NaMg6HfO7 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 Hf(1)O5 square pyramid, corners with four equivalent Na(1)O5 square pyramids, edges with four equivalent Mg(1)O6 octahedra, 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(2), one O(3), and four equivalent O(4) atoms to form MgO6 octahedra that share corners with two equivalent Mg(2)O6 octahedra, corners with four equivalent Mg(1)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, and edges with four equivalent Na(1)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(2), one O(3), and four equivalent O(5) atoms to form MgO6 octahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with four equivalent Mg(2)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 0-3°. 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(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, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Mg(2)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, edges with two equivalent Na(1)O5 square pyramids, and edges with two equivalent Hf(1)O5 square pyramids. The corner-sharing octahedral tilt angles range from 10-14°. Hf(1) is bonded to one O(1) and four equivalent O(5) atoms to form HfO5 square pyramids that share  a cornercorner with one Na(1)O5 square pyramid, corners with four equivalent Hf(1)O5 square pyramids, edges with four equivalent Mg(2)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), four equivalent Mg(4), and one Hf(1) atom to form ONaHfMg4 octahedra that share corners with four equivalent O(1)NaHfMg4 octahedra, edges with four equivalent O(5)Hf2Mg4 octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with four equivalent O(4)Na2Mg4 octahedra. The corner-sharing octahedral tilt angles are 14°. In the second O site, O(2) is bonded to one Mg(1), one Mg(2), and four equivalent Mg(3) atoms to form OMg6 octahedra that share corners with two equivalent O(3)Mg6 octahedra, corners with four equivalent O(2)Mg6 octahedra, edges with four equivalent O(5)Hf2Mg4 octahedra, and edges with four equivalent O(4)Na2Mg4 octahedra. The corner-sharing octahedral tilt angles range from 0-9°. In the third O site, O(3) is bonded to one Mg(1), one Mg(2), and four equivalent Mg(4) atoms to form OMg6 octahedra that share corners with two equivalent O(2)Mg6 octahedra, corners with four equivalent O(3)Mg6 octahedra, edges with four equivalent O(5)Hf2Mg4 octahedra, edges with four equivalent O(4)Na2Mg4 octahedra, and edges with four equivalent O(1)NaHfMg4 octahedra. The corner-sharing octahedral tilt angles range from 0-10°. In the fourth O site, O(4) is bonded to two equivalent Na(1), one Mg(3), one Mg(4), and two equivalent Mg(1) atoms to form ONa2Mg4 octahedra that share corners with two equivalent O(5)Hf2Mg4 octahedra, corners with four equivalent O(4)Na2Mg4 octahedra, edges with two equivalent O(2)Mg6 octahedra, edges with two equivalent O(3)Mg6 octahedra, edges with two equivalent O(1)NaHfMg4 octahedra, and edges with four equivalent O(4)Na2Mg4 octahedra. The corner-sharing octahedral tilt angles range from 0-2°. In the fifth O site, O(5) is bonded to one Mg(3), one Mg(4), two equivalent Mg(2), and two equivalent Hf(1) atoms to form OHf2Mg4 octahedra that share corners with two equivalent O(4)Na2Mg4 octahedra, corners with four equivalent O(5)Hf2Mg4 octahedra, edges with two equivalent O(2)Mg6 octahedra, edges with two equivalent O(3)Mg6 octahedra, edges with two equivalent O(1)NaHfMg4 octahedra, and edges with four equivalent O(5)Hf2Mg4 octahedra. The corner-sharing octahedral tilt angles range from 0-5°.
NaMg6HfO7 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 Hf(1)O5 square pyramid, corners with four equivalent Na(1)O5 square pyramids, edges with four equivalent Mg(1)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. The Na(1)-O(1) bond length is 2.34 Å. All Na(1)-O(4) bond lengths are 2.18 Å. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one O(2), one O(3), and four equivalent O(4) atoms to form MgO6 octahedra that share corners with two equivalent Mg(2)O6 octahedra, corners with four equivalent Mg(1)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, and edges with four equivalent Na(1)O5 square pyramids. The corner-sharing octahedral tilt angles range from 0-1°. The Mg(1)-O(2) bond length is 2.21 Å. The Mg(1)-O(3) bond length is 2.24 Å. All Mg(1)-O(4) bond lengths are 2.18 Å. In the second Mg site, Mg(2) is bonded to one O(2), one O(3), and four equivalent O(5) atoms to form MgO6 octahedra that share corners with two equivalent Mg(1)O6 octahedra, corners with four equivalent Mg(2)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 0-3°. The Mg(2)-O(2) bond length is 2.13 Å. The Mg(2)-O(3) bond length is 2.17 Å. All Mg(2)-O(5) bond lengths are 2.18 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(2) atoms. The Mg(3)-O(4) bond length is 2.05 Å. The Mg(3)-O(5) bond length is 2.37 Å. Both Mg(3)-O(2) bond lengths are 2.19 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, edges with two equivalent Mg(1)O6 octahedra, edges with two equivalent Mg(2)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, edges with two equivalent Na(1)O5 square pyramids, and edges with two equivalent Hf(1)O5 square pyramids. The corner-sharing octahedral tilt angles range from 10-14°. The Mg(4)-O(4) bond length is 2.03 Å. The Mg(4)-O(5) bond length is 2.30 Å. Both Mg(4)-O(1) bond lengths are 2.20 Å. Both Mg(4)-O(3) bond lengths are 2.19 Å. Hf(1) is bonded to one O(1) and four equivalent O(5) atoms to form HfO5 square pyramids that share  a cornercorner with one Na(1)O5 square pyramid, corners with four equivalent Hf(1)O5 square pyramids, edges with four equivalent Mg(2)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. The Hf(1)-O(1) bond length is 2.12 Å. All Hf(1)-O(5) bond lengths are 2.19 Å. There are five inequivalent O sites. In the first O site, O(1) is bonded to one Na(1), four equivalent Mg(4), and one Hf(1) atom to form ONaHfMg4 octahedra that share corners with four equivalent O(1)NaHfMg4 octahedra, edges with four equivalent O(5)Hf2Mg4 octahedra, edges with four equivalent O(3)Mg6 octahedra, and edges with four equivalent O(4)Na2Mg4 octahedra. The corner-sharing octahedral tilt angles are 14°. In the second O site, O(2) is bonded to one Mg(1), one Mg(2), and four equivalent Mg(3) atoms to form OMg6 octahedra that share corners with two equivalent O(3)Mg6 octahedra, corners with four equivalent O(2)Mg6 octahedra, edges with four equivalent O(5)Hf2Mg4 octahedra, and edges with four equivalent O(4)Na2Mg4 octahedra. The corner-sharing octahedral tilt angles range from 0-9°. In the third O site, O(3) is bonded to one Mg(1), one Mg(2), and four equivalent Mg(4) atoms to form OMg6 octahedra that share corners with two equivalent O(2)Mg6 octahedra, corners with four equivalent O(3)Mg6 octahedra, edges with four equivalent O(5)Hf2Mg4 octahedra, edges with four equivalent O(4)Na2Mg4 octahedra, and edges with four equivalent O(1)NaHfMg4 octahedra. The corner-sharing octahedral tilt angles range from 0-10°. In the fourth O site, O(4) is bonded to two equivalent Na(1), one Mg(3), one Mg(4), and two equivalent Mg(1) atoms to form ONa2Mg4 octahedra that share corners with two equivalent O(5)Hf2Mg4 octahedra, corners with four equivalent O(4)Na2Mg4 octahedra, edges with two equivalent O(2)Mg6 octahedra, edges with two equivalent O(3)Mg6 octahedra, edges with two equivalent O(1)NaHfMg4 octahedra, and edges with four equivalent O(4)Na2Mg4 octahedra. The corner-sharing octahedral tilt angles range from 0-2°. In the fifth O site, O(5) is bonded to one Mg(3), one Mg(4), two equivalent Mg(2), and two equivalent Hf(1) atoms to form OHf2Mg4 octahedra that share corners with two equivalent O(4)Na2Mg4 octahedra, corners with four equivalent O(5)Hf2Mg4 octahedra, edges with two equivalent O(2)Mg6 octahedra, edges with two equivalent O(3)Mg6 octahedra, edges with two equivalent O(1)NaHfMg4 octahedra, and edges with four equivalent O(5)Hf2Mg4 octahedra. The corner-sharing octahedral tilt angles range from 0-5°.