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.
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°. The Mg(1)-O(1) bond length is 2.00 Å. All Mg(1)-O(4) bond lengths are 2.01 Å. 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°. The Mg(2)-O(6) bond length is 2.00 Å. All Mg(2)-O(7) bond lengths are 2.00 Å. 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°. The Mg(3)-O(5) bond length is 2.00 Å. All Mg(3)-O(8) bond lengths are 2.01 Å. 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. All Cr(1)-O(3) bond lengths are 2.02 Å. All Cr(1)-O(8) bond lengths are 2.04 Å. 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. All Cr(2)-O(4) bond lengths are 2.03 Å. All Cr(2)-O(7) bond lengths are 2.03 Å. 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. The Cr(3)-O(1) bond length is 2.04 Å. The Cr(3)-O(5) bond length is 2.03 Å. Both Cr(3)-O(3) bond lengths are 2.03 Å. Both Cr(3)-O(7) bond lengths are 2.03 Å. 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. The Cr(4)-O(2) bond length is 2.04 Å. The Cr(4)-O(6) bond length is 2.04 Å. Both Cr(4)-O(4) bond lengths are 2.04 Å. Both Cr(4)-O(8) bond lengths are 2.03 Å. 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°. The Fe(1)-O(2) bond length is 1.98 Å. All Fe(1)-O(3) bond lengths are 2.03 Å. 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.