The material described by Mg3Cr8FeO16 is Spinel-derived structured and crystallizes in the trigonal R3m space group. There are three inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one O(1) and three equivalent O(4) atoms to form MgO4 tetrahedra that share corners with three equivalent Cr(2)O6 octahedra, corners with three equivalent Cr(3)O6 octahedra, and corners with six equivalent Cr(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-59°. In the second Mg site, Mg(2) is bonded to one O(6) and three equivalent O(7) atoms to form MgO4 tetrahedra that share corners with three equivalent Cr(2)O6 octahedra, corners with three equivalent Cr(4)O6 octahedra, and corners with six equivalent Cr(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-59°. In the third Mg site, Mg(3) is bonded to one O(5) and three equivalent O(8) atoms to form MgO4 tetrahedra that share corners with three equivalent Cr(1)O6 octahedra, corners with three equivalent Cr(3)O6 octahedra, and corners with six equivalent Cr(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-59°. There are four inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to three equivalent O(3) and three equivalent O(8) atoms to form CrO6 octahedra that share corners with three equivalent Mg(3)O4 tetrahedra, corners with three equivalent Fe(1)O4 tetrahedra, edges with three equivalent Cr(3)O6 octahedra, and edges with three equivalent Cr(4)O6 octahedra. In the second Cr site, Cr(2) is bonded to three equivalent O(4) and three equivalent O(7) atoms to form CrO6 octahedra that share corners with three equivalent Mg(1)O4 tetrahedra, corners with three equivalent Mg(2)O4 tetrahedra, edges with three equivalent Cr(3)O6 octahedra, and edges with three equivalent Cr(4)O6 octahedra. In the third Cr site, Cr(3) is bonded to one O(1), one O(5), two equivalent O(3), and two equivalent O(7) atoms to form CrO6 octahedra that share  a cornercorner with one Mg(1)O4 tetrahedra,  a cornercorner with one Mg(3)O4 tetrahedra, corners with two equivalent Mg(2)O4 tetrahedra, corners with two equivalent Fe(1)O4 tetrahedra,  an edgeedge with one Cr(1)O6 octahedra,  an edgeedge with one Cr(2)O6 octahedra, and edges with four equivalent Cr(3)O6 octahedra. In the fourth Cr site, Cr(4) is bonded to one O(2), one O(6), two equivalent O(4), and two equivalent O(8) atoms to form CrO6 octahedra that share  a cornercorner with one Mg(2)O4 tetrahedra,  a cornercorner with one Fe(1)O4 tetrahedra, corners with two equivalent Mg(1)O4 tetrahedra, corners with two equivalent Mg(3)O4 tetrahedra,  an edgeedge with one Cr(1)O6 octahedra,  an edgeedge with one Cr(2)O6 octahedra, and edges with four equivalent Cr(4)O6 octahedra. Fe(1) is bonded to one O(2) and three equivalent O(3) atoms to form FeO4 tetrahedra that share corners with three equivalent Cr(1)O6 octahedra, corners with three equivalent Cr(4)O6 octahedra, and corners with six equivalent Cr(3)O6 octahedra. The corner-sharing octahedral tilt angles are 59°. There are eight inequivalent O sites. In the first O site, O(1) is bonded to one Mg(1) and three equivalent Cr(3) atoms to form distorted OMgCr3 trigonal pyramids that share corners with three equivalent O(4)MgCr3 trigonal pyramids, corners with three equivalent O(5)MgCr3 trigonal pyramids, corners with six equivalent O(7)MgCr3 trigonal pyramids, and edges with three equivalent O(3)Cr3Fe trigonal pyramids. In the second O site, O(2) is bonded to three equivalent Cr(4) and one Fe(1) atom to form distorted OCr3Fe trigonal pyramids that share corners with three equivalent O(3)Cr3Fe trigonal pyramids, corners with three equivalent O(6)MgCr3 trigonal pyramids, corners with six equivalent O(8)MgCr3 trigonal pyramids, and edges with three equivalent O(4)MgCr3 trigonal pyramids. In the third O site, O(3) is bonded to one Cr(1), two equivalent Cr(3), and one Fe(1) atom to form distorted OCr3Fe trigonal pyramids that share  a cornercorner with one O(2)Cr3Fe trigonal pyramid, corners with two equivalent O(3)Cr3Fe trigonal pyramids, corners with two equivalent O(5)MgCr3 trigonal pyramids, corners with three equivalent O(8)MgCr3 trigonal pyramids, corners with four equivalent O(7)MgCr3 trigonal pyramids,  an edgeedge with one O(1)MgCr3 trigonal pyramid, and edges with two equivalent O(3)Cr3Fe trigonal pyramids. In the fourth O site, O(4) is bonded to one Mg(1), one Cr(2), and two equivalent Cr(4) atoms to form distorted OMgCr3 trigonal pyramids that share  a cornercorner with one O(1)MgCr3 trigonal pyramid, corners with two equivalent O(4)MgCr3 trigonal pyramids, corners with two equivalent O(6)MgCr3 trigonal pyramids, corners with three equivalent O(7)MgCr3 trigonal pyramids, corners with four equivalent O(8)MgCr3 trigonal pyramids,  an edgeedge with one O(2)Cr3Fe trigonal pyramid, and edges with two equivalent O(4)MgCr3 trigonal pyramids. In the fifth O site, O(5) is bonded to one Mg(3) and three equivalent Cr(3) atoms to form distorted OMgCr3 trigonal pyramids that share corners with three equivalent O(1)MgCr3 trigonal pyramids, corners with three equivalent O(8)MgCr3 trigonal pyramids, corners with six equivalent O(3)Cr3Fe trigonal pyramids, and edges with three equivalent O(7)MgCr3 trigonal pyramids. In the sixth O site, O(6) is bonded to one Mg(2) and three equivalent Cr(4) atoms to form distorted OMgCr3 trigonal pyramids that share corners with three equivalent O(2)Cr3Fe trigonal pyramids, corners with three equivalent O(7)MgCr3 trigonal pyramids, corners with six equivalent O(4)MgCr3 trigonal pyramids, and edges with three equivalent O(8)MgCr3 trigonal pyramids. In the seventh O site, O(7) is bonded to one Mg(2), one Cr(2), and two equivalent Cr(3) atoms to form distorted OMgCr3 trigonal pyramids that share  a cornercorner with one O(6)MgCr3 trigonal pyramid, corners with two equivalent O(1)MgCr3 trigonal pyramids, corners with two equivalent O(7)MgCr3 trigonal pyramids, corners with three equivalent O(4)MgCr3 trigonal pyramids, corners with four equivalent O(3)Cr3Fe trigonal pyramids,  an edgeedge with one O(5)MgCr3 trigonal pyramid, and edges with two equivalent O(7)MgCr3 trigonal pyramids. In the eighth O site, O(8) is bonded to one Mg(3), one Cr(1), and two equivalent Cr(4) atoms to form distorted OMgCr3 trigonal pyramids that share  a cornercorner with one O(5)MgCr3 trigonal pyramid, corners with two equivalent O(2)Cr3Fe trigonal pyramids, corners with two equivalent O(8)MgCr3 trigonal pyramids, corners with three equivalent O(3)Cr3Fe trigonal pyramids, corners with four equivalent O(4)MgCr3 trigonal pyramids,  an edgeedge with one O(6)MgCr3 trigonal pyramid, and edges with two equivalent O(8)MgCr3 trigonal pyramids. is represented by the Crystallographic Information File (CIF) [CIF]
data_Mg3Cr8FeO16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   10.379
_cell_length_b   10.379
_cell_length_c   10.379
_cell_angle_alpha   33.726
_cell_angle_beta   33.726
_cell_angle_gamma   33.726
_symmetry_Int_Tables_number   1
_cell_volume   307.112
_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  0.188  0.188  0.188  1.0
  Mg  Mg1  1  0.812  0.812  0.812  1.0
  Mg  Mg2  1  0.313  0.313  0.313  1.0
  Cr  Cr3  1  1.000  1.000  1.000  1.0
  Cr  Cr4  1  0.500  0.500  0.500  1.0
  Cr  Cr5  1  0.750  0.250  0.250  1.0
  Cr  Cr6  1  0.250  0.750  0.750  1.0
  Cr  Cr7  1  0.250  0.750  0.250  1.0
  Cr  Cr8  1  0.750  0.250  0.750  1.0
  Cr  Cr9  1  0.250  0.250  0.750  1.0
  Cr  Cr10  1  0.750  0.750  0.250  1.0
  Fe  Fe11  1  0.687  0.687  0.687  1.0
  O  O12  1  0.119  0.119  0.119  1.0
  O  O13  1  0.620  0.620  0.620  1.0
  O  O14  1  0.343  0.893  0.893  1.0
  O  O15  1  0.847  0.392  0.392  1.0
  O  O16  1  0.893  0.343  0.893  1.0
  O  O17  1  0.392  0.847  0.392  1.0
  O  O18  1  0.893  0.893  0.343  1.0
  O  O19  1  0.392  0.392  0.847  1.0
  O  O20  1  0.381  0.381  0.381  1.0
  O  O21  1  0.881  0.881  0.881  1.0
  O  O22  1  0.153  0.608  0.608  1.0
  O  O23  1  0.652  0.108  0.108  1.0
  O  O24  1  0.608  0.153  0.608  1.0
  O  O25  1  0.108  0.652  0.108  1.0
  O  O26  1  0.608  0.608  0.153  1.0
  O  O27  1  0.108  0.108  0.652  1.0
[/CIF]
.
The material described by Mg3Cr8FeO16 is Spinel-derived structured and crystallizes in the trigonal R3m space group. There are three inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one O(1) and three equivalent O(4) atoms to form MgO4 tetrahedra that share corners with three equivalent Cr(2)O6 octahedra, corners with three equivalent Cr(3)O6 octahedra, and corners with six equivalent Cr(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-59°. In the second Mg site, Mg(2) is bonded to one O(6) and three equivalent O(7) atoms to form MgO4 tetrahedra that share corners with three equivalent Cr(2)O6 octahedra, corners with three equivalent Cr(4)O6 octahedra, and corners with six equivalent Cr(3)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-59°. In the third Mg site, Mg(3) is bonded to one O(5) and three equivalent O(8) atoms to form MgO4 tetrahedra that share corners with three equivalent Cr(1)O6 octahedra, corners with three equivalent Cr(3)O6 octahedra, and corners with six equivalent Cr(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-59°. There are four inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to three equivalent O(3) and three equivalent O(8) atoms to form CrO6 octahedra that share corners with three equivalent Mg(3)O4 tetrahedra, corners with three equivalent Fe(1)O4 tetrahedra, edges with three equivalent Cr(3)O6 octahedra, and edges with three equivalent Cr(4)O6 octahedra. In the second Cr site, Cr(2) is bonded to three equivalent O(4) and three equivalent O(7) atoms to form CrO6 octahedra that share corners with three equivalent Mg(1)O4 tetrahedra, corners with three equivalent Mg(2)O4 tetrahedra, edges with three equivalent Cr(3)O6 octahedra, and edges with three equivalent Cr(4)O6 octahedra. In the third Cr site, Cr(3) is bonded to one O(1), one O(5), two equivalent O(3), and two equivalent O(7) atoms to form CrO6 octahedra that share  a cornercorner with one Mg(1)O4 tetrahedra,  a cornercorner with one Mg(3)O4 tetrahedra, corners with two equivalent Mg(2)O4 tetrahedra, corners with two equivalent Fe(1)O4 tetrahedra,  an edgeedge with one Cr(1)O6 octahedra,  an edgeedge with one Cr(2)O6 octahedra, and edges with four equivalent Cr(3)O6 octahedra. In the fourth Cr site, Cr(4) is bonded to one O(2), one O(6), two equivalent O(4), and two equivalent O(8) atoms to form CrO6 octahedra that share  a cornercorner with one Mg(2)O4 tetrahedra,  a cornercorner with one Fe(1)O4 tetrahedra, corners with two equivalent Mg(1)O4 tetrahedra, corners with two equivalent Mg(3)O4 tetrahedra,  an edgeedge with one Cr(1)O6 octahedra,  an edgeedge with one Cr(2)O6 octahedra, and edges with four equivalent Cr(4)O6 octahedra. Fe(1) is bonded to one O(2) and three equivalent O(3) atoms to form FeO4 tetrahedra that share corners with three equivalent Cr(1)O6 octahedra, corners with three equivalent Cr(4)O6 octahedra, and corners with six equivalent Cr(3)O6 octahedra. The corner-sharing octahedral tilt angles are 59°. There are eight inequivalent O sites. In the first O site, O(1) is bonded to one Mg(1) and three equivalent Cr(3) atoms to form distorted OMgCr3 trigonal pyramids that share corners with three equivalent O(4)MgCr3 trigonal pyramids, corners with three equivalent O(5)MgCr3 trigonal pyramids, corners with six equivalent O(7)MgCr3 trigonal pyramids, and edges with three equivalent O(3)Cr3Fe trigonal pyramids. In the second O site, O(2) is bonded to three equivalent Cr(4) and one Fe(1) atom to form distorted OCr3Fe trigonal pyramids that share corners with three equivalent O(3)Cr3Fe trigonal pyramids, corners with three equivalent O(6)MgCr3 trigonal pyramids, corners with six equivalent O(8)MgCr3 trigonal pyramids, and edges with three equivalent O(4)MgCr3 trigonal pyramids. In the third O site, O(3) is bonded to one Cr(1), two equivalent Cr(3), and one Fe(1) atom to form distorted OCr3Fe trigonal pyramids that share  a cornercorner with one O(2)Cr3Fe trigonal pyramid, corners with two equivalent O(3)Cr3Fe trigonal pyramids, corners with two equivalent O(5)MgCr3 trigonal pyramids, corners with three equivalent O(8)MgCr3 trigonal pyramids, corners with four equivalent O(7)MgCr3 trigonal pyramids,  an edgeedge with one O(1)MgCr3 trigonal pyramid, and edges with two equivalent O(3)Cr3Fe trigonal pyramids. In the fourth O site, O(4) is bonded to one Mg(1), one Cr(2), and two equivalent Cr(4) atoms to form distorted OMgCr3 trigonal pyramids that share  a cornercorner with one O(1)MgCr3 trigonal pyramid, corners with two equivalent O(4)MgCr3 trigonal pyramids, corners with two equivalent O(6)MgCr3 trigonal pyramids, corners with three equivalent O(7)MgCr3 trigonal pyramids, corners with four equivalent O(8)MgCr3 trigonal pyramids,  an edgeedge with one O(2)Cr3Fe trigonal pyramid, and edges with two equivalent O(4)MgCr3 trigonal pyramids. In the fifth O site, O(5) is bonded to one Mg(3) and three equivalent Cr(3) atoms to form distorted OMgCr3 trigonal pyramids that share corners with three equivalent O(1)MgCr3 trigonal pyramids, corners with three equivalent O(8)MgCr3 trigonal pyramids, corners with six equivalent O(3)Cr3Fe trigonal pyramids, and edges with three equivalent O(7)MgCr3 trigonal pyramids. In the sixth O site, O(6) is bonded to one Mg(2) and three equivalent Cr(4) atoms to form distorted OMgCr3 trigonal pyramids that share corners with three equivalent O(2)Cr3Fe trigonal pyramids, corners with three equivalent O(7)MgCr3 trigonal pyramids, corners with six equivalent O(4)MgCr3 trigonal pyramids, and edges with three equivalent O(8)MgCr3 trigonal pyramids. In the seventh O site, O(7) is bonded to one Mg(2), one Cr(2), and two equivalent Cr(3) atoms to form distorted OMgCr3 trigonal pyramids that share  a cornercorner with one O(6)MgCr3 trigonal pyramid, corners with two equivalent O(1)MgCr3 trigonal pyramids, corners with two equivalent O(7)MgCr3 trigonal pyramids, corners with three equivalent O(4)MgCr3 trigonal pyramids, corners with four equivalent O(3)Cr3Fe trigonal pyramids,  an edgeedge with one O(5)MgCr3 trigonal pyramid, and edges with two equivalent O(7)MgCr3 trigonal pyramids. In the eighth O site, O(8) is bonded to one Mg(3), one Cr(1), and two equivalent Cr(4) atoms to form distorted OMgCr3 trigonal pyramids that share  a cornercorner with one O(5)MgCr3 trigonal pyramid, corners with two equivalent O(2)Cr3Fe trigonal pyramids, corners with two equivalent O(8)MgCr3 trigonal pyramids, corners with three equivalent O(3)Cr3Fe trigonal pyramids, corners with four equivalent O(4)MgCr3 trigonal pyramids,  an edgeedge with one O(6)MgCr3 trigonal pyramid, and edges with two equivalent O(8)MgCr3 trigonal pyramids. is represented by the Crystallographic Information File (CIF) [CIF]
data_Mg3Cr8FeO16
_symmetry_space_group_name_H-M   'P 1'
_cell_length_a   10.379
_cell_length_b   10.379
_cell_length_c   10.379
_cell_angle_alpha   33.726
_cell_angle_beta   33.726
_cell_angle_gamma   33.726
_symmetry_Int_Tables_number   1
_cell_volume   307.112
_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  0.188  0.188  0.188  1.0
  Mg  Mg1  1  0.812  0.812  0.812  1.0
  Mg  Mg2  1  0.313  0.313  0.313  1.0
  Cr  Cr3  1  1.000  1.000  1.000  1.0
  Cr  Cr4  1  0.500  0.500  0.500  1.0
  Cr  Cr5  1  0.750  0.250  0.250  1.0
  Cr  Cr6  1  0.250  0.750  0.750  1.0
  Cr  Cr7  1  0.250  0.750  0.250  1.0
  Cr  Cr8  1  0.750  0.250  0.750  1.0
  Cr  Cr9  1  0.250  0.250  0.750  1.0
  Cr  Cr10  1  0.750  0.750  0.250  1.0
  Fe  Fe11  1  0.687  0.687  0.687  1.0
  O  O12  1  0.119  0.119  0.119  1.0
  O  O13  1  0.620  0.620  0.620  1.0
  O  O14  1  0.343  0.893  0.893  1.0
  O  O15  1  0.847  0.392  0.392  1.0
  O  O16  1  0.893  0.343  0.893  1.0
  O  O17  1  0.392  0.847  0.392  1.0
  O  O18  1  0.893  0.893  0.343  1.0
  O  O19  1  0.392  0.392  0.847  1.0
  O  O20  1  0.381  0.381  0.381  1.0
  O  O21  1  0.881  0.881  0.881  1.0
  O  O22  1  0.153  0.608  0.608  1.0
  O  O23  1  0.652  0.108  0.108  1.0
  O  O24  1  0.608  0.153  0.608  1.0
  O  O25  1  0.108  0.652  0.108  1.0
  O  O26  1  0.608  0.608  0.153  1.0
  O  O27  1  0.108  0.108  0.652  1.0
[/CIF]
.