The compound described by MgFe2O4 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(9) and three equivalent O(1) atoms to form MgO4 tetrahedra that share corners with three equivalent Mg(5)O6 octahedra, corners with three equivalent Fe(5)O6 octahedra, and corners with six equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-58°. In the second Mg site, Mg(2) is bonded to one O(2) and three equivalent O(3) atoms to form MgO4 tetrahedra that share corners with three equivalent Mg(3)O6 octahedra, corners with three equivalent Fe(1)O6 octahedra, and corners with six equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-58°. In the third Mg site, Mg(3) is bonded to three equivalent O(3) and three equivalent O(4) atoms to form MgO6 octahedra that share corners with three equivalent Mg(2)O4 tetrahedra, corners with three equivalent Fe(4)O4 tetrahedra, edges with three equivalent Fe(1)O6 octahedra, and edges with three equivalent Fe(2)O6 octahedra. In the fourth Mg site, Mg(4) is bonded to one O(5) and three equivalent O(7) atoms to form MgO4 tetrahedra that share corners with three equivalent Fe(2)O6 octahedra, corners with three equivalent Fe(3)O6 octahedra, and corners with six equivalent Fe(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-59°. In the fifth Mg site, Mg(5) 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 Fe(6)O4 tetrahedra, edges with three equivalent Fe(1)O6 octahedra, and edges with three equivalent Fe(5)O6 octahedra. In the sixth Mg site, Mg(6) is bonded to one O(12) and three equivalent O(8) atoms to form MgO4 tetrahedra that share corners with three equivalent Fe(3)O6 octahedra, corners with three equivalent Fe(5)O6 octahedra, and corners with six equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-60°. There are six inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to one O(2), one O(6), two equivalent O(1), and two equivalent O(4) atoms to form FeO6 octahedra that share  a cornercorner with one Mg(2)O4 tetrahedra,  a cornercorner with one Fe(6)O4 tetrahedra, corners with two equivalent Mg(1)O4 tetrahedra, corners with two equivalent Fe(4)O4 tetrahedra,  an edgeedge with one Mg(3)O6 octahedra,  an edgeedge with one Mg(5)O6 octahedra, and edges with four equivalent Fe(1)O6 octahedra. In the second Fe site, Fe(2) is bonded to one O(10), one O(5), two equivalent O(3), and two equivalent O(8) atoms to form FeO6 octahedra that share  a cornercorner with one Mg(4)O4 tetrahedra,  a cornercorner with one Fe(4)O4 tetrahedra, corners with two equivalent Mg(2)O4 tetrahedra, corners with two equivalent Mg(6)O4 tetrahedra,  an edgeedge with one Mg(3)O6 octahedra,  an edgeedge with one Fe(3)O6 octahedra, and edges with four equivalent Fe(2)O6 octahedra. In the third Fe site, Fe(3) is bonded to three equivalent O(7) and three equivalent O(8) atoms to form FeO6 octahedra that share corners with three equivalent Mg(4)O4 tetrahedra, corners with three equivalent Mg(6)O4 tetrahedra, edges with three equivalent Fe(2)O6 octahedra, and edges with three equivalent Fe(5)O6 octahedra. In the fourth Fe site, Fe(4) is bonded to one O(10) and three equivalent O(4) atoms to form FeO4 tetrahedra that share corners with three equivalent Mg(3)O6 octahedra, corners with three equivalent Fe(2)O6 octahedra, and corners with six equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-58°. In the fifth Fe site, Fe(5) is bonded to one O(12), one O(9), two equivalent O(11), and two equivalent O(7) atoms to form FeO6 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 Fe(6)O4 tetrahedra,  an edgeedge with one Mg(5)O6 octahedra,  an edgeedge with one Fe(3)O6 octahedra, and edges with four equivalent Fe(5)O6 octahedra. In the sixth Fe site, Fe(6) is bonded to one O(6) and three equivalent O(11) atoms to form FeO4 tetrahedra that share corners with three equivalent Mg(5)O6 octahedra, corners with three equivalent Fe(1)O6 octahedra, and corners with six equivalent Fe(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-58°. 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(5), and two equivalent Fe(1) atoms. In the second O site, O(2) is bonded in a distorted rectangular see-saw-like geometry to one Mg(2) and three equivalent Fe(1) atoms. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Mg(2), one Mg(3), and two equivalent Fe(2) atoms. In the fourth O site, O(4) is bonded to one Mg(3), one Fe(4), and two equivalent Fe(1) atoms to form distorted OMgFe3 trigonal pyramids that share corners with two equivalent O(4)MgFe3 trigonal pyramids,  an edgeedge with one O(6)Fe4 trigonal pyramid, and edges with two equivalent O(4)MgFe3 trigonal pyramids. In the fifth O site, O(5) is bonded in a distorted rectangular see-saw-like geometry to one Mg(4) and three equivalent Fe(2) atoms. In the sixth O site, O(6) is bonded to one Fe(6) and three equivalent Fe(1) atoms to form distorted edge-sharing OFe4 trigonal pyramids. In the seventh O site, O(7) is bonded to one Mg(4), one Fe(3), and two equivalent Fe(5) atoms to form a mixture of distorted corner and edge-sharing OMgFe3 trigonal pyramids. In the eighth O site, O(8) is bonded to one Mg(6), one Fe(3), and two equivalent Fe(2) atoms to form a mixture of distorted corner and edge-sharing OMgFe3 trigonal pyramids. In the ninth O site, O(9) is bonded in a distorted rectangular see-saw-like geometry to one Mg(1) and three equivalent Fe(5) atoms. In the tenth O site, O(10) is bonded in a distorted rectangular see-saw-like geometry to one Fe(4) and three equivalent Fe(2) atoms. In the eleventh O site, O(11) is bonded in a distorted rectangular see-saw-like geometry to one Mg(5), one Fe(6), and two equivalent Fe(5) atoms. In the twelfth O site, O(12) is bonded to one Mg(6) and three equivalent Fe(5) atoms to form distorted corner-sharing OMgFe3 trigonal pyramids. is represented by the CIF file [CIF]
data_Mg(FeO2)2
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.050
_cell_length_b   6.050
_cell_length_c   14.806
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   469.278
_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  0.379  1.0
  Mg  Mg2  1  0.667  0.333  0.336  1.0
  Mg  Mg3  1  0.667  0.333  0.709  1.0
  Mg  Mg4  1  0.333  0.667  0.002  1.0
  Mg  Mg5  1  0.333  0.667  0.623  1.0
  Fe  Fe6  1  0.496  0.993  0.166  1.0
  Fe  Fe7  1  0.496  0.504  0.166  1.0
  Fe  Fe8  1  0.831  0.662  0.499  1.0
  Fe  Fe9  1  0.007  0.504  0.166  1.0
  Fe  Fe10  1  0.831  0.169  0.499  1.0
  Fe  Fe11  1  0.000  0.000  0.663  1.0
  Fe  Fe12  1  0.000  0.000  0.287  1.0
  Fe  Fe13  1  0.165  0.330  0.832  1.0
  Fe  Fe14  1  0.338  0.169  0.499  1.0
  Fe  Fe15  1  0.165  0.835  0.832  1.0
  Fe  Fe16  1  0.670  0.835  0.832  1.0
  Fe  Fe17  1  0.667  0.333  0.956  1.0
  O  O18  1  0.179  0.358  0.090  1.0
  O  O19  1  0.333  0.667  0.242  1.0
  O  O20  1  0.179  0.821  0.090  1.0
  O  O21  1  0.642  0.821  0.090  1.0
  O  O22  1  0.512  0.023  0.424  1.0
  O  O23  1  0.352  0.176  0.245  1.0
  O  O24  1  0.667  0.333  0.575  1.0
  O  O25  1  0.824  0.176  0.245  1.0
  O  O26  1  0.667  0.333  0.089  1.0
  O  O27  1  0.512  0.488  0.424  1.0
  O  O28  1  0.977  0.488  0.424  1.0
  O  O29  1  0.824  0.648  0.245  1.0
  O  O30  1  0.847  0.694  0.754  1.0
  O  O31  1  0.696  0.848  0.580  1.0
  O  O32  1  0.152  0.848  0.580  1.0
  O  O33  1  0.000  0.000  0.908  1.0
  O  O34  1  0.000  0.000  0.420  1.0
  O  O35  1  0.847  0.153  0.754  1.0
  O  O36  1  0.306  0.153  0.754  1.0
  O  O37  1  0.152  0.304  0.580  1.0
  O  O38  1  0.015  0.508  0.912  1.0
  O  O39  1  0.492  0.508  0.912  1.0
  O  O40  1  0.333  0.667  0.761  1.0
  O  O41  1  0.492  0.985  0.912  1.0
[/CIF]
.
The compound described by MgFe2O4 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(9) and three equivalent O(1) atoms to form MgO4 tetrahedra that share corners with three equivalent Mg(5)O6 octahedra, corners with three equivalent Fe(5)O6 octahedra, and corners with six equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-58°. In the second Mg site, Mg(2) is bonded to one O(2) and three equivalent O(3) atoms to form MgO4 tetrahedra that share corners with three equivalent Mg(3)O6 octahedra, corners with three equivalent Fe(1)O6 octahedra, and corners with six equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-58°. In the third Mg site, Mg(3) is bonded to three equivalent O(3) and three equivalent O(4) atoms to form MgO6 octahedra that share corners with three equivalent Mg(2)O4 tetrahedra, corners with three equivalent Fe(4)O4 tetrahedra, edges with three equivalent Fe(1)O6 octahedra, and edges with three equivalent Fe(2)O6 octahedra. In the fourth Mg site, Mg(4) is bonded to one O(5) and three equivalent O(7) atoms to form MgO4 tetrahedra that share corners with three equivalent Fe(2)O6 octahedra, corners with three equivalent Fe(3)O6 octahedra, and corners with six equivalent Fe(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-59°. In the fifth Mg site, Mg(5) 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 Fe(6)O4 tetrahedra, edges with three equivalent Fe(1)O6 octahedra, and edges with three equivalent Fe(5)O6 octahedra. In the sixth Mg site, Mg(6) is bonded to one O(12) and three equivalent O(8) atoms to form MgO4 tetrahedra that share corners with three equivalent Fe(3)O6 octahedra, corners with three equivalent Fe(5)O6 octahedra, and corners with six equivalent Fe(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-60°. There are six inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to one O(2), one O(6), two equivalent O(1), and two equivalent O(4) atoms to form FeO6 octahedra that share  a cornercorner with one Mg(2)O4 tetrahedra,  a cornercorner with one Fe(6)O4 tetrahedra, corners with two equivalent Mg(1)O4 tetrahedra, corners with two equivalent Fe(4)O4 tetrahedra,  an edgeedge with one Mg(3)O6 octahedra,  an edgeedge with one Mg(5)O6 octahedra, and edges with four equivalent Fe(1)O6 octahedra. In the second Fe site, Fe(2) is bonded to one O(10), one O(5), two equivalent O(3), and two equivalent O(8) atoms to form FeO6 octahedra that share  a cornercorner with one Mg(4)O4 tetrahedra,  a cornercorner with one Fe(4)O4 tetrahedra, corners with two equivalent Mg(2)O4 tetrahedra, corners with two equivalent Mg(6)O4 tetrahedra,  an edgeedge with one Mg(3)O6 octahedra,  an edgeedge with one Fe(3)O6 octahedra, and edges with four equivalent Fe(2)O6 octahedra. In the third Fe site, Fe(3) is bonded to three equivalent O(7) and three equivalent O(8) atoms to form FeO6 octahedra that share corners with three equivalent Mg(4)O4 tetrahedra, corners with three equivalent Mg(6)O4 tetrahedra, edges with three equivalent Fe(2)O6 octahedra, and edges with three equivalent Fe(5)O6 octahedra. In the fourth Fe site, Fe(4) is bonded to one O(10) and three equivalent O(4) atoms to form FeO4 tetrahedra that share corners with three equivalent Mg(3)O6 octahedra, corners with three equivalent Fe(2)O6 octahedra, and corners with six equivalent Fe(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-58°. In the fifth Fe site, Fe(5) is bonded to one O(12), one O(9), two equivalent O(11), and two equivalent O(7) atoms to form FeO6 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 Fe(6)O4 tetrahedra,  an edgeedge with one Mg(5)O6 octahedra,  an edgeedge with one Fe(3)O6 octahedra, and edges with four equivalent Fe(5)O6 octahedra. In the sixth Fe site, Fe(6) is bonded to one O(6) and three equivalent O(11) atoms to form FeO4 tetrahedra that share corners with three equivalent Mg(5)O6 octahedra, corners with three equivalent Fe(1)O6 octahedra, and corners with six equivalent Fe(5)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-58°. 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(5), and two equivalent Fe(1) atoms. In the second O site, O(2) is bonded in a distorted rectangular see-saw-like geometry to one Mg(2) and three equivalent Fe(1) atoms. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Mg(2), one Mg(3), and two equivalent Fe(2) atoms. In the fourth O site, O(4) is bonded to one Mg(3), one Fe(4), and two equivalent Fe(1) atoms to form distorted OMgFe3 trigonal pyramids that share corners with two equivalent O(4)MgFe3 trigonal pyramids,  an edgeedge with one O(6)Fe4 trigonal pyramid, and edges with two equivalent O(4)MgFe3 trigonal pyramids. In the fifth O site, O(5) is bonded in a distorted rectangular see-saw-like geometry to one Mg(4) and three equivalent Fe(2) atoms. In the sixth O site, O(6) is bonded to one Fe(6) and three equivalent Fe(1) atoms to form distorted edge-sharing OFe4 trigonal pyramids. In the seventh O site, O(7) is bonded to one Mg(4), one Fe(3), and two equivalent Fe(5) atoms to form a mixture of distorted corner and edge-sharing OMgFe3 trigonal pyramids. In the eighth O site, O(8) is bonded to one Mg(6), one Fe(3), and two equivalent Fe(2) atoms to form a mixture of distorted corner and edge-sharing OMgFe3 trigonal pyramids. In the ninth O site, O(9) is bonded in a distorted rectangular see-saw-like geometry to one Mg(1) and three equivalent Fe(5) atoms. In the tenth O site, O(10) is bonded in a distorted rectangular see-saw-like geometry to one Fe(4) and three equivalent Fe(2) atoms. In the eleventh O site, O(11) is bonded in a distorted rectangular see-saw-like geometry to one Mg(5), one Fe(6), and two equivalent Fe(5) atoms. In the twelfth O site, O(12) is bonded to one Mg(6) and three equivalent Fe(5) atoms to form distorted corner-sharing OMgFe3 trigonal pyramids. is represented by the CIF file [CIF]
data_Mg(FeO2)2
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.050
_cell_length_b   6.050
_cell_length_c   14.806
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   469.278
_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  0.379  1.0
  Mg  Mg2  1  0.667  0.333  0.336  1.0
  Mg  Mg3  1  0.667  0.333  0.709  1.0
  Mg  Mg4  1  0.333  0.667  0.002  1.0
  Mg  Mg5  1  0.333  0.667  0.623  1.0
  Fe  Fe6  1  0.496  0.993  0.166  1.0
  Fe  Fe7  1  0.496  0.504  0.166  1.0
  Fe  Fe8  1  0.831  0.662  0.499  1.0
  Fe  Fe9  1  0.007  0.504  0.166  1.0
  Fe  Fe10  1  0.831  0.169  0.499  1.0
  Fe  Fe11  1  0.000  0.000  0.663  1.0
  Fe  Fe12  1  0.000  0.000  0.287  1.0
  Fe  Fe13  1  0.165  0.330  0.832  1.0
  Fe  Fe14  1  0.338  0.169  0.499  1.0
  Fe  Fe15  1  0.165  0.835  0.832  1.0
  Fe  Fe16  1  0.670  0.835  0.832  1.0
  Fe  Fe17  1  0.667  0.333  0.956  1.0
  O  O18  1  0.179  0.358  0.090  1.0
  O  O19  1  0.333  0.667  0.242  1.0
  O  O20  1  0.179  0.821  0.090  1.0
  O  O21  1  0.642  0.821  0.090  1.0
  O  O22  1  0.512  0.023  0.424  1.0
  O  O23  1  0.352  0.176  0.245  1.0
  O  O24  1  0.667  0.333  0.575  1.0
  O  O25  1  0.824  0.176  0.245  1.0
  O  O26  1  0.667  0.333  0.089  1.0
  O  O27  1  0.512  0.488  0.424  1.0
  O  O28  1  0.977  0.488  0.424  1.0
  O  O29  1  0.824  0.648  0.245  1.0
  O  O30  1  0.847  0.694  0.754  1.0
  O  O31  1  0.696  0.848  0.580  1.0
  O  O32  1  0.152  0.848  0.580  1.0
  O  O33  1  0.000  0.000  0.908  1.0
  O  O34  1  0.000  0.000  0.420  1.0
  O  O35  1  0.847  0.153  0.754  1.0
  O  O36  1  0.306  0.153  0.754  1.0
  O  O37  1  0.152  0.304  0.580  1.0
  O  O38  1  0.015  0.508  0.912  1.0
  O  O39  1  0.492  0.508  0.912  1.0
  O  O40  1  0.333  0.667  0.761  1.0
  O  O41  1  0.492  0.985  0.912  1.0
[/CIF]
.