The structure described by Li2MgTi9O20 crystallizes in the monoclinic Pm space group. There are two inequivalent Li sites. In the first Li site, Li(1) is bonded in a 6-coordinate geometry to one O(1), one O(2), two equivalent O(10), and two equivalent O(6) atoms. In the second Li site, Li(2) is bonded to one O(3), one O(4), two equivalent O(11), and two equivalent O(7) atoms to form distorted LiO6 octahedra that share corners with two equivalent Ti(1)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, and edges with two equivalent Ti(3)O6 octahedra. The corner-sharing octahedral tilt angles are 29°. Mg(1) is bonded in a 6-coordinate geometry to one O(1), one O(2), two equivalent O(5), and two equivalent O(9) atoms. There are five inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(11), one O(3), one O(5), one O(7), one O(8), and one O(9) atom to form distorted TiO6 octahedra that share  a cornercorner with one Li(2)O6 octahedra,  a cornercorner with one Ti(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Ti(4)O6 octahedra, and edges with two equivalent Ti(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 29-54°. In the second Ti site, Ti(2) is bonded to one O(10), one O(12), one O(4), one O(6), one O(7), and one O(8) atom to form TiO6 octahedra that share  a cornercorner with one Ti(2)O6 octahedra, corners with two equivalent Ti(1)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Ti(3)O6 octahedra, and edges with two equivalent Ti(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 29-49°. In the third Ti site, Ti(3) is bonded to one O(1), one O(11), one O(5), one O(6), 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(4)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra, and edges with two equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 30-44°. In the fourth Ti site, Ti(4) is bonded to one O(10), one O(12), one O(2), one O(5), one O(6), and one O(8) atom to form a mixture of distorted corner and edge-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 30-44°. In the fifth Ti site, Ti(5) is bonded in a 6-coordinate geometry to one O(3), one O(4), two equivalent O(12), and two equivalent O(8) atoms. There are twelve inequivalent O sites. In the first O site, O(1) is bonded to one Li(1), one Mg(1), and two equivalent Ti(3) atoms to form distorted OLiMgTi2 trigonal pyramids that share corners with two equivalent O(2)LiMgTi2 trigonal pyramids, corners with two equivalent O(7)LiTi3 trigonal pyramids, edges with two equivalent O(6)LiTi3 trigonal pyramids, and edges with two equivalent O(5)MgTi3 trigonal pyramids. In the second O site, O(2) is bonded to one Li(1), one Mg(1), and two equivalent Ti(4) atoms to form distorted OLiMgTi2 trigonal pyramids that share corners with two equivalent O(1)LiMgTi2 trigonal pyramids, corners with two equivalent O(8)Ti4 trigonal pyramids, edges with two equivalent O(6)LiTi3 trigonal pyramids, and edges with two equivalent O(5)MgTi3 trigonal pyramids. In the third O site, O(3) is bonded to one Li(2), one Ti(5), and two equivalent Ti(1) atoms to form distorted OLiTi3 trigonal pyramids that share corners with two equivalent O(4)LiTi3 trigonal pyramids, corners with two equivalent O(5)MgTi3 trigonal pyramids, edges with two equivalent O(7)LiTi3 trigonal pyramids, and edges with two equivalent O(8)Ti4 trigonal pyramids. In the fourth O site, O(4) is bonded to one Li(2), one Ti(5), and two equivalent Ti(2) atoms to form distorted OLiTi3 trigonal pyramids that share corners with two equivalent O(3)LiTi3 trigonal pyramids, corners with two equivalent O(6)LiTi3 trigonal pyramids, edges with two equivalent O(7)LiTi3 trigonal pyramids, and edges with two equivalent O(8)Ti4 trigonal pyramids. In the fifth O site, O(5) 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(3)LiTi3 trigonal pyramid,  a cornercorner with one O(5)MgTi3 trigonal pyramid, corners with two equivalent O(6)LiTi3 trigonal pyramids,  an edgeedge with one O(1)LiMgTi2 trigonal pyramid,  an edgeedge with one O(2)LiMgTi2 trigonal pyramid,  an edgeedge with one O(7)LiTi3 trigonal pyramid, and  an edgeedge with one O(8)Ti4 trigonal pyramid. In the sixth O site, O(6) is bonded to one Li(1), one Ti(2), one Ti(3), and one Ti(4) atom to form OLiTi3 trigonal pyramids that share  a cornercorner with one O(4)LiTi3 trigonal pyramid,  a cornercorner with one O(6)LiTi3 trigonal pyramid, corners with two equivalent O(5)MgTi3 trigonal pyramids,  an edgeedge with one O(1)LiMgTi2 trigonal pyramid,  an edgeedge with one O(2)LiMgTi2 trigonal pyramid,  an edgeedge with one O(7)LiTi3 trigonal pyramid, and  an edgeedge with one O(8)Ti4 trigonal pyramid. In the seventh O site, O(7) is bonded to one Li(2), one Ti(1), one Ti(2), and one Ti(3) atom to form distorted OLiTi3 trigonal pyramids that share  a cornercorner with one O(1)LiMgTi2 trigonal pyramid,  a cornercorner with one O(7)LiTi3 trigonal pyramid, corners with two equivalent O(8)Ti4 trigonal pyramids,  an edgeedge with one O(3)LiTi3 trigonal pyramid,  an edgeedge with one O(4)LiTi3 trigonal pyramid,  an edgeedge with one O(6)LiTi3 trigonal pyramid, and  an edgeedge with one O(5)MgTi3 trigonal pyramid. In the eighth O site, O(8) is bonded to one Ti(1), one Ti(2), one Ti(4), and one Ti(5) atom to form distorted OTi4 trigonal pyramids that share  a cornercorner with one O(2)LiMgTi2 trigonal pyramid,  a cornercorner with one O(8)Ti4 trigonal pyramid, corners with two equivalent O(7)LiTi3 trigonal pyramids,  an edgeedge with one O(3)LiTi3 trigonal pyramid,  an edgeedge with one O(4)LiTi3 trigonal pyramid,  an edgeedge with one O(6)LiTi3 trigonal pyramid, and  an edgeedge with one O(5)MgTi3 trigonal pyramid. In the ninth O site, O(9) is bonded in a distorted trigonal non-coplanar geometry to one Mg(1), one Ti(1), and one Ti(3) atom. In the tenth O site, O(10) is bonded in a distorted trigonal non-coplanar geometry to one Li(1), one Ti(2), and one Ti(4) atom. In the eleventh O site, O(11) is bonded in a distorted trigonal non-coplanar geometry to one Li(2), one Ti(1), and one Ti(3) atom. In the twelfth O site, O(12) is bonded in a distorted T-shaped geometry to one Ti(2), one Ti(4), and one Ti(5) atom. is represented by the CIF file [CIF]
data_Li2MgTi9O20
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   10.076
_cell_length_b   5.242
_cell_length_c   7.474
_cell_angle_alpha   70.058
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   371.058
_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
  Li  Li0  1  0.500  0.213  0.401  1.0
  Li  Li1  1  0.000  0.284  0.095  1.0
  Mg  Mg2  1  0.500  0.701  0.904  1.0
  Ti  Ti3  1  0.185  0.802  0.939  1.0
  Ti  Ti4  1  0.190  0.305  0.427  1.0
  Ti  Ti5  1  0.318  0.200  0.068  1.0
  Ti  Ti6  1  0.321  0.707  0.568  1.0
  Ti  Ti7  1  0.815  0.802  0.939  1.0
  Ti  Ti8  1  0.810  0.305  0.427  1.0
  Ti  Ti9  1  0.682  0.200  0.068  1.0
  Ti  Ti10  1  0.679  0.707  0.568  1.0
  Ti  Ti11  1  0.000  0.797  0.598  1.0
  O  O12  1  0.500  0.316  0.104  1.0
  O  O13  1  0.500  0.818  0.608  1.0
  O  O14  1  0.000  0.682  0.870  1.0
  O  O15  1  0.000  0.149  0.408  1.0
  O  O16  1  0.311  0.529  0.843  1.0
  O  O17  1  0.303  0.029  0.343  1.0
  O  O18  1  0.185  0.478  0.161  1.0
  O  O19  1  0.183  0.965  0.655  1.0
  O  O20  1  0.689  0.529  0.843  1.0
  O  O21  1  0.697  0.029  0.343  1.0
  O  O22  1  0.815  0.478  0.161  1.0
  O  O23  1  0.817  0.965  0.655  1.0
  O  O24  1  0.363  0.930  0.975  1.0
  O  O25  1  0.359  0.432  0.479  1.0
  O  O26  1  0.137  0.068  0.023  1.0
  O  O27  1  0.128  0.575  0.525  1.0
  O  O28  1  0.636  0.930  0.975  1.0
  O  O29  1  0.641  0.432  0.479  1.0
  O  O30  1  0.863  0.068  0.023  1.0
  O  O31  1  0.872  0.575  0.525  1.0
[/CIF]
.
The structure described by Li2MgTi9O20 crystallizes in the monoclinic Pm space group. There are two inequivalent Li sites. In the first Li site, Li(1) is bonded in a 6-coordinate geometry to one O(1), one O(2), two equivalent O(10), and two equivalent O(6) atoms. In the second Li site, Li(2) is bonded to one O(3), one O(4), two equivalent O(11), and two equivalent O(7) atoms to form distorted LiO6 octahedra that share corners with two equivalent Ti(1)O6 octahedra, edges with two equivalent Ti(1)O6 octahedra, edges with two equivalent Ti(2)O6 octahedra, and edges with two equivalent Ti(3)O6 octahedra. The corner-sharing octahedral tilt angles are 29°. Mg(1) is bonded in a 6-coordinate geometry to one O(1), one O(2), two equivalent O(5), and two equivalent O(9) atoms. There are five inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(11), one O(3), one O(5), one O(7), one O(8), and one O(9) atom to form distorted TiO6 octahedra that share  a cornercorner with one Li(2)O6 octahedra,  a cornercorner with one Ti(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Ti(4)O6 octahedra, and edges with two equivalent Ti(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 29-54°. In the second Ti site, Ti(2) is bonded to one O(10), one O(12), one O(4), one O(6), one O(7), and one O(8) atom to form TiO6 octahedra that share  a cornercorner with one Ti(2)O6 octahedra, corners with two equivalent Ti(1)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Ti(3)O6 octahedra, and edges with two equivalent Ti(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 29-49°. In the third Ti site, Ti(3) is bonded to one O(1), one O(11), one O(5), one O(6), 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(4)O6 octahedra,  an edgeedge with one Li(2)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra, and edges with two equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 30-44°. In the fourth Ti site, Ti(4) is bonded to one O(10), one O(12), one O(2), one O(5), one O(6), and one O(8) atom to form a mixture of distorted corner and edge-sharing TiO6 octahedra. The corner-sharing octahedral tilt angles range from 30-44°. In the fifth Ti site, Ti(5) is bonded in a 6-coordinate geometry to one O(3), one O(4), two equivalent O(12), and two equivalent O(8) atoms. There are twelve inequivalent O sites. In the first O site, O(1) is bonded to one Li(1), one Mg(1), and two equivalent Ti(3) atoms to form distorted OLiMgTi2 trigonal pyramids that share corners with two equivalent O(2)LiMgTi2 trigonal pyramids, corners with two equivalent O(7)LiTi3 trigonal pyramids, edges with two equivalent O(6)LiTi3 trigonal pyramids, and edges with two equivalent O(5)MgTi3 trigonal pyramids. In the second O site, O(2) is bonded to one Li(1), one Mg(1), and two equivalent Ti(4) atoms to form distorted OLiMgTi2 trigonal pyramids that share corners with two equivalent O(1)LiMgTi2 trigonal pyramids, corners with two equivalent O(8)Ti4 trigonal pyramids, edges with two equivalent O(6)LiTi3 trigonal pyramids, and edges with two equivalent O(5)MgTi3 trigonal pyramids. In the third O site, O(3) is bonded to one Li(2), one Ti(5), and two equivalent Ti(1) atoms to form distorted OLiTi3 trigonal pyramids that share corners with two equivalent O(4)LiTi3 trigonal pyramids, corners with two equivalent O(5)MgTi3 trigonal pyramids, edges with two equivalent O(7)LiTi3 trigonal pyramids, and edges with two equivalent O(8)Ti4 trigonal pyramids. In the fourth O site, O(4) is bonded to one Li(2), one Ti(5), and two equivalent Ti(2) atoms to form distorted OLiTi3 trigonal pyramids that share corners with two equivalent O(3)LiTi3 trigonal pyramids, corners with two equivalent O(6)LiTi3 trigonal pyramids, edges with two equivalent O(7)LiTi3 trigonal pyramids, and edges with two equivalent O(8)Ti4 trigonal pyramids. In the fifth O site, O(5) 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(3)LiTi3 trigonal pyramid,  a cornercorner with one O(5)MgTi3 trigonal pyramid, corners with two equivalent O(6)LiTi3 trigonal pyramids,  an edgeedge with one O(1)LiMgTi2 trigonal pyramid,  an edgeedge with one O(2)LiMgTi2 trigonal pyramid,  an edgeedge with one O(7)LiTi3 trigonal pyramid, and  an edgeedge with one O(8)Ti4 trigonal pyramid. In the sixth O site, O(6) is bonded to one Li(1), one Ti(2), one Ti(3), and one Ti(4) atom to form OLiTi3 trigonal pyramids that share  a cornercorner with one O(4)LiTi3 trigonal pyramid,  a cornercorner with one O(6)LiTi3 trigonal pyramid, corners with two equivalent O(5)MgTi3 trigonal pyramids,  an edgeedge with one O(1)LiMgTi2 trigonal pyramid,  an edgeedge with one O(2)LiMgTi2 trigonal pyramid,  an edgeedge with one O(7)LiTi3 trigonal pyramid, and  an edgeedge with one O(8)Ti4 trigonal pyramid. In the seventh O site, O(7) is bonded to one Li(2), one Ti(1), one Ti(2), and one Ti(3) atom to form distorted OLiTi3 trigonal pyramids that share  a cornercorner with one O(1)LiMgTi2 trigonal pyramid,  a cornercorner with one O(7)LiTi3 trigonal pyramid, corners with two equivalent O(8)Ti4 trigonal pyramids,  an edgeedge with one O(3)LiTi3 trigonal pyramid,  an edgeedge with one O(4)LiTi3 trigonal pyramid,  an edgeedge with one O(6)LiTi3 trigonal pyramid, and  an edgeedge with one O(5)MgTi3 trigonal pyramid. In the eighth O site, O(8) is bonded to one Ti(1), one Ti(2), one Ti(4), and one Ti(5) atom to form distorted OTi4 trigonal pyramids that share  a cornercorner with one O(2)LiMgTi2 trigonal pyramid,  a cornercorner with one O(8)Ti4 trigonal pyramid, corners with two equivalent O(7)LiTi3 trigonal pyramids,  an edgeedge with one O(3)LiTi3 trigonal pyramid,  an edgeedge with one O(4)LiTi3 trigonal pyramid,  an edgeedge with one O(6)LiTi3 trigonal pyramid, and  an edgeedge with one O(5)MgTi3 trigonal pyramid. In the ninth O site, O(9) is bonded in a distorted trigonal non-coplanar geometry to one Mg(1), one Ti(1), and one Ti(3) atom. In the tenth O site, O(10) is bonded in a distorted trigonal non-coplanar geometry to one Li(1), one Ti(2), and one Ti(4) atom. In the eleventh O site, O(11) is bonded in a distorted trigonal non-coplanar geometry to one Li(2), one Ti(1), and one Ti(3) atom. In the twelfth O site, O(12) is bonded in a distorted T-shaped geometry to one Ti(2), one Ti(4), and one Ti(5) atom. is represented by the CIF file [CIF]
data_Li2MgTi9O20
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   10.076
_cell_length_b   5.242
_cell_length_c   7.474
_cell_angle_alpha   70.058
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   371.058
_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
  Li  Li0  1  0.500  0.213  0.401  1.0
  Li  Li1  1  0.000  0.284  0.095  1.0
  Mg  Mg2  1  0.500  0.701  0.904  1.0
  Ti  Ti3  1  0.185  0.802  0.939  1.0
  Ti  Ti4  1  0.190  0.305  0.427  1.0
  Ti  Ti5  1  0.318  0.200  0.068  1.0
  Ti  Ti6  1  0.321  0.707  0.568  1.0
  Ti  Ti7  1  0.815  0.802  0.939  1.0
  Ti  Ti8  1  0.810  0.305  0.427  1.0
  Ti  Ti9  1  0.682  0.200  0.068  1.0
  Ti  Ti10  1  0.679  0.707  0.568  1.0
  Ti  Ti11  1  0.000  0.797  0.598  1.0
  O  O12  1  0.500  0.316  0.104  1.0
  O  O13  1  0.500  0.818  0.608  1.0
  O  O14  1  0.000  0.682  0.870  1.0
  O  O15  1  0.000  0.149  0.408  1.0
  O  O16  1  0.311  0.529  0.843  1.0
  O  O17  1  0.303  0.029  0.343  1.0
  O  O18  1  0.185  0.478  0.161  1.0
  O  O19  1  0.183  0.965  0.655  1.0
  O  O20  1  0.689  0.529  0.843  1.0
  O  O21  1  0.697  0.029  0.343  1.0
  O  O22  1  0.815  0.478  0.161  1.0
  O  O23  1  0.817  0.965  0.655  1.0
  O  O24  1  0.363  0.930  0.975  1.0
  O  O25  1  0.359  0.432  0.479  1.0
  O  O26  1  0.137  0.068  0.023  1.0
  O  O27  1  0.128  0.575  0.525  1.0
  O  O28  1  0.636  0.930  0.975  1.0
  O  O29  1  0.641  0.432  0.479  1.0
  O  O30  1  0.863  0.068  0.023  1.0
  O  O31  1  0.872  0.575  0.525  1.0
[/CIF]
.