NaMg4V3O12 crystallizes in the tetragonal I-42d space group. There are two inequivalent Na sites. In the first Na site, Na(1) is bonded in a distorted body-centered cubic geometry to four equivalent O(2) and four equivalent O(3) atoms. In the second Na site, Na(1) is bonded in a distorted body-centered cubic geometry to four equivalent O(2) and four equivalent O(3) atoms. There are five inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(3) atoms to form MgO6 octahedra that share corners with two equivalent Mg(2)O6 octahedra; corners with two equivalent V(1)O4 tetrahedra; corners with four V(2,2)O4 tetrahedra; and edges with two equivalent Mg(2)O6 octahedra. The corner-sharing octahedral tilt angles are 55°. In the second Mg site, Mg(2) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(3) atoms to form MgO6 octahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent V(1)O4 tetrahedra, corners with two equivalent V(2)O4 tetrahedra, edges with two equivalent Mg(1)O6 octahedra, and  an edgeedge with one V(2)O4 tetrahedra. The corner-sharing octahedral tilt angles are 55°. In the third Mg site, Mg(1) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(3) atoms to form MgO6 octahedra that share corners with two equivalent Mg(2)O6 octahedra; corners with two equivalent V(1)O4 tetrahedra; corners with four V(2,2)O4 tetrahedra; and edges with two equivalent Mg(2)O6 octahedra. The corner-sharing octahedral tilt angles are 55°. In the fourth Mg site, Mg(2) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(3) atoms to form MgO6 octahedra that share corners with two Mg(1,1)O6 octahedra; corners with two equivalent V(1)O4 tetrahedra; corners with two equivalent V(2)O4 tetrahedra; edges with two Mg(1,1)O6 octahedra; and  an edgeedge with one V(2)O4 tetrahedra. The corner-sharing octahedral tilt angles are 55°. In the fifth Mg site, Mg(2) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(3) atoms to form MgO6 octahedra that share corners with two Mg(1,1)O6 octahedra; corners with two equivalent V(1)O4 tetrahedra; corners with two equivalent V(2)O4 tetrahedra; edges with two Mg(1,1)O6 octahedra; and  an edgeedge with one V(2)O4 tetrahedra. The corner-sharing octahedral tilt angles are 55°. There are four inequivalent V sites. In the first V site, V(1) is bonded to four equivalent O(1) atoms to form VO4 tetrahedra that share corners with four equivalent Mg(1)O6 octahedra and corners with four equivalent Mg(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 49-50°. In the second V site, V(2) is bonded to two equivalent O(2) and two equivalent O(3) atoms to form VO4 tetrahedra that share corners with two equivalent Mg(2)O6 octahedra, corners with four equivalent Mg(1)O6 octahedra, and  an edgeedge with one Mg(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 45-49°. In the third V site, V(2) is bonded to two equivalent O(2) and two equivalent O(3) atoms to form VO4 tetrahedra that share corners with two equivalent Mg(2)O6 octahedra; corners with four Mg(1,1)O6 octahedra; and  an edgeedge with one Mg(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 45-49°. In the fourth V site, V(2) is bonded to two equivalent O(2) and two equivalent O(3) atoms to form VO4 tetrahedra that share corners with two equivalent Mg(2)O6 octahedra; corners with four Mg(1,1)O6 octahedra; and  an edgeedge with one Mg(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 45-49°. There are three inequivalent O sites. In the first O site, O(1) is bonded in a distorted trigonal planar geometry to one Mg(1), one Mg(2), and one V(1) atom. In the second O site, O(2) is bonded to one Na(1), one Mg(1), one Mg(2), and one V(2) atom to form distorted corner-sharing ONaMg2V trigonal pyramids. In the third O site, O(3) is bonded in a distorted rectangular see-saw-like geometry to one Na(1), one Mg(1), one Mg(2), and one V(2) atom.
NaMg4V3O12 crystallizes in the tetragonal I-42d space group. There are two inequivalent Na sites. In the first Na site, Na(1) is bonded in a distorted body-centered cubic geometry to four equivalent O(2) and four equivalent O(3) atoms. All Na(1)-O(2) bond lengths are 2.71 Å. All Na(1)-O(3) bond lengths are 2.39 Å. In the second Na site, Na(1) is bonded in a distorted body-centered cubic geometry to four equivalent O(2) and four equivalent O(3) atoms. All Na(1)-O(2) bond lengths are 2.71 Å. All Na(1)-O(3) bond lengths are 2.39 Å. There are five inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(3) atoms to form MgO6 octahedra that share corners with two equivalent Mg(2)O6 octahedra; corners with two equivalent V(1)O4 tetrahedra; corners with four V(2,2)O4 tetrahedra; and edges with two equivalent Mg(2)O6 octahedra. The corner-sharing octahedral tilt angles are 55°. Both Mg(1)-O(1) bond lengths are 2.11 Å. Both Mg(1)-O(2) bond lengths are 2.16 Å. Both Mg(1)-O(3) bond lengths are 2.13 Å. In the second Mg site, Mg(2) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(3) atoms to form MgO6 octahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with two equivalent V(1)O4 tetrahedra, corners with two equivalent V(2)O4 tetrahedra, edges with two equivalent Mg(1)O6 octahedra, and  an edgeedge with one V(2)O4 tetrahedra. The corner-sharing octahedral tilt angles are 55°. Both Mg(2)-O(1) bond lengths are 2.04 Å. Both Mg(2)-O(2) bond lengths are 2.10 Å. Both Mg(2)-O(3) bond lengths are 2.19 Å. In the third Mg site, Mg(1) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(3) atoms to form MgO6 octahedra that share corners with two equivalent Mg(2)O6 octahedra; corners with two equivalent V(1)O4 tetrahedra; corners with four V(2,2)O4 tetrahedra; and edges with two equivalent Mg(2)O6 octahedra. The corner-sharing octahedral tilt angles are 55°. Both Mg(1)-O(1) bond lengths are 2.11 Å. Both Mg(1)-O(2) bond lengths are 2.16 Å. Both Mg(1)-O(3) bond lengths are 2.13 Å. In the fourth Mg site, Mg(2) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(3) atoms to form MgO6 octahedra that share corners with two Mg(1,1)O6 octahedra; corners with two equivalent V(1)O4 tetrahedra; corners with two equivalent V(2)O4 tetrahedra; edges with two Mg(1,1)O6 octahedra; and  an edgeedge with one V(2)O4 tetrahedra. The corner-sharing octahedral tilt angles are 55°. Both Mg(2)-O(1) bond lengths are 2.04 Å. Both Mg(2)-O(2) bond lengths are 2.10 Å. Both Mg(2)-O(3) bond lengths are 2.19 Å. In the fifth Mg site, Mg(2) is bonded to two equivalent O(1), two equivalent O(2), and two equivalent O(3) atoms to form MgO6 octahedra that share corners with two Mg(1,1)O6 octahedra; corners with two equivalent V(1)O4 tetrahedra; corners with two equivalent V(2)O4 tetrahedra; edges with two Mg(1,1)O6 octahedra; and  an edgeedge with one V(2)O4 tetrahedra. The corner-sharing octahedral tilt angles are 55°. Both Mg(2)-O(1) bond lengths are 2.04 Å. Both Mg(2)-O(2) bond lengths are 2.10 Å. Both Mg(2)-O(3) bond lengths are 2.19 Å. There are four inequivalent V sites. In the first V site, V(1) is bonded to four equivalent O(1) atoms to form VO4 tetrahedra that share corners with four equivalent Mg(1)O6 octahedra and corners with four equivalent Mg(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 49-50°. All V(1)-O(1) bond lengths are 1.75 Å. In the second V site, V(2) is bonded to two equivalent O(2) and two equivalent O(3) atoms to form VO4 tetrahedra that share corners with two equivalent Mg(2)O6 octahedra, corners with four equivalent Mg(1)O6 octahedra, and  an edgeedge with one Mg(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 45-49°. Both V(2)-O(2) bond lengths are 1.76 Å. Both V(2)-O(3) bond lengths are 1.75 Å. In the third V site, V(2) is bonded to two equivalent O(2) and two equivalent O(3) atoms to form VO4 tetrahedra that share corners with two equivalent Mg(2)O6 octahedra; corners with four Mg(1,1)O6 octahedra; and  an edgeedge with one Mg(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 45-49°. Both V(2)-O(2) bond lengths are 1.76 Å. Both V(2)-O(3) bond lengths are 1.75 Å. In the fourth V site, V(2) is bonded to two equivalent O(2) and two equivalent O(3) atoms to form VO4 tetrahedra that share corners with two equivalent Mg(2)O6 octahedra; corners with four Mg(1,1)O6 octahedra; and  an edgeedge with one Mg(2)O6 octahedra. The corner-sharing octahedral tilt angles range from 45-49°. Both V(2)-O(2) bond lengths are 1.76 Å. Both V(2)-O(3) bond lengths are 1.75 Å. There are three inequivalent O sites. In the first O site, O(1) is bonded in a distorted trigonal planar geometry to one Mg(1), one Mg(2), and one V(1) atom. In the second O site, O(2) is bonded to one Na(1), one Mg(1), one Mg(2), and one V(2) atom to form distorted corner-sharing ONaMg2V trigonal pyramids. In the third O site, O(3) is bonded in a distorted rectangular see-saw-like geometry to one Na(1), one Mg(1), one Mg(2), and one V(2) atom.