NaMg6HfO7 crystallizes in the tetragonal P4mm space group. Na(1) is bonded to one O(1), one O(2), and four equivalent O(4) atoms to form NaO6 octahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with four equivalent Na(1)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, and edges with four equivalent Hf(1)O5 square pyramids. The corner-sharing octahedral tilt angles range from 0-5°. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one O(1), one O(2), and four equivalent O(5) atoms to form MgO6 octahedra that share corners with two equivalent Na(1)O6 octahedra, corners with four equivalent Mg(1)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, and edges with four equivalent Mg(2)O5 square pyramids. The corner-sharing octahedral tilt angles range from 0-1°. In the second Mg site, Mg(2) is bonded to one O(3) and four equivalent O(5) atoms to form MgO5 square pyramids that share  a cornercorner with one Hf(1)O5 square pyramid, corners with four equivalent Mg(2)O5 square pyramids, edges with four equivalent Mg(1)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. In the third Mg site, Mg(3) is bonded in a square co-planar geometry to one O(4), one O(5), and two equivalent O(1) atoms. In the fourth Mg site, Mg(4) is bonded to one O(4), one O(5), two equivalent O(2), and two equivalent O(3) atoms to form MgO6 octahedra that share corners with four equivalent Mg(4)O6 octahedra, edges with two equivalent Na(1)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, edges with two equivalent Mg(2)O5 square pyramids, and edges with two equivalent Hf(1)O5 square pyramids. The corner-sharing octahedral tilt angles range from 2-4°. Hf(1) is bonded to one O(3) and four equivalent O(4) atoms to form HfO5 square pyramids that share  a cornercorner with one Mg(2)O5 square pyramid, corners with four equivalent Hf(1)O5 square pyramids, edges with four equivalent Na(1)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. 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(3) atoms to form ONaMg5 octahedra that share corners with two equivalent O(2)NaMg5 octahedra, corners with four equivalent O(1)NaMg5 octahedra, edges with four equivalent O(5)Mg6 octahedra, and edges with four equivalent O(4)Na2Hf2Mg2 octahedra. The corner-sharing octahedral tilt angles range from 0-5°. In the second O site, O(2) is bonded to one Na(1), one Mg(1), and four equivalent Mg(4) atoms to form ONaMg5 octahedra that share corners with two equivalent O(1)NaMg5 octahedra, corners with four equivalent O(2)NaMg5 octahedra, edges with four equivalent O(3)HfMg5 octahedra, edges with four equivalent O(5)Mg6 octahedra, and edges with four equivalent O(4)Na2Hf2Mg2 octahedra. The corner-sharing octahedral tilt angles range from 0-4°. In the third O site, O(3) is bonded to one Mg(2), four equivalent Mg(4), and one Hf(1) atom to form OHfMg5 octahedra that share corners with four equivalent O(3)HfMg5 octahedra, edges with four equivalent O(5)Mg6 octahedra, edges with four equivalent O(4)Na2Hf2Mg2 octahedra, and edges with four equivalent O(2)NaMg5 octahedra. The corner-sharing octahedral tilt angles are 2°. In the fourth O site, O(4) is bonded to two equivalent Na(1), one Mg(3), one Mg(4), and two equivalent Hf(1) atoms to form ONa2Hf2Mg2 octahedra that share corners with two equivalent O(5)Mg6 octahedra, corners with four equivalent O(4)Na2Hf2Mg2 octahedra, edges with two equivalent O(3)HfMg5 octahedra, edges with two equivalent O(1)NaMg5 octahedra, edges with two equivalent O(2)NaMg5 octahedra, and edges with four equivalent O(4)Na2Hf2Mg2 octahedra. The corner-sharing octahedral tilt angles range from 0-5°. 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)Na2Hf2Mg2 octahedra, corners with four equivalent O(5)Mg6 octahedra, edges with two equivalent O(3)HfMg5 octahedra, edges with two equivalent O(1)NaMg5 octahedra, edges with two equivalent O(2)NaMg5 octahedra, and edges with four equivalent O(5)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 0-2°.
NaMg6HfO7 crystallizes in the tetragonal P4mm space group. Na(1) is bonded to one O(1), one O(2), and four equivalent O(4) atoms to form NaO6 octahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with four equivalent Na(1)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, and edges with four equivalent Hf(1)O5 square pyramids. The corner-sharing octahedral tilt angles range from 0-5°. The Na(1)-O(1) bond length is 2.35 Å. The Na(1)-O(2) bond length is 2.40 Å. All Na(1)-O(4) bond lengths are 2.16 Å. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one O(1), one O(2), and four equivalent O(5) atoms to form MgO6 octahedra that share corners with two equivalent Na(1)O6 octahedra, corners with four equivalent Mg(1)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, and edges with four equivalent Mg(2)O5 square pyramids. The corner-sharing octahedral tilt angles range from 0-1°. The Mg(1)-O(1) bond length is 2.06 Å. The Mg(1)-O(2) bond length is 2.07 Å. All Mg(1)-O(5) bond lengths are 2.16 Å. In the second Mg site, Mg(2) is bonded to one O(3) and four equivalent O(5) atoms to form MgO5 square pyramids that share  a cornercorner with one Hf(1)O5 square pyramid, corners with four equivalent Mg(2)O5 square pyramids, edges with four equivalent Mg(1)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. The Mg(2)-O(3) bond length is 2.15 Å. All Mg(2)-O(5) bond lengths are 2.16 Å. In the third Mg site, Mg(3) is bonded in a square co-planar geometry to one O(4), one O(5), and two equivalent O(1) atoms. The Mg(3)-O(4) bond length is 2.35 Å. The Mg(3)-O(5) bond length is 2.16 Å. Both Mg(3)-O(1) bond lengths are 2.16 Å. In the fourth Mg site, Mg(4) is bonded to one O(4), one O(5), two equivalent O(2), and two equivalent O(3) atoms to form MgO6 octahedra that share corners with four equivalent Mg(4)O6 octahedra, edges with two equivalent Na(1)O6 octahedra, edges with two equivalent Mg(1)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, edges with two equivalent Mg(2)O5 square pyramids, and edges with two equivalent Hf(1)O5 square pyramids. The corner-sharing octahedral tilt angles range from 2-4°. The Mg(4)-O(4) bond length is 2.23 Å. The Mg(4)-O(5) bond length is 2.14 Å. Both Mg(4)-O(2) bond lengths are 2.16 Å. Both Mg(4)-O(3) bond lengths are 2.16 Å. Hf(1) is bonded to one O(3) and four equivalent O(4) atoms to form HfO5 square pyramids that share  a cornercorner with one Mg(2)O5 square pyramid, corners with four equivalent Hf(1)O5 square pyramids, edges with four equivalent Na(1)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. The Hf(1)-O(3) bond length is 2.27 Å. All Hf(1)-O(4) bond lengths are 2.16 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(3) atoms to form ONaMg5 octahedra that share corners with two equivalent O(2)NaMg5 octahedra, corners with four equivalent O(1)NaMg5 octahedra, edges with four equivalent O(5)Mg6 octahedra, and edges with four equivalent O(4)Na2Hf2Mg2 octahedra. The corner-sharing octahedral tilt angles range from 0-5°. In the second O site, O(2) is bonded to one Na(1), one Mg(1), and four equivalent Mg(4) atoms to form ONaMg5 octahedra that share corners with two equivalent O(1)NaMg5 octahedra, corners with four equivalent O(2)NaMg5 octahedra, edges with four equivalent O(3)HfMg5 octahedra, edges with four equivalent O(5)Mg6 octahedra, and edges with four equivalent O(4)Na2Hf2Mg2 octahedra. The corner-sharing octahedral tilt angles range from 0-4°. In the third O site, O(3) is bonded to one Mg(2), four equivalent Mg(4), and one Hf(1) atom to form OHfMg5 octahedra that share corners with four equivalent O(3)HfMg5 octahedra, edges with four equivalent O(5)Mg6 octahedra, edges with four equivalent O(4)Na2Hf2Mg2 octahedra, and edges with four equivalent O(2)NaMg5 octahedra. The corner-sharing octahedral tilt angles are 2°. In the fourth O site, O(4) is bonded to two equivalent Na(1), one Mg(3), one Mg(4), and two equivalent Hf(1) atoms to form ONa2Hf2Mg2 octahedra that share corners with two equivalent O(5)Mg6 octahedra, corners with four equivalent O(4)Na2Hf2Mg2 octahedra, edges with two equivalent O(3)HfMg5 octahedra, edges with two equivalent O(1)NaMg5 octahedra, edges with two equivalent O(2)NaMg5 octahedra, and edges with four equivalent O(4)Na2Hf2Mg2 octahedra. The corner-sharing octahedral tilt angles range from 0-5°. 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)Na2Hf2Mg2 octahedra, corners with four equivalent O(5)Mg6 octahedra, edges with two equivalent O(3)HfMg5 octahedra, edges with two equivalent O(1)NaMg5 octahedra, edges with two equivalent O(2)NaMg5 octahedra, and edges with four equivalent O(5)Mg6 octahedra. The corner-sharing octahedral tilt angles range from 0-2°.