The structure described by MgCr8Fe3O16 is Spinel-derived structured and crystallizes in the tetragonal P-4m2 space group. Mg(1) is bonded to four equivalent O(2) atoms to form MgO4 tetrahedra that share corners with four equivalent Cr(2)O6 octahedra and corners with eight equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-59°. There are two inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(1), two equivalent O(2), and three equivalent O(4) atoms to form CrO6 octahedra that share  a cornercorner with one Fe(1)O4 tetrahedra, corners with two equivalent Mg(1)O4 tetrahedra, corners with three equivalent Fe(2)O4 tetrahedra, edges with two equivalent Cr(2)O6 octahedra, and edges with four equivalent Cr(1)O6 octahedra. In the second Cr site, Cr(2) is bonded to one O(2), two equivalent O(1), and three equivalent O(3) atoms to form CrO6 octahedra that share  a cornercorner with one Mg(1)O4 tetrahedra, corners with two equivalent Fe(1)O4 tetrahedra, corners with three equivalent Fe(2)O4 tetrahedra, edges with two equivalent Cr(1)O6 octahedra, and edges with four equivalent Cr(2)O6 octahedra. There are two inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to four equivalent O(1) atoms to form FeO4 tetrahedra that share corners with four equivalent Cr(1)O6 octahedra and corners with eight equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles are 59°. In the second Fe site, Fe(2) is bonded to two equivalent O(3) and two equivalent O(4) atoms to form FeO4 tetrahedra that share corners with six equivalent Cr(1)O6 octahedra and corners with six equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 59-60°. There are four inequivalent O sites. In the first O site, O(1) is bonded to one Cr(1), two equivalent Cr(2), and one Fe(1) atom to form distorted OCr3Fe trigonal pyramids that share corners with three equivalent O(1)Cr3Fe trigonal pyramids, corners with three equivalent O(4)Cr3Fe trigonal pyramids, corners with six equivalent O(3)Cr3Fe trigonal pyramids,  an edgeedge with one O(1)Cr3Fe trigonal pyramid, and edges with two equivalent O(2)MgCr3 trigonal pyramids. In the second O site, O(2) is bonded to one Mg(1), one Cr(2), and two equivalent Cr(1) atoms to form distorted OMgCr3 trigonal pyramids that share corners with three equivalent O(3)Cr3Fe trigonal pyramids, corners with three equivalent O(2)MgCr3 trigonal pyramids, corners with six equivalent O(4)Cr3Fe trigonal pyramids,  an edgeedge with one O(2)MgCr3 trigonal pyramid, and edges with two equivalent O(1)Cr3Fe trigonal pyramids. In the third O site, O(3) is bonded to three equivalent Cr(2) and one Fe(2) atom to form distorted OCr3Fe trigonal pyramids that share  a cornercorner with one O(3)Cr3Fe trigonal pyramid, corners with two equivalent O(4)Cr3Fe trigonal pyramids, corners with three equivalent O(2)MgCr3 trigonal pyramids, corners with six equivalent O(1)Cr3Fe trigonal pyramids, and edges with three equivalent O(3)Cr3Fe trigonal pyramids. In the fourth O site, O(4) is bonded to three equivalent Cr(1) and one Fe(2) atom to form distorted OCr3Fe trigonal pyramids that share  a cornercorner with one O(4)Cr3Fe trigonal pyramid, corners with two equivalent O(3)Cr3Fe trigonal pyramids, corners with three equivalent O(1)Cr3Fe trigonal pyramids, corners with six equivalent O(2)MgCr3 trigonal pyramids, and edges with three equivalent O(4)Cr3Fe trigonal pyramids. is represented by the CIF card [CIF]
data_MgCr8Fe3O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.053
_cell_length_b   6.053
_cell_length_c   8.510
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   311.772
_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  0.500  0.500  0.500  1.0
  Cr  Cr1  1  0.251  0.000  0.375  1.0
  Cr  Cr2  1  0.750  0.500  0.875  1.0
  Cr  Cr3  1  0.749  0.000  0.375  1.0
  Cr  Cr4  1  0.250  0.500  0.875  1.0
  Cr  Cr5  1  0.500  0.250  0.125  1.0
  Cr  Cr6  1  0.000  0.749  0.625  1.0
  Cr  Cr7  1  0.500  0.750  0.125  1.0
  Cr  Cr8  1  0.000  0.251  0.625  1.0
  Fe  Fe9  1  0.000  0.000  0.000  1.0
  Fe  Fe10  1  0.500  0.000  0.750  1.0
  Fe  Fe11  1  0.000  0.500  0.250  1.0
  O  O12  1  0.724  0.000  0.138  1.0
  O  O13  1  0.227  0.500  0.636  1.0
  O  O14  1  0.276  0.000  0.138  1.0
  O  O15  1  0.773  0.500  0.636  1.0
  O  O16  1  0.500  0.773  0.364  1.0
  O  O17  1  0.000  0.276  0.862  1.0
  O  O18  1  0.500  0.227  0.364  1.0
  O  O19  1  0.000  0.724  0.862  1.0
  O  O20  1  0.277  0.500  0.113  1.0
  O  O21  1  0.777  0.000  0.613  1.0
  O  O22  1  0.723  0.500  0.113  1.0
  O  O23  1  0.223  0.000  0.613  1.0
  O  O24  1  0.500  0.723  0.887  1.0
  O  O25  1  0.000  0.223  0.387  1.0
  O  O26  1  0.500  0.277  0.887  1.0
  O  O27  1  0.000  0.777  0.387  1.0
[/CIF]
.
The structure described by MgCr8Fe3O16 is Spinel-derived structured and crystallizes in the tetragonal P-4m2 space group. Mg(1) is bonded to four equivalent O(2) atoms to form MgO4 tetrahedra that share corners with four equivalent Cr(2)O6 octahedra and corners with eight equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-59°. There are two inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(1), two equivalent O(2), and three equivalent O(4) atoms to form CrO6 octahedra that share  a cornercorner with one Fe(1)O4 tetrahedra, corners with two equivalent Mg(1)O4 tetrahedra, corners with three equivalent Fe(2)O4 tetrahedra, edges with two equivalent Cr(2)O6 octahedra, and edges with four equivalent Cr(1)O6 octahedra. In the second Cr site, Cr(2) is bonded to one O(2), two equivalent O(1), and three equivalent O(3) atoms to form CrO6 octahedra that share  a cornercorner with one Mg(1)O4 tetrahedra, corners with two equivalent Fe(1)O4 tetrahedra, corners with three equivalent Fe(2)O4 tetrahedra, edges with two equivalent Cr(1)O6 octahedra, and edges with four equivalent Cr(2)O6 octahedra. There are two inequivalent Fe sites. In the first Fe site, Fe(1) is bonded to four equivalent O(1) atoms to form FeO4 tetrahedra that share corners with four equivalent Cr(1)O6 octahedra and corners with eight equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles are 59°. In the second Fe site, Fe(2) is bonded to two equivalent O(3) and two equivalent O(4) atoms to form FeO4 tetrahedra that share corners with six equivalent Cr(1)O6 octahedra and corners with six equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 59-60°. There are four inequivalent O sites. In the first O site, O(1) is bonded to one Cr(1), two equivalent Cr(2), and one Fe(1) atom to form distorted OCr3Fe trigonal pyramids that share corners with three equivalent O(1)Cr3Fe trigonal pyramids, corners with three equivalent O(4)Cr3Fe trigonal pyramids, corners with six equivalent O(3)Cr3Fe trigonal pyramids,  an edgeedge with one O(1)Cr3Fe trigonal pyramid, and edges with two equivalent O(2)MgCr3 trigonal pyramids. In the second O site, O(2) is bonded to one Mg(1), one Cr(2), and two equivalent Cr(1) atoms to form distorted OMgCr3 trigonal pyramids that share corners with three equivalent O(3)Cr3Fe trigonal pyramids, corners with three equivalent O(2)MgCr3 trigonal pyramids, corners with six equivalent O(4)Cr3Fe trigonal pyramids,  an edgeedge with one O(2)MgCr3 trigonal pyramid, and edges with two equivalent O(1)Cr3Fe trigonal pyramids. In the third O site, O(3) is bonded to three equivalent Cr(2) and one Fe(2) atom to form distorted OCr3Fe trigonal pyramids that share  a cornercorner with one O(3)Cr3Fe trigonal pyramid, corners with two equivalent O(4)Cr3Fe trigonal pyramids, corners with three equivalent O(2)MgCr3 trigonal pyramids, corners with six equivalent O(1)Cr3Fe trigonal pyramids, and edges with three equivalent O(3)Cr3Fe trigonal pyramids. In the fourth O site, O(4) is bonded to three equivalent Cr(1) and one Fe(2) atom to form distorted OCr3Fe trigonal pyramids that share  a cornercorner with one O(4)Cr3Fe trigonal pyramid, corners with two equivalent O(3)Cr3Fe trigonal pyramids, corners with three equivalent O(1)Cr3Fe trigonal pyramids, corners with six equivalent O(2)MgCr3 trigonal pyramids, and edges with three equivalent O(4)Cr3Fe trigonal pyramids. is represented by the CIF card [CIF]
data_MgCr8Fe3O16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   6.053
_cell_length_b   6.053
_cell_length_c   8.510
_cell_angle_alpha   90.000
_cell_angle_beta   90.000
_cell_angle_gamma   90.000
_symmetry_Int_Tables_number   1
_cell_volume   311.772
_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  0.500  0.500  0.500  1.0
  Cr  Cr1  1  0.251  0.000  0.375  1.0
  Cr  Cr2  1  0.750  0.500  0.875  1.0
  Cr  Cr3  1  0.749  0.000  0.375  1.0
  Cr  Cr4  1  0.250  0.500  0.875  1.0
  Cr  Cr5  1  0.500  0.250  0.125  1.0
  Cr  Cr6  1  0.000  0.749  0.625  1.0
  Cr  Cr7  1  0.500  0.750  0.125  1.0
  Cr  Cr8  1  0.000  0.251  0.625  1.0
  Fe  Fe9  1  0.000  0.000  0.000  1.0
  Fe  Fe10  1  0.500  0.000  0.750  1.0
  Fe  Fe11  1  0.000  0.500  0.250  1.0
  O  O12  1  0.724  0.000  0.138  1.0
  O  O13  1  0.227  0.500  0.636  1.0
  O  O14  1  0.276  0.000  0.138  1.0
  O  O15  1  0.773  0.500  0.636  1.0
  O  O16  1  0.500  0.773  0.364  1.0
  O  O17  1  0.000  0.276  0.862  1.0
  O  O18  1  0.500  0.227  0.364  1.0
  O  O19  1  0.000  0.724  0.862  1.0
  O  O20  1  0.277  0.500  0.113  1.0
  O  O21  1  0.777  0.000  0.613  1.0
  O  O22  1  0.723  0.500  0.113  1.0
  O  O23  1  0.223  0.000  0.613  1.0
  O  O24  1  0.500  0.723  0.887  1.0
  O  O25  1  0.000  0.223  0.387  1.0
  O  O26  1  0.500  0.277  0.887  1.0
  O  O27  1  0.000  0.777  0.387  1.0
[/CIF]
.