The material described by MgCr4O8 crystallizes in the orthorhombic Imm2 space group. Mg(1) is bonded to two equivalent O(2) and two equivalent O(4) atoms to form distorted MgO4 trigonal pyramids that share corners with six equivalent Cr(3)O6 octahedra, corners with two equivalent Cr(1)O4 tetrahedra, and  an edgeedge with one Cr(2)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 61-79°. There are three inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to two equivalent O(3) and two equivalent O(4) atoms to form CrO4 tetrahedra that share corners with six equivalent Cr(3)O6 octahedra and corners with two equivalent Mg(1)O4 trigonal pyramids. The corner-sharing octahedral tilt angles range from 42-60°. In the second Cr site, Cr(2) is bonded to two equivalent O(1) and two equivalent O(2) atoms to form CrO4 tetrahedra that share corners with six equivalent Cr(3)O6 octahedra and  an edgeedge with one Mg(1)O4 trigonal pyramid. The corner-sharing octahedral tilt angles range from 55-61°. In the third Cr site, Cr(3) is bonded to one O(1), one O(4), two equivalent O(2), and two equivalent O(3) atoms to form CrO6 octahedra that share corners with three equivalent Cr(1)O4 tetrahedra, corners with three equivalent Cr(2)O4 tetrahedra, corners with three equivalent Mg(1)O4 trigonal pyramids, and edges with two equivalent Cr(3)O6 octahedra. There are four inequivalent O sites. In the first O site, O(1) is bonded in a bent 120 degrees geometry to one Cr(2) and one Cr(3) atom. In the second O site, O(2) is bonded to one Mg(1), one Cr(2), and two equivalent Cr(3) atoms to form distorted edge-sharing OMgCr3 tetrahedra. In the third O site, O(3) is bonded in a distorted trigonal planar geometry to one Cr(1) and two equivalent Cr(3) atoms. In the fourth O site, O(4) is bonded in a distorted trigonal planar geometry to one Mg(1), one Cr(1), 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   5.902
_cell_length_b   5.904
_cell_length_c   6.316
_cell_angle_alpha   57.678
_cell_angle_beta   57.669
_cell_angle_gamma   57.169
_symmetry_Int_Tables_number   1
_cell_volume   146.669
_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  0.922  0.923  0.578  1.0
  Cr  Cr1  1  0.004  0.004  0.996  1.0
  Cr  Cr2  1  0.266  0.265  0.235  1.0
  Cr  Cr3  1  0.611  0.611  0.148  1.0
  Cr  Cr4  1  0.610  0.610  0.631  1.0
  O  O5  1  0.374  0.375  0.363  1.0
  O  O6  1  0.354  0.856  0.395  1.0
  O  O7  1  0.374  0.374  0.889  1.0
  O  O8  1  0.856  0.354  0.395  1.0
  O  O9  1  0.395  0.847  0.879  1.0
  O  O10  1  0.847  0.395  0.879  1.0
  O  O11  1  0.855  0.855  0.355  1.0
  O  O12  1  0.855  0.856  0.935  1.0
[/CIF]
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The material described by MgCr4O8 crystallizes in the orthorhombic Imm2 space group. Mg(1) is bonded to two equivalent O(2) and two equivalent O(4) atoms to form distorted MgO4 trigonal pyramids that share corners with six equivalent Cr(3)O6 octahedra, corners with two equivalent Cr(1)O4 tetrahedra, and  an edgeedge with one Cr(2)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 61-79°. There are three inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to two equivalent O(3) and two equivalent O(4) atoms to form CrO4 tetrahedra that share corners with six equivalent Cr(3)O6 octahedra and corners with two equivalent Mg(1)O4 trigonal pyramids. The corner-sharing octahedral tilt angles range from 42-60°. In the second Cr site, Cr(2) is bonded to two equivalent O(1) and two equivalent O(2) atoms to form CrO4 tetrahedra that share corners with six equivalent Cr(3)O6 octahedra and  an edgeedge with one Mg(1)O4 trigonal pyramid. The corner-sharing octahedral tilt angles range from 55-61°. In the third Cr site, Cr(3) is bonded to one O(1), one O(4), two equivalent O(2), and two equivalent O(3) atoms to form CrO6 octahedra that share corners with three equivalent Cr(1)O4 tetrahedra, corners with three equivalent Cr(2)O4 tetrahedra, corners with three equivalent Mg(1)O4 trigonal pyramids, and edges with two equivalent Cr(3)O6 octahedra. There are four inequivalent O sites. In the first O site, O(1) is bonded in a bent 120 degrees geometry to one Cr(2) and one Cr(3) atom. In the second O site, O(2) is bonded to one Mg(1), one Cr(2), and two equivalent Cr(3) atoms to form distorted edge-sharing OMgCr3 tetrahedra. In the third O site, O(3) is bonded in a distorted trigonal planar geometry to one Cr(1) and two equivalent Cr(3) atoms. In the fourth O site, O(4) is bonded in a distorted trigonal planar geometry to one Mg(1), one Cr(1), 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   5.902
_cell_length_b   5.904
_cell_length_c   6.316
_cell_angle_alpha   57.678
_cell_angle_beta   57.669
_cell_angle_gamma   57.169
_symmetry_Int_Tables_number   1
_cell_volume   146.669
_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  0.922  0.923  0.578  1.0
  Cr  Cr1  1  0.004  0.004  0.996  1.0
  Cr  Cr2  1  0.266  0.265  0.235  1.0
  Cr  Cr3  1  0.611  0.611  0.148  1.0
  Cr  Cr4  1  0.610  0.610  0.631  1.0
  O  O5  1  0.374  0.375  0.363  1.0
  O  O6  1  0.354  0.856  0.395  1.0
  O  O7  1  0.374  0.374  0.889  1.0
  O  O8  1  0.856  0.354  0.395  1.0
  O  O9  1  0.395  0.847  0.879  1.0
  O  O10  1  0.847  0.395  0.879  1.0
  O  O11  1  0.855  0.855  0.355  1.0
  O  O12  1  0.855  0.856  0.935  1.0
[/CIF]
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