Mg4ZrN4 crystallizes in the triclinic P-1 space group. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one N(1), one N(2), one N(3), and one N(4) atom to form distorted MgN4 tetrahedra that share  a cornercorner with one Mg(3)N5 square pyramid, corners with three equivalent Mg(4)N5 square pyramids, corners with four equivalent Zr(1)N4 tetrahedra,  an edgeedge with one Mg(4)N5 square pyramid, and edges with two equivalent Mg(3)N5 square pyramids. In the second Mg site, Mg(2) is bonded in a 4-coordinate geometry to two equivalent N(2) and two equivalent N(3) atoms. In the third Mg site, Mg(3) is bonded to one N(3), two equivalent N(1), and two equivalent N(4) atoms to form MgN5 square pyramids that share corners with three equivalent Mg(4)N5 square pyramids,  a cornercorner with one Mg(1)N4 tetrahedra, corners with three equivalent Zr(1)N4 tetrahedra, edges with two equivalent Mg(3)N5 square pyramids, edges with three equivalent Mg(4)N5 square pyramids,  an edgeedge with one Zr(1)N4 tetrahedra, and edges with two equivalent Mg(1)N4 tetrahedra. In the fourth Mg site, Mg(4) is bonded to one N(3), two equivalent N(1), and two equivalent N(4) atoms to form distorted MgN5 square pyramids that share corners with three equivalent Mg(3)N5 square pyramids,  a cornercorner with one Zr(1)N4 tetrahedra, corners with three equivalent Mg(1)N4 tetrahedra, edges with two equivalent Mg(4)N5 square pyramids, edges with three equivalent Mg(3)N5 square pyramids,  an edgeedge with one Mg(1)N4 tetrahedra, and edges with two equivalent Zr(1)N4 tetrahedra. Zr(1) is bonded to one N(1), one N(2), one N(3), and one N(4) atom to form ZrN4 tetrahedra that share  a cornercorner with one Mg(4)N5 square pyramid, corners with three equivalent Mg(3)N5 square pyramids, corners with four equivalent Mg(1)N4 tetrahedra,  an edgeedge with one Mg(3)N5 square pyramid, and edges with two equivalent Mg(4)N5 square pyramids. There are four inequivalent N sites. In the first N site, N(1) is bonded to one Mg(1), two equivalent Mg(3), two equivalent Mg(4), and one Zr(1) atom to form NMg5Zr octahedra that share corners with two equivalent N(3)Mg5Zr octahedra, corners with two equivalent N(4)Mg5Zr octahedra, corners with two equivalent N(2)Mg3Zr tetrahedra, edges with two equivalent N(1)Mg5Zr octahedra, edges with two equivalent N(3)Mg5Zr octahedra, and edges with four equivalent N(4)Mg5Zr octahedra. The corner-sharing octahedral tilt angles range from 11-16°. In the second N site, N(2) is bonded to one Mg(1), two equivalent Mg(2), and one Zr(1) atom to form NMg3Zr tetrahedra that share corners with two equivalent N(1)Mg5Zr octahedra, corners with two equivalent N(4)Mg5Zr octahedra, corners with six equivalent N(3)Mg5Zr octahedra, and  an edgeedge with one N(2)Mg3Zr tetrahedra. The corner-sharing octahedral tilt angles range from 55-65°. In the third N site, N(3) is bonded to one Mg(1), one Mg(3), one Mg(4), two equivalent Mg(2), and one Zr(1) atom to form NMg5Zr octahedra that share corners with two equivalent N(1)Mg5Zr octahedra, corners with six equivalent N(2)Mg3Zr tetrahedra,  an edgeedge with one N(3)Mg5Zr octahedra, edges with two equivalent N(1)Mg5Zr octahedra, and edges with three equivalent N(4)Mg5Zr octahedra. The corner-sharing octahedral tilt angles range from 11-15°. In the fourth N site, N(4) is bonded to one Mg(1), two equivalent Mg(3), two equivalent Mg(4), and one Zr(1) atom to form distorted NMg5Zr octahedra that share corners with two equivalent N(1)Mg5Zr octahedra, corners with two equivalent N(2)Mg3Zr tetrahedra, edges with two equivalent N(4)Mg5Zr octahedra, edges with three equivalent N(3)Mg5Zr octahedra, and edges with four equivalent N(1)Mg5Zr octahedra. The corner-sharing octahedral tilt angles range from 12-16°.
Mg4ZrN4 crystallizes in the triclinic P-1 space group. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one N(1), one N(2), one N(3), and one N(4) atom to form distorted MgN4 tetrahedra that share  a cornercorner with one Mg(3)N5 square pyramid, corners with three equivalent Mg(4)N5 square pyramids, corners with four equivalent Zr(1)N4 tetrahedra,  an edgeedge with one Mg(4)N5 square pyramid, and edges with two equivalent Mg(3)N5 square pyramids. The Mg(1)-N(1) bond length is 2.16 Å. The Mg(1)-N(2) bond length is 2.05 Å. The Mg(1)-N(3) bond length is 2.13 Å. The Mg(1)-N(4) bond length is 2.09 Å. In the second Mg site, Mg(2) is bonded in a 4-coordinate geometry to two equivalent N(2) and two equivalent N(3) atoms. There is one shorter (2.11 Å) and one longer (2.13 Å) Mg(2)-N(2) bond length. There is one shorter (2.24 Å) and one longer (2.28 Å) Mg(2)-N(3) bond length. In the third Mg site, Mg(3) is bonded to one N(3), two equivalent N(1), and two equivalent N(4) atoms to form MgN5 square pyramids that share corners with three equivalent Mg(4)N5 square pyramids,  a cornercorner with one Mg(1)N4 tetrahedra, corners with three equivalent Zr(1)N4 tetrahedra, edges with two equivalent Mg(3)N5 square pyramids, edges with three equivalent Mg(4)N5 square pyramids,  an edgeedge with one Zr(1)N4 tetrahedra, and edges with two equivalent Mg(1)N4 tetrahedra. The Mg(3)-N(3) bond length is 2.45 Å. There is one shorter (2.19 Å) and one longer (2.30 Å) Mg(3)-N(1) bond length. There is one shorter (2.12 Å) and one longer (2.28 Å) Mg(3)-N(4) bond length. In the fourth Mg site, Mg(4) is bonded to one N(3), two equivalent N(1), and two equivalent N(4) atoms to form distorted MgN5 square pyramids that share corners with three equivalent Mg(3)N5 square pyramids,  a cornercorner with one Zr(1)N4 tetrahedra, corners with three equivalent Mg(1)N4 tetrahedra, edges with two equivalent Mg(4)N5 square pyramids, edges with three equivalent Mg(3)N5 square pyramids,  an edgeedge with one Mg(1)N4 tetrahedra, and edges with two equivalent Zr(1)N4 tetrahedra. The Mg(4)-N(3) bond length is 2.22 Å. There is one shorter (2.20 Å) and one longer (2.24 Å) Mg(4)-N(1) bond length. There is one shorter (2.14 Å) and one longer (2.68 Å) Mg(4)-N(4) bond length. Zr(1) is bonded to one N(1), one N(2), one N(3), and one N(4) atom to form ZrN4 tetrahedra that share  a cornercorner with one Mg(4)N5 square pyramid, corners with three equivalent Mg(3)N5 square pyramids, corners with four equivalent Mg(1)N4 tetrahedra,  an edgeedge with one Mg(3)N5 square pyramid, and edges with two equivalent Mg(4)N5 square pyramids. The Zr(1)-N(1) bond length is 2.14 Å. The Zr(1)-N(2) bond length is 2.08 Å. The Zr(1)-N(3) bond length is 2.09 Å. The Zr(1)-N(4) bond length is 2.07 Å. There are four inequivalent N sites. In the first N site, N(1) is bonded to one Mg(1), two equivalent Mg(3), two equivalent Mg(4), and one Zr(1) atom to form NMg5Zr octahedra that share corners with two equivalent N(3)Mg5Zr octahedra, corners with two equivalent N(4)Mg5Zr octahedra, corners with two equivalent N(2)Mg3Zr tetrahedra, edges with two equivalent N(1)Mg5Zr octahedra, edges with two equivalent N(3)Mg5Zr octahedra, and edges with four equivalent N(4)Mg5Zr octahedra. The corner-sharing octahedral tilt angles range from 11-16°. In the second N site, N(2) is bonded to one Mg(1), two equivalent Mg(2), and one Zr(1) atom to form NMg3Zr tetrahedra that share corners with two equivalent N(1)Mg5Zr octahedra, corners with two equivalent N(4)Mg5Zr octahedra, corners with six equivalent N(3)Mg5Zr octahedra, and  an edgeedge with one N(2)Mg3Zr tetrahedra. The corner-sharing octahedral tilt angles range from 55-65°. In the third N site, N(3) is bonded to one Mg(1), one Mg(3), one Mg(4), two equivalent Mg(2), and one Zr(1) atom to form NMg5Zr octahedra that share corners with two equivalent N(1)Mg5Zr octahedra, corners with six equivalent N(2)Mg3Zr tetrahedra,  an edgeedge with one N(3)Mg5Zr octahedra, edges with two equivalent N(1)Mg5Zr octahedra, and edges with three equivalent N(4)Mg5Zr octahedra. The corner-sharing octahedral tilt angles range from 11-15°. In the fourth N site, N(4) is bonded to one Mg(1), two equivalent Mg(3), two equivalent Mg(4), and one Zr(1) atom to form distorted NMg5Zr octahedra that share corners with two equivalent N(1)Mg5Zr octahedra, corners with two equivalent N(2)Mg3Zr tetrahedra, edges with two equivalent N(4)Mg5Zr octahedra, edges with three equivalent N(3)Mg5Zr octahedra, and edges with four equivalent N(1)Mg5Zr octahedra. The corner-sharing octahedral tilt angles range from 12-16°.