trigonal pyramid,  a cornercorner with one O(4)MgTi3 trigonal pyramid, corners with two equivalent O(5)Ti4 trigonal pyramids,  an edgeedge with one O(1)MgTi3 trigonal pyramid,  an edgeedge with one O(10)MgTi3 trigonal pyramid,  an edgeedge with one O(11)MgTi3 trigonal pyramid, and  an edgeedge with one O(3)MgTi3 trigonal pyramid. In the ninth O site, O(5) is bonded to one Ti(1), one Ti(2), one Ti(3), and one Ti(5) atom to form distorted OTi4 trigonal pyramids that share  a cornercorner with one O(2)Mg2Ti2 trigonal pyramid,  a cornercorner with one O(5)Ti4 trigonal pyramid, corners with two equivalent O(4)MgTi3 trigonal pyramids,  an edgeedge with one O(1)MgTi3 trigonal pyramid,  an edgeedge with one O(10)MgTi3 trigonal pyramid,  an edgeedge with one O(11)MgTi3 trigonal pyramid, and  an edgeedge with one O(3)MgTi3 trigonal pyramid. In the tenth O site, O(6) is bonded in a distorted T-shaped geometry to one Mg(1), one Ti(2), and one Ti(4) atom. In the eleventh O site, O(7) is bonded in a distorted trigonal non-coplanar geometry to one Mg(1), one Ti(1), and one Ti(3) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_Mg3Ti9O20
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   10.688
_cell_length_b   10.688
_cell_length_c   5.215
_cell_angle_alpha   82.703
_cell_angle_beta   82.699
_cell_angle_gamma   138.736
_symmetry_Int_Tables_number   1
_cell_volume   366.457
_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  0.223  0.725  0.609  1.0
  Mg  Mg1  1  0.725  0.223  0.609  1.0
  Mg  Mg2  1  0.280  0.280  0.388  1.0
  Ti  Ti3  1  0.965  0.647  0.275  1.0
  Ti  Ti4  1  0.534  0.347  0.733  1.0
  Ti  Ti5  1  0.347  0.534  0.733  1.0
  Ti  Ti6  1  0.852  0.039  0.728  1.0
  Ti  Ti7  1  0.467  0.152  0.268  1.0
  Ti  Ti8  1  0.647  0.965  0.275  1.0
  Ti  Ti9  1  0.152  0.467  0.268  1.0
  Ti  Ti10  1  0.779  0.779  0.390  1.0
  Ti  Ti11  1  0.039  0.852  0.728  1.0
  O  O12  1  0.375  0.688  0.374  1.0
  O  O13  1  0.015  0.516  0.440  1.0
  O  O14  1  0.496  0.496  0.549  1.0
  O  O15  1  0.310  0.129  0.627  1.0
  O  O16  1  0.129  0.310  0.627  1.0
  O  O17  1  0.811  0.628  0.623  1.0
  O  O18  1  0.580  0.215  0.907  1.0
  O  O19  1  0.718  0.079  0.910  1.0
  O  O20  1  0.215  0.580  0.907  1.0
  O  O21  1  0.079  0.718  0.910  1.0
  O  O22  1  0.285  0.422  0.091  1.0
  O  O23  1  0.785  0.916  0.098  1.0
  O  O24  1  0.916  0.785  0.098  1.0
  O  O25  1  0.422  0.285  0.091  1.0
  O  O26  1  0.688  0.375  0.374  1.0
  O  O27  1  0.188  0.876  0.378  1.0
  O  O28  1  0.876  0.188  0.378  1.0
  O  O29  1  0.516  0.015  0.440  1.0
  O  O30  1  0.981  0.981  0.554  1.0
  O  O31  1  0.628  0.811  0.623  1.0
[/CIF]
.