The material structure described by MgTiFeO4 crystallizes in the triclinic P1 space group. Mg(1) is bonded to one O(1), one O(2), two equivalent O(3), and two equivalent O(4) atoms to form distorted MgO6 octahedra that share corners with three equivalent Ti(1)O5 trigonal bipyramids, corners with three equivalent Fe(1)O5 trigonal bipyramids, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Ti(1)O5 trigonal bipyramids, and edges with two equivalent Fe(1)O5 trigonal bipyramids. Ti(1) is bonded to one O(1), one O(3), one O(4), and two equivalent O(2) atoms to form TiO5 trigonal bipyramids that share corners with three equivalent Mg(1)O6 octahedra, corners with two equivalent Ti(1)O5 trigonal bipyramids, edges with two equivalent Mg(1)O6 octahedra, and edges with three equivalent Fe(1)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 30-51°. Fe(1) is bonded to one O(2), one O(3), one O(4), and two equivalent O(1) atoms to form distorted FeO5 trigonal bipyramids that share corners with three equivalent Mg(1)O6 octahedra, corners with two equivalent Fe(1)O5 trigonal bipyramids, edges with two equivalent Mg(1)O6 octahedra, and edges with three equivalent Ti(1)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 39-62°. There are four inequivalent O sites. In the first O site, O(1) is bonded to one Mg(1), one Ti(1), and two equivalent Fe(1) atoms to form distorted OMgTiFe2 tetrahedra that share corners with two equivalent O(1)MgTiFe2 tetrahedra,  a cornercorner with one O(4)Mg2TiFe trigonal pyramid,  a cornercorner with one O(2)MgTi2Fe trigonal pyramid, corners with five equivalent O(3)Mg2TiFe trigonal pyramids, edges with two equivalent O(4)Mg2TiFe trigonal pyramids, and edges with two equivalent O(2)MgTi2Fe trigonal pyramids. In the second O site, O(2) is bonded to one Mg(1), two equivalent Ti(1), and one Fe(1) atom to form distorted OMgTi2Fe trigonal pyramids that share  a cornercorner with one O(1)MgTiFe2 tetrahedra,  a cornercorner with one O(3)Mg2TiFe trigonal pyramid, corners with two equivalent O(2)MgTi2Fe trigonal pyramids, corners with five equivalent O(4)Mg2TiFe trigonal pyramids, edges with two equivalent O(1)MgTiFe2 tetrahedra, and edges with two equivalent O(3)Mg2TiFe trigonal pyramids. In the third O site, O(3) is bonded to two equivalent Mg(1), one Ti(1), and one Fe(1) atom to form OMg2TiFe trigonal pyramids that share corners with five equivalent O(1)MgTiFe2 tetrahedra,  a cornercorner with one O(2)MgTi2Fe trigonal pyramid, corners with two equivalent O(3)Mg2TiFe trigonal pyramids, corners with two equivalent O(4)Mg2TiFe trigonal pyramids, edges with two equivalent O(4)Mg2TiFe trigonal pyramids, and edges with two equivalent O(2)MgTi2Fe trigonal pyramids. In the fourth O site, O(4) is bonded to two equivalent Mg(1), one Ti(1), and one Fe(1) atom to form distorted OMg2TiFe trigonal pyramids that share  a cornercorner with one O(1)MgTiFe2 tetrahedra, corners with two equivalent O(3)Mg2TiFe trigonal pyramids, corners with two equivalent O(4)Mg2TiFe trigonal pyramids, corners with five equivalent O(2)MgTi2Fe trigonal pyramids, edges with two equivalent O(1)MgTiFe2 tetrahedra, and edges with two equivalent O(3)Mg2TiFe trigonal pyramids. is represented by the Crystallographic Information File (CIF) [CIF]
data_MgTiFeO4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.401
_cell_length_b   5.651
_cell_length_c   6.436
_cell_angle_alpha   130.723
_cell_angle_beta   148.741
_cell_angle_gamma   59.655
_symmetry_Int_Tables_number   1
_cell_volume   90.737
_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
  Mg  Mg0  1  0.402  0.145  0.777  1.0
  Ti  Ti1  1  0.734  0.363  0.619  1.0
  Fe  Fe2  1  0.034  0.875  0.882  1.0
  O  O3  1  0.542  0.138  0.584  1.0
  O  O4  1  0.226  0.172  0.956  1.0
  O  O5  1  0.910  0.413  0.498  1.0
  O  O6  1  0.784  0.776  0.946  1.0
[/CIF]
.
The material structure described by MgTiFeO4 crystallizes in the triclinic P1 space group. Mg(1) is bonded to one O(1), one O(2), two equivalent O(3), and two equivalent O(4) atoms to form distorted MgO6 octahedra that share corners with three equivalent Ti(1)O5 trigonal bipyramids, corners with three equivalent Fe(1)O5 trigonal bipyramids, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Ti(1)O5 trigonal bipyramids, and edges with two equivalent Fe(1)O5 trigonal bipyramids. Ti(1) is bonded to one O(1), one O(3), one O(4), and two equivalent O(2) atoms to form TiO5 trigonal bipyramids that share corners with three equivalent Mg(1)O6 octahedra, corners with two equivalent Ti(1)O5 trigonal bipyramids, edges with two equivalent Mg(1)O6 octahedra, and edges with three equivalent Fe(1)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 30-51°. Fe(1) is bonded to one O(2), one O(3), one O(4), and two equivalent O(1) atoms to form distorted FeO5 trigonal bipyramids that share corners with three equivalent Mg(1)O6 octahedra, corners with two equivalent Fe(1)O5 trigonal bipyramids, edges with two equivalent Mg(1)O6 octahedra, and edges with three equivalent Ti(1)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 39-62°. There are four inequivalent O sites. In the first O site, O(1) is bonded to one Mg(1), one Ti(1), and two equivalent Fe(1) atoms to form distorted OMgTiFe2 tetrahedra that share corners with two equivalent O(1)MgTiFe2 tetrahedra,  a cornercorner with one O(4)Mg2TiFe trigonal pyramid,  a cornercorner with one O(2)MgTi2Fe trigonal pyramid, corners with five equivalent O(3)Mg2TiFe trigonal pyramids, edges with two equivalent O(4)Mg2TiFe trigonal pyramids, and edges with two equivalent O(2)MgTi2Fe trigonal pyramids. In the second O site, O(2) is bonded to one Mg(1), two equivalent Ti(1), and one Fe(1) atom to form distorted OMgTi2Fe trigonal pyramids that share  a cornercorner with one O(1)MgTiFe2 tetrahedra,  a cornercorner with one O(3)Mg2TiFe trigonal pyramid, corners with two equivalent O(2)MgTi2Fe trigonal pyramids, corners with five equivalent O(4)Mg2TiFe trigonal pyramids, edges with two equivalent O(1)MgTiFe2 tetrahedra, and edges with two equivalent O(3)Mg2TiFe trigonal pyramids. In the third O site, O(3) is bonded to two equivalent Mg(1), one Ti(1), and one Fe(1) atom to form OMg2TiFe trigonal pyramids that share corners with five equivalent O(1)MgTiFe2 tetrahedra,  a cornercorner with one O(2)MgTi2Fe trigonal pyramid, corners with two equivalent O(3)Mg2TiFe trigonal pyramids, corners with two equivalent O(4)Mg2TiFe trigonal pyramids, edges with two equivalent O(4)Mg2TiFe trigonal pyramids, and edges with two equivalent O(2)MgTi2Fe trigonal pyramids. In the fourth O site, O(4) is bonded to two equivalent Mg(1), one Ti(1), and one Fe(1) atom to form distorted OMg2TiFe trigonal pyramids that share  a cornercorner with one O(1)MgTiFe2 tetrahedra, corners with two equivalent O(3)Mg2TiFe trigonal pyramids, corners with two equivalent O(4)Mg2TiFe trigonal pyramids, corners with five equivalent O(2)MgTi2Fe trigonal pyramids, edges with two equivalent O(1)MgTiFe2 tetrahedra, and edges with two equivalent O(3)Mg2TiFe trigonal pyramids. is represented by the Crystallographic Information File (CIF) [CIF]
data_MgTiFeO4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.401
_cell_length_b   5.651
_cell_length_c   6.436
_cell_angle_alpha   130.723
_cell_angle_beta   148.741
_cell_angle_gamma   59.655
_symmetry_Int_Tables_number   1
_cell_volume   90.737
_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
  Mg  Mg0  1  0.402  0.145  0.777  1.0
  Ti  Ti1  1  0.734  0.363  0.619  1.0
  Fe  Fe2  1  0.034  0.875  0.882  1.0
  O  O3  1  0.542  0.138  0.584  1.0
  O  O4  1  0.226  0.172  0.956  1.0
  O  O5  1  0.910  0.413  0.498  1.0
  O  O6  1  0.784  0.776  0.946  1.0
[/CIF]
.