The crystal structure described by MgTiFeO4 crystallizes in the orthorhombic Imm2 space group. Mg(1) is bonded to one O(2), one O(4), two equivalent O(1), and two equivalent O(3) atoms to form distorted MgO6 octahedra that share corners with four equivalent Mg(1)O6 octahedra,  a cornercorner with one Fe(1)O5 trigonal bipyramid, edges with four equivalent Ti(1)O6 octahedra, and edges with four equivalent Fe(1)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 11-33°. Ti(1) is bonded to one O(1), one O(3), two equivalent O(2), and two equivalent O(4) atoms to form TiO6 octahedra that share corners with four equivalent Ti(1)O6 octahedra, corners with two equivalent Fe(1)O5 trigonal bipyramids, edges with four equivalent Mg(1)O6 octahedra, and edges with two equivalent Fe(1)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 2-9°. Fe(1) is bonded to one O(2), two equivalent O(1), and two equivalent O(3) atoms to form FeO5 trigonal bipyramids that share  a cornercorner with one Mg(1)O6 octahedra, corners with two equivalent Ti(1)O6 octahedra, corners with four equivalent Fe(1)O5 trigonal bipyramids, edges with two equivalent Ti(1)O6 octahedra, and edges with four equivalent Mg(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-67°. There are four inequivalent O sites. In the first O site, O(1) is bonded to two equivalent Mg(1), one Ti(1), and two equivalent Fe(1) atoms to form a mixture of corner and edge-sharing OMg2TiFe2 trigonal bipyramids. In the second O site, O(2) is bonded in a square co-planar geometry to one Mg(1), two equivalent Ti(1), and one Fe(1) atom. In the third O site, O(3) is bonded to two equivalent Mg(1), one Ti(1), and two equivalent Fe(1) atoms to form a mixture of corner and edge-sharing OMg2TiFe2 trigonal bipyramids. In the fourth O site, O(4) is bonded in a distorted T-shaped geometry to one Mg(1) and two equivalent Ti(1) atoms. is represented by the CIF card [CIF]
data_MgTiFeO4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.566
_cell_length_b   5.565
_cell_length_c   5.565
_cell_angle_alpha   139.287
_cell_angle_beta   135.455
_cell_angle_gamma   61.921
_symmetry_Int_Tables_number   1
_cell_volume   77.960
_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  0.466  0.466  1.000  1.0
  Ti  Ti1  1  0.740  0.240  0.500  1.0
  Fe  Fe2  1  0.031  0.031  1.000  1.0
  O  O3  1  0.527  0.027  0.500  1.0
  O  O4  1  0.245  0.245  0.000  1.0
  O  O5  1  0.944  0.444  0.500  1.0
  O  O6  1  0.725  0.725  0.000  1.0
[/CIF]
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The crystal structure described by MgTiFeO4 crystallizes in the orthorhombic Imm2 space group. Mg(1) is bonded to one O(2), one O(4), two equivalent O(1), and two equivalent O(3) atoms to form distorted MgO6 octahedra that share corners with four equivalent Mg(1)O6 octahedra,  a cornercorner with one Fe(1)O5 trigonal bipyramid, edges with four equivalent Ti(1)O6 octahedra, and edges with four equivalent Fe(1)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 11-33°. Ti(1) is bonded to one O(1), one O(3), two equivalent O(2), and two equivalent O(4) atoms to form TiO6 octahedra that share corners with four equivalent Ti(1)O6 octahedra, corners with two equivalent Fe(1)O5 trigonal bipyramids, edges with four equivalent Mg(1)O6 octahedra, and edges with two equivalent Fe(1)O5 trigonal bipyramids. The corner-sharing octahedral tilt angles range from 2-9°. Fe(1) is bonded to one O(2), two equivalent O(1), and two equivalent O(3) atoms to form FeO5 trigonal bipyramids that share  a cornercorner with one Mg(1)O6 octahedra, corners with two equivalent Ti(1)O6 octahedra, corners with four equivalent Fe(1)O5 trigonal bipyramids, edges with two equivalent Ti(1)O6 octahedra, and edges with four equivalent Mg(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-67°. There are four inequivalent O sites. In the first O site, O(1) is bonded to two equivalent Mg(1), one Ti(1), and two equivalent Fe(1) atoms to form a mixture of corner and edge-sharing OMg2TiFe2 trigonal bipyramids. In the second O site, O(2) is bonded in a square co-planar geometry to one Mg(1), two equivalent Ti(1), and one Fe(1) atom. In the third O site, O(3) is bonded to two equivalent Mg(1), one Ti(1), and two equivalent Fe(1) atoms to form a mixture of corner and edge-sharing OMg2TiFe2 trigonal bipyramids. In the fourth O site, O(4) is bonded in a distorted T-shaped geometry to one Mg(1) and two equivalent Ti(1) atoms. is represented by the CIF card [CIF]
data_MgTiFeO4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.566
_cell_length_b   5.565
_cell_length_c   5.565
_cell_angle_alpha   139.287
_cell_angle_beta   135.455
_cell_angle_gamma   61.921
_symmetry_Int_Tables_number   1
_cell_volume   77.960
_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  0.466  0.466  1.000  1.0
  Ti  Ti1  1  0.740  0.240  0.500  1.0
  Fe  Fe2  1  0.031  0.031  1.000  1.0
  O  O3  1  0.527  0.027  0.500  1.0
  O  O4  1  0.245  0.245  0.000  1.0
  O  O5  1  0.944  0.444  0.500  1.0
  O  O6  1  0.725  0.725  0.000  1.0
[/CIF]
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