The structure described by MgCr2O4 crystallizes in the orthorhombic Pbcm space group. Mg(1) is bonded in a 8-coordinate geometry to two equivalent O(2), two equivalent O(3), and four equivalent O(1) atoms. Cr(1) is bonded to one O(3), two equivalent O(2), and three equivalent O(1) atoms to form a mixture of corner and edge-sharing CrO6 octahedra. The corner-sharing octahedral tilt angles range from 0-56°. There are three inequivalent O sites. In the first O site, O(1) is bonded to two equivalent Mg(1) and three equivalent Cr(1) atoms to form distorted OMg2Cr3 trigonal bipyramids that share corners with five equivalent O(3)Mg2Cr2 tetrahedra, corners with two equivalent O(1)Mg2Cr3 trigonal bipyramids,  an edgeedge with one O(3)Mg2Cr2 tetrahedra, and edges with five equivalent O(1)Mg2Cr3 trigonal bipyramids. In the second O site, O(2) is bonded in a distorted rectangular see-saw-like geometry to two equivalent Mg(1) and four equivalent Cr(1) atoms. In the third O site, O(3) is bonded to two equivalent Mg(1) and two equivalent Cr(1) atoms to form OMg2Cr2 tetrahedra that share corners with two equivalent O(3)Mg2Cr2 tetrahedra, corners with ten equivalent O(1)Mg2Cr3 trigonal bipyramids, and edges with two equivalent O(1)Mg2Cr3 trigonal bipyramids. is represented by the Crystallographic Information File (CIF) [CIF]
data_MgCr2O4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   2.926
_cell_length_b   9.670
_cell_length_c   9.818
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   277.803
_cell_formula_units_Z   4
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  0.212  0.359  0.750  1.0
  Mg  Mg1  1  0.212  0.141  0.250  1.0
  Mg  Mg2  1  0.788  0.859  0.750  1.0
  Mg  Mg3  1  0.788  0.641  0.250  1.0
  Cr  Cr4  1  0.740  0.117  0.928  1.0
  Cr  Cr5  1  0.740  0.383  0.428  1.0
  Cr  Cr6  1  0.260  0.883  0.428  1.0
  Cr  Cr7  1  0.740  0.383  0.072  1.0
  Cr  Cr8  1  0.260  0.883  0.072  1.0
  Cr  Cr9  1  0.740  0.117  0.572  1.0
  Cr  Cr10  1  0.260  0.617  0.572  1.0
  Cr  Cr11  1  0.260  0.617  0.928  1.0
  O  O12  1  0.243  0.980  0.614  1.0
  O  O13  1  0.757  0.020  0.386  1.0
  O  O14  1  0.238  0.250  0.500  1.0
  O  O15  1  0.757  0.480  0.614  1.0
  O  O16  1  0.757  0.480  0.886  1.0
  O  O17  1  0.718  0.287  0.250  1.0
  O  O18  1  0.243  0.520  0.386  1.0
  O  O19  1  0.282  0.787  0.250  1.0
  O  O20  1  0.238  0.250  0.000  1.0
  O  O21  1  0.762  0.750  0.500  1.0
  O  O22  1  0.243  0.980  0.886  1.0
  O  O23  1  0.282  0.713  0.750  1.0
  O  O24  1  0.718  0.213  0.750  1.0
  O  O25  1  0.762  0.750  0.000  1.0
  O  O26  1  0.243  0.520  0.114  1.0
  O  O27  1  0.757  0.020  0.114  1.0
[/CIF]
.
The structure described by MgCr2O4 crystallizes in the orthorhombic Pbcm space group. Mg(1) is bonded in a 8-coordinate geometry to two equivalent O(2), two equivalent O(3), and four equivalent O(1) atoms. Cr(1) is bonded to one O(3), two equivalent O(2), and three equivalent O(1) atoms to form a mixture of corner and edge-sharing CrO6 octahedra. The corner-sharing octahedral tilt angles range from 0-56°. There are three inequivalent O sites. In the first O site, O(1) is bonded to two equivalent Mg(1) and three equivalent Cr(1) atoms to form distorted OMg2Cr3 trigonal bipyramids that share corners with five equivalent O(3)Mg2Cr2 tetrahedra, corners with two equivalent O(1)Mg2Cr3 trigonal bipyramids,  an edgeedge with one O(3)Mg2Cr2 tetrahedra, and edges with five equivalent O(1)Mg2Cr3 trigonal bipyramids. In the second O site, O(2) is bonded in a distorted rectangular see-saw-like geometry to two equivalent Mg(1) and four equivalent Cr(1) atoms. In the third O site, O(3) is bonded to two equivalent Mg(1) and two equivalent Cr(1) atoms to form OMg2Cr2 tetrahedra that share corners with two equivalent O(3)Mg2Cr2 tetrahedra, corners with ten equivalent O(1)Mg2Cr3 trigonal bipyramids, and edges with two equivalent O(1)Mg2Cr3 trigonal bipyramids. is represented by the Crystallographic Information File (CIF) [CIF]
data_MgCr2O4
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   2.926
_cell_length_b   9.670
_cell_length_c   9.818
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   277.803
_cell_formula_units_Z   4
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  0.212  0.359  0.750  1.0
  Mg  Mg1  1  0.212  0.141  0.250  1.0
  Mg  Mg2  1  0.788  0.859  0.750  1.0
  Mg  Mg3  1  0.788  0.641  0.250  1.0
  Cr  Cr4  1  0.740  0.117  0.928  1.0
  Cr  Cr5  1  0.740  0.383  0.428  1.0
  Cr  Cr6  1  0.260  0.883  0.428  1.0
  Cr  Cr7  1  0.740  0.383  0.072  1.0
  Cr  Cr8  1  0.260  0.883  0.072  1.0
  Cr  Cr9  1  0.740  0.117  0.572  1.0
  Cr  Cr10  1  0.260  0.617  0.572  1.0
  Cr  Cr11  1  0.260  0.617  0.928  1.0
  O  O12  1  0.243  0.980  0.614  1.0
  O  O13  1  0.757  0.020  0.386  1.0
  O  O14  1  0.238  0.250  0.500  1.0
  O  O15  1  0.757  0.480  0.614  1.0
  O  O16  1  0.757  0.480  0.886  1.0
  O  O17  1  0.718  0.287  0.250  1.0
  O  O18  1  0.243  0.520  0.386  1.0
  O  O19  1  0.282  0.787  0.250  1.0
  O  O20  1  0.238  0.250  0.000  1.0
  O  O21  1  0.762  0.750  0.500  1.0
  O  O22  1  0.243  0.980  0.886  1.0
  O  O23  1  0.282  0.713  0.750  1.0
  O  O24  1  0.718  0.213  0.750  1.0
  O  O25  1  0.762  0.750  0.000  1.0
  O  O26  1  0.243  0.520  0.114  1.0
  O  O27  1  0.757  0.020  0.114  1.0
[/CIF]
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