The crystal structure described by Mg2Cr3O8 crystallizes in the hexagonal P6_3mc space group. There are two inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form MgO6 octahedra that share corners with six equivalent Cr(1)O6 octahedra, corners with three equivalent Mg(2)O4 tetrahedra, and edges with three equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles are 51°. In the second Mg site, Mg(2) is bonded to one O(4) and three equivalent O(2) atoms to form MgO4 tetrahedra that share corners with three equivalent Mg(1)O6 octahedra and corners with nine equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-62°. Cr(1) is bonded to one O(3), one O(4), two equivalent O(1), and two equivalent O(2) atoms to form CrO6 octahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with three equivalent Mg(2)O4 tetrahedra,  an edgeedge with one Mg(1)O6 octahedra, and edges with four equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles are 51°. There are four inequivalent O sites. In the first O site, O(1) is bonded in a distorted trigonal planar geometry to one Mg(1) and two equivalent Cr(1) atoms. In the second O site, O(2) is bonded to one Mg(1), one Mg(2), and two equivalent Cr(1) atoms to form OMg2Cr2 tetrahedra that share corners with two equivalent O(2)Mg2Cr2 tetrahedra,  a cornercorner with one O(4)MgCr3 trigonal pyramid, edges with two equivalent O(2)Mg2Cr2 tetrahedra, and  an edgeedge with one O(4)MgCr3 trigonal pyramid. In the third O site, O(3) is bonded in a distorted T-shaped geometry to three equivalent Cr(1) atoms. In the fourth O site, O(4) is bonded to one Mg(2) and three equivalent Cr(1) atoms to form a mixture of distorted corner and edge-sharing OMgCr3 trigonal pyramids. is represented by the CIF card [CIF]
data_Mg2Cr3O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.858
_cell_length_b   5.858
_cell_length_c   9.496
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   282.238
_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  0.667  0.333  0.020  1.0
  Mg  Mg1  1  0.333  0.667  0.520  1.0
  Mg  Mg2  1  0.667  0.333  0.422  1.0
  Mg  Mg3  1  0.333  0.667  0.922  1.0
  Cr  Cr4  1  0.673  0.836  0.244  1.0
  Cr  Cr5  1  0.836  0.164  0.744  1.0
  Cr  Cr6  1  0.164  0.327  0.244  1.0
  Cr  Cr7  1  0.836  0.673  0.744  1.0
  Cr  Cr8  1  0.327  0.164  0.744  1.0
  Cr  Cr9  1  0.164  0.836  0.244  1.0
  O  O10  1  0.837  0.163  0.149  1.0
  O  O11  1  0.673  0.837  0.649  1.0
  O  O12  1  0.163  0.327  0.649  1.0
  O  O13  1  0.837  0.673  0.149  1.0
  O  O14  1  0.327  0.163  0.149  1.0
  O  O15  1  0.163  0.837  0.649  1.0
  O  O16  1  0.519  0.481  0.863  1.0
  O  O17  1  0.038  0.519  0.363  1.0
  O  O18  1  0.481  0.962  0.363  1.0
  O  O19  1  0.519  0.038  0.863  1.0
  O  O20  1  0.000  0.000  0.353  1.0
  O  O21  1  0.000  0.000  0.853  1.0
  O  O22  1  0.333  0.667  0.132  1.0
  O  O23  1  0.962  0.481  0.863  1.0
  O  O24  1  0.481  0.519  0.363  1.0
  O  O25  1  0.667  0.333  0.632  1.0
[/CIF]
.
The crystal structure described by Mg2Cr3O8 crystallizes in the hexagonal P6_3mc space group. There are two inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to three equivalent O(1) and three equivalent O(2) atoms to form MgO6 octahedra that share corners with six equivalent Cr(1)O6 octahedra, corners with three equivalent Mg(2)O4 tetrahedra, and edges with three equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles are 51°. In the second Mg site, Mg(2) is bonded to one O(4) and three equivalent O(2) atoms to form MgO4 tetrahedra that share corners with three equivalent Mg(1)O6 octahedra and corners with nine equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-62°. Cr(1) is bonded to one O(3), one O(4), two equivalent O(1), and two equivalent O(2) atoms to form CrO6 octahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with three equivalent Mg(2)O4 tetrahedra,  an edgeedge with one Mg(1)O6 octahedra, and edges with four equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles are 51°. There are four inequivalent O sites. In the first O site, O(1) is bonded in a distorted trigonal planar geometry to one Mg(1) and two equivalent Cr(1) atoms. In the second O site, O(2) is bonded to one Mg(1), one Mg(2), and two equivalent Cr(1) atoms to form OMg2Cr2 tetrahedra that share corners with two equivalent O(2)Mg2Cr2 tetrahedra,  a cornercorner with one O(4)MgCr3 trigonal pyramid, edges with two equivalent O(2)Mg2Cr2 tetrahedra, and  an edgeedge with one O(4)MgCr3 trigonal pyramid. In the third O site, O(3) is bonded in a distorted T-shaped geometry to three equivalent Cr(1) atoms. In the fourth O site, O(4) is bonded to one Mg(2) and three equivalent Cr(1) atoms to form a mixture of distorted corner and edge-sharing OMgCr3 trigonal pyramids. is represented by the CIF card [CIF]
data_Mg2Cr3O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.858
_cell_length_b   5.858
_cell_length_c   9.496
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   120.000
_symmetry_Int_Tables_number   1
_cell_volume   282.238
_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  0.667  0.333  0.020  1.0
  Mg  Mg1  1  0.333  0.667  0.520  1.0
  Mg  Mg2  1  0.667  0.333  0.422  1.0
  Mg  Mg3  1  0.333  0.667  0.922  1.0
  Cr  Cr4  1  0.673  0.836  0.244  1.0
  Cr  Cr5  1  0.836  0.164  0.744  1.0
  Cr  Cr6  1  0.164  0.327  0.244  1.0
  Cr  Cr7  1  0.836  0.673  0.744  1.0
  Cr  Cr8  1  0.327  0.164  0.744  1.0
  Cr  Cr9  1  0.164  0.836  0.244  1.0
  O  O10  1  0.837  0.163  0.149  1.0
  O  O11  1  0.673  0.837  0.649  1.0
  O  O12  1  0.163  0.327  0.649  1.0
  O  O13  1  0.837  0.673  0.149  1.0
  O  O14  1  0.327  0.163  0.149  1.0
  O  O15  1  0.163  0.837  0.649  1.0
  O  O16  1  0.519  0.481  0.863  1.0
  O  O17  1  0.038  0.519  0.363  1.0
  O  O18  1  0.481  0.962  0.363  1.0
  O  O19  1  0.519  0.038  0.863  1.0
  O  O20  1  0.000  0.000  0.353  1.0
  O  O21  1  0.000  0.000  0.853  1.0
  O  O22  1  0.333  0.667  0.132  1.0
  O  O23  1  0.962  0.481  0.863  1.0
  O  O24  1  0.481  0.519  0.363  1.0
  O  O25  1  0.667  0.333  0.632  1.0
[/CIF]
.