MgZn(CoO2)4 crystallizes in the triclinic P1 space group. Mg(1) is bonded to one O(2), one O(3), two equivalent O(1), and two equivalent O(4) atoms to form distorted MgO6 octahedra that share corners with two equivalent Co(1)O6 octahedra, corners with two equivalent Co(4)O6 pentagonal pyramids, corners with two equivalent Zn(1)O5 square pyramids, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Co(3)O6 octahedra,  an edgeedge with one Co(4)O6 pentagonal pyramid, and  a faceface with one Co(1)O6 octahedra. The corner-sharing octahedral tilt angles are 39°. There are four inequivalent Co sites. In the first Co site, Co(1) is bonded to one O(2), one O(7), two equivalent O(4), and two equivalent O(5) atoms to form CoO6 octahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent Co(3)O6 octahedra, edges with two equivalent Co(1)O6 octahedra, edges with two equivalent Co(4)O6 pentagonal pyramids, edges with two equivalent Zn(1)O5 square pyramids, and  a faceface with one Mg(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 39-48°. In the second Co site, Co(2) is bonded in a 5-coordinate geometry to one O(8), two equivalent O(3), and two equivalent O(6) atoms. In the third Co site, Co(3) is bonded to one O(1), one O(6), two equivalent O(2), and two equivalent O(8) atoms to form CoO6 octahedra that share corners with two equivalent Co(1)O6 octahedra, corners with two equivalent Zn(1)O5 square pyramids, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Co(3)O6 octahedra, and edges with two equivalent Co(4)O6 pentagonal pyramids. The corner-sharing octahedral tilt angles are 48°. In the fourth Co site, Co(4) is bonded to one O(5), one O(8), two equivalent O(1), and two equivalent O(7) atoms to form distorted CoO6 pentagonal pyramids that share corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent Zn(1)O5 square pyramids,  an edgeedge with one Mg(1)O6 octahedra, edges with two equivalent Co(1)O6 octahedra, edges with two equivalent Co(3)O6 octahedra, edges with two equivalent Co(4)O6 pentagonal pyramids, and  an edgeedge with one Zn(1)O5 square pyramid. The corner-sharing octahedral tilt angles are 13°. Zn(1) is bonded to one O(4), two equivalent O(6), and two equivalent O(7) atoms to form ZnO5 square pyramids that share corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent Co(3)O6 octahedra, corners with two equivalent Co(4)O6 pentagonal pyramids, edges with two equivalent Co(1)O6 octahedra,  an edgeedge with one Co(4)O6 pentagonal pyramid, and edges with two equivalent Zn(1)O5 square pyramids. The corner-sharing octahedral tilt angles range from 50-56°. There are eight inequivalent O sites. In the first O site, O(1) is bonded to two equivalent Mg(1), one Co(3), and two equivalent Co(4) atoms to form OMg2Co3 square pyramids that share corners with two equivalent O(7)Zn2Co3 square pyramids, corners with two equivalent O(4)Mg2ZnCo2 trigonal bipyramids,  an edgeedge with one O(7)Zn2Co3 square pyramid, edges with two equivalent O(1)Mg2Co3 square pyramids,  an edgeedge with one O(4)Mg2ZnCo2 trigonal bipyramid, edges with two equivalent O(8)Co4 trigonal pyramids, and edges with two equivalent O(2)MgCo3 trigonal pyramids. In the second O site, O(2) is bonded to one Mg(1), one Co(1), and two equivalent Co(3) atoms to form OMgCo3 trigonal pyramids that share  a cornercorner with one O(7)Zn2Co3 square pyramid, corners with two equivalent O(8)Co4 trigonal pyramids, corners with two equivalent O(2)MgCo3 trigonal pyramids, edges with two equivalent O(1)Mg2Co3 square pyramids, edges with two equivalent O(4)Mg2ZnCo2 trigonal bipyramids, and  an edgeedge with one O(8)Co4 trigonal pyramid. In the third O site, O(3) is bonded in a trigonal non-coplanar geometry to one Mg(1) and two equivalent Co(2) atoms. In the fourth O site, O(4) is bonded to two equivalent Mg(1), two equivalent Co(1), and one Zn(1) atom to form distorted OMg2ZnCo2 trigonal bipyramids that share corners with two equivalent O(1)Mg2Co3 square pyramids,  an edgeedge with one O(1)Mg2Co3 square pyramid, edges with two equivalent O(7)Zn2Co3 square pyramids, edges with two equivalent O(4)Mg2ZnCo2 trigonal bipyramids, and edges with two equivalent O(2)MgCo3 trigonal pyramids. In the fifth O site, O(5) is bonded in a trigonal non-coplanar geometry to one Co(4) and two equivalent Co(1) atoms. In the sixth O site, O(6) is bonded in a 5-coordinate geometry to one Co(3), two equivalent Co(2), and two equivalent Zn(1) atoms. In the seventh O site, O(7) is bonded to one Co(1), two equivalent Co(4), and two equivalent Zn(1) atoms to form OZn2Co3 square pyramids that share corners with two equivalent O(1)Mg2Co3 square pyramids,  a cornercorner with one O(2)MgCo3 trigonal pyramid, corners with two equivalent O(8)Co4 trigonal pyramids,  an edgeedge with one O(1)Mg2Co3 square pyramid, edges with two equivalent O(7)Zn2Co3 square pyramids, and edges with two equivalent O(4)Mg2ZnCo2 trigonal bipyramids. In the eighth O site, O(8) is bonded to one Co(2), one Co(4), and two equivalent Co(3) atoms to form distorted OCo4 trigonal pyramids that share corners with two equivalent O(7)Zn2Co3 square pyramids, corners with two equivalent O(8)Co4 trigonal pyramids, corners with two equivalent O(2)MgCo3 trigonal pyramids, edges with two equivalent O(1)Mg2Co3 square pyramids, and  an edgeedge with one O(2)MgCo3 trigonal pyramid.
MgZn(CoO2)4 crystallizes in the triclinic P1 space group. Mg(1) is bonded to one O(2), one O(3), two equivalent O(1), and two equivalent O(4) atoms to form distorted MgO6 octahedra that share corners with two equivalent Co(1)O6 octahedra, corners with two equivalent Co(4)O6 pentagonal pyramids, corners with two equivalent Zn(1)O5 square pyramids, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Co(3)O6 octahedra,  an edgeedge with one Co(4)O6 pentagonal pyramid, and  a faceface with one Co(1)O6 octahedra. The corner-sharing octahedral tilt angles are 39°. The Mg(1)-O(2) bond length is 2.19 Å. The Mg(1)-O(3) bond length is 2.01 Å. Both Mg(1)-O(1) bond lengths are 2.02 Å. There is one shorter (2.18 Å) and one longer (2.19 Å) Mg(1)-O(4) bond length. There are four inequivalent Co sites. In the first Co site, Co(1) is bonded to one O(2), one O(7), two equivalent O(4), and two equivalent O(5) atoms to form CoO6 octahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent Co(3)O6 octahedra, edges with two equivalent Co(1)O6 octahedra, edges with two equivalent Co(4)O6 pentagonal pyramids, edges with two equivalent Zn(1)O5 square pyramids, and  a faceface with one Mg(1)O6 octahedra. The corner-sharing octahedral tilt angles range from 39-48°. The Co(1)-O(2) bond length is 1.89 Å. The Co(1)-O(7) bond length is 1.95 Å. Both Co(1)-O(4) bond lengths are 2.01 Å. Both Co(1)-O(5) bond lengths are 1.87 Å. In the second Co site, Co(2) is bonded in a 5-coordinate geometry to one O(8), two equivalent O(3), and two equivalent O(6) atoms. The Co(2)-O(8) bond length is 1.85 Å. Both Co(2)-O(3) bond lengths are 1.85 Å. There is one shorter (2.33 Å) and one longer (2.35 Å) Co(2)-O(6) bond length. In the third Co site, Co(3) is bonded to one O(1), one O(6), two equivalent O(2), and two equivalent O(8) atoms to form CoO6 octahedra that share corners with two equivalent Co(1)O6 octahedra, corners with two equivalent Zn(1)O5 square pyramids, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Co(3)O6 octahedra, and edges with two equivalent Co(4)O6 pentagonal pyramids. The corner-sharing octahedral tilt angles are 48°. The Co(3)-O(1) bond length is 2.10 Å. The Co(3)-O(6) bond length is 1.97 Å. Both Co(3)-O(2) bond lengths are 1.97 Å. Both Co(3)-O(8) bond lengths are 2.06 Å. In the fourth Co site, Co(4) is bonded to one O(5), one O(8), two equivalent O(1), and two equivalent O(7) atoms to form distorted CoO6 pentagonal pyramids that share corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent Zn(1)O5 square pyramids,  an edgeedge with one Mg(1)O6 octahedra, edges with two equivalent Co(1)O6 octahedra, edges with two equivalent Co(3)O6 octahedra, edges with two equivalent Co(4)O6 pentagonal pyramids, and  an edgeedge with one Zn(1)O5 square pyramid. The corner-sharing octahedral tilt angles are 13°. The Co(4)-O(5) bond length is 2.07 Å. The Co(4)-O(8) bond length is 2.04 Å. Both Co(4)-O(1) bond lengths are 2.13 Å. There is one shorter (2.18 Å) and one longer (2.19 Å) Co(4)-O(7) bond length. Zn(1) is bonded to one O(4), two equivalent O(6), and two equivalent O(7) atoms to form ZnO5 square pyramids that share corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent Co(3)O6 octahedra, corners with two equivalent Co(4)O6 pentagonal pyramids, edges with two equivalent Co(1)O6 octahedra,  an edgeedge with one Co(4)O6 pentagonal pyramid, and edges with two equivalent Zn(1)O5 square pyramids. The corner-sharing octahedral tilt angles range from 50-56°. The Zn(1)-O(4) bond length is 2.13 Å. Both Zn(1)-O(6) bond lengths are 2.07 Å. Both Zn(1)-O(7) bond lengths are 2.08 Å. There are eight inequivalent O sites. In the first O site, O(1) is bonded to two equivalent Mg(1), one Co(3), and two equivalent Co(4) atoms to form OMg2Co3 square pyramids that share corners with two equivalent O(7)Zn2Co3 square pyramids, corners with two equivalent O(4)Mg2ZnCo2 trigonal bipyramids,  an edgeedge with one O(7)Zn2Co3 square pyramid, edges with two equivalent O(1)Mg2Co3 square pyramids,  an edgeedge with one O(4)Mg2ZnCo2 trigonal bipyramid, edges with two equivalent O(8)Co4 trigonal pyramids, and edges with two equivalent O(2)MgCo3 trigonal pyramids. In the second O site, O(2) is bonded to one Mg(1), one Co(1), and two equivalent Co(3) atoms to form OMgCo3 trigonal pyramids that share  a cornercorner with one O(7)Zn2Co3 square pyramid, corners with two equivalent O(8)Co4 trigonal pyramids, corners with two equivalent O(2)MgCo3 trigonal pyramids, edges with two equivalent O(1)Mg2Co3 square pyramids, edges with two equivalent O(4)Mg2ZnCo2 trigonal bipyramids, and  an edgeedge with one O(8)Co4 trigonal pyramid. In the third O site, O(3) is bonded in a trigonal non-coplanar geometry to one Mg(1) and two equivalent Co(2) atoms. In the fourth O site, O(4) is bonded to two equivalent Mg(1), two equivalent Co(1), and one Zn(1) atom to form distorted OMg2ZnCo2 trigonal bipyramids that share corners with two equivalent O(1)Mg2Co3 square pyramids,  an edgeedge with one O(1)Mg2Co3 square pyramid, edges with two equivalent O(7)Zn2Co3 square pyramids, edges with two equivalent O(4)Mg2ZnCo2 trigonal bipyramids, and edges with two equivalent O(2)MgCo3 trigonal pyramids. In the fifth O site, O(5) is bonded in a trigonal non-coplanar geometry to one Co(4) and two equivalent Co(1) atoms. In the sixth O site, O(6) is bonded in a 5-coordinate geometry to one Co(3), two equivalent Co(2), and two equivalent Zn(1) atoms. In the seventh O site, O(7) is bonded to one Co(1), two equivalent Co(4), and two equivalent Zn(1) atoms to form OZn2Co3 square pyramids that share corners with two equivalent O(1)Mg2Co3 square pyramids,  a cornercorner with one O(2)MgCo3 trigonal pyramid, corners with two equivalent O(8)Co4 trigonal pyramids,  an edgeedge with one O(1)Mg2Co3 square pyramid, edges with two equivalent O(7)Zn2Co3 square pyramids, and edges with two equivalent O(4)Mg2ZnCo2 trigonal bipyramids. In the eighth O site, O(8) is bonded to one Co(2), one Co(4), and two equivalent Co(3) atoms to form distorted OCo4 trigonal pyramids that share corners with two equivalent O(7)Zn2Co3 square pyramids, corners with two equivalent O(8)Co4 trigonal pyramids, corners with two equivalent O(2)MgCo3 trigonal pyramids, edges with two equivalent O(1)Mg2Co3 square pyramids, and  an edgeedge with one O(2)MgCo3 trigonal pyramid.