The structure described by Li3MgTi8O16 is Spinel-derived structured and crystallizes in the trigonal R3m space group. There are three inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(6) and three equivalent O(1) atoms to form LiO4 tetrahedra that share corners with three equivalent Ti(2)O6 octahedra, corners with three equivalent Ti(4)O6 octahedra, and corners with six equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 59-62°. In the second Li site, Li(2) is bonded to one O(7) and three equivalent O(4) atoms to form LiO4 tetrahedra that share corners with three equivalent Mg(1)O6 octahedra, corners with three equivalent Ti(4)O6 octahedra, and corners with six equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-60°. In the third Li site, Li(3) is bonded to one O(3) and three equivalent O(8) atoms to form LiO4 tetrahedra that share corners with three equivalent Ti(1)O6 octahedra, corners with three equivalent Ti(2)O6 octahedra, and corners with six equivalent Ti(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-60°. Mg(1) is bonded to three equivalent O(4) and three equivalent O(5) atoms to form MgO6 octahedra that share corners with three equivalent Li(2)O4 tetrahedra, corners with three equivalent Ti(3)O4 tetrahedra, edges with three equivalent Ti(1)O6 octahedra, and edges with three equivalent Ti(4)O6 octahedra. There are four inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(2), one O(3), two equivalent O(1), and two equivalent O(4) atoms to form TiO6 octahedra that share  a cornercorner with one Li(3)O4 tetrahedra,  a cornercorner with one Ti(3)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra, corners with two equivalent Li(2)O4 tetrahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra, and edges with four equivalent Ti(1)O6 octahedra. In the second Ti site, Ti(2) is bonded to three equivalent O(1) and three equivalent O(8) atoms to form TiO6 octahedra that share corners with three equivalent Li(1)O4 tetrahedra, corners with three equivalent Li(3)O4 tetrahedra, edges with three equivalent Ti(1)O6 octahedra, and edges with three equivalent Ti(4)O6 octahedra. In the third Ti site, Ti(3) is bonded to one O(2) and three equivalent O(5) atoms to form TiO4 tetrahedra that share corners with three equivalent Mg(1)O6 octahedra, corners with three equivalent Ti(1)O6 octahedra, and corners with six equivalent Ti(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-58°. In the fourth Ti site, Ti(4) is bonded to one O(6), one O(7), two equivalent O(5), and two equivalent O(8) atoms to form TiO6 octahedra that share  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 tetrahedra, corners with two equivalent Li(3)O4 tetrahedra, corners with two equivalent Ti(3)O4 tetrahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra, and edges with four equivalent Ti(4)O6 octahedra. There are eight inequivalent O sites. In the first O site, O(1) is bonded to one Li(1), one Ti(2), and two equivalent Ti(1) atoms to form a mixture of distorted corner and edge-sharing OLiTi3 tetrahedra. In the second O site, O(2) is bonded in a distorted rectangular see-saw-like geometry to one Ti(3) and three equivalent Ti(1) atoms. In the third O site, O(3) is bonded to one Li(3) and three equivalent Ti(1) atoms to form distorted corner-sharing OLiTi3 trigonal pyramids. In the fourth O site, O(4) is bonded in a rectangular see-saw-like geometry to one Li(2), one Mg(1), and two equivalent Ti(1) atoms. In the fifth O site, O(5) is bonded in a distorted rectangular see-saw-like geometry to one Mg(1), one Ti(3), and two equivalent Ti(4) atoms. In the sixth O site, O(6) is bonded to one Li(1) and three equivalent Ti(4) atoms to form corner-sharing OLiTi3 tetrahedra. In the seventh O site, O(7) is bonded in a distorted rectangular see-saw-like geometry to one Li(2) and three equivalent Ti(4) atoms. In the eighth O site, O(8) is bonded to one Li(3), one Ti(2), and two equivalent Ti(4) atoms to form a mixture of distorted corner and edge-sharing OLiTi3 trigonal pyramids. is represented by the CIF file [CIF]
data_Li3MgTi8O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   10.463
_cell_length_b   10.463
_cell_length_c   10.463
_cell_angle_alpha   33.253
_cell_angle_beta   33.253
_cell_angle_gamma   33.253
_symmetry_Int_Tables_number   1
_cell_volume   306.652
_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  0.188  0.188  0.188  1.0
  Li  Li1  1  0.310  0.310  0.310  1.0
  Li  Li2  1  0.813  0.813  0.813  1.0
  Mg  Mg3  1  0.999  0.999  0.999  1.0
  Ti  Ti4  1  0.754  0.754  0.242  1.0
  Ti  Ti5  1  0.501  0.501  0.501  1.0
  Ti  Ti6  1  0.242  0.754  0.754  1.0
  Ti  Ti7  1  0.754  0.242  0.754  1.0
  Ti  Ti8  1  0.688  0.688  0.688  1.0
  Ti  Ti9  1  0.256  0.256  0.745  1.0
  Ti  Ti10  1  0.256  0.745  0.256  1.0
  Ti  Ti11  1  0.745  0.256  0.256  1.0
  O  O12  1  0.395  0.841  0.395  1.0
  O  O13  1  0.841  0.395  0.395  1.0
  O  O14  1  0.395  0.395  0.841  1.0
  O  O15  1  0.623  0.623  0.623  1.0
  O  O16  1  0.880  0.880  0.880  1.0
  O  O17  1  0.106  0.106  0.649  1.0
  O  O18  1  0.106  0.649  0.106  1.0
  O  O19  1  0.649  0.106  0.106  1.0
  O  O20  1  0.882  0.365  0.882  1.0
  O  O21  1  0.365  0.882  0.882  1.0
  O  O22  1  0.882  0.882  0.365  1.0
  O  O23  1  0.118  0.118  0.118  1.0
  O  O24  1  0.381  0.381  0.381  1.0
  O  O25  1  0.608  0.608  0.153  1.0
  O  O26  1  0.153  0.608  0.608  1.0
  O  O27  1  0.608  0.153  0.608  1.0
[/CIF]
.
The structure described by Li3MgTi8O16 is Spinel-derived structured and crystallizes in the trigonal R3m space group. There are three inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(6) and three equivalent O(1) atoms to form LiO4 tetrahedra that share corners with three equivalent Ti(2)O6 octahedra, corners with three equivalent Ti(4)O6 octahedra, and corners with six equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 59-62°. In the second Li site, Li(2) is bonded to one O(7) and three equivalent O(4) atoms to form LiO4 tetrahedra that share corners with three equivalent Mg(1)O6 octahedra, corners with three equivalent Ti(4)O6 octahedra, and corners with six equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-60°. In the third Li site, Li(3) is bonded to one O(3) and three equivalent O(8) atoms to form LiO4 tetrahedra that share corners with three equivalent Ti(1)O6 octahedra, corners with three equivalent Ti(2)O6 octahedra, and corners with six equivalent Ti(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-60°. Mg(1) is bonded to three equivalent O(4) and three equivalent O(5) atoms to form MgO6 octahedra that share corners with three equivalent Li(2)O4 tetrahedra, corners with three equivalent Ti(3)O4 tetrahedra, edges with three equivalent Ti(1)O6 octahedra, and edges with three equivalent Ti(4)O6 octahedra. There are four inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(2), one O(3), two equivalent O(1), and two equivalent O(4) atoms to form TiO6 octahedra that share  a cornercorner with one Li(3)O4 tetrahedra,  a cornercorner with one Ti(3)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra, corners with two equivalent Li(2)O4 tetrahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra, and edges with four equivalent Ti(1)O6 octahedra. In the second Ti site, Ti(2) is bonded to three equivalent O(1) and three equivalent O(8) atoms to form TiO6 octahedra that share corners with three equivalent Li(1)O4 tetrahedra, corners with three equivalent Li(3)O4 tetrahedra, edges with three equivalent Ti(1)O6 octahedra, and edges with three equivalent Ti(4)O6 octahedra. In the third Ti site, Ti(3) is bonded to one O(2) and three equivalent O(5) atoms to form TiO4 tetrahedra that share corners with three equivalent Mg(1)O6 octahedra, corners with three equivalent Ti(1)O6 octahedra, and corners with six equivalent Ti(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-58°. In the fourth Ti site, Ti(4) is bonded to one O(6), one O(7), two equivalent O(5), and two equivalent O(8) atoms to form TiO6 octahedra that share  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(2)O4 tetrahedra, corners with two equivalent Li(3)O4 tetrahedra, corners with two equivalent Ti(3)O4 tetrahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra, and edges with four equivalent Ti(4)O6 octahedra. There are eight inequivalent O sites. In the first O site, O(1) is bonded to one Li(1), one Ti(2), and two equivalent Ti(1) atoms to form a mixture of distorted corner and edge-sharing OLiTi3 tetrahedra. In the second O site, O(2) is bonded in a distorted rectangular see-saw-like geometry to one Ti(3) and three equivalent Ti(1) atoms. In the third O site, O(3) is bonded to one Li(3) and three equivalent Ti(1) atoms to form distorted corner-sharing OLiTi3 trigonal pyramids. In the fourth O site, O(4) is bonded in a rectangular see-saw-like geometry to one Li(2), one Mg(1), and two equivalent Ti(1) atoms. In the fifth O site, O(5) is bonded in a distorted rectangular see-saw-like geometry to one Mg(1), one Ti(3), and two equivalent Ti(4) atoms. In the sixth O site, O(6) is bonded to one Li(1) and three equivalent Ti(4) atoms to form corner-sharing OLiTi3 tetrahedra. In the seventh O site, O(7) is bonded in a distorted rectangular see-saw-like geometry to one Li(2) and three equivalent Ti(4) atoms. In the eighth O site, O(8) is bonded to one Li(3), one Ti(2), and two equivalent Ti(4) atoms to form a mixture of distorted corner and edge-sharing OLiTi3 trigonal pyramids. is represented by the CIF file [CIF]
data_Li3MgTi8O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   10.463
_cell_length_b   10.463
_cell_length_c   10.463
_cell_angle_alpha   33.253
_cell_angle_beta   33.253
_cell_angle_gamma   33.253
_symmetry_Int_Tables_number   1
_cell_volume   306.652
_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  0.188  0.188  0.188  1.0
  Li  Li1  1  0.310  0.310  0.310  1.0
  Li  Li2  1  0.813  0.813  0.813  1.0
  Mg  Mg3  1  0.999  0.999  0.999  1.0
  Ti  Ti4  1  0.754  0.754  0.242  1.0
  Ti  Ti5  1  0.501  0.501  0.501  1.0
  Ti  Ti6  1  0.242  0.754  0.754  1.0
  Ti  Ti7  1  0.754  0.242  0.754  1.0
  Ti  Ti8  1  0.688  0.688  0.688  1.0
  Ti  Ti9  1  0.256  0.256  0.745  1.0
  Ti  Ti10  1  0.256  0.745  0.256  1.0
  Ti  Ti11  1  0.745  0.256  0.256  1.0
  O  O12  1  0.395  0.841  0.395  1.0
  O  O13  1  0.841  0.395  0.395  1.0
  O  O14  1  0.395  0.395  0.841  1.0
  O  O15  1  0.623  0.623  0.623  1.0
  O  O16  1  0.880  0.880  0.880  1.0
  O  O17  1  0.106  0.106  0.649  1.0
  O  O18  1  0.106  0.649  0.106  1.0
  O  O19  1  0.649  0.106  0.106  1.0
  O  O20  1  0.882  0.365  0.882  1.0
  O  O21  1  0.365  0.882  0.882  1.0
  O  O22  1  0.882  0.882  0.365  1.0
  O  O23  1  0.118  0.118  0.118  1.0
  O  O24  1  0.381  0.381  0.381  1.0
  O  O25  1  0.608  0.608  0.153  1.0
  O  O26  1  0.153  0.608  0.608  1.0
  O  O27  1  0.608  0.153  0.608  1.0
[/CIF]
.