MgCr2O4 is Spinel-like structured and crystallizes in the trigonal R3m space group. There are two inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one O(3) and three equivalent O(4) atoms to form MgO4 tetrahedra that share corners with three equivalent Mg(2)O6 octahedra and corners with nine equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-59°. In the second Mg site, Mg(2) is bonded to three equivalent O(1) and three equivalent O(4) atoms to form MgO6 octahedra that share corners with three equivalent Mg(1)O4 tetrahedra, corners with three equivalent Cr(1)O4 tetrahedra, and edges with six equivalent Cr(2)O6 octahedra. There are two inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(2) and three equivalent O(1) atoms to form CrO4 tetrahedra that share corners with three equivalent Mg(2)O6 octahedra and corners with nine equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-59°. In the second Cr site, Cr(2) is bonded to one O(2), one O(3), two equivalent O(1), and two equivalent O(4) atoms to form CrO6 octahedra that share corners with three equivalent Mg(1)O4 tetrahedra, corners with three equivalent Cr(1)O4 tetrahedra, edges with two equivalent Mg(2)O6 octahedra, and edges with four equivalent Cr(2)O6 octahedra. There are four inequivalent O sites. In the first O site, O(1) is bonded to one Mg(2), one Cr(1), and two equivalent Cr(2) atoms to form distorted OMgCr3 trigonal pyramids that share  a cornercorner with one O(2)Cr4 trigonal pyramid, corners with two equivalent O(1)MgCr3 trigonal pyramids, corners with seven equivalent O(4)Mg2Cr2 trigonal pyramids,  an edgeedge with one O(2)Cr4 trigonal pyramid, and edges with two equivalent O(1)MgCr3 trigonal pyramids. In the second O site, O(2) is bonded to one Cr(1) and three equivalent Cr(2) atoms to form distorted OCr4 trigonal pyramids that share corners with three equivalent O(1)MgCr3 trigonal pyramids, corners with six equivalent O(4)Mg2Cr2 trigonal pyramids, and edges with three equivalent O(1)MgCr3 trigonal pyramids. In the third O site, O(3) is bonded in a distorted rectangular see-saw-like geometry to one Mg(1) and three equivalent Cr(2) atoms. In the fourth O site, O(4) is bonded to one Mg(1), one Mg(2), and two equivalent Cr(2) atoms to form distorted OMg2Cr2 trigonal pyramids that share corners with two equivalent O(2)Cr4 trigonal pyramids, corners with two equivalent O(4)Mg2Cr2 trigonal pyramids, corners with seven equivalent O(1)MgCr3 trigonal pyramids, and edges with two equivalent O(4)Mg2Cr2 trigonal pyramids.
MgCr2O4 is Spinel-like structured and crystallizes in the trigonal R3m space group. There are two inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one O(3) and three equivalent O(4) atoms to form MgO4 tetrahedra that share corners with three equivalent Mg(2)O6 octahedra and corners with nine equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-59°. The Mg(1)-O(3) bond length is 2.05 Å. All Mg(1)-O(4) bond lengths are 1.98 Å. In the second Mg site, Mg(2) is bonded to three equivalent O(1) and three equivalent O(4) atoms to form MgO6 octahedra that share corners with three equivalent Mg(1)O4 tetrahedra, corners with three equivalent Cr(1)O4 tetrahedra, and edges with six equivalent Cr(2)O6 octahedra. All Mg(2)-O(1) bond lengths are 2.13 Å. All Mg(2)-O(4) bond lengths are 2.06 Å. There are two inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(2) and three equivalent O(1) atoms to form CrO4 tetrahedra that share corners with three equivalent Mg(2)O6 octahedra and corners with nine equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-59°. The Cr(1)-O(2) bond length is 2.09 Å. All Cr(1)-O(1) bond lengths are 1.93 Å. In the second Cr site, Cr(2) is bonded to one O(2), one O(3), two equivalent O(1), and two equivalent O(4) atoms to form CrO6 octahedra that share corners with three equivalent Mg(1)O4 tetrahedra, corners with three equivalent Cr(1)O4 tetrahedra, edges with two equivalent Mg(2)O6 octahedra, and edges with four equivalent Cr(2)O6 octahedra. The Cr(2)-O(2) bond length is 2.05 Å. The Cr(2)-O(3) bond length is 2.03 Å. Both Cr(2)-O(1) bond lengths are 2.06 Å. Both Cr(2)-O(4) bond lengths are 2.00 Å. There are four inequivalent O sites. In the first O site, O(1) is bonded to one Mg(2), one Cr(1), and two equivalent Cr(2) atoms to form distorted OMgCr3 trigonal pyramids that share  a cornercorner with one O(2)Cr4 trigonal pyramid, corners with two equivalent O(1)MgCr3 trigonal pyramids, corners with seven equivalent O(4)Mg2Cr2 trigonal pyramids,  an edgeedge with one O(2)Cr4 trigonal pyramid, and edges with two equivalent O(1)MgCr3 trigonal pyramids. In the second O site, O(2) is bonded to one Cr(1) and three equivalent Cr(2) atoms to form distorted OCr4 trigonal pyramids that share corners with three equivalent O(1)MgCr3 trigonal pyramids, corners with six equivalent O(4)Mg2Cr2 trigonal pyramids, and edges with three equivalent O(1)MgCr3 trigonal pyramids. In the third O site, O(3) is bonded in a distorted rectangular see-saw-like geometry to one Mg(1) and three equivalent Cr(2) atoms. In the fourth O site, O(4) is bonded to one Mg(1), one Mg(2), and two equivalent Cr(2) atoms to form distorted OMg2Cr2 trigonal pyramids that share corners with two equivalent O(2)Cr4 trigonal pyramids, corners with two equivalent O(4)Mg2Cr2 trigonal pyramids, corners with seven equivalent O(1)MgCr3 trigonal pyramids, and edges with two equivalent O(4)Mg2Cr2 trigonal pyramids.