NaMg6BO7 crystallizes in the tetragonal P4mm space group. Na(1) is bonded to one O(1) and four equivalent O(4) atoms to form NaO5 square pyramids that share  a cornercorner with one Mg(1)O5 square pyramid, corners with four equivalent Na(1)O5 square pyramids, and edges with four equivalent Mg(4)O6 octahedra. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one O(1) and four equivalent O(5) atoms to form MgO5 square pyramids that share  a cornercorner with one Na(1)O5 square pyramid, corners with four equivalent Mg(1)O5 square pyramids, edges with four equivalent Mg(4)O6 octahedra, and edges with four equivalent Mg(2)O5 square pyramids. In the second Mg site, Mg(2) is bonded to one O(2) and four equivalent O(5) atoms to form distorted MgO5 square pyramids that share corners with four equivalent Mg(4)O6 octahedra, corners with four equivalent Mg(2)O5 square pyramids, and edges with four equivalent Mg(1)O5 square pyramids. The corner-sharing octahedral tilt angles are 82°. In the third Mg site, Mg(3) is bonded in a 4-coordinate geometry to one O(4), one O(5), and two equivalent O(2) atoms. In the fourth Mg site, Mg(4) is bonded to one O(4), one O(5), two equivalent O(1), and two equivalent O(3) atoms to form MgO6 octahedra that share corners with four equivalent Mg(4)O6 octahedra, corners with two equivalent Mg(2)O5 square pyramids, edges with four equivalent Mg(4)O6 octahedra, edges with two equivalent Na(1)O5 square pyramids, and edges with two equivalent Mg(1)O5 square pyramids. The corner-sharing octahedral tilt angles range from 9-18°. B(1) is bonded in a distorted single-bond geometry to one O(3) and four equivalent O(4) atoms. There are five inequivalent O sites. In the first O site, O(1) is bonded to one Na(1), one Mg(1), and four equivalent Mg(4) atoms to form ONaMg5 octahedra that share corners with four equivalent O(1)NaMg5 octahedra, edges with four equivalent O(5)Mg6 octahedra, and edges with four equivalent O(4)Na2Mg2B2 octahedra. The corner-sharing octahedral tilt angles are 9°. In the second O site, O(2) is bonded to one Mg(2) and four equivalent Mg(3) atoms to form OMg5 square pyramids that share corners with four equivalent O(4)Na2Mg2B2 octahedra, corners with four equivalent O(2)Mg5 square pyramids, and edges with four equivalent O(5)Mg6 octahedra. The corner-sharing octahedral tilt angles are 81°. In the third O site, O(3) is bonded in a 5-coordinate geometry to four equivalent Mg(4) and one B(1) atom. In the fourth O site, O(4) is bonded to two equivalent Na(1), one Mg(3), one Mg(4), and two equivalent B(1) atoms to form ONa2Mg2B2 octahedra that share corners with two equivalent O(5)Mg6 octahedra, corners with four equivalent O(4)Na2Mg2B2 octahedra, corners with two equivalent O(2)Mg5 square pyramids, edges with two equivalent O(1)NaMg5 octahedra, and edges with four equivalent O(4)Na2Mg2B2 octahedra. The corner-sharing octahedral tilt angles range from 0-20°. In the fifth O site, O(5) is bonded to one Mg(3), one Mg(4), two equivalent Mg(1), and two equivalent Mg(2) atoms to form OMg6 octahedra that share corners with two equivalent O(4)Na2Mg2B2 octahedra, corners with four equivalent O(5)Mg6 octahedra, edges with two equivalent O(1)NaMg5 octahedra, edges with four equivalent O(5)Mg6 octahedra, and edges with two equivalent O(2)Mg5 square pyramids. The corner-sharing octahedral tilt angles range from 0-16°.
NaMg6BO7 crystallizes in the tetragonal P4mm space group. Na(1) is bonded to one O(1) and four equivalent O(4) atoms to form NaO5 square pyramids that share  a cornercorner with one Mg(1)O5 square pyramid, corners with four equivalent Na(1)O5 square pyramids, and edges with four equivalent Mg(4)O6 octahedra. The Na(1)-O(1) bond length is 2.24 Å. All Na(1)-O(4) bond lengths are 2.12 Å. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one O(1) and four equivalent O(5) atoms to form MgO5 square pyramids that share  a cornercorner with one Na(1)O5 square pyramid, corners with four equivalent Mg(1)O5 square pyramids, edges with four equivalent Mg(4)O6 octahedra, and edges with four equivalent Mg(2)O5 square pyramids. The Mg(1)-O(1) bond length is 2.03 Å. All Mg(1)-O(5) bond lengths are 2.12 Å. In the second Mg site, Mg(2) is bonded to one O(2) and four equivalent O(5) atoms to form distorted MgO5 square pyramids that share corners with four equivalent Mg(4)O6 octahedra, corners with four equivalent Mg(2)O5 square pyramids, and edges with four equivalent Mg(1)O5 square pyramids. The corner-sharing octahedral tilt angles are 82°. The Mg(2)-O(2) bond length is 1.99 Å. All Mg(2)-O(5) bond lengths are 2.14 Å. In the third Mg site, Mg(3) is bonded in a 4-coordinate geometry to one O(4), one O(5), and two equivalent O(2) atoms. The Mg(3)-O(4) bond length is 2.04 Å. The Mg(3)-O(5) bond length is 2.61 Å. Both Mg(3)-O(2) bond lengths are 2.14 Å. In the fourth Mg site, Mg(4) is bonded to one O(4), one O(5), two equivalent O(1), and two equivalent O(3) atoms to form MgO6 octahedra that share corners with four equivalent Mg(4)O6 octahedra, corners with two equivalent Mg(2)O5 square pyramids, edges with four equivalent Mg(4)O6 octahedra, edges with two equivalent Na(1)O5 square pyramids, and edges with two equivalent Mg(1)O5 square pyramids. The corner-sharing octahedral tilt angles range from 9-18°. The Mg(4)-O(4) bond length is 2.09 Å. The Mg(4)-O(5) bond length is 2.16 Å. Both Mg(4)-O(1) bond lengths are 2.12 Å. Both Mg(4)-O(3) bond lengths are 2.14 Å. B(1) is bonded in a distorted single-bond geometry to one O(3) and four equivalent O(4) atoms. The B(1)-O(3) bond length is 1.39 Å. All B(1)-O(4) bond lengths are 2.15 Å. There are five inequivalent O sites. In the first O site, O(1) is bonded to one Na(1), one Mg(1), and four equivalent Mg(4) atoms to form ONaMg5 octahedra that share corners with four equivalent O(1)NaMg5 octahedra, edges with four equivalent O(5)Mg6 octahedra, and edges with four equivalent O(4)Na2Mg2B2 octahedra. The corner-sharing octahedral tilt angles are 9°. In the second O site, O(2) is bonded to one Mg(2) and four equivalent Mg(3) atoms to form OMg5 square pyramids that share corners with four equivalent O(4)Na2Mg2B2 octahedra, corners with four equivalent O(2)Mg5 square pyramids, and edges with four equivalent O(5)Mg6 octahedra. The corner-sharing octahedral tilt angles are 81°. In the third O site, O(3) is bonded in a 5-coordinate geometry to four equivalent Mg(4) and one B(1) atom. In the fourth O site, O(4) is bonded to two equivalent Na(1), one Mg(3), one Mg(4), and two equivalent B(1) atoms to form ONa2Mg2B2 octahedra that share corners with two equivalent O(5)Mg6 octahedra, corners with four equivalent O(4)Na2Mg2B2 octahedra, corners with two equivalent O(2)Mg5 square pyramids, edges with two equivalent O(1)NaMg5 octahedra, and edges with four equivalent O(4)Na2Mg2B2 octahedra. The corner-sharing octahedral tilt angles range from 0-20°. In the fifth O site, O(5) is bonded to one Mg(3), one Mg(4), two equivalent Mg(1), and two equivalent Mg(2) atoms to form OMg6 octahedra that share corners with two equivalent O(4)Na2Mg2B2 octahedra, corners with four equivalent O(5)Mg6 octahedra, edges with two equivalent O(1)NaMg5 octahedra, edges with four equivalent O(5)Mg6 octahedra, and edges with two equivalent O(2)Mg5 square pyramids. The corner-sharing octahedral tilt angles range from 0-16°.