Mg6HfBO7 crystallizes in the tetragonal P4mm space group. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one B(1), one O(1), and four equivalent O(5) atoms to form distorted MgBO5 square pyramids that share corners with four equivalent Mg(1)BO5 square pyramids, edges with four equivalent Mg(3)B2O4 octahedra, edges with four equivalent Mg(2)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. 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 Hf(1)O6 octahedra, corners with four equivalent Mg(2)O6 octahedra, edges with four equivalent Mg(3)B2O4 octahedra, edges with four equivalent Mg(4)O6 octahedra, and edges with four equivalent Mg(1)BO5 square pyramids. The corner-sharing octahedral tilt angles range from 0-1°. In the third Mg site, Mg(3) is bonded to two equivalent B(1), one O(4), one O(5), and two equivalent O(2) atoms to form MgB2O4 octahedra that share corners with two equivalent Mg(4)O6 octahedra, corners with four equivalent Mg(3)B2O4 octahedra, edges with two equivalent Mg(2)O6 octahedra, edges with two equivalent Hf(1)O6 octahedra, edges with four equivalent Mg(3)B2O4 octahedra, and edges with two equivalent Mg(1)BO5 square pyramids. The corner-sharing octahedral tilt angles range from 0-18°. 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 two equivalent Mg(3)B2O4 octahedra, corners with four equivalent Mg(4)O6 octahedra, edges with two equivalent Mg(2)O6 octahedra, edges with two equivalent Hf(1)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, and edges with two equivalent Mg(1)BO5 square pyramids. The corner-sharing octahedral tilt angles range from 0-10°. Hf(1) is bonded to one O(2), one O(3), and four equivalent O(4) atoms to form HfO6 octahedra that share corners with two equivalent Mg(2)O6 octahedra, corners with four equivalent Hf(1)O6 octahedra, edges with four equivalent Mg(3)B2O4 octahedra, and edges with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-5°. B(1) is bonded to one Mg(1) and four equivalent Mg(3) atoms to form distorted BMg5 square pyramids that share  a cornercorner with one O(1)Mg5 square pyramid, corners with four equivalent B(1)Mg5 square pyramids, edges with four equivalent O(2)HfMg5 octahedra, and edges with four equivalent O(5)Mg6 octahedra. There are five inequivalent O sites. In the first O site, O(1) is bonded to one Mg(1) and four equivalent Mg(4) atoms to form OMg5 square pyramids that share  a cornercorner with one B(1)Mg5 square pyramid, corners with four equivalent O(1)Mg5 square pyramids, edges with four equivalent O(3)HfMg5 octahedra, and edges with four equivalent O(5)Mg6 octahedra. In the second O site, O(2) is bonded to one Mg(2), four equivalent Mg(3), and one Hf(1) atom to form OHfMg5 octahedra that share corners with two equivalent O(3)HfMg5 octahedra, corners with four equivalent O(2)HfMg5 octahedra, edges with four equivalent O(5)Mg6 octahedra, and edges with four equivalent B(1)Mg5 square pyramids. The corner-sharing octahedral tilt angles range from 0-8°. 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 two equivalent O(2)HfMg5 octahedra, corners with four equivalent O(3)HfMg5 octahedra, edges with four equivalent O(5)Mg6 octahedra, and edges with four equivalent O(1)Mg5 square pyramids. The corner-sharing octahedral tilt angles range from 0-3°. In the fourth O site, O(4) is bonded in a square co-planar geometry to one Mg(3), one Mg(4), and two equivalent Hf(1) atoms. 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 four equivalent O(5)Mg6 octahedra, edges with two equivalent O(2)HfMg5 octahedra, edges with two equivalent O(3)HfMg5 octahedra, edges with four equivalent O(5)Mg6 octahedra, edges with two equivalent B(1)Mg5 square pyramids, and edges with two equivalent O(1)Mg5 square pyramids. The corner-sharing octahedral tilt angles range from 1-3°.
Mg6HfBO7 crystallizes in the tetragonal P4mm space group. There are four inequivalent Mg sites. In the first Mg site, Mg(1) is bonded to one B(1), one O(1), and four equivalent O(5) atoms to form distorted MgBO5 square pyramids that share corners with four equivalent Mg(1)BO5 square pyramids, edges with four equivalent Mg(3)B2O4 octahedra, edges with four equivalent Mg(2)O6 octahedra, and edges with four equivalent Mg(4)O6 octahedra. The Mg(1)-B(1) bond length is 2.51 Å. The Mg(1)-O(1) bond length is 1.97 Å. All Mg(1)-O(5) bond lengths are 2.16 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 Hf(1)O6 octahedra, corners with four equivalent Mg(2)O6 octahedra, edges with four equivalent Mg(3)B2O4 octahedra, edges with four equivalent Mg(4)O6 octahedra, and edges with four equivalent Mg(1)BO5 square pyramids. The corner-sharing octahedral tilt angles range from 0-1°. The Mg(2)-O(2) bond length is 2.29 Å. The Mg(2)-O(3) bond length is 2.25 Å. All Mg(2)-O(5) bond lengths are 2.16 Å. In the third Mg site, Mg(3) is bonded to two equivalent B(1), one O(4), one O(5), and two equivalent O(2) atoms to form MgB2O4 octahedra that share corners with two equivalent Mg(4)O6 octahedra, corners with four equivalent Mg(3)B2O4 octahedra, edges with two equivalent Mg(2)O6 octahedra, edges with two equivalent Hf(1)O6 octahedra, edges with four equivalent Mg(3)B2O4 octahedra, and edges with two equivalent Mg(1)BO5 square pyramids. The corner-sharing octahedral tilt angles range from 0-18°. Both Mg(3)-B(1) bond lengths are 2.19 Å. The Mg(3)-O(4) bond length is 2.37 Å. The Mg(3)-O(5) bond length is 2.12 Å. Both Mg(3)-O(2) bond lengths are 2.17 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 two equivalent Mg(3)B2O4 octahedra, corners with four equivalent Mg(4)O6 octahedra, edges with two equivalent Mg(2)O6 octahedra, edges with two equivalent Hf(1)O6 octahedra, edges with four equivalent Mg(4)O6 octahedra, and edges with two equivalent Mg(1)BO5 square pyramids. The corner-sharing octahedral tilt angles range from 0-10°. The Mg(4)-O(4) bond length is 2.11 Å. The Mg(4)-O(5) bond length is 2.21 Å. Both Mg(4)-O(1) bond lengths are 2.17 Å. Both Mg(4)-O(3) bond lengths are 2.16 Å. Hf(1) is bonded to one O(2), one O(3), and four equivalent O(4) atoms to form HfO6 octahedra that share corners with two equivalent Mg(2)O6 octahedra, corners with four equivalent Hf(1)O6 octahedra, edges with four equivalent Mg(3)B2O4 octahedra, and edges with four equivalent Mg(4)O6 octahedra. The corner-sharing octahedral tilt angles range from 0-5°. The Hf(1)-O(2) bond length is 2.13 Å. The Hf(1)-O(3) bond length is 2.15 Å. All Hf(1)-O(4) bond lengths are 2.16 Å. B(1) is bonded to one Mg(1) and four equivalent Mg(3) atoms to form distorted BMg5 square pyramids that share  a cornercorner with one O(1)Mg5 square pyramid, corners with four equivalent B(1)Mg5 square pyramids, edges with four equivalent O(2)HfMg5 octahedra, and edges with four equivalent O(5)Mg6 octahedra. There are five inequivalent O sites. In the first O site, O(1) is bonded to one Mg(1) and four equivalent Mg(4) atoms to form OMg5 square pyramids that share  a cornercorner with one B(1)Mg5 square pyramid, corners with four equivalent O(1)Mg5 square pyramids, edges with four equivalent O(3)HfMg5 octahedra, and edges with four equivalent O(5)Mg6 octahedra. In the second O site, O(2) is bonded to one Mg(2), four equivalent Mg(3), and one Hf(1) atom to form OHfMg5 octahedra that share corners with two equivalent O(3)HfMg5 octahedra, corners with four equivalent O(2)HfMg5 octahedra, edges with four equivalent O(5)Mg6 octahedra, and edges with four equivalent B(1)Mg5 square pyramids. The corner-sharing octahedral tilt angles range from 0-8°. 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 two equivalent O(2)HfMg5 octahedra, corners with four equivalent O(3)HfMg5 octahedra, edges with four equivalent O(5)Mg6 octahedra, and edges with four equivalent O(1)Mg5 square pyramids. The corner-sharing octahedral tilt angles range from 0-3°. In the fourth O site, O(4) is bonded in a square co-planar geometry to one Mg(3), one Mg(4), and two equivalent Hf(1) atoms. 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 four equivalent O(5)Mg6 octahedra, edges with two equivalent O(2)HfMg5 octahedra, edges with two equivalent O(3)HfMg5 octahedra, edges with four equivalent O(5)Mg6 octahedra, edges with two equivalent B(1)Mg5 square pyramids, and edges with two equivalent O(1)Mg5 square pyramids. The corner-sharing octahedral tilt angles range from 1-3°.