The compound described by Li5MgTi12O24 is Spinel-derived structured and crystallizes in the trigonal P3m1 space group. There are five inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(11) and three equivalent O(1) atoms to form LiO4 tetrahedra that share corners with three equivalent Ti(4)O6 octahedra, corners with three equivalent Ti(5)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(8) and three equivalent O(3) atoms to form LiO4 tetrahedra that share corners with three equivalent Ti(2)O6 octahedra, corners with three equivalent Ti(3)O6 octahedra, and corners with six equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-60°. In the third Li site, Li(3) is bonded to one O(6) and three equivalent O(5) atoms to form LiO4 tetrahedra that share corners with three equivalent Ti(1)O6 octahedra, corners with three equivalent Ti(3)O6 octahedra, and corners with six equivalent Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 59-61°. In the fourth Li site, Li(4) is bonded to one O(12) 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(5)O6 octahedra, and corners with six equivalent Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-60°. In the fifth Li site, Li(5) is bonded to one O(2) and three equivalent O(9) atoms to form LiO4 tetrahedra that share corners with three equivalent Ti(1)O6 octahedra, corners with three equivalent Ti(4)O6 octahedra, and corners with six equivalent Ti(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-61°. Mg(1) is bonded to three equivalent O(10) and three equivalent O(4) atoms to form MgO6 octahedra that share corners with three equivalent Li(4)O4 tetrahedra, corners with three equivalent Ti(6)O4 tetrahedra, edges with three equivalent Ti(2)O6 octahedra, and edges with three equivalent Ti(5)O6 octahedra. There are six inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(2), one O(6), two equivalent O(1), and two equivalent O(3) atoms to form TiO6 octahedra that share  a cornercorner with one Li(3)O4 tetrahedra,  a cornercorner with one Li(5)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra, corners with two equivalent Li(2)O4 tetrahedra,  an edgeedge with one Ti(3)O6 octahedra,  an edgeedge with one Ti(4)O6 octahedra, and edges with four equivalent Ti(1)O6 octahedra. In the second Ti site, Ti(2) is bonded to one O(7), one O(8), two equivalent O(4), and two equivalent O(5) atoms to form TiO6 octahedra that share  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Ti(6)O4 tetrahedra, corners with two equivalent Li(3)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Ti(3)O6 octahedra, and edges with four equivalent Ti(2)O6 octahedra. In the third Ti site, Ti(3) is bonded to three equivalent O(3) and three equivalent O(5) atoms to form TiO6 octahedra that share corners with three equivalent Li(2)O4 tetrahedra, corners with three equivalent Li(3)O4 tetrahedra, edges with three equivalent Ti(1)O6 octahedra, and edges with three equivalent Ti(2)O6 octahedra. In the fourth Ti site, Ti(4) is bonded to three equivalent O(1) and three equivalent O(9) atoms to form TiO6 octahedra that share corners with three equivalent Li(1)O4 tetrahedra, corners with three equivalent Li(5)O4 tetrahedra, edges with three equivalent Ti(1)O6 octahedra, and edges with three equivalent Ti(5)O6 octahedra. In the fifth Ti site, Ti(5) is bonded to one O(11), one O(12), two equivalent O(10), and two equivalent O(9) atoms to form TiO6 octahedra that share  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(5)O4 tetrahedra, corners with two equivalent Ti(6)O4 tetrahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Ti(4)O6 octahedra, and edges with four equivalent Ti(5)O6 octahedra. In the sixth Ti site, Ti(6) is bonded to one O(7) and three equivalent O(10) atoms to form TiO4 tetrahedra that share corners with three equivalent Mg(1)O6 octahedra, corners with three equivalent Ti(2)O6 octahedra, and corners with six equivalent Ti(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-58°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded to one Li(1), one Ti(4), and two equivalent Ti(1) atoms to form a mixture of distorted corner and edge-sharing OLiTi3 trigonal pyramids. In the second O site, O(2) is bonded to one Li(5) and three equivalent Ti(1) atoms to form a mixture of distorted corner and edge-sharing OLiTi3 trigonal pyramids. In the third O site, O(3) is bonded to one Li(2), one Ti(3), and two equivalent Ti(1) atoms to form a mixture of distorted corner and edge-sharing OLiTi3 trigonal pyramids. In the fourth O site, O(4) is bonded to one Li(4), one Mg(1), and two equivalent Ti(2) atoms to form distorted OLiMgTi2 trigonal pyramids that share corners with four equivalent O(5)LiTi3 tetrahedra, corners with two equivalent O(4)LiMgTi2 trigonal pyramids,  an edgeedge with one O(8)LiTi3 trigonal pyramid, and edges with two equivalent O(4)LiMgTi2 trigonal pyramids. In the fifth O site, O(5) is bonded to one Li(3), one Ti(3), and two equivalent Ti(2) atoms to form distorted OLiTi3 tetrahedra that share corners with two equivalent O(5)LiTi3 tetrahedra,  a cornercorner with one O(6)LiTi3 trigonal pyramid, corners with two equivalent O(8)LiTi3 trigonal pyramids, corners with three equivalent O(3)LiTi3 trigonal pyramids, corners with four equivalent O(4)LiMgTi2 trigonal pyramids, and edges with two equivalent O(5)LiTi3 tetrahedra. In the sixth O site, O(6) is bonded to one Li(3) and three equivalent Ti(1) atoms to form a mixture of distorted corner and edge-sharing OLiTi3 trigonal pyramids. In the seventh O site, O(7) is bonded in a distorted rectangular see-saw-like geometry to one Ti(6) and three equivalent Ti(2) atoms. In the eighth O site, O(8) is bonded to one Li(2) and three equivalent Ti(2) atoms to form distorted OLiTi3 trigonal pyramids that share corners with six equivalent O(5)LiTi3 tetrahedra, corners with three equivalent O(3)LiTi3 trigonal pyramids, and edges with three equivalent O(4)LiMgTi2 trigonal pyramids. In the ninth O site, O(9) is bonded in a rectangular see-saw-like geometry to one Li(5), one Ti(4), and two equivalent Ti(5) atoms. In the tenth O site, O(10) is bonded in a distorted rectangular see-saw-like geometry to one Mg(1), one Ti(6), and two equivalent Ti(5) atoms. In the eleventh O site, O(11) is bonded to one Li(1) and three equivalent Ti(5) atoms to form corner-sharing OLiTi3 tetrahedra. In the twelfth O site, O(12) is bonded in a rectangular see-saw-like geometry to one Li(4) and three equivalent Ti(5) atoms. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li5MgTi12O24
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.995
_cell_length_b   5.995
_cell_length_c   14.758
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   459.301
_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  0.667  0.333  0.042  1.0
  Li  Li1  1  0.667  0.333  0.290  1.0
  Li  Li2  1  0.333  0.667  0.376  1.0
  Li  Li3  1  0.333  0.667  0.620  1.0
  Li  Li4  1  0.000  0.000  0.962  1.0
  Mg  Mg5  1  0.667  0.333  0.664  1.0
  Ti  Ti6  1  0.167  0.334  0.167  1.0
  Ti  Ti7  1  0.829  0.171  0.499  1.0
  Ti  Ti8  1  0.167  0.833  0.167  1.0
  Ti  Ti9  1  0.000  0.000  0.333  1.0
  Ti  Ti10  1  0.333  0.667  0.002  1.0
  Ti  Ti11  1  0.666  0.833  0.167  1.0
  Ti  Ti12  1  0.342  0.171  0.499  1.0
  Ti  Ti13  1  0.829  0.658  0.499  1.0
  Ti  Ti14  1  0.009  0.504  0.838  1.0
  Ti  Ti15  1  0.000  0.000  0.710  1.0
  Ti  Ti16  1  0.496  0.504  0.838  1.0
  Ti  Ti17  1  0.496  0.991  0.838  1.0
  O  O18  1  0.033  0.517  0.088  1.0
  O  O19  1  0.483  0.517  0.088  1.0
  O  O20  1  0.000  0.000  0.097  1.0
  O  O21  1  0.851  0.149  0.246  1.0
  O  O22  1  0.851  0.701  0.246  1.0
  O  O23  1  0.299  0.149  0.246  1.0
  O  O24  1  0.971  0.486  0.574  1.0
  O  O25  1  0.483  0.967  0.088  1.0
  O  O26  1  0.148  0.296  0.421  1.0
  O  O27  1  0.148  0.852  0.421  1.0
  O  O28  1  0.333  0.667  0.237  1.0
  O  O29  1  0.000  0.000  0.579  1.0
  O  O30  1  0.667  0.333  0.427  1.0
  O  O31  1  0.514  0.486  0.574  1.0
  O  O32  1  0.514  0.029  0.574  1.0
  O  O33  1  0.182  0.364  0.913  1.0
  O  O34  1  0.704  0.852  0.421  1.0
  O  O35  1  0.345  0.172  0.753  1.0
  O  O36  1  0.828  0.655  0.753  1.0
  O  O37  1  0.828  0.172  0.753  1.0
  O  O38  1  0.667  0.333  0.902  1.0
  O  O39  1  0.333  0.667  0.763  1.0
  O  O40  1  0.182  0.818  0.913  1.0
  O  O41  1  0.636  0.818  0.913  1.0
[/CIF]
.
The compound described by Li5MgTi12O24 is Spinel-derived structured and crystallizes in the trigonal P3m1 space group. There are five inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(11) and three equivalent O(1) atoms to form LiO4 tetrahedra that share corners with three equivalent Ti(4)O6 octahedra, corners with three equivalent Ti(5)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(8) and three equivalent O(3) atoms to form LiO4 tetrahedra that share corners with three equivalent Ti(2)O6 octahedra, corners with three equivalent Ti(3)O6 octahedra, and corners with six equivalent Ti(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-60°. In the third Li site, Li(3) is bonded to one O(6) and three equivalent O(5) atoms to form LiO4 tetrahedra that share corners with three equivalent Ti(1)O6 octahedra, corners with three equivalent Ti(3)O6 octahedra, and corners with six equivalent Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 59-61°. In the fourth Li site, Li(4) is bonded to one O(12) 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(5)O6 octahedra, and corners with six equivalent Ti(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-60°. In the fifth Li site, Li(5) is bonded to one O(2) and three equivalent O(9) atoms to form LiO4 tetrahedra that share corners with three equivalent Ti(1)O6 octahedra, corners with three equivalent Ti(4)O6 octahedra, and corners with six equivalent Ti(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-61°. Mg(1) is bonded to three equivalent O(10) and three equivalent O(4) atoms to form MgO6 octahedra that share corners with three equivalent Li(4)O4 tetrahedra, corners with three equivalent Ti(6)O4 tetrahedra, edges with three equivalent Ti(2)O6 octahedra, and edges with three equivalent Ti(5)O6 octahedra. There are six inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(2), one O(6), two equivalent O(1), and two equivalent O(3) atoms to form TiO6 octahedra that share  a cornercorner with one Li(3)O4 tetrahedra,  a cornercorner with one Li(5)O4 tetrahedra, corners with two equivalent Li(1)O4 tetrahedra, corners with two equivalent Li(2)O4 tetrahedra,  an edgeedge with one Ti(3)O6 octahedra,  an edgeedge with one Ti(4)O6 octahedra, and edges with four equivalent Ti(1)O6 octahedra. In the second Ti site, Ti(2) is bonded to one O(7), one O(8), two equivalent O(4), and two equivalent O(5) atoms to form TiO6 octahedra that share  a cornercorner with one Li(2)O4 tetrahedra,  a cornercorner with one Ti(6)O4 tetrahedra, corners with two equivalent Li(3)O4 tetrahedra, corners with two equivalent Li(4)O4 tetrahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Ti(3)O6 octahedra, and edges with four equivalent Ti(2)O6 octahedra. In the third Ti site, Ti(3) is bonded to three equivalent O(3) and three equivalent O(5) atoms to form TiO6 octahedra that share corners with three equivalent Li(2)O4 tetrahedra, corners with three equivalent Li(3)O4 tetrahedra, edges with three equivalent Ti(1)O6 octahedra, and edges with three equivalent Ti(2)O6 octahedra. In the fourth Ti site, Ti(4) is bonded to three equivalent O(1) and three equivalent O(9) atoms to form TiO6 octahedra that share corners with three equivalent Li(1)O4 tetrahedra, corners with three equivalent Li(5)O4 tetrahedra, edges with three equivalent Ti(1)O6 octahedra, and edges with three equivalent Ti(5)O6 octahedra. In the fifth Ti site, Ti(5) is bonded to one O(11), one O(12), two equivalent O(10), and two equivalent O(9) atoms to form TiO6 octahedra that share  a cornercorner with one Li(1)O4 tetrahedra,  a cornercorner with one Li(4)O4 tetrahedra, corners with two equivalent Li(5)O4 tetrahedra, corners with two equivalent Ti(6)O4 tetrahedra,  an edgeedge with one Mg(1)O6 octahedra,  an edgeedge with one Ti(4)O6 octahedra, and edges with four equivalent Ti(5)O6 octahedra. In the sixth Ti site, Ti(6) is bonded to one O(7) and three equivalent O(10) atoms to form TiO4 tetrahedra that share corners with three equivalent Mg(1)O6 octahedra, corners with three equivalent Ti(2)O6 octahedra, and corners with six equivalent Ti(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-58°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded to one Li(1), one Ti(4), and two equivalent Ti(1) atoms to form a mixture of distorted corner and edge-sharing OLiTi3 trigonal pyramids. In the second O site, O(2) is bonded to one Li(5) and three equivalent Ti(1) atoms to form a mixture of distorted corner and edge-sharing OLiTi3 trigonal pyramids. In the third O site, O(3) is bonded to one Li(2), one Ti(3), and two equivalent Ti(1) atoms to form a mixture of distorted corner and edge-sharing OLiTi3 trigonal pyramids. In the fourth O site, O(4) is bonded to one Li(4), one Mg(1), and two equivalent Ti(2) atoms to form distorted OLiMgTi2 trigonal pyramids that share corners with four equivalent O(5)LiTi3 tetrahedra, corners with two equivalent O(4)LiMgTi2 trigonal pyramids,  an edgeedge with one O(8)LiTi3 trigonal pyramid, and edges with two equivalent O(4)LiMgTi2 trigonal pyramids. In the fifth O site, O(5) is bonded to one Li(3), one Ti(3), and two equivalent Ti(2) atoms to form distorted OLiTi3 tetrahedra that share corners with two equivalent O(5)LiTi3 tetrahedra,  a cornercorner with one O(6)LiTi3 trigonal pyramid, corners with two equivalent O(8)LiTi3 trigonal pyramids, corners with three equivalent O(3)LiTi3 trigonal pyramids, corners with four equivalent O(4)LiMgTi2 trigonal pyramids, and edges with two equivalent O(5)LiTi3 tetrahedra. In the sixth O site, O(6) is bonded to one Li(3) and three equivalent Ti(1) atoms to form a mixture of distorted corner and edge-sharing OLiTi3 trigonal pyramids. In the seventh O site, O(7) is bonded in a distorted rectangular see-saw-like geometry to one Ti(6) and three equivalent Ti(2) atoms. In the eighth O site, O(8) is bonded to one Li(2) and three equivalent Ti(2) atoms to form distorted OLiTi3 trigonal pyramids that share corners with six equivalent O(5)LiTi3 tetrahedra, corners with three equivalent O(3)LiTi3 trigonal pyramids, and edges with three equivalent O(4)LiMgTi2 trigonal pyramids. In the ninth O site, O(9) is bonded in a rectangular see-saw-like geometry to one Li(5), one Ti(4), and two equivalent Ti(5) atoms. In the tenth O site, O(10) is bonded in a distorted rectangular see-saw-like geometry to one Mg(1), one Ti(6), and two equivalent Ti(5) atoms. In the eleventh O site, O(11) is bonded to one Li(1) and three equivalent Ti(5) atoms to form corner-sharing OLiTi3 tetrahedra. In the twelfth O site, O(12) is bonded in a rectangular see-saw-like geometry to one Li(4) and three equivalent Ti(5) atoms. is represented by the Crystallographic Information File (CIF) [CIF]
data_Li5MgTi12O24
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.995
_cell_length_b   5.995
_cell_length_c   14.758
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   459.301
_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  0.667  0.333  0.042  1.0
  Li  Li1  1  0.667  0.333  0.290  1.0
  Li  Li2  1  0.333  0.667  0.376  1.0
  Li  Li3  1  0.333  0.667  0.620  1.0
  Li  Li4  1  0.000  0.000  0.962  1.0
  Mg  Mg5  1  0.667  0.333  0.664  1.0
  Ti  Ti6  1  0.167  0.334  0.167  1.0
  Ti  Ti7  1  0.829  0.171  0.499  1.0
  Ti  Ti8  1  0.167  0.833  0.167  1.0
  Ti  Ti9  1  0.000  0.000  0.333  1.0
  Ti  Ti10  1  0.333  0.667  0.002  1.0
  Ti  Ti11  1  0.666  0.833  0.167  1.0
  Ti  Ti12  1  0.342  0.171  0.499  1.0
  Ti  Ti13  1  0.829  0.658  0.499  1.0
  Ti  Ti14  1  0.009  0.504  0.838  1.0
  Ti  Ti15  1  0.000  0.000  0.710  1.0
  Ti  Ti16  1  0.496  0.504  0.838  1.0
  Ti  Ti17  1  0.496  0.991  0.838  1.0
  O  O18  1  0.033  0.517  0.088  1.0
  O  O19  1  0.483  0.517  0.088  1.0
  O  O20  1  0.000  0.000  0.097  1.0
  O  O21  1  0.851  0.149  0.246  1.0
  O  O22  1  0.851  0.701  0.246  1.0
  O  O23  1  0.299  0.149  0.246  1.0
  O  O24  1  0.971  0.486  0.574  1.0
  O  O25  1  0.483  0.967  0.088  1.0
  O  O26  1  0.148  0.296  0.421  1.0
  O  O27  1  0.148  0.852  0.421  1.0
  O  O28  1  0.333  0.667  0.237  1.0
  O  O29  1  0.000  0.000  0.579  1.0
  O  O30  1  0.667  0.333  0.427  1.0
  O  O31  1  0.514  0.486  0.574  1.0
  O  O32  1  0.514  0.029  0.574  1.0
  O  O33  1  0.182  0.364  0.913  1.0
  O  O34  1  0.704  0.852  0.421  1.0
  O  O35  1  0.345  0.172  0.753  1.0
  O  O36  1  0.828  0.655  0.753  1.0
  O  O37  1  0.828  0.172  0.753  1.0
  O  O38  1  0.667  0.333  0.902  1.0
  O  O39  1  0.333  0.667  0.763  1.0
  O  O40  1  0.182  0.818  0.913  1.0
  O  O41  1  0.636  0.818  0.913  1.0
[/CIF]
.