The crystal structure described by Li2Mg3Ti6O16 crystallizes in the monoclinic P2_1 space group. There are two inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(1), one O(13), one O(2), one O(4), one O(7), and one O(8) atom to form LiO6 octahedra that share  a cornercorner with one Mg(1)O4 tetrahedra,  a cornercorner with one Mg(3)O4 tetrahedra, corners with two equivalent Li(2)O4 tetrahedra, corners with two equivalent Mg(2)O4 tetrahedra,  an edgeedge with one Ti(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra,  an edgeedge with one Ti(4)O6 octahedra,  an edgeedge with one Ti(5)O6 octahedra, and edges with two equivalent Ti(3)O6 octahedra. In the second Li site, Li(2) is bonded to one O(14), one O(15), one O(4), and one O(8) atom to form LiO4 tetrahedra that share  a cornercorner with one Ti(1)O6 octahedra,  a cornercorner with one Ti(2)O6 octahedra,  a cornercorner with one Ti(6)O6 octahedra, corners with two equivalent Li(1)O6 octahedra, corners with two equivalent Ti(3)O6 octahedra, corners with two equivalent Ti(4)O6 octahedra, and corners with two equivalent Ti(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 53-65°. There are three inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one O(12), one O(16), one O(6), and one O(7) atom to form MgO4 tetrahedra that share  a cornercorner with one Li(1)O6 octahedra,  a cornercorner with one Ti(3)O6 octahedra,  a cornercorner with one Ti(4)O6 octahedra,  a cornercorner with one Ti(5)O6 octahedra, corners with two equivalent Ti(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra, and corners with two equivalent Ti(6)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-65°. In the second Mg site, Mg(2) is bonded to one O(1), one O(2), one O(3), and one O(5) atom to form MgO4 tetrahedra that share  a cornercorner with one Ti(4)O6 octahedra,  a cornercorner with one Ti(5)O6 octahedra,  a cornercorner with one Ti(6)O6 octahedra, corners with two equivalent Li(1)O6 octahedra, corners with two equivalent Ti(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra, and corners with two equivalent Ti(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 53-65°. In the third Mg site, Mg(3) is bonded to one O(10), one O(11), one O(13), and one O(9) atom to form MgO4 tetrahedra that share  a cornercorner with one Li(1)O6 octahedra,  a cornercorner with one Ti(1)O6 octahedra,  a cornercorner with one Ti(2)O6 octahedra,  a cornercorner with one Ti(3)O6 octahedra, corners with two equivalent Ti(4)O6 octahedra, corners with two equivalent Ti(5)O6 octahedra, and corners with two equivalent Ti(6)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-63°. There are six inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(3), one O(5), one O(6), one O(7), one O(8), and one O(9) atom to form TiO6 octahedra that share  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Mg(3)O4 tetrahedra, corners with two equivalent Mg(1)O4 tetrahedra, corners with two equivalent Mg(2)O4 tetrahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Ti(3)O6 octahedra,  an edgeedge with one Ti(6)O6 octahedra, and edges with two equivalent Ti(2)O6 octahedra. In the second Ti site, Ti(2) is bonded to one O(10), one O(3), one O(4), one O(5), one O(6), and one O(7) atom to form TiO6 octahedra that share  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Mg(3)O4 tetrahedra, corners with two equivalent Mg(1)O4 tetrahedra, corners with two equivalent Mg(2)O4 tetrahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Ti(3)O6 octahedra,  an edgeedge with one Ti(6)O6 octahedra, and edges with two equivalent Ti(1)O6 octahedra. In the third Ti site, Ti(3) is bonded to one O(1), one O(11), one O(2), one O(4), one O(6), and one O(8) atom to form TiO6 octahedra that share  a cornercorner with one Mg(1)O4 tetrahedra,  a cornercorner with one Mg(3)O4 tetrahedra, corners with two equivalent Li(2)O4 tetrahedra, corners with two equivalent Mg(2)O4 tetrahedra,  an edgeedge with one Ti(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra,  an edgeedge with one Ti(4)O6 octahedra,  an edgeedge with one Ti(5)O6 octahedra, and edges with two equivalent Li(1)O6 octahedra. In the fourth Ti site, Ti(4) is bonded to one O(1), one O(11), one O(13), one O(14), one O(15), and one O(16) atom to form TiO6 octahedra that share  a cornercorner with one Mg(1)O4 tetrahedra,  a cornercorner with one Mg(2)O4 tetrahedra, corners with two equivalent Li(2)O4 tetrahedra, corners with two equivalent Mg(3)O4 tetrahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Ti(3)O6 octahedra,  an edgeedge with one Ti(6)O6 octahedra, and edges with two equivalent Ti(5)O6 octahedra. In the fifth Ti site, Ti(5) is bonded to one O(11), one O(12), one O(13), one O(14), one O(15), and one O(2) atom to form TiO6 octahedra that share  a cornercorner with one Mg(1)O4 tetrahedra,  a cornercorner with one Mg(2)O4 tetrahedra, corners with two equivalent Li(2)O4 tetrahedra, corners with two equivalent Mg(3)O4 tetrahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Ti(3)O6 octahedra,  an edgeedge with one Ti(6)O6 octahedra, and edges with two equivalent Ti(4)O6 octahedra. In the sixth Ti site, Ti(6) is bonded to one O(10), one O(12), one O(14), one O(16), one O(3), and one O(9) atom to form TiO6 octahedra that share  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Mg(2)O4 tetrahedra, corners with two equivalent Mg(1)O4 tetrahedra, corners with two equivalent Mg(3)O4 tetrahedra,  an edgeedge with one Ti(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra,  an edgeedge with one Ti(4)O6 octahedra, and  an edgeedge with one Ti(5)O6 octahedra. There are sixteen inequivalent O sites. In the first O site, O(1) is bonded to one Li(1), one Mg(2), one Ti(3), and one Ti(4) atom to form OLiMgTi2 trigonal pyramids that share  a cornercorner with one O(2)LiMgTi2 trigonal pyramid,  a cornercorner with one O(7)LiMgTi2 trigonal pyramid,  a cornercorner with one O(14)LiTi3 trigonal pyramid,  a cornercorner with one O(6)MgTi3 trigonal pyramid, corners with two equivalent O(4)Li2Ti2 trigonal pyramids, corners with two equivalent O(8)Li2Ti2 trigonal pyramids,  an edgeedge with one O(13)LiMgTi2 trigonal pyramid,  an edgeedge with one O(2)LiMgTi2 trigonal pyramid, and  an edgeedge with one O(11)MgTi3 trigonal pyramid. In the second O site, O(2) is bonded to one Li(1), one Mg(2), one Ti(3), and one Ti(5) atom to form distorted OLiMgTi2 trigonal pyramids that share  a cornercorner with one O(1)LiMgTi2 trigonal pyramid,  a cornercorner with one O(7)LiMgTi2 trigonal pyramid,  a cornercorner with one O(14)LiTi3 trigonal pyramid,  a cornercorner with one O(6)MgTi3 trigonal pyramid, corners with two equivalent O(4)Li2Ti2 trigonal pyramids, corners with two equivalent O(8)Li2Ti2 trigonal pyramids,  an edgeedge with one O(1)LiMgTi2 trigonal pyramid,  an edgeedge with one O(13)LiMgTi2 trigonal pyramid, and  an edgeedge with one O(11)MgTi3 trigonal pyramid. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Mg(2), one Ti(1), one Ti(2), and one Ti(6) atom. In the fourth O site, O(4) is bonded to one Li(1), one Li(2), one Ti(2), and one Ti(3) atom to form distorted OLi2Ti2 trigonal pyramids that share  a cornercorner with one O(8)Li2Ti2 trigonal pyramid,  a cornercorner with one O(13)LiMgTi2 trigonal pyramid,  a cornercorner with one O(14)LiTi3 trigonal pyramid,  a cornercorner with one O(11)MgTi3 trigonal pyramid, corners with two equivalent O(1)LiMgTi2 trigonal pyramids, corners with two equivalent O(2)LiMgTi2 trigonal pyramids,  an edgeedge with one O(8)Li2Ti2 trigonal pyramid,  an edgeedge with one O(7)LiMgTi2 trigonal pyramid, and  an edgeedge with one O(6)MgTi3 trigonal pyramid. In the fifth O site, O(5) is bonded in a trigonal planar geometry to one Mg(2), one Ti(1), and one Ti(2) atom. In the sixth O site, O(6) 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(1)LiMgTi2 trigonal pyramid,  a cornercorner with one O(2)LiMgTi2 trigonal pyramid,  a cornercorner with one O(7)LiMgTi2 trigonal pyramid,  a cornercorner with one O(11)MgTi3 trigonal pyramid,  an edgeedge with one O(4)Li2Ti2 trigonal pyramid,  an edgeedge with one O(8)Li2Ti2 trigonal pyramid, and  an edgeedge with one O(7)LiMgTi2 trigonal pyramid. In the seventh O site, O(7) is bonded to one Li(1), one Mg(1), one Ti(1), and one Ti(2) atom to form distorted OLiMgTi2 trigonal pyramids that share  a cornercorner with one O(1)LiMgTi2 trigonal pyramid,  a cornercorner with one O(13)LiMgTi2 trigonal pyramid,  a cornercorner with one O(2)LiMgTi2 trigonal pyramid,  a cornercorner with one O(6)MgTi3 trigonal pyramid,  an edgeedge with one O(4)Li2Ti2 trigonal pyramid,  an edgeedge with one O(8)Li2Ti2 trigonal pyramid, and  an edgeedge with one O(6)MgTi3 trigonal pyramid. In the eighth O site, O(8) is bonded to one Li(1), one Li(2), one Ti(1), and one Ti(3) atom to form distorted OLi2Ti2 trigonal pyramids that share  a cornercorner with one O(4)Li2Ti2 trigonal pyramid,  a cornercorner with one O(13)LiMgTi2 trigonal pyramid,  a cornercorner with one O(14)LiTi3 trigonal pyramid,  a cornercorner with one O(11)MgTi3 trigonal pyramid, corners with two equivalent O(1)LiMgTi2 trigonal pyramids, corners with two equivalent O(2)LiMgTi2 trigonal pyramids,  an edgeedge with one O(4)Li2Ti2 trigonal pyramid,  an edgeedge with one O(7)LiMgTi2 trigonal pyramid, and  an edgeedge with one O(6)MgTi3 trigonal pyramid. In the ninth O site, O(9) is bonded in a trigonal planar geometry to one Mg(3), one Ti(1), and one Ti(6) atom. In the tenth O site, O(10) is bonded in a trigonal planar geometry to one Mg(3), one Ti(2), and one Ti(6) atom. In the eleventh O site, O(11) is bonded to one Mg(3), one Ti(3), one Ti(4), and one Ti(5) atom to form distorted OMgTi3 trigonal pyramids that share  a cornercorner with one O(4)Li2Ti2 trigonal pyramid,  a cornercorner with one O(8)Li2Ti2 trigonal pyramid,  a cornercorner with one O(13)LiMgTi2 trigonal pyramid,  a cornercorner with one O(6)MgTi3 trigonal pyramid, corners with two equivalent O(14)LiTi3 trigonal pyramids,  an edgeedge with one O(1)LiMgTi2 trigonal pyramid,  an edgeedge with one O(13)LiMgTi2 trigonal pyramid, and  an edgeedge with one O(2)LiMgTi2 trigonal pyramid. In the twelfth O site, O(12) is bonded in a trigonal planar geometry to one Mg(1), one Ti(5), and one Ti(6) atom. In the thirteenth O site, O(13) is bonded to one Li(1), one Mg(3), one Ti(4), and one Ti(5) atom to form distorted OLiMgTi2 trigonal pyramids that share  a cornercorner with one O(4)Li2Ti2 trigonal pyramid,  a cornercorner with one O(8)Li2Ti2 trigonal pyramid,  a cornercorner with one O(7)LiMgTi2 trigonal pyramid,  a cornercorner with one O(11)MgTi3 trigonal pyramid, corners with two equivalent O(14)LiTi3 trigonal pyramids,  an edgeedge with one O(1)LiMgTi2 trigonal pyramid,  an edgeedge with one O(2)LiMgTi2 trigonal pyramid, and  an edgeedge with one O(11)MgTi3 trigonal pyramid. In the fourteenth O site, O(14) is bonded to one Li(2), one Ti(4), one Ti(5), and one Ti(6) atom to form distorted OLiTi3 trigonal pyramids that share  a cornercorner with one O(4)Li2Ti2 trigonal pyramid,  a cornercorner with one O(8)Li2Ti2 trigonal pyramid,  a cornercorner with one O(1)LiMgTi2 trigonal pyramid,  a cornercorner with one O(2)LiMgTi2 trigonal pyramid, corners with two equivalent O(13)LiMgTi2 trigonal pyramids, and corners with two equivalent O(11)MgTi3 trigonal pyramids. In the fifteenth O site, O(15) is bonded in a trigonal planar geometry to one Li(2), one Ti(4), and one Ti(5) atom. In the sixteenth O site, O(16) is bonded in a trigonal planar geometry to one Mg(1), one Ti(4), and one Ti(6) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li2Mg3Ti6O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.474
_cell_length_b   8.478
_cell_length_c   8.483
_cell_angle_alpha   89.738
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   609.464
_cell_formula_units_Z   2
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  0.624  0.875  0.626  1.0
  Li  Li1  1  0.124  0.125  0.374  1.0
  Li  Li2  1  0.502  0.005  0.248  1.0
  Li  Li3  1  0.002  0.995  0.752  1.0
  Mg  Mg4  1  0.495  0.498  0.744  1.0
  Mg  Mg5  1  0.247  0.750  0.506  1.0
  Mg  Mg6  1  0.747  0.250  0.494  1.0
  Mg  Mg7  1  0.995  0.502  0.256  1.0
  Mg  Mg8  1  0.755  0.758  0.002  1.0
  Mg  Mg9  1  0.255  0.242  0.998  1.0
  Ti  Ti10  1  0.868  0.625  0.634  1.0
  Ti  Ti11  1  0.115  0.364  0.632  1.0
  Ti  Ti12  1  0.373  0.117  0.616  1.0
  Ti  Ti13  1  0.873  0.883  0.384  1.0
  Ti  Ti14  1  0.615  0.636  0.368  1.0
  Ti  Ti15  1  0.368  0.375  0.366  1.0
  Ti  Ti16  1  0.136  0.873  0.130  1.0
  Ti  Ti17  1  0.880  0.132  0.117  1.0
  Ti  Ti18  1  0.625  0.381  0.116  1.0
  Ti  Ti19  1  0.125  0.619  0.884  1.0
  Ti  Ti20  1  0.380  0.868  0.883  1.0
  Ti  Ti21  1  0.636  0.127  0.870  1.0
  O  O22  1  0.611  0.131  0.644  1.0
  O  O23  1  0.372  0.895  0.639  1.0
  O  O24  1  0.110  0.612  0.638  1.0
  O  O25  1  0.140  0.145  0.628  1.0
  O  O26  1  0.896  0.392  0.607  1.0
  O  O27  1  0.362  0.361  0.612  1.0
  O  O28  1  0.645  0.620  0.611  1.0
  O  O29  1  0.878  0.858  0.603  1.0
  O  O30  1  0.378  0.142  0.397  1.0
  O  O31  1  0.145  0.380  0.389  1.0
  O  O32  1  0.862  0.639  0.388  1.0
  O  O33  1  0.396  0.608  0.393  1.0
  O  O34  1  0.640  0.855  0.372  1.0
  O  O35  1  0.610  0.388  0.362  1.0
  O  O36  1  0.872  0.105  0.361  1.0
  O  O37  1  0.111  0.869  0.356  1.0
  O  O38  1  0.392  0.360  0.147  1.0
  O  O39  1  0.643  0.604  0.141  1.0
  O  O40  1  0.888  0.890  0.140  1.0
  O  O41  1  0.858  0.352  0.143  1.0
  O  O42  1  0.106  0.111  0.122  1.0
  O  O43  1  0.641  0.140  0.109  1.0
  O  O44  1  0.354  0.890  0.108  1.0
  O  O45  1  0.108  0.641  0.105  1.0
  O  O46  1  0.608  0.359  0.895  1.0
  O  O47  1  0.854  0.110  0.892  1.0
  O  O48  1  0.141  0.860  0.891  1.0
  O  O49  1  0.606  0.889  0.878  1.0
  O  O50  1  0.358  0.648  0.857  1.0
  O  O51  1  0.388  0.110  0.860  1.0
  O  O52  1  0.143  0.396  0.859  1.0
  O  O53  1  0.892  0.640  0.853  1.0
[/CIF]
.
The crystal structure described by Li2Mg3Ti6O16 crystallizes in the monoclinic P2_1 space group. There are two inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(1), one O(13), one O(2), one O(4), one O(7), and one O(8) atom to form LiO6 octahedra that share  a cornercorner with one Mg(1)O4 tetrahedra,  a cornercorner with one Mg(3)O4 tetrahedra, corners with two equivalent Li(2)O4 tetrahedra, corners with two equivalent Mg(2)O4 tetrahedra,  an edgeedge with one Ti(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra,  an edgeedge with one Ti(4)O6 octahedra,  an edgeedge with one Ti(5)O6 octahedra, and edges with two equivalent Ti(3)O6 octahedra. In the second Li site, Li(2) is bonded to one O(14), one O(15), one O(4), and one O(8) atom to form LiO4 tetrahedra that share  a cornercorner with one Ti(1)O6 octahedra,  a cornercorner with one Ti(2)O6 octahedra,  a cornercorner with one Ti(6)O6 octahedra, corners with two equivalent Li(1)O6 octahedra, corners with two equivalent Ti(3)O6 octahedra, corners with two equivalent Ti(4)O6 octahedra, and corners with two equivalent Ti(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 53-65°. There are three inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one O(12), one O(16), one O(6), and one O(7) atom to form MgO4 tetrahedra that share  a cornercorner with one Li(1)O6 octahedra,  a cornercorner with one Ti(3)O6 octahedra,  a cornercorner with one Ti(4)O6 octahedra,  a cornercorner with one Ti(5)O6 octahedra, corners with two equivalent Ti(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra, and corners with two equivalent Ti(6)O6 octahedra. The corner-sharing octahedral tilt angles range from 51-65°. In the second Mg site, Mg(2) is bonded to one O(1), one O(2), one O(3), and one O(5) atom to form MgO4 tetrahedra that share  a cornercorner with one Ti(4)O6 octahedra,  a cornercorner with one Ti(5)O6 octahedra,  a cornercorner with one Ti(6)O6 octahedra, corners with two equivalent Li(1)O6 octahedra, corners with two equivalent Ti(1)O6 octahedra, corners with two equivalent Ti(2)O6 octahedra, and corners with two equivalent Ti(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 53-65°. In the third Mg site, Mg(3) is bonded to one O(10), one O(11), one O(13), and one O(9) atom to form MgO4 tetrahedra that share  a cornercorner with one Li(1)O6 octahedra,  a cornercorner with one Ti(1)O6 octahedra,  a cornercorner with one Ti(2)O6 octahedra,  a cornercorner with one Ti(3)O6 octahedra, corners with two equivalent Ti(4)O6 octahedra, corners with two equivalent Ti(5)O6 octahedra, and corners with two equivalent Ti(6)O6 octahedra. The corner-sharing octahedral tilt angles range from 52-63°. There are six inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(3), one O(5), one O(6), one O(7), one O(8), and one O(9) atom to form TiO6 octahedra that share  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Mg(3)O4 tetrahedra, corners with two equivalent Mg(1)O4 tetrahedra, corners with two equivalent Mg(2)O4 tetrahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Ti(3)O6 octahedra,  an edgeedge with one Ti(6)O6 octahedra, and edges with two equivalent Ti(2)O6 octahedra. In the second Ti site, Ti(2) is bonded to one O(10), one O(3), one O(4), one O(5), one O(6), and one O(7) atom to form TiO6 octahedra that share  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Mg(3)O4 tetrahedra, corners with two equivalent Mg(1)O4 tetrahedra, corners with two equivalent Mg(2)O4 tetrahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Ti(3)O6 octahedra,  an edgeedge with one Ti(6)O6 octahedra, and edges with two equivalent Ti(1)O6 octahedra. In the third Ti site, Ti(3) is bonded to one O(1), one O(11), one O(2), one O(4), one O(6), and one O(8) atom to form TiO6 octahedra that share  a cornercorner with one Mg(1)O4 tetrahedra,  a cornercorner with one Mg(3)O4 tetrahedra, corners with two equivalent Li(2)O4 tetrahedra, corners with two equivalent Mg(2)O4 tetrahedra,  an edgeedge with one Ti(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra,  an edgeedge with one Ti(4)O6 octahedra,  an edgeedge with one Ti(5)O6 octahedra, and edges with two equivalent Li(1)O6 octahedra. In the fourth Ti site, Ti(4) is bonded to one O(1), one O(11), one O(13), one O(14), one O(15), and one O(16) atom to form TiO6 octahedra that share  a cornercorner with one Mg(1)O4 tetrahedra,  a cornercorner with one Mg(2)O4 tetrahedra, corners with two equivalent Li(2)O4 tetrahedra, corners with two equivalent Mg(3)O4 tetrahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Ti(3)O6 octahedra,  an edgeedge with one Ti(6)O6 octahedra, and edges with two equivalent Ti(5)O6 octahedra. In the fifth Ti site, Ti(5) is bonded to one O(11), one O(12), one O(13), one O(14), one O(15), and one O(2) atom to form TiO6 octahedra that share  a cornercorner with one Mg(1)O4 tetrahedra,  a cornercorner with one Mg(2)O4 tetrahedra, corners with two equivalent Li(2)O4 tetrahedra, corners with two equivalent Mg(3)O4 tetrahedra,  an edgeedge with one Li(1)O6 octahedra,  an edgeedge with one Ti(3)O6 octahedra,  an edgeedge with one Ti(6)O6 octahedra, and edges with two equivalent Ti(4)O6 octahedra. In the sixth Ti site, Ti(6) is bonded to one O(10), one O(12), one O(14), one O(16), one O(3), and one O(9) atom to form TiO6 octahedra that share  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Mg(2)O4 tetrahedra, corners with two equivalent Mg(1)O4 tetrahedra, corners with two equivalent Mg(3)O4 tetrahedra,  an edgeedge with one Ti(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra,  an edgeedge with one Ti(4)O6 octahedra, and  an edgeedge with one Ti(5)O6 octahedra. There are sixteen inequivalent O sites. In the first O site, O(1) is bonded to one Li(1), one Mg(2), one Ti(3), and one Ti(4) atom to form OLiMgTi2 trigonal pyramids that share  a cornercorner with one O(2)LiMgTi2 trigonal pyramid,  a cornercorner with one O(7)LiMgTi2 trigonal pyramid,  a cornercorner with one O(14)LiTi3 trigonal pyramid,  a cornercorner with one O(6)MgTi3 trigonal pyramid, corners with two equivalent O(4)Li2Ti2 trigonal pyramids, corners with two equivalent O(8)Li2Ti2 trigonal pyramids,  an edgeedge with one O(13)LiMgTi2 trigonal pyramid,  an edgeedge with one O(2)LiMgTi2 trigonal pyramid, and  an edgeedge with one O(11)MgTi3 trigonal pyramid. In the second O site, O(2) is bonded to one Li(1), one Mg(2), one Ti(3), and one Ti(5) atom to form distorted OLiMgTi2 trigonal pyramids that share  a cornercorner with one O(1)LiMgTi2 trigonal pyramid,  a cornercorner with one O(7)LiMgTi2 trigonal pyramid,  a cornercorner with one O(14)LiTi3 trigonal pyramid,  a cornercorner with one O(6)MgTi3 trigonal pyramid, corners with two equivalent O(4)Li2Ti2 trigonal pyramids, corners with two equivalent O(8)Li2Ti2 trigonal pyramids,  an edgeedge with one O(1)LiMgTi2 trigonal pyramid,  an edgeedge with one O(13)LiMgTi2 trigonal pyramid, and  an edgeedge with one O(11)MgTi3 trigonal pyramid. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Mg(2), one Ti(1), one Ti(2), and one Ti(6) atom. In the fourth O site, O(4) is bonded to one Li(1), one Li(2), one Ti(2), and one Ti(3) atom to form distorted OLi2Ti2 trigonal pyramids that share  a cornercorner with one O(8)Li2Ti2 trigonal pyramid,  a cornercorner with one O(13)LiMgTi2 trigonal pyramid,  a cornercorner with one O(14)LiTi3 trigonal pyramid,  a cornercorner with one O(11)MgTi3 trigonal pyramid, corners with two equivalent O(1)LiMgTi2 trigonal pyramids, corners with two equivalent O(2)LiMgTi2 trigonal pyramids,  an edgeedge with one O(8)Li2Ti2 trigonal pyramid,  an edgeedge with one O(7)LiMgTi2 trigonal pyramid, and  an edgeedge with one O(6)MgTi3 trigonal pyramid. In the fifth O site, O(5) is bonded in a trigonal planar geometry to one Mg(2), one Ti(1), and one Ti(2) atom. In the sixth O site, O(6) 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(1)LiMgTi2 trigonal pyramid,  a cornercorner with one O(2)LiMgTi2 trigonal pyramid,  a cornercorner with one O(7)LiMgTi2 trigonal pyramid,  a cornercorner with one O(11)MgTi3 trigonal pyramid,  an edgeedge with one O(4)Li2Ti2 trigonal pyramid,  an edgeedge with one O(8)Li2Ti2 trigonal pyramid, and  an edgeedge with one O(7)LiMgTi2 trigonal pyramid. In the seventh O site, O(7) is bonded to one Li(1), one Mg(1), one Ti(1), and one Ti(2) atom to form distorted OLiMgTi2 trigonal pyramids that share  a cornercorner with one O(1)LiMgTi2 trigonal pyramid,  a cornercorner with one O(13)LiMgTi2 trigonal pyramid,  a cornercorner with one O(2)LiMgTi2 trigonal pyramid,  a cornercorner with one O(6)MgTi3 trigonal pyramid,  an edgeedge with one O(4)Li2Ti2 trigonal pyramid,  an edgeedge with one O(8)Li2Ti2 trigonal pyramid, and  an edgeedge with one O(6)MgTi3 trigonal pyramid. In the eighth O site, O(8) is bonded to one Li(1), one Li(2), one Ti(1), and one Ti(3) atom to form distorted OLi2Ti2 trigonal pyramids that share  a cornercorner with one O(4)Li2Ti2 trigonal pyramid,  a cornercorner with one O(13)LiMgTi2 trigonal pyramid,  a cornercorner with one O(14)LiTi3 trigonal pyramid,  a cornercorner with one O(11)MgTi3 trigonal pyramid, corners with two equivalent O(1)LiMgTi2 trigonal pyramids, corners with two equivalent O(2)LiMgTi2 trigonal pyramids,  an edgeedge with one O(4)Li2Ti2 trigonal pyramid,  an edgeedge with one O(7)LiMgTi2 trigonal pyramid, and  an edgeedge with one O(6)MgTi3 trigonal pyramid. In the ninth O site, O(9) is bonded in a trigonal planar geometry to one Mg(3), one Ti(1), and one Ti(6) atom. In the tenth O site, O(10) is bonded in a trigonal planar geometry to one Mg(3), one Ti(2), and one Ti(6) atom. In the eleventh O site, O(11) is bonded to one Mg(3), one Ti(3), one Ti(4), and one Ti(5) atom to form distorted OMgTi3 trigonal pyramids that share  a cornercorner with one O(4)Li2Ti2 trigonal pyramid,  a cornercorner with one O(8)Li2Ti2 trigonal pyramid,  a cornercorner with one O(13)LiMgTi2 trigonal pyramid,  a cornercorner with one O(6)MgTi3 trigonal pyramid, corners with two equivalent O(14)LiTi3 trigonal pyramids,  an edgeedge with one O(1)LiMgTi2 trigonal pyramid,  an edgeedge with one O(13)LiMgTi2 trigonal pyramid, and  an edgeedge with one O(2)LiMgTi2 trigonal pyramid. In the twelfth O site, O(12) is bonded in a trigonal planar geometry to one Mg(1), one Ti(5), and one Ti(6) atom. In the thirteenth O site, O(13) is bonded to one Li(1), one Mg(3), one Ti(4), and one Ti(5) atom to form distorted OLiMgTi2 trigonal pyramids that share  a cornercorner with one O(4)Li2Ti2 trigonal pyramid,  a cornercorner with one O(8)Li2Ti2 trigonal pyramid,  a cornercorner with one O(7)LiMgTi2 trigonal pyramid,  a cornercorner with one O(11)MgTi3 trigonal pyramid, corners with two equivalent O(14)LiTi3 trigonal pyramids,  an edgeedge with one O(1)LiMgTi2 trigonal pyramid,  an edgeedge with one O(2)LiMgTi2 trigonal pyramid, and  an edgeedge with one O(11)MgTi3 trigonal pyramid. In the fourteenth O site, O(14) is bonded to one Li(2), one Ti(4), one Ti(5), and one Ti(6) atom to form distorted OLiTi3 trigonal pyramids that share  a cornercorner with one O(4)Li2Ti2 trigonal pyramid,  a cornercorner with one O(8)Li2Ti2 trigonal pyramid,  a cornercorner with one O(1)LiMgTi2 trigonal pyramid,  a cornercorner with one O(2)LiMgTi2 trigonal pyramid, corners with two equivalent O(13)LiMgTi2 trigonal pyramids, and corners with two equivalent O(11)MgTi3 trigonal pyramids. In the fifteenth O site, O(15) is bonded in a trigonal planar geometry to one Li(2), one Ti(4), and one Ti(5) atom. In the sixteenth O site, O(16) is bonded in a trigonal planar geometry to one Mg(1), one Ti(4), and one Ti(6) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li2Mg3Ti6O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   8.474
_cell_length_b   8.478
_cell_length_c   8.483
_cell_angle_alpha   89.738
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   609.464
_cell_formula_units_Z   2
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  0.624  0.875  0.626  1.0
  Li  Li1  1  0.124  0.125  0.374  1.0
  Li  Li2  1  0.502  0.005  0.248  1.0
  Li  Li3  1  0.002  0.995  0.752  1.0
  Mg  Mg4  1  0.495  0.498  0.744  1.0
  Mg  Mg5  1  0.247  0.750  0.506  1.0
  Mg  Mg6  1  0.747  0.250  0.494  1.0
  Mg  Mg7  1  0.995  0.502  0.256  1.0
  Mg  Mg8  1  0.755  0.758  0.002  1.0
  Mg  Mg9  1  0.255  0.242  0.998  1.0
  Ti  Ti10  1  0.868  0.625  0.634  1.0
  Ti  Ti11  1  0.115  0.364  0.632  1.0
  Ti  Ti12  1  0.373  0.117  0.616  1.0
  Ti  Ti13  1  0.873  0.883  0.384  1.0
  Ti  Ti14  1  0.615  0.636  0.368  1.0
  Ti  Ti15  1  0.368  0.375  0.366  1.0
  Ti  Ti16  1  0.136  0.873  0.130  1.0
  Ti  Ti17  1  0.880  0.132  0.117  1.0
  Ti  Ti18  1  0.625  0.381  0.116  1.0
  Ti  Ti19  1  0.125  0.619  0.884  1.0
  Ti  Ti20  1  0.380  0.868  0.883  1.0
  Ti  Ti21  1  0.636  0.127  0.870  1.0
  O  O22  1  0.611  0.131  0.644  1.0
  O  O23  1  0.372  0.895  0.639  1.0
  O  O24  1  0.110  0.612  0.638  1.0
  O  O25  1  0.140  0.145  0.628  1.0
  O  O26  1  0.896  0.392  0.607  1.0
  O  O27  1  0.362  0.361  0.612  1.0
  O  O28  1  0.645  0.620  0.611  1.0
  O  O29  1  0.878  0.858  0.603  1.0
  O  O30  1  0.378  0.142  0.397  1.0
  O  O31  1  0.145  0.380  0.389  1.0
  O  O32  1  0.862  0.639  0.388  1.0
  O  O33  1  0.396  0.608  0.393  1.0
  O  O34  1  0.640  0.855  0.372  1.0
  O  O35  1  0.610  0.388  0.362  1.0
  O  O36  1  0.872  0.105  0.361  1.0
  O  O37  1  0.111  0.869  0.356  1.0
  O  O38  1  0.392  0.360  0.147  1.0
  O  O39  1  0.643  0.604  0.141  1.0
  O  O40  1  0.888  0.890  0.140  1.0
  O  O41  1  0.858  0.352  0.143  1.0
  O  O42  1  0.106  0.111  0.122  1.0
  O  O43  1  0.641  0.140  0.109  1.0
  O  O44  1  0.354  0.890  0.108  1.0
  O  O45  1  0.108  0.641  0.105  1.0
  O  O46  1  0.608  0.359  0.895  1.0
  O  O47  1  0.854  0.110  0.892  1.0
  O  O48  1  0.141  0.860  0.891  1.0
  O  O49  1  0.606  0.889  0.878  1.0
  O  O50  1  0.358  0.648  0.857  1.0
  O  O51  1  0.388  0.110  0.860  1.0
  O  O52  1  0.143  0.396  0.859  1.0
  O  O53  1  0.892  0.640  0.853  1.0
[/CIF]
.