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(6), two equivalent O(1), and two equivalent O(5) atoms to form MgO6 octahedra that share corners with three equivalent Cr(1)O4 tetrahedra, edges with two equivalent Cr(3)O6 octahedra, and edges with four equivalent Cr(2)O6 octahedra. 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 CrO4 tetrahedra that share corners with three equivalent Mg(1)O6 octahedra, corners with three equivalent Cr(3)O6 octahedra, and corners with six equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-59°. In the second Cr site, Cr(2) 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 Cr(1)O4 tetrahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Cr(2)O6 octahedra, and edges with two equivalent Cr(3)O6 octahedra. In the third Cr site, Cr(3) is bonded to one O(3), one O(4), two equivalent O(1), and two equivalent O(5) atoms to form CrO6 octahedra that share corners with three equivalent Cr(1)O4 tetrahedra, edges with two equivalent Mg(1)O6 octahedra, and edges with four equivalent Cr(2)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 distorted OMgCr3 trigonal pyramids that share  a cornercorner with one O(3)Cr4 trigonal pyramid,  a cornercorner with one O(1)MgCr3 trigonal pyramid,  an edgeedge with one O(3)Cr4 trigonal pyramid, and  an edgeedge with one O(1)MgCr3 trigonal pyramid. In the second O site, O(2) is bonded in a distorted rectangular see-saw-like geometry to one Mg(1), one Cr(1), and two equivalent Cr(2) atoms. In the third O site, O(3) is bonded to one Cr(1), one Cr(3), and two equivalent Cr(2) atoms to form a mixture of distorted corner and edge-sharing OCr4 trigonal pyramids. In the fourth O site, O(4) is bonded in a distorted T-shaped geometry to one Cr(3) and two equivalent Cr(2) atoms. In the fifth O site, O(5) is bonded in a distorted T-shaped geometry to one Mg(1), one Cr(2), and one Cr(3) atom. In the sixth O site, O(6) is bonded in a distorted T-shaped geometry to one Mg(1) and two equivalent Cr(2) atoms. is represented by the Crystallographic Information File (CIF) [CIF]
data_MgCr4O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.965
_cell_length_b   5.922
_cell_length_c   5.935
_cell_angle_alpha   60.072
_cell_angle_beta   60.010
_cell_angle_gamma   60.240
_symmetry_Int_Tables_number   1
_cell_volume   148.598
_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  0.123  0.629  0.620  1.0
  Cr  Cr1  1  0.261  0.248  0.243  1.0
  Cr  Cr2  1  0.632  0.112  0.625  1.0
  Cr  Cr3  1  0.645  0.630  0.095  1.0
  Cr  Cr4  1  0.632  0.631  0.625  1.0
  O  O5  1  0.389  0.377  0.375  1.0
  O  O6  1  0.383  0.379  0.859  1.0
  O  O7  1  0.389  0.858  0.375  1.0
  O  O8  1  0.869  0.378  0.375  1.0
  O  O9  1  0.420  0.858  0.864  1.0
  O  O10  1  0.838  0.415  0.881  1.0
  O  O11  1  0.850  0.865  0.419  1.0
  O  O12  1  0.838  0.865  0.881  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(6), two equivalent O(1), and two equivalent O(5) atoms to form MgO6 octahedra that share corners with three equivalent Cr(1)O4 tetrahedra, edges with two equivalent Cr(3)O6 octahedra, and edges with four equivalent Cr(2)O6 octahedra. 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 CrO4 tetrahedra that share corners with three equivalent Mg(1)O6 octahedra, corners with three equivalent Cr(3)O6 octahedra, and corners with six equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-59°. In the second Cr site, Cr(2) 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 Cr(1)O4 tetrahedra, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Cr(2)O6 octahedra, and edges with two equivalent Cr(3)O6 octahedra. In the third Cr site, Cr(3) is bonded to one O(3), one O(4), two equivalent O(1), and two equivalent O(5) atoms to form CrO6 octahedra that share corners with three equivalent Cr(1)O4 tetrahedra, edges with two equivalent Mg(1)O6 octahedra, and edges with four equivalent Cr(2)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 distorted OMgCr3 trigonal pyramids that share  a cornercorner with one O(3)Cr4 trigonal pyramid,  a cornercorner with one O(1)MgCr3 trigonal pyramid,  an edgeedge with one O(3)Cr4 trigonal pyramid, and  an edgeedge with one O(1)MgCr3 trigonal pyramid. In the second O site, O(2) is bonded in a distorted rectangular see-saw-like geometry to one Mg(1), one Cr(1), and two equivalent Cr(2) atoms. In the third O site, O(3) is bonded to one Cr(1), one Cr(3), and two equivalent Cr(2) atoms to form a mixture of distorted corner and edge-sharing OCr4 trigonal pyramids. In the fourth O site, O(4) is bonded in a distorted T-shaped geometry to one Cr(3) and two equivalent Cr(2) atoms. In the fifth O site, O(5) is bonded in a distorted T-shaped geometry to one Mg(1), one Cr(2), and one Cr(3) atom. In the sixth O site, O(6) is bonded in a distorted T-shaped geometry to one Mg(1) and two equivalent Cr(2) atoms. is represented by the Crystallographic Information File (CIF) [CIF]
data_MgCr4O8
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   5.965
_cell_length_b   5.922
_cell_length_c   5.935
_cell_angle_alpha   60.072
_cell_angle_beta   60.010
_cell_angle_gamma   60.240
_symmetry_Int_Tables_number   1
_cell_volume   148.598
_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  0.123  0.629  0.620  1.0
  Cr  Cr1  1  0.261  0.248  0.243  1.0
  Cr  Cr2  1  0.632  0.112  0.625  1.0
  Cr  Cr3  1  0.645  0.630  0.095  1.0
  Cr  Cr4  1  0.632  0.631  0.625  1.0
  O  O5  1  0.389  0.377  0.375  1.0
  O  O6  1  0.383  0.379  0.859  1.0
  O  O7  1  0.389  0.858  0.375  1.0
  O  O8  1  0.869  0.378  0.375  1.0
  O  O9  1  0.420  0.858  0.864  1.0
  O  O10  1  0.838  0.415  0.881  1.0
  O  O11  1  0.850  0.865  0.419  1.0
  O  O12  1  0.838  0.865  0.881  1.0
[/CIF]
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