The crystal structure described by MgCr4O8 is beta indium sulfide-derived structured and crystallizes in the monoclinic Cm space group. Mg(1) is bonded to one O(2), one O(3), and two equivalent O(1) atoms to form MgO4 tetrahedra that share corners with three equivalent Cr(1)O6 octahedra, 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 58-61°. There are three inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(3), one O(5), two equivalent O(1), and two equivalent O(6) atoms to form CrO6 octahedra that share corners with three equivalent Mg(1)O4 tetrahedra, edges with two equivalent Cr(2)O6 octahedra, and edges with four equivalent Cr(3)O6 octahedra. In the second Cr site, Cr(2) is bonded to one O(2), 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, edges with two equivalent Cr(1)O6 octahedra, 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, edges with two equivalent Cr(1)O6 octahedra, 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 to one Mg(1), one Cr(1), one Cr(2), and one Cr(3) atom to form a mixture of distorted edge and corner-sharing OMgCr3 trigonal pyramids. In the second O site, O(2) is bonded to one Mg(1), one Cr(2), and two equivalent Cr(3) atoms to form a mixture of distorted edge and corner-sharing OMgCr3 tetrahedra. In the third O site, O(3) is bonded to one Mg(1), one Cr(1), and two equivalent Cr(3) atoms to form a mixture of distorted edge and corner-sharing OMgCr3 trigonal pyramids. In the fourth O site, O(4) is bonded in a distorted trigonal non-coplanar geometry to one Cr(2) and two equivalent Cr(3) atoms. In the fifth O site, O(5) is bonded in a distorted trigonal non-coplanar geometry to one Cr(1) and two equivalent Cr(3) atoms. In the sixth O site, O(6) is bonded in a distorted T-shaped geometry to one Cr(1), one Cr(2), and one Cr(3) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_MgCr4O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.070
_cell_length_b   5.957
_cell_length_c   5.954
_cell_angle_alpha   59.729
_cell_angle_beta   59.389
_cell_angle_gamma   59.325
_symmetry_Int_Tables_number   1
_cell_volume   150.425
_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  0.125  0.125  0.126  1.0
  Cr  Cr1  1  0.506  0.989  0.498  1.0
  Cr  Cr2  1  0.506  0.500  0.987  1.0
  Cr  Cr3  1  0.001  0.501  0.501  1.0
  Cr  Cr4  1  0.497  0.501  0.502  1.0
  O  O5  1  0.271  0.258  0.257  1.0
  O  O6  1  0.714  0.258  0.257  1.0
  O  O7  1  0.266  0.711  0.256  1.0
  O  O8  1  0.266  0.256  0.712  1.0
  O  O9  1  0.727  0.305  0.741  1.0
  O  O10  1  0.726  0.740  0.307  1.0
  O  O11  1  0.297  0.741  0.740  1.0
  O  O12  1  0.722  0.741  0.740  1.0
[/CIF]
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The crystal structure described by MgCr4O8 is beta indium sulfide-derived structured and crystallizes in the monoclinic Cm space group. Mg(1) is bonded to one O(2), one O(3), and two equivalent O(1) atoms to form MgO4 tetrahedra that share corners with three equivalent Cr(1)O6 octahedra, 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 58-61°. There are three inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(3), one O(5), two equivalent O(1), and two equivalent O(6) atoms to form CrO6 octahedra that share corners with three equivalent Mg(1)O4 tetrahedra, edges with two equivalent Cr(2)O6 octahedra, and edges with four equivalent Cr(3)O6 octahedra. In the second Cr site, Cr(2) is bonded to one O(2), 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, edges with two equivalent Cr(1)O6 octahedra, 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, edges with two equivalent Cr(1)O6 octahedra, 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 to one Mg(1), one Cr(1), one Cr(2), and one Cr(3) atom to form a mixture of distorted edge and corner-sharing OMgCr3 trigonal pyramids. In the second O site, O(2) is bonded to one Mg(1), one Cr(2), and two equivalent Cr(3) atoms to form a mixture of distorted edge and corner-sharing OMgCr3 tetrahedra. In the third O site, O(3) is bonded to one Mg(1), one Cr(1), and two equivalent Cr(3) atoms to form a mixture of distorted edge and corner-sharing OMgCr3 trigonal pyramids. In the fourth O site, O(4) is bonded in a distorted trigonal non-coplanar geometry to one Cr(2) and two equivalent Cr(3) atoms. In the fifth O site, O(5) is bonded in a distorted trigonal non-coplanar geometry to one Cr(1) and two equivalent Cr(3) atoms. In the sixth O site, O(6) is bonded in a distorted T-shaped geometry to one Cr(1), one Cr(2), and one Cr(3) atom. is represented by the Crystallographic Information File (CIF) [CIF]
data_MgCr4O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.070
_cell_length_b   5.957
_cell_length_c   5.954
_cell_angle_alpha   59.729
_cell_angle_beta   59.389
_cell_angle_gamma   59.325
_symmetry_Int_Tables_number   1
_cell_volume   150.425
_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  0.125  0.125  0.126  1.0
  Cr  Cr1  1  0.506  0.989  0.498  1.0
  Cr  Cr2  1  0.506  0.500  0.987  1.0
  Cr  Cr3  1  0.001  0.501  0.501  1.0
  Cr  Cr4  1  0.497  0.501  0.502  1.0
  O  O5  1  0.271  0.258  0.257  1.0
  O  O6  1  0.714  0.258  0.257  1.0
  O  O7  1  0.266  0.711  0.256  1.0
  O  O8  1  0.266  0.256  0.712  1.0
  O  O9  1  0.727  0.305  0.741  1.0
  O  O10  1  0.726  0.740  0.307  1.0
  O  O11  1  0.297  0.741  0.740  1.0
  O  O12  1  0.722  0.741  0.740  1.0
[/CIF]
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