The material structure described by MgTi2O4 is Spinel-like structured and crystallizes in the trigonal P3m1 space group. There are six inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one O(10) and three equivalent O(1) atoms to form MgO4 tetrahedra that share corners with three equivalent Mg(3)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 55-60°. In the second Mg site, Mg(2) is bonded to one O(2) and three equivalent O(4) atoms to form MgO4 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 56-59°. In the third Mg site, Mg(3) is bonded to three equivalent O(1) and three equivalent O(11) atoms to form MgO6 octahedra that share corners with three equivalent Mg(1)O4 tetrahedra, corners with three equivalent Ti(6)O4 tetrahedra, edges with three equivalent Ti(1)O6 octahedra, and edges with three equivalent Ti(4)O6 octahedra. In the fourth Mg site, Mg(4) is bonded to one O(6) and three equivalent O(8) atoms to form MgO4 tetrahedra that share corners with three equivalent Ti(2)O6 octahedra, corners with three equivalent Ti(5)O6 octahedra, and corners with six equivalent Ti(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-59°. In the fifth Mg site, Mg(5) is bonded to one O(9) and three equivalent O(3) atoms to form MgO4 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 57-59°. In the sixth Mg site, Mg(6) is bonded to one O(12) and three equivalent O(7) atoms to form MgO4 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(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-59°. There are six inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(2), one O(5), two equivalent O(1), and two equivalent O(3) atoms to form TiO6 octahedra that share  a cornercorner with one Mg(2)O4 tetrahedra,  a cornercorner with one Ti(6)O4 tetrahedra, corners with two equivalent Mg(1)O4 tetrahedra, corners with two equivalent Mg(5)O4 tetrahedra,  an edgeedge with one Mg(3)O6 octahedra,  an edgeedge with one Ti(3)O6 octahedra, and edges with four equivalent Ti(1)O6 octahedra. In the second Ti site, Ti(2) is bonded to one O(6), one O(9), two equivalent O(4), and two equivalent O(7) atoms to form TiO6 octahedra that share  a cornercorner with one Mg(4)O4 tetrahedra,  a cornercorner with one Mg(5)O4 tetrahedra, corners with two equivalent Mg(2)O4 tetrahedra, corners with two equivalent Mg(6)O4 tetrahedra,  an edgeedge with one Ti(3)O6 octahedra,  an edgeedge with one Ti(5)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(4) atoms to form TiO6 octahedra that share corners with three equivalent Mg(2)O4 tetrahedra, corners with three equivalent Mg(5)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 one O(10), one O(12), two equivalent O(11), and two equivalent O(8) atoms to form TiO6 octahedra that share  a cornercorner with one Mg(1)O4 tetrahedra,  a cornercorner with one Mg(6)O4 tetrahedra, corners with two equivalent Mg(4)O4 tetrahedra, corners with two equivalent Ti(6)O4 tetrahedra,  an edgeedge with one Mg(3)O6 octahedra,  an edgeedge with one Ti(5)O6 octahedra, and edges with four equivalent Ti(4)O6 octahedra. In the fifth Ti site, Ti(5) is bonded to three equivalent O(7) and three equivalent O(8) atoms to form TiO6 octahedra that share corners with three equivalent Mg(4)O4 tetrahedra, corners with three equivalent Mg(6)O4 tetrahedra, edges with three equivalent Ti(2)O6 octahedra, and edges with three equivalent Ti(4)O6 octahedra. In the sixth Ti site, Ti(6) is bonded to one O(5) and three equivalent O(11) atoms to form TiO4 tetrahedra that share corners with three equivalent Mg(3)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 53-58°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a distorted rectangular see-saw-like geometry to one Mg(1), one Mg(3), and two equivalent Ti(1) atoms. In the second O site, O(2) is bonded to one Mg(2) and three equivalent Ti(1) atoms to form distorted corner-sharing OMgTi3 trigonal pyramids. In the third O site, O(3) is bonded to one Mg(5), one Ti(3), and two equivalent Ti(1) atoms to form a mixture of distorted edge and corner-sharing OMgTi3 trigonal pyramids. In the fourth O site, O(4) is bonded in a rectangular see-saw-like geometry to one Mg(2), one Ti(3), and two equivalent Ti(2) atoms. In the fifth O site, O(5) is bonded in a rectangular see-saw-like geometry to one Ti(6) and three equivalent Ti(1) atoms. In the sixth O site, O(6) is bonded to one Mg(4) and three equivalent Ti(2) atoms to form distorted corner-sharing OMgTi3 trigonal pyramids. In the seventh O site, O(7) is bonded to one Mg(6), one Ti(5), and two equivalent Ti(2) atoms to form a mixture of distorted edge and corner-sharing OMgTi3 trigonal pyramids. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Mg(4), one Ti(5), and two equivalent Ti(4) atoms. In the ninth O site, O(9) is bonded in a distorted rectangular see-saw-like geometry to one Mg(5) and three equivalent Ti(2) atoms. In the tenth O site, O(10) is bonded in a rectangular see-saw-like geometry to one Mg(1) and three equivalent Ti(4) atoms. In the eleventh O site, O(11) is bonded to one Mg(3), one Ti(6), and two equivalent Ti(4) atoms to form a mixture of distorted edge and corner-sharing OMgTi3 trigonal pyramids. In the twelfth O site, O(12) is bonded to one Mg(6) and three equivalent Ti(4) atoms to form a mixture of distorted edge and corner-sharing OMgTi3 trigonal pyramids. is represented by the Crystallographic Information File (CIF) [CIF]
data_MgTi2O4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.011
_cell_length_b   6.011
_cell_length_c   14.931
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   467.238
_cell_formula_units_Z   6
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  0.000  0.000  0.045  1.0
  Mg  Mg1  1  0.333  0.667  0.371  1.0
  Mg  Mg2  1  0.333  0.667  0.003  1.0
  Mg  Mg3  1  0.667  0.333  0.705  1.0
  Mg  Mg4  1  0.000  0.000  0.292  1.0
  Mg  Mg5  1  0.333  0.667  0.626  1.0
  Ti  Ti6  1  0.990  0.495  0.167  1.0
  Ti  Ti7  1  0.505  0.010  0.167  1.0
  Ti  Ti8  1  0.334  0.167  0.500  1.0
  Ti  Ti9  1  0.505  0.495  0.167  1.0
  Ti  Ti10  1  0.667  0.333  0.340  1.0
  Ti  Ti11  1  0.833  0.666  0.500  1.0
  Ti  Ti12  1  0.677  0.838  0.831  1.0
  Ti  Ti13  1  0.833  0.167  0.500  1.0
  Ti  Ti14  1  0.162  0.838  0.831  1.0
  Ti  Ti15  1  0.000  0.000  0.666  1.0
  Ti  Ti16  1  0.162  0.323  0.831  1.0
  Ti  Ti17  1  0.667  0.333  0.953  1.0
  O  O18  1  0.178  0.357  0.091  1.0
  O  O19  1  0.333  0.667  0.240  1.0
  O  O20  1  0.178  0.822  0.091  1.0
  O  O21  1  0.643  0.822  0.091  1.0
  O  O22  1  0.360  0.180  0.250  1.0
  O  O23  1  0.509  0.017  0.420  1.0
  O  O24  1  0.820  0.180  0.250  1.0
  O  O25  1  0.667  0.333  0.081  1.0
  O  O26  1  0.509  0.491  0.420  1.0
  O  O27  1  0.667  0.333  0.574  1.0
  O  O28  1  0.820  0.640  0.250  1.0
  O  O29  1  0.983  0.491  0.420  1.0
  O  O30  1  0.689  0.845  0.581  1.0
  O  O31  1  0.842  0.684  0.751  1.0
  O  O32  1  0.155  0.845  0.581  1.0
  O  O33  1  0.000  0.000  0.425  1.0
  O  O34  1  0.000  0.000  0.911  1.0
  O  O35  1  0.842  0.158  0.751  1.0
  O  O36  1  0.155  0.311  0.581  1.0
  O  O37  1  0.316  0.158  0.751  1.0
  O  O38  1  0.014  0.507  0.914  1.0
  O  O39  1  0.333  0.667  0.759  1.0
  O  O40  1  0.493  0.507  0.914  1.0
  O  O41  1  0.493  0.986  0.914  1.0
[/CIF]
.
The material structure described by MgTi2O4 is Spinel-like structured and crystallizes in the trigonal P3m1 space group. There are six inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one O(10) and three equivalent O(1) atoms to form MgO4 tetrahedra that share corners with three equivalent Mg(3)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 55-60°. In the second Mg site, Mg(2) is bonded to one O(2) and three equivalent O(4) atoms to form MgO4 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 56-59°. In the third Mg site, Mg(3) is bonded to three equivalent O(1) and three equivalent O(11) atoms to form MgO6 octahedra that share corners with three equivalent Mg(1)O4 tetrahedra, corners with three equivalent Ti(6)O4 tetrahedra, edges with three equivalent Ti(1)O6 octahedra, and edges with three equivalent Ti(4)O6 octahedra. In the fourth Mg site, Mg(4) is bonded to one O(6) and three equivalent O(8) atoms to form MgO4 tetrahedra that share corners with three equivalent Ti(2)O6 octahedra, corners with three equivalent Ti(5)O6 octahedra, and corners with six equivalent Ti(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-59°. In the fifth Mg site, Mg(5) is bonded to one O(9) and three equivalent O(3) atoms to form MgO4 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 57-59°. In the sixth Mg site, Mg(6) is bonded to one O(12) and three equivalent O(7) atoms to form MgO4 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(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-59°. There are six inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to one O(2), one O(5), two equivalent O(1), and two equivalent O(3) atoms to form TiO6 octahedra that share  a cornercorner with one Mg(2)O4 tetrahedra,  a cornercorner with one Ti(6)O4 tetrahedra, corners with two equivalent Mg(1)O4 tetrahedra, corners with two equivalent Mg(5)O4 tetrahedra,  an edgeedge with one Mg(3)O6 octahedra,  an edgeedge with one Ti(3)O6 octahedra, and edges with four equivalent Ti(1)O6 octahedra. In the second Ti site, Ti(2) is bonded to one O(6), one O(9), two equivalent O(4), and two equivalent O(7) atoms to form TiO6 octahedra that share  a cornercorner with one Mg(4)O4 tetrahedra,  a cornercorner with one Mg(5)O4 tetrahedra, corners with two equivalent Mg(2)O4 tetrahedra, corners with two equivalent Mg(6)O4 tetrahedra,  an edgeedge with one Ti(3)O6 octahedra,  an edgeedge with one Ti(5)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(4) atoms to form TiO6 octahedra that share corners with three equivalent Mg(2)O4 tetrahedra, corners with three equivalent Mg(5)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 one O(10), one O(12), two equivalent O(11), and two equivalent O(8) atoms to form TiO6 octahedra that share  a cornercorner with one Mg(1)O4 tetrahedra,  a cornercorner with one Mg(6)O4 tetrahedra, corners with two equivalent Mg(4)O4 tetrahedra, corners with two equivalent Ti(6)O4 tetrahedra,  an edgeedge with one Mg(3)O6 octahedra,  an edgeedge with one Ti(5)O6 octahedra, and edges with four equivalent Ti(4)O6 octahedra. In the fifth Ti site, Ti(5) is bonded to three equivalent O(7) and three equivalent O(8) atoms to form TiO6 octahedra that share corners with three equivalent Mg(4)O4 tetrahedra, corners with three equivalent Mg(6)O4 tetrahedra, edges with three equivalent Ti(2)O6 octahedra, and edges with three equivalent Ti(4)O6 octahedra. In the sixth Ti site, Ti(6) is bonded to one O(5) and three equivalent O(11) atoms to form TiO4 tetrahedra that share corners with three equivalent Mg(3)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 53-58°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded in a distorted rectangular see-saw-like geometry to one Mg(1), one Mg(3), and two equivalent Ti(1) atoms. In the second O site, O(2) is bonded to one Mg(2) and three equivalent Ti(1) atoms to form distorted corner-sharing OMgTi3 trigonal pyramids. In the third O site, O(3) is bonded to one Mg(5), one Ti(3), and two equivalent Ti(1) atoms to form a mixture of distorted edge and corner-sharing OMgTi3 trigonal pyramids. In the fourth O site, O(4) is bonded in a rectangular see-saw-like geometry to one Mg(2), one Ti(3), and two equivalent Ti(2) atoms. In the fifth O site, O(5) is bonded in a rectangular see-saw-like geometry to one Ti(6) and three equivalent Ti(1) atoms. In the sixth O site, O(6) is bonded to one Mg(4) and three equivalent Ti(2) atoms to form distorted corner-sharing OMgTi3 trigonal pyramids. In the seventh O site, O(7) is bonded to one Mg(6), one Ti(5), and two equivalent Ti(2) atoms to form a mixture of distorted edge and corner-sharing OMgTi3 trigonal pyramids. In the eighth O site, O(8) is bonded in a rectangular see-saw-like geometry to one Mg(4), one Ti(5), and two equivalent Ti(4) atoms. In the ninth O site, O(9) is bonded in a distorted rectangular see-saw-like geometry to one Mg(5) and three equivalent Ti(2) atoms. In the tenth O site, O(10) is bonded in a rectangular see-saw-like geometry to one Mg(1) and three equivalent Ti(4) atoms. In the eleventh O site, O(11) is bonded to one Mg(3), one Ti(6), and two equivalent Ti(4) atoms to form a mixture of distorted edge and corner-sharing OMgTi3 trigonal pyramids. In the twelfth O site, O(12) is bonded to one Mg(6) and three equivalent Ti(4) atoms to form a mixture of distorted edge and corner-sharing OMgTi3 trigonal pyramids. is represented by the Crystallographic Information File (CIF) [CIF]
data_MgTi2O4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.011
_cell_length_b   6.011
_cell_length_c   14.931
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   467.238
_cell_formula_units_Z   6
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  0.000  0.000  0.045  1.0
  Mg  Mg1  1  0.333  0.667  0.371  1.0
  Mg  Mg2  1  0.333  0.667  0.003  1.0
  Mg  Mg3  1  0.667  0.333  0.705  1.0
  Mg  Mg4  1  0.000  0.000  0.292  1.0
  Mg  Mg5  1  0.333  0.667  0.626  1.0
  Ti  Ti6  1  0.990  0.495  0.167  1.0
  Ti  Ti7  1  0.505  0.010  0.167  1.0
  Ti  Ti8  1  0.334  0.167  0.500  1.0
  Ti  Ti9  1  0.505  0.495  0.167  1.0
  Ti  Ti10  1  0.667  0.333  0.340  1.0
  Ti  Ti11  1  0.833  0.666  0.500  1.0
  Ti  Ti12  1  0.677  0.838  0.831  1.0
  Ti  Ti13  1  0.833  0.167  0.500  1.0
  Ti  Ti14  1  0.162  0.838  0.831  1.0
  Ti  Ti15  1  0.000  0.000  0.666  1.0
  Ti  Ti16  1  0.162  0.323  0.831  1.0
  Ti  Ti17  1  0.667  0.333  0.953  1.0
  O  O18  1  0.178  0.357  0.091  1.0
  O  O19  1  0.333  0.667  0.240  1.0
  O  O20  1  0.178  0.822  0.091  1.0
  O  O21  1  0.643  0.822  0.091  1.0
  O  O22  1  0.360  0.180  0.250  1.0
  O  O23  1  0.509  0.017  0.420  1.0
  O  O24  1  0.820  0.180  0.250  1.0
  O  O25  1  0.667  0.333  0.081  1.0
  O  O26  1  0.509  0.491  0.420  1.0
  O  O27  1  0.667  0.333  0.574  1.0
  O  O28  1  0.820  0.640  0.250  1.0
  O  O29  1  0.983  0.491  0.420  1.0
  O  O30  1  0.689  0.845  0.581  1.0
  O  O31  1  0.842  0.684  0.751  1.0
  O  O32  1  0.155  0.845  0.581  1.0
  O  O33  1  0.000  0.000  0.425  1.0
  O  O34  1  0.000  0.000  0.911  1.0
  O  O35  1  0.842  0.158  0.751  1.0
  O  O36  1  0.155  0.311  0.581  1.0
  O  O37  1  0.316  0.158  0.751  1.0
  O  O38  1  0.014  0.507  0.914  1.0
  O  O39  1  0.333  0.667  0.759  1.0
  O  O40  1  0.493  0.507  0.914  1.0
  O  O41  1  0.493  0.986  0.914  1.0
[/CIF]
.