MgCr2O4 is Spinel-like structured and crystallizes in the trigonal P3m1 space group. There are six inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one O(10) and three equivalent O(1) atoms to form MgO4 tetrahedra that share corners with three equivalent Mg(3)O6 octahedra, corners with three equivalent Cr(4)O6 octahedra, and corners with six equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-58°. In the second Mg site, Mg(2) is bonded to one O(2) and three equivalent O(4) 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(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-59°. In the third Mg site, Mg(3) is bonded to three equivalent O(1) and three equivalent O(11) atoms to form MgO6 octahedra that share corners with three equivalent Mg(1)O4 tetrahedra, corners with three equivalent Cr(6)O4 tetrahedra, edges with three equivalent Cr(1)O6 octahedra, and edges with three equivalent Cr(4)O6 octahedra. In the fourth Mg site, Mg(4) is bonded to one O(6) and three equivalent O(8) atoms to form MgO4 tetrahedra that share corners with three equivalent Cr(2)O6 octahedra, corners with three equivalent Cr(5)O6 octahedra, and corners with six equivalent Cr(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-59°. In the fifth Mg site, Mg(5) is bonded to one O(9) and three equivalent O(3) 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(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-59°. In the sixth Mg site, Mg(6) is bonded to one O(12) and three equivalent O(7) atoms to form MgO4 tetrahedra that share corners with three equivalent Cr(4)O6 octahedra, corners with three equivalent Cr(5)O6 octahedra, and corners with six equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-59°. There are six inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(2), one O(5), two equivalent O(1), and two equivalent O(3) atoms to form CrO6 octahedra that share  a cornercorner with one Mg(2)O4 tetrahedra,  a cornercorner with one Cr(6)O4 tetrahedra, corners with two equivalent Mg(1)O4 tetrahedra, corners with two equivalent Mg(5)O4 tetrahedra,  an edgeedge with one Mg(3)O6 octahedra,  an edgeedge with one Cr(3)O6 octahedra, and edges with four equivalent Cr(1)O6 octahedra. In the second Cr site, Cr(2) is bonded to one O(6), one O(9), two equivalent O(4), and two equivalent O(7) atoms to form CrO6 octahedra that share  a cornercorner with one Mg(4)O4 tetrahedra,  a cornercorner with one Mg(5)O4 tetrahedra, corners with two equivalent Mg(2)O4 tetrahedra, corners with two equivalent Mg(6)O4 tetrahedra,  an edgeedge with one Cr(3)O6 octahedra,  an edgeedge with one Cr(5)O6 octahedra, and edges with four equivalent Cr(2)O6 octahedra. In the third Cr site, Cr(3) is bonded to three equivalent O(3) and three equivalent O(4) atoms to form CrO6 octahedra that share corners with three equivalent Mg(2)O4 tetrahedra, corners with three equivalent Mg(5)O4 tetrahedra, edges with three equivalent Cr(1)O6 octahedra, and edges with three equivalent Cr(2)O6 octahedra. In the fourth Cr site, Cr(4) is bonded to one O(10), one O(12), two equivalent O(11), and two equivalent O(8) atoms to form CrO6 octahedra that share  a cornercorner with one Mg(1)O4 tetrahedra,  a cornercorner with one Mg(6)O4 tetrahedra, corners with two equivalent Mg(4)O4 tetrahedra, corners with two equivalent Cr(6)O4 tetrahedra,  an edgeedge with one Mg(3)O6 octahedra,  an edgeedge with one Cr(5)O6 octahedra, and edges with four equivalent Cr(4)O6 octahedra. In the fifth Cr site, Cr(5) is bonded to three equivalent O(7) and three equivalent O(8) atoms to form CrO6 octahedra that share corners with three equivalent Mg(4)O4 tetrahedra, corners with three equivalent Mg(6)O4 tetrahedra, edges with three equivalent Cr(2)O6 octahedra, and edges with three equivalent Cr(4)O6 octahedra. In the sixth Cr site, Cr(6) is bonded to one O(5) and three equivalent O(11) atoms to form CrO4 tetrahedra that share corners with three equivalent Mg(3)O6 octahedra, corners with three equivalent Cr(1)O6 octahedra, and corners with six equivalent Cr(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-61°. There are twelve inequivalent O sites. In the first O site, O(1) is bonded to one Mg(1), one Mg(3), and two equivalent Cr(1) atoms to form distorted OMg2Cr2 trigonal pyramids that share  a cornercorner with one O(10)MgCr3 trigonal pyramid, corners with two equivalent O(5)Cr4 trigonal pyramids, corners with two equivalent O(1)Mg2Cr2 trigonal pyramids, corners with four equivalent O(3)MgCr3 trigonal pyramids,  an edgeedge with one O(2)MgCr3 trigonal pyramid, and edges with two equivalent O(1)Mg2Cr2 trigonal pyramids. In the second O site, O(2) is bonded to one Mg(2) and three equivalent Cr(1) atoms to form distorted OMgCr3 trigonal pyramids that share corners with three equivalent O(5)Cr4 trigonal pyramids, corners with three equivalent O(4)MgCr3 trigonal pyramids, corners with six equivalent O(3)MgCr3 trigonal pyramids, and edges with three equivalent O(1)Mg2Cr2 trigonal pyramids. In the third O site, O(3) is bonded to one Mg(5), one Cr(3), and two equivalent Cr(1) atoms to form distorted OMgCr3 trigonal pyramids that share  a cornercorner with one O(9)MgCr3 trigonal pyramid, corners with two equivalent O(2)MgCr3 trigonal pyramids, corners with two equivalent O(3)MgCr3 trigonal pyramids, corners with three equivalent O(4)MgCr3 trigonal pyramids, corners with four equivalent O(1)Mg2Cr2 trigonal pyramids,  an edgeedge with one O(5)Cr4 trigonal pyramid, and edges with two equivalent O(3)MgCr3 trigonal pyramids. In the fourth O site, O(4) is bonded to one Mg(2), one Cr(3), and two equivalent Cr(2) atoms to form a mixture of distorted corner and edge-sharing OMgCr3 trigonal pyramids. In the fifth O site, O(5) is bonded to one Cr(6) and three equivalent Cr(1) atoms to form distorted OCr4 trigonal pyramids that share corners with three equivalent O(2)MgCr3 trigonal pyramids, corners with six equivalent O(1)Mg2Cr2 trigonal pyramids, and edges with three equivalent O(3)MgCr3 trigonal pyramids. In the sixth O site, O(6) is bonded to one Mg(4) and three equivalent Cr(2) atoms to form a mixture of distorted corner and edge-sharing OMgCr3 trigonal pyramids. In the seventh O site, O(7) is bonded to one Mg(6), one Cr(5), and two equivalent Cr(2) atoms to form a mixture of distorted corner and edge-sharing OMgCr3 trigonal pyramids. In the eighth O site, O(8) is bonded to one Mg(4), one Cr(5), and two equivalent Cr(4) atoms to form a mixture of distorted corner and edge-sharing OMgCr3 trigonal pyramids. In the ninth O site, O(9) is bonded to one Mg(5) and three equivalent Cr(2) atoms to form a mixture of distorted corner and edge-sharing OMgCr3 trigonal pyramids. In the tenth O site, O(10) is bonded to one Mg(1) and three equivalent Cr(4) atoms to form distorted OMgCr3 trigonal pyramids that share corners with three equivalent O(1)Mg2Cr2 trigonal pyramids, corners with three equivalent O(12)MgCr3 trigonal pyramids, and edges with three equivalent O(8)MgCr3 trigonal pyramids. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Mg(3), one Cr(6), and two equivalent Cr(4) atoms. In the twelfth O site, O(12) is bonded to one Mg(6) and three equivalent Cr(4) atoms to form distorted corner-sharing OMgCr3 trigonal pyramids.
MgCr2O4 is Spinel-like structured and crystallizes in the trigonal P3m1 space group. There are six inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one O(10) and three equivalent O(1) atoms to form MgO4 tetrahedra that share corners with three equivalent Mg(3)O6 octahedra, corners with three equivalent Cr(4)O6 octahedra, and corners with six equivalent Cr(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-58°. The Mg(1)-O(10) bond length is 2.07 Å. All Mg(1)-O(1) bond lengths are 1.96 Å. In the second Mg site, Mg(2) is bonded to one O(2) and three equivalent O(4) 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(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-59°. The Mg(2)-O(2) bond length is 1.99 Å. All Mg(2)-O(4) bond lengths are 1.99 Å. In the third Mg site, Mg(3) is bonded to three equivalent O(1) and three equivalent O(11) atoms to form MgO6 octahedra that share corners with three equivalent Mg(1)O4 tetrahedra, corners with three equivalent Cr(6)O4 tetrahedra, edges with three equivalent Cr(1)O6 octahedra, and edges with three equivalent Cr(4)O6 octahedra. All Mg(3)-O(1) bond lengths are 2.04 Å. All Mg(3)-O(11) bond lengths are 2.16 Å. In the fourth Mg site, Mg(4) is bonded to one O(6) and three equivalent O(8) atoms to form MgO4 tetrahedra that share corners with three equivalent Cr(2)O6 octahedra, corners with three equivalent Cr(5)O6 octahedra, and corners with six equivalent Cr(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-59°. The Mg(4)-O(6) bond length is 1.99 Å. All Mg(4)-O(8) bond lengths are 2.00 Å. In the fifth Mg site, Mg(5) is bonded to one O(9) and three equivalent O(3) 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(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 57-59°. The Mg(5)-O(9) bond length is 2.02 Å. All Mg(5)-O(3) bond lengths are 1.99 Å. In the sixth Mg site, Mg(6) is bonded to one O(12) and three equivalent O(7) atoms to form MgO4 tetrahedra that share corners with three equivalent Cr(4)O6 octahedra, corners with three equivalent Cr(5)O6 octahedra, and corners with six equivalent Cr(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 58-59°. The Mg(6)-O(12) bond length is 2.02 Å. All Mg(6)-O(7) bond lengths are 1.99 Å. There are six inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(2), one O(5), two equivalent O(1), and two equivalent O(3) atoms to form CrO6 octahedra that share  a cornercorner with one Mg(2)O4 tetrahedra,  a cornercorner with one Cr(6)O4 tetrahedra, corners with two equivalent Mg(1)O4 tetrahedra, corners with two equivalent Mg(5)O4 tetrahedra,  an edgeedge with one Mg(3)O6 octahedra,  an edgeedge with one Cr(3)O6 octahedra, and edges with four equivalent Cr(1)O6 octahedra. The Cr(1)-O(2) bond length is 2.02 Å. The Cr(1)-O(5) bond length is 2.06 Å. Both Cr(1)-O(1) bond lengths are 2.01 Å. Both Cr(1)-O(3) bond lengths are 2.03 Å. In the second Cr site, Cr(2) is bonded to one O(6), one O(9), two equivalent O(4), and two equivalent O(7) atoms to form CrO6 octahedra that share  a cornercorner with one Mg(4)O4 tetrahedra,  a cornercorner with one Mg(5)O4 tetrahedra, corners with two equivalent Mg(2)O4 tetrahedra, corners with two equivalent Mg(6)O4 tetrahedra,  an edgeedge with one Cr(3)O6 octahedra,  an edgeedge with one Cr(5)O6 octahedra, and edges with four equivalent Cr(2)O6 octahedra. The Cr(2)-O(6) bond length is 2.03 Å. The Cr(2)-O(9) bond length is 2.03 Å. Both Cr(2)-O(4) bond lengths are 2.02 Å. Both Cr(2)-O(7) bond lengths are 2.04 Å. In the third Cr site, Cr(3) is bonded to three equivalent O(3) and three equivalent O(4) atoms to form CrO6 octahedra that share corners with three equivalent Mg(2)O4 tetrahedra, corners with three equivalent Mg(5)O4 tetrahedra, edges with three equivalent Cr(1)O6 octahedra, and edges with three equivalent Cr(2)O6 octahedra. All Cr(3)-O(3) bond lengths are 2.01 Å. All Cr(3)-O(4) bond lengths are 2.04 Å. In the fourth Cr site, Cr(4) is bonded to one O(10), one O(12), two equivalent O(11), and two equivalent O(8) atoms to form CrO6 octahedra that share  a cornercorner with one Mg(1)O4 tetrahedra,  a cornercorner with one Mg(6)O4 tetrahedra, corners with two equivalent Mg(4)O4 tetrahedra, corners with two equivalent Cr(6)O4 tetrahedra,  an edgeedge with one Mg(3)O6 octahedra,  an edgeedge with one Cr(5)O6 octahedra, and edges with four equivalent Cr(4)O6 octahedra. The Cr(4)-O(10) bond length is 2.03 Å. The Cr(4)-O(12) bond length is 2.03 Å. Both Cr(4)-O(11) bond lengths are 2.04 Å. Both Cr(4)-O(8) bond lengths are 2.02 Å. In the fifth Cr site, Cr(5) is bonded to three equivalent O(7) and three equivalent O(8) atoms to form CrO6 octahedra that share corners with three equivalent Mg(4)O4 tetrahedra, corners with three equivalent Mg(6)O4 tetrahedra, edges with three equivalent Cr(2)O6 octahedra, and edges with three equivalent Cr(4)O6 octahedra. All Cr(5)-O(7) bond lengths are 2.02 Å. All Cr(5)-O(8) bond lengths are 2.03 Å. In the sixth Cr site, Cr(6) is bonded to one O(5) and three equivalent O(11) atoms to form CrO4 tetrahedra that share corners with three equivalent Mg(3)O6 octahedra, corners with three equivalent Cr(1)O6 octahedra, and corners with six equivalent Cr(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 56-61°. The Cr(6)-O(5) bond length is 2.00 Å. All Cr(6)-O(11) bond lengths are 1.93 Å. There are twelve inequivalent O sites. In the first O site, O(1) is bonded to one Mg(1), one Mg(3), and two equivalent Cr(1) atoms to form distorted OMg2Cr2 trigonal pyramids that share  a cornercorner with one O(10)MgCr3 trigonal pyramid, corners with two equivalent O(5)Cr4 trigonal pyramids, corners with two equivalent O(1)Mg2Cr2 trigonal pyramids, corners with four equivalent O(3)MgCr3 trigonal pyramids,  an edgeedge with one O(2)MgCr3 trigonal pyramid, and edges with two equivalent O(1)Mg2Cr2 trigonal pyramids. In the second O site, O(2) is bonded to one Mg(2) and three equivalent Cr(1) atoms to form distorted OMgCr3 trigonal pyramids that share corners with three equivalent O(5)Cr4 trigonal pyramids, corners with three equivalent O(4)MgCr3 trigonal pyramids, corners with six equivalent O(3)MgCr3 trigonal pyramids, and edges with three equivalent O(1)Mg2Cr2 trigonal pyramids. In the third O site, O(3) is bonded to one Mg(5), one Cr(3), and two equivalent Cr(1) atoms to form distorted OMgCr3 trigonal pyramids that share  a cornercorner with one O(9)MgCr3 trigonal pyramid, corners with two equivalent O(2)MgCr3 trigonal pyramids, corners with two equivalent O(3)MgCr3 trigonal pyramids, corners with three equivalent O(4)MgCr3 trigonal pyramids, corners with four equivalent O(1)Mg2Cr2 trigonal pyramids,  an edgeedge with one O(5)Cr4 trigonal pyramid, and edges with two equivalent O(3)MgCr3 trigonal pyramids. In the fourth O site, O(4) is bonded to one Mg(2), one Cr(3), and two equivalent Cr(2) atoms to form a mixture of distorted corner and edge-sharing OMgCr3 trigonal pyramids. In the fifth O site, O(5) is bonded to one Cr(6) and three equivalent Cr(1) atoms to form distorted OCr4 trigonal pyramids that share corners with three equivalent O(2)MgCr3 trigonal pyramids, corners with six equivalent O(1)Mg2Cr2 trigonal pyramids, and edges with three equivalent O(3)MgCr3 trigonal pyramids. In the sixth O site, O(6) is bonded to one Mg(4) and three equivalent Cr(2) atoms to form a mixture of distorted corner and edge-sharing OMgCr3 trigonal pyramids. In the seventh O site, O(7) is bonded to one Mg(6), one Cr(5), and two equivalent Cr(2) atoms to form a mixture of distorted corner and edge-sharing OMgCr3 trigonal pyramids. In the eighth O site, O(8) is bonded to one Mg(4), one Cr(5), and two equivalent Cr(4) atoms to form a mixture of distorted corner and edge-sharing OMgCr3 trigonal pyramids. In the ninth O site, O(9) is bonded to one Mg(5) and three equivalent Cr(2) atoms to form a mixture of distorted corner and edge-sharing OMgCr3 trigonal pyramids. In the tenth O site, O(10) is bonded to one Mg(1) and three equivalent Cr(4) atoms to form distorted OMgCr3 trigonal pyramids that share corners with three equivalent O(1)Mg2Cr2 trigonal pyramids, corners with three equivalent O(12)MgCr3 trigonal pyramids, and edges with three equivalent O(8)MgCr3 trigonal pyramids. In the eleventh O site, O(11) is bonded in a rectangular see-saw-like geometry to one Mg(3), one Cr(6), and two equivalent Cr(4) atoms. In the twelfth O site, O(12) is bonded to one Mg(6) and three equivalent Cr(4) atoms to form distorted corner-sharing OMgCr3 trigonal pyramids.