MgCr2(CoO4)2 crystallizes in the triclinic P1 space group. Mg(1) is bonded to one O(2), one O(5), one O(6), and one O(8) atom to form distorted MgO4 tetrahedra that share corners with three equivalent Co(1)O6 octahedra, corners with three equivalent Co(2)O6 octahedra, corners with two equivalent Cr(2)O4 tetrahedra, and  an edgeedge with one Cr(1)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 66-68°. There are two inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(1), one O(5), one O(6), and one O(7) atom to form CrO4 tetrahedra that share corners with three equivalent Co(1)O6 octahedra, corners with three equivalent Co(2)O6 octahedra, and  an edgeedge with one Mg(1)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 51-58°. In the second Cr site, Cr(2) is bonded to one O(2), one O(3), one O(4), and one O(8) atom to form CrO4 tetrahedra that share corners with three equivalent Co(1)O6 octahedra, corners with three equivalent Co(2)O6 octahedra, and corners with two equivalent Mg(1)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 49-51°. There are two inequivalent Co sites. In the first Co site, Co(1) is bonded to one O(2), one O(3), one O(4), one O(5), one O(6), and one O(7) atom to form CoO6 octahedra that share corners with three equivalent Mg(1)O4 tetrahedra, corners with three equivalent Cr(1)O4 tetrahedra, corners with three equivalent Cr(2)O4 tetrahedra, and edges with two equivalent Co(2)O6 octahedra. In the second Co site, Co(2) is bonded to one O(1), one O(3), one O(4), one O(5), one O(6), and one O(8) atom to form CoO6 octahedra that share corners with three equivalent Mg(1)O4 tetrahedra, corners with three equivalent Cr(1)O4 tetrahedra, corners with three equivalent Cr(2)O4 tetrahedra, and edges with two equivalent Co(1)O6 octahedra. There are eight inequivalent O sites. In the first O site, O(1) is bonded in a bent 120 degrees geometry to one Cr(1) and one Co(2) atom. In the second O site, O(2) is bonded in a trigonal planar geometry to one Mg(1), one Cr(2), and one Co(1) atom. In the third O site, O(3) is bonded in a distorted trigonal planar geometry to one Cr(2), one Co(1), and one Co(2) atom. In the fourth O site, O(4) is bonded in a distorted trigonal planar geometry to one Cr(2), one Co(1), and one Co(2) atom. In the fifth O site, O(5) is bonded to one Mg(1), one Cr(1), one Co(1), and one Co(2) atom to form distorted edge-sharing OMgCrCo2 tetrahedra. In the sixth O site, O(6) is bonded to one Mg(1), one Cr(1), one Co(1), and one Co(2) atom to form distorted edge-sharing OMgCrCo2 tetrahedra. In the seventh O site, O(7) is bonded in a bent 120 degrees geometry to one Cr(1) and one Co(1) atom. In the eighth O site, O(8) is bonded in a trigonal planar geometry to one Mg(1), one Cr(2), and one Co(2) atom.
MgCr2(CoO4)2 crystallizes in the triclinic P1 space group. Mg(1) is bonded to one O(2), one O(5), one O(6), and one O(8) atom to form distorted MgO4 tetrahedra that share corners with three equivalent Co(1)O6 octahedra, corners with three equivalent Co(2)O6 octahedra, corners with two equivalent Cr(2)O4 tetrahedra, and  an edgeedge with one Cr(1)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 66-68°. The Mg(1)-O(2) bond length is 1.97 Å. The Mg(1)-O(5) bond length is 2.05 Å. The Mg(1)-O(6) bond length is 2.05 Å. The Mg(1)-O(8) bond length is 1.97 Å. There are two inequivalent Cr sites. In the first Cr site, Cr(1) is bonded to one O(1), one O(5), one O(6), and one O(7) atom to form CrO4 tetrahedra that share corners with three equivalent Co(1)O6 octahedra, corners with three equivalent Co(2)O6 octahedra, and  an edgeedge with one Mg(1)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 51-58°. The Cr(1)-O(1) bond length is 1.65 Å. The Cr(1)-O(5) bond length is 1.84 Å. The Cr(1)-O(6) bond length is 1.84 Å. The Cr(1)-O(7) bond length is 1.65 Å. In the second Cr site, Cr(2) is bonded to one O(2), one O(3), one O(4), and one O(8) atom to form CrO4 tetrahedra that share corners with three equivalent Co(1)O6 octahedra, corners with three equivalent Co(2)O6 octahedra, and corners with two equivalent Mg(1)O4 tetrahedra. The corner-sharing octahedral tilt angles range from 49-51°. The Cr(2)-O(2) bond length is 1.77 Å. The Cr(2)-O(3) bond length is 1.72 Å. The Cr(2)-O(4) bond length is 1.72 Å. The Cr(2)-O(8) bond length is 1.77 Å. There are two inequivalent Co sites. In the first Co site, Co(1) is bonded to one O(2), one O(3), one O(4), one O(5), one O(6), and one O(7) atom to form CoO6 octahedra that share corners with three equivalent Mg(1)O4 tetrahedra, corners with three equivalent Cr(1)O4 tetrahedra, corners with three equivalent Cr(2)O4 tetrahedra, and edges with two equivalent Co(2)O6 octahedra. The Co(1)-O(2) bond length is 2.04 Å. The Co(1)-O(3) bond length is 2.10 Å. The Co(1)-O(4) bond length is 2.12 Å. The Co(1)-O(5) bond length is 2.20 Å. The Co(1)-O(6) bond length is 2.20 Å. The Co(1)-O(7) bond length is 2.06 Å. In the second Co site, Co(2) is bonded to one O(1), one O(3), one O(4), one O(5), one O(6), and one O(8) atom to form CoO6 octahedra that share corners with three equivalent Mg(1)O4 tetrahedra, corners with three equivalent Cr(1)O4 tetrahedra, corners with three equivalent Cr(2)O4 tetrahedra, and edges with two equivalent Co(1)O6 octahedra. The Co(2)-O(1) bond length is 2.06 Å. The Co(2)-O(3) bond length is 2.10 Å. The Co(2)-O(4) bond length is 2.12 Å. The Co(2)-O(5) bond length is 2.20 Å. The Co(2)-O(6) bond length is 2.20 Å. The Co(2)-O(8) bond length is 2.04 Å. There are eight inequivalent O sites. In the first O site, O(1) is bonded in a bent 120 degrees geometry to one Cr(1) and one Co(2) atom. In the second O site, O(2) is bonded in a trigonal planar geometry to one Mg(1), one Cr(2), and one Co(1) atom. In the third O site, O(3) is bonded in a distorted trigonal planar geometry to one Cr(2), one Co(1), and one Co(2) atom. In the fourth O site, O(4) is bonded in a distorted trigonal planar geometry to one Cr(2), one Co(1), and one Co(2) atom. In the fifth O site, O(5) is bonded to one Mg(1), one Cr(1), one Co(1), and one Co(2) atom to form distorted edge-sharing OMgCrCo2 tetrahedra. In the sixth O site, O(6) is bonded to one Mg(1), one Cr(1), one Co(1), and one Co(2) atom to form distorted edge-sharing OMgCrCo2 tetrahedra. In the seventh O site, O(7) is bonded in a bent 120 degrees geometry to one Cr(1) and one Co(1) atom. In the eighth O site, O(8) is bonded in a trigonal planar geometry to one Mg(1), one Cr(2), and one Co(2) atom.