The structure described by MgCr4O6 crystallizes in the orthorhombic Cmcm space group. Mg(1) is bonded in a 6-coordinate geometry to two equivalent O(4) and four equivalent O(2) atoms. There are two inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(2), two equivalent O(1), and three equivalent O(3) atoms to form a mixture of edge and corner-sharing CrO6 octahedra. The corner-sharing octahedral tilt angles range from 0-11°. In the second Cr site, Cr(2) is bonded to one O(1), one O(4), two equivalent O(2), and two equivalent O(3) atoms to form a mixture of edge and corner-sharing CrO6 octahedra. The corner-sharing octahedral tilt angles range from 0-63°. There are four inequivalent O sites. In the first O site, O(1) is bonded to two equivalent Cr(2) and four equivalent Cr(1) atoms to form OCr6 octahedra that share corners with four equivalent O(3)Cr5 square pyramids, corners with two equivalent O(4)Mg2Cr2 tetrahedra, edges with two equivalent O(1)Cr6 octahedra, edges with six equivalent O(3)Cr5 square pyramids, and edges with four equivalent O(2)Mg2Cr3 trigonal bipyramids. In the second O site, O(2) is bonded to two equivalent Mg(1), one Cr(1), and two equivalent Cr(2) atoms to form distorted OMg2Cr3 trigonal bipyramids that share corners with five equivalent O(3)Cr5 square pyramids, corners with four equivalent O(4)Mg2Cr2 tetrahedra, corners with two equivalent O(2)Mg2Cr3 trigonal bipyramids, edges with two equivalent O(1)Cr6 octahedra,  an edgeedge with one O(3)Cr5 square pyramid,  an edgeedge with one O(4)Mg2Cr2 tetrahedra, and edges with three equivalent O(2)Mg2Cr3 trigonal bipyramids. In the third O site, O(3) is bonded to two equivalent Cr(2) and three equivalent Cr(1) atoms to form OCr5 square pyramids that share corners with two equivalent O(1)Cr6 octahedra, corners with two equivalent O(4)Mg2Cr2 tetrahedra, corners with five equivalent O(2)Mg2Cr3 trigonal bipyramids, edges with three equivalent O(1)Cr6 octahedra, edges with four equivalent O(3)Cr5 square pyramids, and  an edgeedge with one O(2)Mg2Cr3 trigonal bipyramid. The corner-sharing octahedral tilt angles are 5°. In the fourth O site, O(4) is bonded to two equivalent Mg(1) and two equivalent Cr(2) atoms to form OMg2Cr2 tetrahedra that share corners with two equivalent O(1)Cr6 octahedra, corners with four equivalent O(3)Cr5 square pyramids, corners with two equivalent O(4)Mg2Cr2 tetrahedra, corners with eight equivalent O(2)Mg2Cr3 trigonal bipyramids, and edges with two equivalent O(2)Mg2Cr3 trigonal bipyramids. The corner-sharing octahedral tilt angles are 7°. is represented by the CIF file [CIF]
data_MgCr4O6
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.283
_cell_length_b   5.283
_cell_length_c   15.243
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   147.032
_symmetry_Int_Tables_number   1
_cell_volume   231.544
_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  0.341  0.659  0.750  1.0
  Mg  Mg1  1  0.659  0.341  0.250  1.0
  Cr  Cr2  1  0.136  0.864  0.046  1.0
  Cr  Cr3  1  0.595  0.405  0.636  1.0
  Cr  Cr4  1  0.864  0.136  0.954  1.0
  Cr  Cr5  1  0.405  0.595  0.364  1.0
  Cr  Cr6  1  0.136  0.864  0.454  1.0
  Cr  Cr7  1  0.864  0.136  0.546  1.0
  Cr  Cr8  1  0.405  0.595  0.136  1.0
  Cr  Cr9  1  0.595  0.405  0.864  1.0
  O  O10  1  0.500  0.500  0.500  1.0
  O  O11  1  0.500  0.500  0.000  1.0
  O  O12  1  0.958  0.042  0.838  1.0
  O  O13  1  0.042  0.958  0.162  1.0
  O  O14  1  0.042  0.958  0.338  1.0
  O  O15  1  0.958  0.042  0.662  1.0
  O  O16  1  0.213  0.787  0.918  1.0
  O  O17  1  0.787  0.213  0.082  1.0
  O  O18  1  0.787  0.213  0.418  1.0
  O  O19  1  0.213  0.787  0.582  1.0
  O  O20  1  0.699  0.301  0.750  1.0
  O  O21  1  0.301  0.699  0.250  1.0
[/CIF]
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The structure described by MgCr4O6 crystallizes in the orthorhombic Cmcm space group. Mg(1) is bonded in a 6-coordinate geometry to two equivalent O(4) and four equivalent O(2) atoms. There are two inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(2), two equivalent O(1), and three equivalent O(3) atoms to form a mixture of edge and corner-sharing CrO6 octahedra. The corner-sharing octahedral tilt angles range from 0-11°. In the second Cr site, Cr(2) is bonded to one O(1), one O(4), two equivalent O(2), and two equivalent O(3) atoms to form a mixture of edge and corner-sharing CrO6 octahedra. The corner-sharing octahedral tilt angles range from 0-63°. There are four inequivalent O sites. In the first O site, O(1) is bonded to two equivalent Cr(2) and four equivalent Cr(1) atoms to form OCr6 octahedra that share corners with four equivalent O(3)Cr5 square pyramids, corners with two equivalent O(4)Mg2Cr2 tetrahedra, edges with two equivalent O(1)Cr6 octahedra, edges with six equivalent O(3)Cr5 square pyramids, and edges with four equivalent O(2)Mg2Cr3 trigonal bipyramids. In the second O site, O(2) is bonded to two equivalent Mg(1), one Cr(1), and two equivalent Cr(2) atoms to form distorted OMg2Cr3 trigonal bipyramids that share corners with five equivalent O(3)Cr5 square pyramids, corners with four equivalent O(4)Mg2Cr2 tetrahedra, corners with two equivalent O(2)Mg2Cr3 trigonal bipyramids, edges with two equivalent O(1)Cr6 octahedra,  an edgeedge with one O(3)Cr5 square pyramid,  an edgeedge with one O(4)Mg2Cr2 tetrahedra, and edges with three equivalent O(2)Mg2Cr3 trigonal bipyramids. In the third O site, O(3) is bonded to two equivalent Cr(2) and three equivalent Cr(1) atoms to form OCr5 square pyramids that share corners with two equivalent O(1)Cr6 octahedra, corners with two equivalent O(4)Mg2Cr2 tetrahedra, corners with five equivalent O(2)Mg2Cr3 trigonal bipyramids, edges with three equivalent O(1)Cr6 octahedra, edges with four equivalent O(3)Cr5 square pyramids, and  an edgeedge with one O(2)Mg2Cr3 trigonal bipyramid. The corner-sharing octahedral tilt angles are 5°. In the fourth O site, O(4) is bonded to two equivalent Mg(1) and two equivalent Cr(2) atoms to form OMg2Cr2 tetrahedra that share corners with two equivalent O(1)Cr6 octahedra, corners with four equivalent O(3)Cr5 square pyramids, corners with two equivalent O(4)Mg2Cr2 tetrahedra, corners with eight equivalent O(2)Mg2Cr3 trigonal bipyramids, and edges with two equivalent O(2)Mg2Cr3 trigonal bipyramids. The corner-sharing octahedral tilt angles are 7°. is represented by the CIF file [CIF]
data_MgCr4O6
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.283
_cell_length_b   5.283
_cell_length_c   15.243
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   147.032
_symmetry_Int_Tables_number   1
_cell_volume   231.544
_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  0.341  0.659  0.750  1.0
  Mg  Mg1  1  0.659  0.341  0.250  1.0
  Cr  Cr2  1  0.136  0.864  0.046  1.0
  Cr  Cr3  1  0.595  0.405  0.636  1.0
  Cr  Cr4  1  0.864  0.136  0.954  1.0
  Cr  Cr5  1  0.405  0.595  0.364  1.0
  Cr  Cr6  1  0.136  0.864  0.454  1.0
  Cr  Cr7  1  0.864  0.136  0.546  1.0
  Cr  Cr8  1  0.405  0.595  0.136  1.0
  Cr  Cr9  1  0.595  0.405  0.864  1.0
  O  O10  1  0.500  0.500  0.500  1.0
  O  O11  1  0.500  0.500  0.000  1.0
  O  O12  1  0.958  0.042  0.838  1.0
  O  O13  1  0.042  0.958  0.162  1.0
  O  O14  1  0.042  0.958  0.338  1.0
  O  O15  1  0.958  0.042  0.662  1.0
  O  O16  1  0.213  0.787  0.918  1.0
  O  O17  1  0.787  0.213  0.082  1.0
  O  O18  1  0.787  0.213  0.418  1.0
  O  O19  1  0.213  0.787  0.582  1.0
  O  O20  1  0.699  0.301  0.750  1.0
  O  O21  1  0.301  0.699  0.250  1.0
[/CIF]
.