The material described by MnTi2O4 is Spinel structured and crystallizes in the trigonal R3m space group. There are four inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to three equivalent O(3) and three equivalent O(8) atoms to form TiO6 octahedra that share corners with three equivalent Mn(3)O4 tetrahedra, corners with three equivalent Mn(4)O4 tetrahedra, edges with three equivalent Ti(3)O6 octahedra, and edges with three equivalent Ti(4)O6 octahedra. In the second Ti site, Ti(2) is bonded to three equivalent O(4) and three equivalent O(7) atoms to form TiO6 octahedra that share corners with three equivalent Mn(1)O4 tetrahedra, corners with three equivalent Mn(2)O4 tetrahedra, edges with three equivalent Ti(3)O6 octahedra, and edges with three equivalent Ti(4)O6 octahedra. In the third Ti site, Ti(3) is bonded to one O(1), one O(5), two equivalent O(3), and two equivalent O(7) atoms to form TiO6 octahedra that share  a cornercorner with one Mn(1)O4 tetrahedra,  a cornercorner with one Mn(4)O4 tetrahedra, corners with two equivalent Mn(2)O4 tetrahedra, corners with two equivalent Mn(3)O4 tetrahedra,  an edgeedge with one Ti(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra, and edges with four equivalent Ti(3)O6 octahedra. In the fourth Ti site, Ti(4) is bonded to one O(2), one O(6), two equivalent O(4), and two equivalent O(8) atoms to form TiO6 octahedra that share  a cornercorner with one Mn(2)O4 tetrahedra,  a cornercorner with one Mn(3)O4 tetrahedra, corners with two equivalent Mn(1)O4 tetrahedra, corners with two equivalent Mn(4)O4 tetrahedra,  an edgeedge with one Ti(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra, and edges with four equivalent Ti(4)O6 octahedra. There are four inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to one O(5) and three equivalent O(4) atoms to form MnO4 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(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-60°. In the second Mn site, Mn(2) is bonded to one O(2) and three equivalent O(7) atoms to form MnO4 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(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-60°. In the third Mn site, Mn(3) is bonded to one O(6) and three equivalent O(3) atoms to form MnO4 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(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-60°. In the fourth Mn site, Mn(4) is bonded to one O(1) and three equivalent O(8) atoms to form MnO4 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(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-60°. There are eight inequivalent O sites. In the first O site, O(1) is bonded in a distorted rectangular see-saw-like geometry to three equivalent Ti(3) and one Mn(4) atom. In the second O site, O(2) is bonded to three equivalent Ti(4) and one Mn(2) atom to form a mixture of distorted corner and edge-sharing OTi3Mn tetrahedra. In the third O site, O(3) is bonded to one Ti(1), two equivalent Ti(3), and one Mn(3) atom to form a mixture of distorted corner and edge-sharing OTi3Mn tetrahedra. In the fourth O site, O(4) is bonded to one Ti(2), two equivalent Ti(4), and one Mn(1) atom to form a mixture of distorted corner and edge-sharing OTi3Mn trigonal pyramids. In the fifth O site, O(5) is bonded to three equivalent Ti(3) and one Mn(1) atom to form a mixture of distorted corner and edge-sharing OTi3Mn tetrahedra. In the sixth O site, O(6) is bonded in a distorted rectangular see-saw-like geometry to three equivalent Ti(4) and one Mn(3) atom. In the seventh O site, O(7) is bonded to one Ti(2), two equivalent Ti(3), and one Mn(2) atom to form a mixture of distorted corner and edge-sharing OTi3Mn trigonal pyramids. In the eighth O site, O(8) is bonded to one Ti(1), two equivalent Ti(4), and one Mn(4) atom to form a mixture of distorted corner and edge-sharing OTi3Mn trigonal pyramids. is represented by the CIF file [CIF]
data_Ti2MnO4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.112
_cell_length_b   6.112
_cell_length_c   6.124
_cell_angle_alpha   60.128
_cell_angle_beta   60.130
_cell_angle_gamma   60.012
_symmetry_Int_Tables_number   1
_cell_volume   162.114
_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
  Mn  Mn0  1  0.125  0.625  0.124  1.0
  Mn  Mn1  1  0.875  0.375  0.875  1.0
  O  O2  1  0.739  0.239  0.283  1.0
  O  O3  1  0.261  0.215  0.262  1.0
  O  O4  1  0.261  0.761  0.716  1.0
  O  O5  1  0.739  0.239  0.738  1.0
  O  O6  1  0.285  0.238  0.738  1.0
  O  O7  1  0.715  0.761  0.262  1.0
  O  O8  1  0.738  0.785  0.738  1.0
  O  O9  1  0.261  0.761  0.262  1.0
  Ti  Ti10  1  0.500  1.000  0.000  1.0
  Ti  Ti11  1  1.000  0.000  0.500  1.0
  Ti  Ti12  1  0.500  0.500  0.500  1.0
  Ti  Ti13  1  0.500  0.000  0.500  1.0
[/CIF]
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The material described by MnTi2O4 is Spinel structured and crystallizes in the trigonal R3m space group. There are four inequivalent Ti sites. In the first Ti site, Ti(1) is bonded to three equivalent O(3) and three equivalent O(8) atoms to form TiO6 octahedra that share corners with three equivalent Mn(3)O4 tetrahedra, corners with three equivalent Mn(4)O4 tetrahedra, edges with three equivalent Ti(3)O6 octahedra, and edges with three equivalent Ti(4)O6 octahedra. In the second Ti site, Ti(2) is bonded to three equivalent O(4) and three equivalent O(7) atoms to form TiO6 octahedra that share corners with three equivalent Mn(1)O4 tetrahedra, corners with three equivalent Mn(2)O4 tetrahedra, edges with three equivalent Ti(3)O6 octahedra, and edges with three equivalent Ti(4)O6 octahedra. In the third Ti site, Ti(3) is bonded to one O(1), one O(5), two equivalent O(3), and two equivalent O(7) atoms to form TiO6 octahedra that share  a cornercorner with one Mn(1)O4 tetrahedra,  a cornercorner with one Mn(4)O4 tetrahedra, corners with two equivalent Mn(2)O4 tetrahedra, corners with two equivalent Mn(3)O4 tetrahedra,  an edgeedge with one Ti(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra, and edges with four equivalent Ti(3)O6 octahedra. In the fourth Ti site, Ti(4) is bonded to one O(2), one O(6), two equivalent O(4), and two equivalent O(8) atoms to form TiO6 octahedra that share  a cornercorner with one Mn(2)O4 tetrahedra,  a cornercorner with one Mn(3)O4 tetrahedra, corners with two equivalent Mn(1)O4 tetrahedra, corners with two equivalent Mn(4)O4 tetrahedra,  an edgeedge with one Ti(1)O6 octahedra,  an edgeedge with one Ti(2)O6 octahedra, and edges with four equivalent Ti(4)O6 octahedra. There are four inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to one O(5) and three equivalent O(4) atoms to form MnO4 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(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-60°. In the second Mn site, Mn(2) is bonded to one O(2) and three equivalent O(7) atoms to form MnO4 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(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-60°. In the third Mn site, Mn(3) is bonded to one O(6) and three equivalent O(3) atoms to form MnO4 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(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-60°. In the fourth Mn site, Mn(4) is bonded to one O(1) and three equivalent O(8) atoms to form MnO4 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(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-60°. There are eight inequivalent O sites. In the first O site, O(1) is bonded in a distorted rectangular see-saw-like geometry to three equivalent Ti(3) and one Mn(4) atom. In the second O site, O(2) is bonded to three equivalent Ti(4) and one Mn(2) atom to form a mixture of distorted corner and edge-sharing OTi3Mn tetrahedra. In the third O site, O(3) is bonded to one Ti(1), two equivalent Ti(3), and one Mn(3) atom to form a mixture of distorted corner and edge-sharing OTi3Mn tetrahedra. In the fourth O site, O(4) is bonded to one Ti(2), two equivalent Ti(4), and one Mn(1) atom to form a mixture of distorted corner and edge-sharing OTi3Mn trigonal pyramids. In the fifth O site, O(5) is bonded to three equivalent Ti(3) and one Mn(1) atom to form a mixture of distorted corner and edge-sharing OTi3Mn tetrahedra. In the sixth O site, O(6) is bonded in a distorted rectangular see-saw-like geometry to three equivalent Ti(4) and one Mn(3) atom. In the seventh O site, O(7) is bonded to one Ti(2), two equivalent Ti(3), and one Mn(2) atom to form a mixture of distorted corner and edge-sharing OTi3Mn trigonal pyramids. In the eighth O site, O(8) is bonded to one Ti(1), two equivalent Ti(4), and one Mn(4) atom to form a mixture of distorted corner and edge-sharing OTi3Mn trigonal pyramids. is represented by the CIF file [CIF]
data_Ti2MnO4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.112
_cell_length_b   6.112
_cell_length_c   6.124
_cell_angle_alpha   60.128
_cell_angle_beta   60.130
_cell_angle_gamma   60.012
_symmetry_Int_Tables_number   1
_cell_volume   162.114
_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
  Mn  Mn0  1  0.125  0.625  0.124  1.0
  Mn  Mn1  1  0.875  0.375  0.875  1.0
  O  O2  1  0.739  0.239  0.283  1.0
  O  O3  1  0.261  0.215  0.262  1.0
  O  O4  1  0.261  0.761  0.716  1.0
  O  O5  1  0.739  0.239  0.738  1.0
  O  O6  1  0.285  0.238  0.738  1.0
  O  O7  1  0.715  0.761  0.262  1.0
  O  O8  1  0.738  0.785  0.738  1.0
  O  O9  1  0.261  0.761  0.262  1.0
  Ti  Ti10  1  0.500  1.000  0.000  1.0
  Ti  Ti11  1  1.000  0.000  0.500  1.0
  Ti  Ti12  1  0.500  0.500  0.500  1.0
  Ti  Ti13  1  0.500  0.000  0.500  1.0
[/CIF]
.