Hf2ON2 crystallizes in the monoclinic Pm space group. There are twelve inequivalent Hf sites. In the first Hf site, Hf(1) is bonded in a 7-coordinate geometry to one N(1), one N(10), one N(11), two equivalent O(1), and two equivalent O(3) atoms. In the second Hf site, Hf(2) is bonded in a 7-coordinate geometry to one N(1), one N(12), one N(2), two equivalent O(1), and two equivalent O(2) atoms. In the third Hf site, Hf(3) is bonded to one N(4), two equivalent N(1), two equivalent N(3), and one O(3) atom to form HfN5O octahedra that share corners with two equivalent Hf(4)N4O2 octahedra,  an edgeedge with one Hf(4)N4O2 octahedra, edges with two equivalent Hf(3)N5O octahedra, and edges with two equivalent Hf(6)N4O3 pentagonal bipyramids. The corner-sharing octahedral tilt angles are 10°. In the fourth Hf site, Hf(4) is bonded to two equivalent N(2), two equivalent N(3), one O(2), and one O(4) atom to form distorted HfN4O2 octahedra that share corners with two equivalent Hf(3)N5O octahedra,  an edgeedge with one Hf(3)N5O octahedra, edges with two equivalent Hf(4)N4O2 octahedra, and edges with two equivalent Hf(6)N4O3 pentagonal bipyramids. The corner-sharing octahedral tilt angles are 10°. In the fifth Hf site, Hf(5) is bonded in a 6-coordinate geometry to one N(1), one N(2), two equivalent N(4), one O(6), and two equivalent O(5) atoms. In the sixth Hf site, Hf(6) is bonded to one N(3), one N(6), two equivalent N(4), one O(6), and two equivalent O(4) atoms to form distorted HfN4O3 pentagonal bipyramids that share  a cornercorner with one Hf(9)N6 octahedra, edges with two equivalent Hf(4)N4O2 octahedra, edges with two equivalent Hf(3)N5O octahedra, and edges with two equivalent Hf(6)N4O3 pentagonal bipyramids. The corner-sharing octahedral tilt angles are 50°. In the seventh Hf site, Hf(7) is bonded in a 7-coordinate geometry to one N(7), two equivalent N(5), two equivalent N(6), one O(4), and one O(5) atom. In the eighth Hf site, Hf(8) is bonded in a 6-coordinate geometry to one N(8), two equivalent N(5), one O(5), and two equivalent O(6) atoms. In the ninth Hf site, Hf(9) is bonded to one N(11), one N(6), two equivalent N(7), and two equivalent N(8) atoms to form HfN6 octahedra that share corners with two equivalent Hf(10)N6 octahedra,  a cornercorner with one Hf(6)N4O3 pentagonal bipyramid,  an edgeedge with one Hf(10)N6 octahedra, and edges with two equivalent Hf(9)N6 octahedra. The corner-sharing octahedral tilt angles are 15°. In the tenth Hf site, Hf(10) is bonded to one N(10), one N(5), two equivalent N(7), and two equivalent N(9) atoms to form a mixture of edge and corner-sharing HfN6 octahedra. The corner-sharing octahedral tilt angles are 15°. In the eleventh Hf site, Hf(11) is bonded in a 7-coordinate geometry to one N(8), one N(9), two equivalent N(11), two equivalent N(12), and one O(1) atom. In the twelfth Hf site, Hf(12) is bonded in a 7-coordinate geometry to one N(9), two equivalent N(10), two equivalent N(12), one O(2), and one O(3) atom. There are twelve inequivalent N sites. In the first N site, N(1) is bonded in a 5-coordinate geometry to one Hf(1), one Hf(2), one Hf(5), and two equivalent Hf(3) atoms. In the second N site, N(2) is bonded to one Hf(2), one Hf(5), and two equivalent Hf(4) atoms to form distorted NHf4 tetrahedra that share corners with two equivalent N(3)Hf5 square pyramids, corners with two equivalent O(1)Hf5 square pyramids, corners with two equivalent N(2)Hf4 tetrahedra, corners with two equivalent O(4)Hf4 tetrahedra,  a cornercorner with one N(12)Hf5 trigonal bipyramid, corners with two equivalent N(4)Hf5 trigonal bipyramids,  a cornercorner with one O(6)Hf4 trigonal pyramid,  an edgeedge with one N(3)Hf5 square pyramid, and edges with two equivalent O(2)Hf4 tetrahedra. In the third N site, N(3) is bonded to one Hf(6), two equivalent Hf(3), and two equivalent Hf(4) atoms to form NHf5 square pyramids that share  a cornercorner with one N(6)Hf4 tetrahedra, corners with two equivalent N(2)Hf4 tetrahedra, corners with two equivalent O(2)Hf4 tetrahedra, corners with two equivalent O(3)Hf4 tetrahedra,  a cornercorner with one O(6)Hf4 trigonal pyramid, edges with two equivalent N(3)Hf5 square pyramids,  an edgeedge with one N(2)Hf4 tetrahedra, edges with two equivalent O(4)Hf4 tetrahedra, and edges with two equivalent N(4)Hf5 trigonal bipyramids. In the fourth N site, N(4) is bonded to one Hf(3), two equivalent Hf(5), and two equivalent Hf(6) atoms to form distorted NHf5 trigonal bipyramids that share  a cornercorner with one O(3)Hf4 tetrahedra, corners with two equivalent N(2)Hf4 tetrahedra, corners with two equivalent N(6)Hf4 tetrahedra, corners with two equivalent O(4)Hf4 tetrahedra, edges with two equivalent N(3)Hf5 square pyramids,  an edgeedge with one O(4)Hf4 tetrahedra, edges with two equivalent N(4)Hf5 trigonal bipyramids, and edges with two equivalent O(6)Hf4 trigonal pyramids. In the fifth N site, N(5) is bonded to one Hf(10), two equivalent Hf(7), and two equivalent Hf(8) atoms to form distorted NHf5 square pyramids that share  a cornercorner with one N(10)Hf4 tetrahedra, corners with two equivalent N(6)Hf4 tetrahedra, corners with two equivalent O(4)Hf4 tetrahedra, corners with two equivalent N(8)Hf4 trigonal pyramids, corners with two equivalent O(6)Hf4 trigonal pyramids, edges with two equivalent N(5)Hf5 square pyramids, edges with two equivalent N(7)Hf5 square pyramids,  an edgeedge with one N(6)Hf4 tetrahedra, and  an edgeedge with one O(6)Hf4 trigonal pyramid. In the sixth N site, N(6) is bonded to one Hf(6), one Hf(9), and two equivalent Hf(7) atoms to form NHf4 tetrahedra that share  a cornercorner with one N(3)Hf5 square pyramid, corners with two equivalent N(5)Hf5 square pyramids,  a cornercorner with one N(11)Hf4 tetrahedra, corners with two equivalent N(6)Hf4 tetrahedra, corners with two equivalent N(4)Hf5 trigonal bipyramids,  a cornercorner with one O(6)Hf4 trigonal pyramid, corners with two equivalent N(8)Hf4 trigonal pyramids,  an edgeedge with one N(5)Hf5 square pyramid, edges with two equivalent N(7)Hf5 square pyramids, and edges with two equivalent O(4)Hf4 tetrahedra. In the seventh N site, N(7) is bonded to one Hf(7), two equivalent Hf(10), and two equivalent Hf(9) atoms to form NHf5 square pyramids that share  a cornercorner with one O(4)Hf4 tetrahedra, corners with two equivalent N(10)Hf4 tetrahedra, corners with two equivalent N(11)Hf4 tetrahedra, corners with two equivalent N(8)Hf4 trigonal pyramids, edges with two equivalent N(5)Hf5 square pyramids, edges with two equivalent N(7)Hf5 square pyramids, edges with two equivalent N(6)Hf4 tetrahedra, and  an edgeedge with one N(8)Hf4 trigonal pyramid. In the eighth N site, N(8) is bonded to one Hf(11), one Hf(8), and two equivalent Hf(9) atoms to form distorted NHf4 trigonal pyramids that share  a cornercorner with one O(1)Hf5 square pyramid, corners with two equivalent N(5)Hf5 square pyramids, corners with two equivalent N(7)Hf5 square pyramids, corners with two equivalent N(6)Hf4 tetrahedra, corners with two equivalent N(12)Hf5 trigonal bipyramids, corners with two equivalent N(8)Hf4 trigonal pyramids, corners with two equivalent O(6)Hf4 trigonal pyramids,  an edgeedge with one N(7)Hf5 square pyramid, and edges with two equivalent N(11)Hf4 tetrahedra. In the ninth N site, N(9) is bonded in a 4-coordinate geometry to one Hf(11), one Hf(12), and two equivalent Hf(10) atoms. In the tenth N site, N(10) is bonded to one Hf(1), one Hf(10), and two equivalent Hf(12) atoms to form NHf4 tetrahedra that share  a cornercorner with one N(5)Hf5 square pyramid, corners with two equivalent N(7)Hf5 square pyramids, corners with two equivalent O(1)Hf5 square pyramids,  a cornercorner with one N(11)Hf4 tetrahedra, corners with two equivalent N(10)Hf4 tetrahedra, corners with two equivalent O(2)Hf4 tetrahedra, corners with two equivalent N(12)Hf5 trigonal bipyramids, edges with two equivalent O(3)Hf4 tetrahedra, and  an edgeedge with one N(12)Hf5 trigonal bipyramid. In the eleventh N site, N(11) is bonded to one Hf(1), one Hf(9), and two equivalent Hf(11) atoms to form NHf4 tetrahedra that share corners with two equivalent N(7)Hf5 square pyramids,  a cornercorner with one N(10)Hf4 tetrahedra,  a cornercorner with one N(6)Hf4 tetrahedra, corners with two equivalent N(11)Hf4 tetrahedra, corners with two equivalent O(3)Hf4 tetrahedra, corners with two equivalent N(12)Hf5 trigonal bipyramids, edges with two equivalent O(1)Hf5 square pyramids,  an edgeedge with one N(12)Hf5 trigonal bipyramid, and edges with two equivalent N(8)Hf4 trigonal pyramids. In the twelfth N site, N(12) is bonded to one Hf(2), two equivalent Hf(11), and two equivalent Hf(12) atoms to form distorted NHf5 trigonal bipyramids that share  a cornercorner with one N(2)Hf4 tetrahedra, corners with two equivalent N(10)Hf4 tetrahedra, corners with two equivalent N(11)Hf4 tetrahedra, corners with two equivalent O(3)Hf4 tetrahedra, corners with two equivalent N(8)Hf4 trigonal pyramids, edges with two equivalent O(1)Hf5 square pyramids,  an edgeedge with one N(10)Hf4 tetrahedra,  an edgeedge with one N(11)Hf4 tetrahedra, edges with two equivalent O(2)Hf4 tetrahedra, and edges with two equivalent N(12)Hf5 trigonal bipyramids. There are six inequivalent O sites. In the first O site, O(1) is bonded to one Hf(11), two equivalent Hf(1), and two equivalent Hf(2) atoms to form OHf5 square pyramids that share corners with two equivalent N(10)Hf4 tetrahedra, corners with two equivalent N(2)Hf4 tetrahedra, corners with two equivalent O(2)Hf4 tetrahedra, corners with two equivalent O(3)Hf4 tetrahedra,  a cornercorner with one N(8)Hf4 trigonal pyramid, edges with two equivalent O(1)Hf5 square pyramids,  an edgeedge with one O(2)Hf4 tetrahedra,  an edgeedge with one O(3)Hf4 tetrahedra, edges with two equivalent N(11)Hf4 tetrahedra, and edges with two equivalent N(12)Hf5 trigonal bipyramids. In the second O site, O(2) is bonded to one Hf(12), one Hf(4), and two equivalent Hf(2) atoms to form OHf4 tetrahedra that share corners with two equivalent N(3)Hf5 square pyramids, corners with two equivalent O(1)Hf5 square pyramids,  a cornercorner with one O(3)Hf4 tetrahedra,  a cornercorner with one O(4)Hf4 tetrahedra, corners with two equivalent N(10)Hf4 tetrahedra, corners with two equivalent O(2)Hf4 tetrahedra,  an edgeedge with one O(1)Hf5 square pyramid, edges with two equivalent N(2)Hf4 tetrahedra, and edges with two equivalent N(12)Hf5 trigonal bipyramids. In the third O site, O(3) is bonded to one Hf(12), one Hf(3), and two equivalent Hf(1) atoms to form distorted OHf4 tetrahedra that share corners with two equivalent N(3)Hf5 square pyramids, corners with two equivalent O(1)Hf5 square pyramids,  a cornercorner with one O(2)Hf4 tetrahedra, corners with two equivalent N(11)Hf4 tetrahedra, corners with two equivalent O(3)Hf4 tetrahedra,  a cornercorner with one N(4)Hf5 trigonal bipyramid, corners with two equivalent N(12)Hf5 trigonal bipyramids,  an edgeedge with one O(1)Hf5 square pyramid, and edges with two equivalent N(10)Hf4 tetrahedra. In the fourth O site, O(4) is bonded to one Hf(4), one Hf(7), and two equivalent Hf(6) atoms to form distorted OHf4 tetrahedra that share  a cornercorner with one N(7)Hf5 square pyramid, corners with two equivalent N(5)Hf5 square pyramids,  a cornercorner with one O(2)Hf4 tetrahedra, corners with two equivalent N(2)Hf4 tetrahedra, corners with two equivalent O(4)Hf4 tetrahedra, corners with two equivalent N(4)Hf5 trigonal bipyramids, corners with two equivalent O(6)Hf4 trigonal pyramids, edges with two equivalent N(3)Hf5 square pyramids, edges with two equivalent N(6)Hf4 tetrahedra, and  an edgeedge with one N(4)Hf5 trigonal bipyramid. In the fifth O site, O(5) is bonded in a 4-coordinate geometry to one Hf(7), one Hf(8), and two equivalent Hf(5) atoms. In the sixth O site, O(6) is bonded to one Hf(5), one Hf(6), and two equivalent Hf(8) atoms to form distorted OHf4 trigonal pyramids that share  a cornercorner with one N(3)Hf5 square pyramid, corners with two equivalent N(5)Hf5 square pyramids,  a cornercorner with one N(2)Hf4 tetrahedra,  a cornercorner with one N(6)Hf4 tetrahedra, corners with two equivalent O(4)Hf4 tetrahedra, corners with two equivalent N(8)Hf4 trigonal pyramids, corners with two equivalent O(6)Hf4 trigonal pyramids,  an edgeedge with one N(5)Hf5 square pyramid, and edges with two equivalent N(4)Hf5 trigonal bipyramids.
Hf2ON2 crystallizes in the monoclinic Pm space group. There are twelve inequivalent Hf sites. In the first Hf site, Hf(1) is bonded in a 7-coordinate geometry to one N(1), one N(10), one N(11), two equivalent O(1), and two equivalent O(3) atoms. The Hf(1)-N(1) bond length is 2.49 Å. The Hf(1)-N(10) bond length is 2.06 Å. The Hf(1)-N(11) bond length is 2.11 Å. Both Hf(1)-O(1) bond lengths are 2.28 Å. Both Hf(1)-O(3) bond lengths are 2.16 Å. In the second Hf site, Hf(2) is bonded in a 7-coordinate geometry to one N(1), one N(12), one N(2), two equivalent O(1), and two equivalent O(2) atoms. The Hf(2)-N(1) bond length is 2.14 Å. The Hf(2)-N(12) bond length is 2.14 Å. The Hf(2)-N(2) bond length is 2.30 Å. Both Hf(2)-O(1) bond lengths are 2.33 Å. Both Hf(2)-O(2) bond lengths are 2.14 Å. In the third Hf site, Hf(3) is bonded to one N(4), two equivalent N(1), two equivalent N(3), and one O(3) atom to form HfN5O octahedra that share corners with two equivalent Hf(4)N4O2 octahedra,  an edgeedge with one Hf(4)N4O2 octahedra, edges with two equivalent Hf(3)N5O octahedra, and edges with two equivalent Hf(6)N4O3 pentagonal bipyramids. The corner-sharing octahedral tilt angles are 10°. The Hf(3)-N(4) bond length is 2.14 Å. Both Hf(3)-N(1) bond lengths are 2.10 Å. Both Hf(3)-N(3) bond lengths are 2.31 Å. The Hf(3)-O(3) bond length is 2.15 Å. In the fourth Hf site, Hf(4) is bonded to two equivalent N(2), two equivalent N(3), one O(2), and one O(4) atom to form distorted HfN4O2 octahedra that share corners with two equivalent Hf(3)N5O octahedra,  an edgeedge with one Hf(3)N5O octahedra, edges with two equivalent Hf(4)N4O2 octahedra, and edges with two equivalent Hf(6)N4O3 pentagonal bipyramids. The corner-sharing octahedral tilt angles are 10°. Both Hf(4)-N(2) bond lengths are 2.13 Å. Both Hf(4)-N(3) bond lengths are 2.27 Å. The Hf(4)-O(2) bond length is 2.14 Å. The Hf(4)-O(4) bond length is 2.08 Å. In the fifth Hf site, Hf(5) is bonded in a 6-coordinate geometry to one N(1), one N(2), two equivalent N(4), one O(6), and two equivalent O(5) atoms. The Hf(5)-N(1) bond length is 2.99 Å. The Hf(5)-N(2) bond length is 2.08 Å. Both Hf(5)-N(4) bond lengths are 2.29 Å. The Hf(5)-O(6) bond length is 2.29 Å. Both Hf(5)-O(5) bond lengths are 2.11 Å. In the sixth Hf site, Hf(6) is bonded to one N(3), one N(6), two equivalent N(4), one O(6), and two equivalent O(4) atoms to form distorted HfN4O3 pentagonal bipyramids that share  a cornercorner with one Hf(9)N6 octahedra, edges with two equivalent Hf(4)N4O2 octahedra, edges with two equivalent Hf(3)N5O octahedra, and edges with two equivalent Hf(6)N4O3 pentagonal bipyramids. The corner-sharing octahedral tilt angles are 50°. The Hf(6)-N(3) bond length is 2.37 Å. The Hf(6)-N(6) bond length is 2.10 Å. Both Hf(6)-N(4) bond lengths are 2.31 Å. The Hf(6)-O(6) bond length is 2.24 Å. Both Hf(6)-O(4) bond lengths are 2.16 Å. In the seventh Hf site, Hf(7) is bonded in a 7-coordinate geometry to one N(7), two equivalent N(5), two equivalent N(6), one O(4), and one O(5) atom. The Hf(7)-N(7) bond length is 2.16 Å. Both Hf(7)-N(5) bond lengths are 2.41 Å. Both Hf(7)-N(6) bond lengths are 2.09 Å. The Hf(7)-O(4) bond length is 2.24 Å. The Hf(7)-O(5) bond length is 2.46 Å. In the eighth Hf site, Hf(8) is bonded in a 6-coordinate geometry to one N(8), two equivalent N(5), one O(5), and two equivalent O(6) atoms. The Hf(8)-N(8) bond length is 2.05 Å. Both Hf(8)-N(5) bond lengths are 2.19 Å. The Hf(8)-O(5) bond length is 2.43 Å. Both Hf(8)-O(6) bond lengths are 2.21 Å. In the ninth Hf site, Hf(9) is bonded to one N(11), one N(6), two equivalent N(7), and two equivalent N(8) atoms to form HfN6 octahedra that share corners with two equivalent Hf(10)N6 octahedra,  a cornercorner with one Hf(6)N4O3 pentagonal bipyramid,  an edgeedge with one Hf(10)N6 octahedra, and edges with two equivalent Hf(9)N6 octahedra. The corner-sharing octahedral tilt angles are 15°. The Hf(9)-N(11) bond length is 2.14 Å. The Hf(9)-N(6) bond length is 2.21 Å. Both Hf(9)-N(7) bond lengths are 2.29 Å. Both Hf(9)-N(8) bond lengths are 2.13 Å. In the tenth Hf site, Hf(10) is bonded to one N(10), one N(5), two equivalent N(7), and two equivalent N(9) atoms to form a mixture of edge and corner-sharing HfN6 octahedra. The corner-sharing octahedral tilt angles are 15°. The Hf(10)-N(10) bond length is 2.12 Å. The Hf(10)-N(5) bond length is 2.21 Å. Both Hf(10)-N(7) bond lengths are 2.31 Å. Both Hf(10)-N(9) bond lengths are 2.10 Å. In the eleventh Hf site, Hf(11) is bonded in a 7-coordinate geometry to one N(8), one N(9), two equivalent N(11), two equivalent N(12), and one O(1) atom. The Hf(11)-N(8) bond length is 2.30 Å. The Hf(11)-N(9) bond length is 2.15 Å. Both Hf(11)-N(11) bond lengths are 2.16 Å. Both Hf(11)-N(12) bond lengths are 2.37 Å. The Hf(11)-O(1) bond length is 2.28 Å. In the twelfth Hf site, Hf(12) is bonded in a 7-coordinate geometry to one N(9), two equivalent N(10), two equivalent N(12), one O(2), and one O(3) atom. The Hf(12)-N(9) bond length is 2.34 Å. Both Hf(12)-N(10) bond lengths are 2.14 Å. Both Hf(12)-N(12) bond lengths are 2.26 Å. The Hf(12)-O(2) bond length is 2.29 Å. The Hf(12)-O(3) bond length is 2.21 Å. There are twelve inequivalent N sites. In the first N site, N(1) is bonded in a 5-coordinate geometry to one Hf(1), one Hf(2), one Hf(5), and two equivalent Hf(3) atoms. In the second N site, N(2) is bonded to one Hf(2), one Hf(5), and two equivalent Hf(4) atoms to form distorted NHf4 tetrahedra that share corners with two equivalent N(3)Hf5 square pyramids, corners with two equivalent O(1)Hf5 square pyramids, corners with two equivalent N(2)Hf4 tetrahedra, corners with two equivalent O(4)Hf4 tetrahedra,  a cornercorner with one N(12)Hf5 trigonal bipyramid, corners with two equivalent N(4)Hf5 trigonal bipyramids,  a cornercorner with one O(6)Hf4 trigonal pyramid,  an edgeedge with one N(3)Hf5 square pyramid, and edges with two equivalent O(2)Hf4 tetrahedra. In the third N site, N(3) is bonded to one Hf(6), two equivalent Hf(3), and two equivalent Hf(4) atoms to form NHf5 square pyramids that share  a cornercorner with one N(6)Hf4 tetrahedra, corners with two equivalent N(2)Hf4 tetrahedra, corners with two equivalent O(2)Hf4 tetrahedra, corners with two equivalent O(3)Hf4 tetrahedra,  a cornercorner with one O(6)Hf4 trigonal pyramid, edges with two equivalent N(3)Hf5 square pyramids,  an edgeedge with one N(2)Hf4 tetrahedra, edges with two equivalent O(4)Hf4 tetrahedra, and edges with two equivalent N(4)Hf5 trigonal bipyramids. In the fourth N site, N(4) is bonded to one Hf(3), two equivalent Hf(5), and two equivalent Hf(6) atoms to form distorted NHf5 trigonal bipyramids that share  a cornercorner with one O(3)Hf4 tetrahedra, corners with two equivalent N(2)Hf4 tetrahedra, corners with two equivalent N(6)Hf4 tetrahedra, corners with two equivalent O(4)Hf4 tetrahedra, edges with two equivalent N(3)Hf5 square pyramids,  an edgeedge with one O(4)Hf4 tetrahedra, edges with two equivalent N(4)Hf5 trigonal bipyramids, and edges with two equivalent O(6)Hf4 trigonal pyramids. In the fifth N site, N(5) is bonded to one Hf(10), two equivalent Hf(7), and two equivalent Hf(8) atoms to form distorted NHf5 square pyramids that share  a cornercorner with one N(10)Hf4 tetrahedra, corners with two equivalent N(6)Hf4 tetrahedra, corners with two equivalent O(4)Hf4 tetrahedra, corners with two equivalent N(8)Hf4 trigonal pyramids, corners with two equivalent O(6)Hf4 trigonal pyramids, edges with two equivalent N(5)Hf5 square pyramids, edges with two equivalent N(7)Hf5 square pyramids,  an edgeedge with one N(6)Hf4 tetrahedra, and  an edgeedge with one O(6)Hf4 trigonal pyramid. In the sixth N site, N(6) is bonded to one Hf(6), one Hf(9), and two equivalent Hf(7) atoms to form NHf4 tetrahedra that share  a cornercorner with one N(3)Hf5 square pyramid, corners with two equivalent N(5)Hf5 square pyramids,  a cornercorner with one N(11)Hf4 tetrahedra, corners with two equivalent N(6)Hf4 tetrahedra, corners with two equivalent N(4)Hf5 trigonal bipyramids,  a cornercorner with one O(6)Hf4 trigonal pyramid, corners with two equivalent N(8)Hf4 trigonal pyramids,  an edgeedge with one N(5)Hf5 square pyramid, edges with two equivalent N(7)Hf5 square pyramids, and edges with two equivalent O(4)Hf4 tetrahedra. In the seventh N site, N(7) is bonded to one Hf(7), two equivalent Hf(10), and two equivalent Hf(9) atoms to form NHf5 square pyramids that share  a cornercorner with one O(4)Hf4 tetrahedra, corners with two equivalent N(10)Hf4 tetrahedra, corners with two equivalent N(11)Hf4 tetrahedra, corners with two equivalent N(8)Hf4 trigonal pyramids, edges with two equivalent N(5)Hf5 square pyramids, edges with two equivalent N(7)Hf5 square pyramids, edges with two equivalent N(6)Hf4 tetrahedra, and  an edgeedge with one N(8)Hf4 trigonal pyramid. In the eighth N site, N(8) is bonded to one Hf(11), one Hf(8), and two equivalent Hf(9) atoms to form distorted NHf4 trigonal pyramids that share  a cornercorner with one O(1)Hf5 square pyramid, corners with two equivalent N(5)Hf5 square pyramids, corners with two equivalent N(7)Hf5 square pyramids, corners with two equivalent N(6)Hf4 tetrahedra, corners with two equivalent N(12)Hf5 trigonal bipyramids, corners with two equivalent N(8)Hf4 trigonal pyramids, corners with two equivalent O(6)Hf4 trigonal pyramids,  an edgeedge with one N(7)Hf5 square pyramid, and edges with two equivalent N(11)Hf4 tetrahedra. In the ninth N site, N(9) is bonded in a 4-coordinate geometry to one Hf(11), one Hf(12), and two equivalent Hf(10) atoms. In the tenth N site, N(10) is bonded to one Hf(1), one Hf(10), and two equivalent Hf(12) atoms to form NHf4 tetrahedra that share  a cornercorner with one N(5)Hf5 square pyramid, corners with two equivalent N(7)Hf5 square pyramids, corners with two equivalent O(1)Hf5 square pyramids,  a cornercorner with one N(11)Hf4 tetrahedra, corners with two equivalent N(10)Hf4 tetrahedra, corners with two equivalent O(2)Hf4 tetrahedra, corners with two equivalent N(12)Hf5 trigonal bipyramids, edges with two equivalent O(3)Hf4 tetrahedra, and  an edgeedge with one N(12)Hf5 trigonal bipyramid. In the eleventh N site, N(11) is bonded to one Hf(1), one Hf(9), and two equivalent Hf(11) atoms to form NHf4 tetrahedra that share corners with two equivalent N(7)Hf5 square pyramids,  a cornercorner with one N(10)Hf4 tetrahedra,  a cornercorner with one N(6)Hf4 tetrahedra, corners with two equivalent N(11)Hf4 tetrahedra, corners with two equivalent O(3)Hf4 tetrahedra, corners with two equivalent N(12)Hf5 trigonal bipyramids, edges with two equivalent O(1)Hf5 square pyramids,  an edgeedge with one N(12)Hf5 trigonal bipyramid, and edges with two equivalent N(8)Hf4 trigonal pyramids. In the twelfth N site, N(12) is bonded to one Hf(2), two equivalent Hf(11), and two equivalent Hf(12) atoms to form distorted NHf5 trigonal bipyramids that share  a cornercorner with one N(2)Hf4 tetrahedra, corners with two equivalent N(10)Hf4 tetrahedra, corners with two equivalent N(11)Hf4 tetrahedra, corners with two equivalent O(3)Hf4 tetrahedra, corners with two equivalent N(8)Hf4 trigonal pyramids, edges with two equivalent O(1)Hf5 square pyramids,  an edgeedge with one N(10)Hf4 tetrahedra,  an edgeedge with one N(11)Hf4 tetrahedra, edges with two equivalent O(2)Hf4 tetrahedra, and edges with two equivalent N(12)Hf5 trigonal bipyramids. There are six inequivalent O sites. In the first O site, O(1) is bonded to one Hf(11), two equivalent Hf(1), and two equivalent Hf(2) atoms to form OHf5 square pyramids that share corners with two equivalent N(10)Hf4 tetrahedra, corners with two equivalent N(2)Hf4 tetrahedra, corners with two equivalent O(2)Hf4 tetrahedra, corners with two equivalent O(3)Hf4 tetrahedra,  a cornercorner with one N(8)Hf4 trigonal pyramid, edges with two equivalent O(1)Hf5 square pyramids,  an edgeedge with one O(2)Hf4 tetrahedra,  an edgeedge with one O(3)Hf4 tetrahedra, edges with two equivalent N(11)Hf4 tetrahedra, and edges with two equivalent N(12)Hf5 trigonal bipyramids. In the second O site, O(2) is bonded to one Hf(12), one Hf(4), and two equivalent Hf(2) atoms to form OHf4 tetrahedra that share corners with two equivalent N(3)Hf5 square pyramids, corners with two equivalent O(1)Hf5 square pyramids,  a cornercorner with one O(3)Hf4 tetrahedra,  a cornercorner with one O(4)Hf4 tetrahedra, corners with two equivalent N(10)Hf4 tetrahedra, corners with two equivalent O(2)Hf4 tetrahedra,  an edgeedge with one O(1)Hf5 square pyramid, edges with two equivalent N(2)Hf4 tetrahedra, and edges with two equivalent N(12)Hf5 trigonal bipyramids. In the third O site, O(3) is bonded to one Hf(12), one Hf(3), and two equivalent Hf(1) atoms to form distorted OHf4 tetrahedra that share corners with two equivalent N(3)Hf5 square pyramids, corners with two equivalent O(1)Hf5 square pyramids,  a cornercorner with one O(2)Hf4 tetrahedra, corners with two equivalent N(11)Hf4 tetrahedra, corners with two equivalent O(3)Hf4 tetrahedra,  a cornercorner with one N(4)Hf5 trigonal bipyramid, corners with two equivalent N(12)Hf5 trigonal bipyramids,  an edgeedge with one O(1)Hf5 square pyramid, and edges with two equivalent N(10)Hf4 tetrahedra. In the fourth O site, O(4) is bonded to one Hf(4), one Hf(7), and two equivalent Hf(6) atoms to form distorted OHf4 tetrahedra that share  a cornercorner with one N(7)Hf5 square pyramid, corners with two equivalent N(5)Hf5 square pyramids,  a cornercorner with one O(2)Hf4 tetrahedra, corners with two equivalent N(2)Hf4 tetrahedra, corners with two equivalent O(4)Hf4 tetrahedra, corners with two equivalent N(4)Hf5 trigonal bipyramids, corners with two equivalent O(6)Hf4 trigonal pyramids, edges with two equivalent N(3)Hf5 square pyramids, edges with two equivalent N(6)Hf4 tetrahedra, and  an edgeedge with one N(4)Hf5 trigonal bipyramid. In the fifth O site, O(5) is bonded in a 4-coordinate geometry to one Hf(7), one Hf(8), and two equivalent Hf(5) atoms. In the sixth O site, O(6) is bonded to one Hf(5), one Hf(6), and two equivalent Hf(8) atoms to form distorted OHf4 trigonal pyramids that share  a cornercorner with one N(3)Hf5 square pyramid, corners with two equivalent N(5)Hf5 square pyramids,  a cornercorner with one N(2)Hf4 tetrahedra,  a cornercorner with one N(6)Hf4 tetrahedra, corners with two equivalent O(4)Hf4 tetrahedra, corners with two equivalent N(8)Hf4 trigonal pyramids, corners with two equivalent O(6)Hf4 trigonal pyramids,  an edgeedge with one N(5)Hf5 square pyramid, and edges with two equivalent N(4)Hf5 trigonal bipyramids.