The structure described by MgCr4O8 crystallizes in the monoclinic Cm space group. Mg(1) is bonded to one O(4), one O(5), and two equivalent O(6) atoms to form MgO4 tetrahedra that share corners with three equivalent Cr(2)O6 octahedra and corners with six equivalent Cr(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-57°. There are three inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(2), one O(3), and two equivalent O(1) atoms to form corner-sharing CrO4 tetrahedra. The corner-sharing octahedral tilt angles range from 56-58°. In the second Cr site, Cr(2) is bonded to one O(3), one O(4), two equivalent O(1), and two equivalent O(6) atoms to form CrO6 octahedra that share corners with three equivalent Mg(1)O4 tetrahedra, corners with three equivalent Cr(1)O4 tetrahedra, and edges with four equivalent Cr(3)O6 octahedra. In the third Cr site, Cr(3) is bonded to one O(1), one O(2), one O(3), one O(4), one O(5), and one O(6) atom 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 Cr(2)O6 octahedra, and edges with two equivalent Cr(3)O6 octahedra. There are six inequivalent O sites. In the first O site, O(1) is bonded in a distorted trigonal planar geometry to one Cr(1), one Cr(2), and one Cr(3) atom. In the second O site, O(2) is bonded in a distorted trigonal planar geometry to one Cr(1) and two equivalent Cr(3) atoms. In the third O site, O(3) is bonded in a distorted trigonal pyramidal geometry to one Cr(1), one Cr(2), and two equivalent Cr(3) atoms. In the fourth O site, O(4) is bonded in a distorted rectangular see-saw-like geometry to one Mg(1), one Cr(2), and two equivalent Cr(3) atoms. In the fifth O site, O(5) is bonded in a trigonal planar geometry to one Mg(1) and two equivalent Cr(3) atoms. In the sixth O site, O(6) is bonded in a trigonal planar geometry to one Mg(1), one Cr(2), and one Cr(3) atom. is represented by the CIF card [CIF]
data_MgCr4O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.867
_cell_length_b   5.970
_cell_length_c   5.970
_cell_angle_alpha   59.991
_cell_angle_beta   59.398
_cell_angle_gamma   59.367
_symmetry_Int_Tables_number   1
_cell_volume   146.473
_cell_formula_units_Z   1
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  0.989  0.002  0.004  1.0
  Cr  Cr1  1  0.268  0.244  0.244  1.0
  Cr  Cr2  1  0.632  0.112  0.628  1.0
  Cr  Cr3  1  0.632  0.627  0.113  1.0
  Cr  Cr4  1  0.633  0.627  0.628  1.0
  O  O5  1  0.396  0.367  0.367  1.0
  O  O6  1  0.396  0.368  0.869  1.0
  O  O7  1  0.396  0.869  0.368  1.0
  O  O8  1  0.863  0.378  0.379  1.0
  O  O9  1  0.404  0.865  0.866  1.0
  O  O10  1  0.834  0.405  0.880  1.0
  O  O11  1  0.834  0.879  0.406  1.0
  O  O12  1  0.834  0.879  0.881  1.0
[/CIF]
.
The structure described by MgCr4O8 crystallizes in the monoclinic Cm space group. Mg(1) is bonded to one O(4), one O(5), and two equivalent O(6) atoms to form MgO4 tetrahedra that share corners with three equivalent Cr(2)O6 octahedra and corners with six equivalent Cr(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 55-57°. There are three inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(2), one O(3), and two equivalent O(1) atoms to form corner-sharing CrO4 tetrahedra. The corner-sharing octahedral tilt angles range from 56-58°. In the second Cr site, Cr(2) is bonded to one O(3), one O(4), two equivalent O(1), and two equivalent O(6) atoms to form CrO6 octahedra that share corners with three equivalent Mg(1)O4 tetrahedra, corners with three equivalent Cr(1)O4 tetrahedra, and edges with four equivalent Cr(3)O6 octahedra. In the third Cr site, Cr(3) is bonded to one O(1), one O(2), one O(3), one O(4), one O(5), and one O(6) atom 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 Cr(2)O6 octahedra, and edges with two equivalent Cr(3)O6 octahedra. There are six inequivalent O sites. In the first O site, O(1) is bonded in a distorted trigonal planar geometry to one Cr(1), one Cr(2), and one Cr(3) atom. In the second O site, O(2) is bonded in a distorted trigonal planar geometry to one Cr(1) and two equivalent Cr(3) atoms. In the third O site, O(3) is bonded in a distorted trigonal pyramidal geometry to one Cr(1), one Cr(2), and two equivalent Cr(3) atoms. In the fourth O site, O(4) is bonded in a distorted rectangular see-saw-like geometry to one Mg(1), one Cr(2), and two equivalent Cr(3) atoms. In the fifth O site, O(5) is bonded in a trigonal planar geometry to one Mg(1) and two equivalent Cr(3) atoms. In the sixth O site, O(6) is bonded in a trigonal planar geometry to one Mg(1), one Cr(2), and one Cr(3) atom. is represented by the CIF card [CIF]
data_MgCr4O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.867
_cell_length_b   5.970
_cell_length_c   5.970
_cell_angle_alpha   59.991
_cell_angle_beta   59.398
_cell_angle_gamma   59.367
_symmetry_Int_Tables_number   1
_cell_volume   146.473
_cell_formula_units_Z   1
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  0.989  0.002  0.004  1.0
  Cr  Cr1  1  0.268  0.244  0.244  1.0
  Cr  Cr2  1  0.632  0.112  0.628  1.0
  Cr  Cr3  1  0.632  0.627  0.113  1.0
  Cr  Cr4  1  0.633  0.627  0.628  1.0
  O  O5  1  0.396  0.367  0.367  1.0
  O  O6  1  0.396  0.368  0.869  1.0
  O  O7  1  0.396  0.869  0.368  1.0
  O  O8  1  0.863  0.378  0.379  1.0
  O  O9  1  0.404  0.865  0.866  1.0
  O  O10  1  0.834  0.405  0.880  1.0
  O  O11  1  0.834  0.879  0.406  1.0
  O  O12  1  0.834  0.879  0.881  1.0
[/CIF]
.