The compound described by MgCr2O4 is Spinel-like structured and crystallizes in the trigonal R3m space group. There are two inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one O(3) and three equivalent O(4) atoms to form MgO4 tetrahedra that share corners with three equivalent Mg(2)O6 octahedra and corners with nine equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-59°. In the second Mg site, Mg(2) is bonded to three equivalent O(1) and three equivalent O(4) atoms to form MgO6 octahedra that share corners with three equivalent Mg(1)O4 tetrahedra, corners with three equivalent Cr(1)O4 tetrahedra, and edges with six equivalent Cr(2)O6 octahedra. There are two inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(2) and three equivalent O(1) atoms to form CrO4 tetrahedra that share corners with three equivalent Mg(2)O6 octahedra and corners with nine equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-59°. In the second Cr site, Cr(2) is bonded to one O(2), one O(3), two equivalent O(1), and two equivalent O(4) atoms to form CrO6 octahedra that share corners with three equivalent Mg(1)O4 tetrahedra, corners with three equivalent Cr(1)O4 tetrahedra, edges with two equivalent Mg(2)O6 octahedra, and edges with four equivalent Cr(2)O6 octahedra. There are four inequivalent O sites. In the first O site, O(1) is bonded to one Mg(2), one Cr(1), and two equivalent Cr(2) atoms to form distorted OMgCr3 trigonal pyramids that share  a cornercorner with one O(2)Cr4 trigonal pyramid, corners with two equivalent O(1)MgCr3 trigonal pyramids, corners with seven equivalent O(4)Mg2Cr2 trigonal pyramids,  an edgeedge with one O(2)Cr4 trigonal pyramid, and edges with two equivalent O(1)MgCr3 trigonal pyramids. In the second O site, O(2) is bonded to one Cr(1) and three equivalent Cr(2) atoms to form distorted OCr4 trigonal pyramids that share corners with three equivalent O(1)MgCr3 trigonal pyramids, corners with six equivalent O(4)Mg2Cr2 trigonal pyramids, and edges with three equivalent O(1)MgCr3 trigonal pyramids. In the third O site, O(3) is bonded in a distorted rectangular see-saw-like geometry to one Mg(1) and three equivalent Cr(2) atoms. In the fourth O site, O(4) is bonded to one Mg(1), one Mg(2), and two equivalent Cr(2) atoms to form distorted OMg2Cr2 trigonal pyramids that share corners with two equivalent O(2)Cr4 trigonal pyramids, corners with two equivalent O(4)Mg2Cr2 trigonal pyramids, corners with seven equivalent O(1)MgCr3 trigonal pyramids, and edges with two equivalent O(4)Mg2Cr2 trigonal pyramids. is represented by the CIF card [CIF]
data_MgCr2O4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.037
_cell_length_b   6.037
_cell_length_c   6.037
_cell_angle_alpha   59.441
_cell_angle_beta   59.441
_cell_angle_gamma   59.441
_symmetry_Int_Tables_number   1
_cell_volume   153.610
_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  0.003  0.003  0.003  1.0
  Mg  Mg1  1  0.627  0.627  0.627  1.0
  Cr  Cr2  1  0.245  0.245  0.245  1.0
  Cr  Cr3  1  0.626  0.626  0.120  1.0
  Cr  Cr4  1  0.120  0.626  0.626  1.0
  Cr  Cr5  1  0.626  0.120  0.626  1.0
  O  O6  1  0.378  0.851  0.378  1.0
  O  O7  1  0.851  0.378  0.378  1.0
  O  O8  1  0.378  0.378  0.851  1.0
  O  O9  1  0.385  0.385  0.385  1.0
  O  O10  1  0.865  0.865  0.865  1.0
  O  O11  1  0.869  0.869  0.407  1.0
  O  O12  1  0.407  0.869  0.869  1.0
  O  O13  1  0.869  0.407  0.869  1.0
[/CIF]
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The compound described by MgCr2O4 is Spinel-like structured and crystallizes in the trigonal R3m space group. There are two inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one O(3) and three equivalent O(4) atoms to form MgO4 tetrahedra that share corners with three equivalent Mg(2)O6 octahedra and corners with nine equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-59°. In the second Mg site, Mg(2) is bonded to three equivalent O(1) and three equivalent O(4) atoms to form MgO6 octahedra that share corners with three equivalent Mg(1)O4 tetrahedra, corners with three equivalent Cr(1)O4 tetrahedra, and edges with six equivalent Cr(2)O6 octahedra. There are two inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(2) and three equivalent O(1) atoms to form CrO4 tetrahedra that share corners with three equivalent Mg(2)O6 octahedra and corners with nine equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-59°. In the second Cr site, Cr(2) is bonded to one O(2), one O(3), two equivalent O(1), and two equivalent O(4) atoms to form CrO6 octahedra that share corners with three equivalent Mg(1)O4 tetrahedra, corners with three equivalent Cr(1)O4 tetrahedra, edges with two equivalent Mg(2)O6 octahedra, and edges with four equivalent Cr(2)O6 octahedra. There are four inequivalent O sites. In the first O site, O(1) is bonded to one Mg(2), one Cr(1), and two equivalent Cr(2) atoms to form distorted OMgCr3 trigonal pyramids that share  a cornercorner with one O(2)Cr4 trigonal pyramid, corners with two equivalent O(1)MgCr3 trigonal pyramids, corners with seven equivalent O(4)Mg2Cr2 trigonal pyramids,  an edgeedge with one O(2)Cr4 trigonal pyramid, and edges with two equivalent O(1)MgCr3 trigonal pyramids. In the second O site, O(2) is bonded to one Cr(1) and three equivalent Cr(2) atoms to form distorted OCr4 trigonal pyramids that share corners with three equivalent O(1)MgCr3 trigonal pyramids, corners with six equivalent O(4)Mg2Cr2 trigonal pyramids, and edges with three equivalent O(1)MgCr3 trigonal pyramids. In the third O site, O(3) is bonded in a distorted rectangular see-saw-like geometry to one Mg(1) and three equivalent Cr(2) atoms. In the fourth O site, O(4) is bonded to one Mg(1), one Mg(2), and two equivalent Cr(2) atoms to form distorted OMg2Cr2 trigonal pyramids that share corners with two equivalent O(2)Cr4 trigonal pyramids, corners with two equivalent O(4)Mg2Cr2 trigonal pyramids, corners with seven equivalent O(1)MgCr3 trigonal pyramids, and edges with two equivalent O(4)Mg2Cr2 trigonal pyramids. is represented by the CIF card [CIF]
data_MgCr2O4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.037
_cell_length_b   6.037
_cell_length_c   6.037
_cell_angle_alpha   59.441
_cell_angle_beta   59.441
_cell_angle_gamma   59.441
_symmetry_Int_Tables_number   1
_cell_volume   153.610
_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  0.003  0.003  0.003  1.0
  Mg  Mg1  1  0.627  0.627  0.627  1.0
  Cr  Cr2  1  0.245  0.245  0.245  1.0
  Cr  Cr3  1  0.626  0.626  0.120  1.0
  Cr  Cr4  1  0.120  0.626  0.626  1.0
  Cr  Cr5  1  0.626  0.120  0.626  1.0
  O  O6  1  0.378  0.851  0.378  1.0
  O  O7  1  0.851  0.378  0.378  1.0
  O  O8  1  0.378  0.378  0.851  1.0
  O  O9  1  0.385  0.385  0.385  1.0
  O  O10  1  0.865  0.865  0.865  1.0
  O  O11  1  0.869  0.869  0.407  1.0
  O  O12  1  0.407  0.869  0.869  1.0
  O  O13  1  0.869  0.407  0.869  1.0
[/CIF]
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