The structure described by MgMn2O4 crystallizes in the triclinic P-1 space group. There are two inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(4) atoms to form MgO6 octahedra that share corners with six equivalent Mn(4)O6 octahedra, edges with two equivalent Mg(2)O6 octahedra, edges with two equivalent Mn(1)O6 octahedra, edges with two equivalent Mn(2)O6 octahedra, and edges with two equivalent Mn(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 9-19°. In the second Mg site, Mg(2) is bonded to two equivalent O(2), two equivalent O(3), and two equivalent O(4) atoms to form MgO6 octahedra that share corners with six equivalent Mn(2)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Mn(1)O6 octahedra, edges with two equivalent Mn(3)O6 octahedra, and edges with two equivalent Mn(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 8-10°. There are four inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(3) atoms to form MnO6 octahedra that share edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Mg(2)O6 octahedra, edges with two equivalent Mn(2)O6 octahedra, edges with two equivalent Mn(3)O6 octahedra, and edges with two equivalent Mn(4)O6 octahedra. In the second Mn site, Mn(2) is bonded to two equivalent O(2), two equivalent O(3), and two equivalent O(4) atoms to form MnO6 octahedra that share corners with six equivalent Mg(2)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Mn(1)O6 octahedra, edges with two equivalent Mn(3)O6 octahedra, and edges with two equivalent Mn(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 8-10°. In the third Mn site, Mn(3) is bonded to two equivalent O(1), two equivalent O(3), and two equivalent O(4) atoms to form MnO6 octahedra that share edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Mg(2)O6 octahedra, edges with two equivalent Mn(1)O6 octahedra, edges with two equivalent Mn(2)O6 octahedra, and edges with two equivalent Mn(4)O6 octahedra. In the fourth Mn site, Mn(4) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(4) atoms to form MnO6 octahedra that share corners with six equivalent Mg(1)O6 octahedra, edges with two equivalent Mg(2)O6 octahedra, edges with two equivalent Mn(1)O6 octahedra, edges with two equivalent Mn(2)O6 octahedra, and edges with two equivalent Mn(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 9-19°. There are four inequivalent O sites. In the first O site, O(1) is bonded in a distorted see-saw-like geometry to one Mg(1), one Mn(1), one Mn(3), and one Mn(4) atom. In the second O site, O(2) is bonded to one Mg(1), one Mg(2), one Mn(1), one Mn(2), and one Mn(4) atom to form a mixture of corner and edge-sharing OMg2Mn3 square pyramids. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Mg(2), one Mn(1), one Mn(2), and one Mn(3) atom. In the fourth O site, O(4) is bonded to one Mg(1), one Mg(2), one Mn(2), one Mn(3), and one Mn(4) atom to form a mixture of corner and edge-sharing OMg2Mn3 square pyramids. is represented by the CIF file [CIF]
data_MgMn2O4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.817
_cell_length_b   6.085
_cell_length_c   6.114
_cell_angle_alpha   118.364
_cell_angle_beta   117.744
_cell_angle_gamma   91.127
_symmetry_Int_Tables_number   1
_cell_volume   160.263
_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
  Mg  Mg0  1  0.000  0.000  0.000  1.0
  Mg  Mg1  1  0.000  0.500  0.500  1.0
  Mn  Mn2  1  0.500  0.000  0.000  1.0
  Mn  Mn3  1  0.500  0.000  0.500  1.0
  Mn  Mn4  1  0.000  0.000  0.500  1.0
  Mn  Mn5  1  0.500  0.500  0.000  1.0
  O  O6  1  0.770  0.808  0.070  1.0
  O  O7  1  0.247  0.758  0.965  1.0
  O  O8  1  0.754  0.211  0.496  1.0
  O  O9  1  0.240  0.217  0.489  1.0
  O  O10  1  0.246  0.789  0.504  1.0
  O  O11  1  0.753  0.242  0.035  1.0
  O  O12  1  0.760  0.783  0.511  1.0
  O  O13  1  0.230  0.192  0.930  1.0
[/CIF]
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The structure described by MgMn2O4 crystallizes in the triclinic P-1 space group. There are two inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(4) atoms to form MgO6 octahedra that share corners with six equivalent Mn(4)O6 octahedra, edges with two equivalent Mg(2)O6 octahedra, edges with two equivalent Mn(1)O6 octahedra, edges with two equivalent Mn(2)O6 octahedra, and edges with two equivalent Mn(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 9-19°. In the second Mg site, Mg(2) is bonded to two equivalent O(2), two equivalent O(3), and two equivalent O(4) atoms to form MgO6 octahedra that share corners with six equivalent Mn(2)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Mn(1)O6 octahedra, edges with two equivalent Mn(3)O6 octahedra, and edges with two equivalent Mn(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 8-10°. There are four inequivalent Mn sites. In the first Mn site, Mn(1) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(3) atoms to form MnO6 octahedra that share edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Mg(2)O6 octahedra, edges with two equivalent Mn(2)O6 octahedra, edges with two equivalent Mn(3)O6 octahedra, and edges with two equivalent Mn(4)O6 octahedra. In the second Mn site, Mn(2) is bonded to two equivalent O(2), two equivalent O(3), and two equivalent O(4) atoms to form MnO6 octahedra that share corners with six equivalent Mg(2)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Mn(1)O6 octahedra, edges with two equivalent Mn(3)O6 octahedra, and edges with two equivalent Mn(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 8-10°. In the third Mn site, Mn(3) is bonded to two equivalent O(1), two equivalent O(3), and two equivalent O(4) atoms to form MnO6 octahedra that share edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Mg(2)O6 octahedra, edges with two equivalent Mn(1)O6 octahedra, edges with two equivalent Mn(2)O6 octahedra, and edges with two equivalent Mn(4)O6 octahedra. In the fourth Mn site, Mn(4) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(4) atoms to form MnO6 octahedra that share corners with six equivalent Mg(1)O6 octahedra, edges with two equivalent Mg(2)O6 octahedra, edges with two equivalent Mn(1)O6 octahedra, edges with two equivalent Mn(2)O6 octahedra, and edges with two equivalent Mn(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 9-19°. There are four inequivalent O sites. In the first O site, O(1) is bonded in a distorted see-saw-like geometry to one Mg(1), one Mn(1), one Mn(3), and one Mn(4) atom. In the second O site, O(2) is bonded to one Mg(1), one Mg(2), one Mn(1), one Mn(2), and one Mn(4) atom to form a mixture of corner and edge-sharing OMg2Mn3 square pyramids. In the third O site, O(3) is bonded in a rectangular see-saw-like geometry to one Mg(2), one Mn(1), one Mn(2), and one Mn(3) atom. In the fourth O site, O(4) is bonded to one Mg(1), one Mg(2), one Mn(2), one Mn(3), and one Mn(4) atom to form a mixture of corner and edge-sharing OMg2Mn3 square pyramids. is represented by the CIF file [CIF]
data_MgMn2O4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.817
_cell_length_b   6.085
_cell_length_c   6.114
_cell_angle_alpha   118.364
_cell_angle_beta   117.744
_cell_angle_gamma   91.127
_symmetry_Int_Tables_number   1
_cell_volume   160.263
_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
  Mg  Mg0  1  0.000  0.000  0.000  1.0
  Mg  Mg1  1  0.000  0.500  0.500  1.0
  Mn  Mn2  1  0.500  0.000  0.000  1.0
  Mn  Mn3  1  0.500  0.000  0.500  1.0
  Mn  Mn4  1  0.000  0.000  0.500  1.0
  Mn  Mn5  1  0.500  0.500  0.000  1.0
  O  O6  1  0.770  0.808  0.070  1.0
  O  O7  1  0.247  0.758  0.965  1.0
  O  O8  1  0.754  0.211  0.496  1.0
  O  O9  1  0.240  0.217  0.489  1.0
  O  O10  1  0.246  0.789  0.504  1.0
  O  O11  1  0.753  0.242  0.035  1.0
  O  O12  1  0.760  0.783  0.511  1.0
  O  O13  1  0.230  0.192  0.930  1.0
[/CIF]
.