Li6Hf2O7 crystallizes in the monoclinic C2/c space group. There are three inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(2), two equivalent O(1), and two equivalent O(3) atoms to form LiO5 square pyramids that share corners with two equivalent Li(1)O5 square pyramids, corners with two equivalent Li(2)O5 square pyramids, corners with five equivalent Li(3)O5 square pyramids, edges with four equivalent Hf(1)O6 octahedra,  an edgeedge with one Li(1)O5 square pyramid,  an edgeedge with one Li(3)O5 square pyramid, and edges with two equivalent Li(2)O5 square pyramids. In the second Li site, Li(2) is bonded to one O(1), one O(3), one O(4), and two equivalent O(2) atoms to form distorted LiO5 square pyramids that share corners with three equivalent Hf(1)O6 octahedra,  a cornercorner with one Li(2)O5 square pyramid, corners with two equivalent Li(1)O5 square pyramids, corners with three equivalent Li(3)O5 square pyramids, edges with three equivalent Hf(1)O6 octahedra,  an edgeedge with one Li(2)O5 square pyramid, edges with two equivalent Li(1)O5 square pyramids, and edges with two equivalent Li(3)O5 square pyramids. The corner-sharing octahedral tilt angles range from 1-16°. In the third Li site, Li(3) is bonded to one O(1), one O(2), one O(4), and two equivalent O(3) atoms to form LiO5 square pyramids that share  a cornercorner with one Li(3)O5 square pyramid, corners with three equivalent Li(2)O5 square pyramids, corners with five equivalent Li(1)O5 square pyramids, edges with four equivalent Hf(1)O6 octahedra,  an edgeedge with one Li(1)O5 square pyramid,  an edgeedge with one Li(3)O5 square pyramid, and edges with two equivalent Li(2)O5 square pyramids. Hf(1) is bonded to one O(3), one O(4), two equivalent O(1), and two equivalent O(2) atoms to form HfO6 octahedra that share corners with three equivalent Hf(1)O6 octahedra, corners with three equivalent Li(2)O5 square pyramids,  an edgeedge with one Hf(1)O6 octahedra, edges with three equivalent Li(2)O5 square pyramids, edges with four equivalent Li(1)O5 square pyramids, and edges with four equivalent Li(3)O5 square pyramids. The corner-sharing octahedral tilt angles range from 5-9°. There are four inequivalent O sites. In the first O site, O(1) is bonded to one Li(2), one Li(3), two equivalent Li(1), and two equivalent Hf(1) atoms to form OLi4Hf2 octahedra that share corners with three equivalent O(2)Li4Hf2 octahedra, corners with three equivalent O(3)Li5Hf octahedra, edges with two equivalent O(1)Li4Hf2 octahedra, edges with two equivalent O(4)Li4Hf2 octahedra, edges with three equivalent O(2)Li4Hf2 octahedra, and edges with three equivalent O(3)Li5Hf octahedra. The corner-sharing octahedral tilt angles range from 3-22°. In the second O site, O(2) is bonded to one Li(1), one Li(3), two equivalent Li(2), and two equivalent Hf(1) atoms to form OLi4Hf2 octahedra that share corners with three equivalent O(1)Li4Hf2 octahedra, corners with three equivalent O(4)Li4Hf2 octahedra,  an edgeedge with one O(4)Li4Hf2 octahedra, edges with two equivalent O(2)Li4Hf2 octahedra, edges with three equivalent O(1)Li4Hf2 octahedra, and edges with four equivalent O(3)Li5Hf octahedra. The corner-sharing octahedral tilt angles range from 6-24°. In the third O site, O(3) is bonded to one Li(2), two equivalent Li(1), two equivalent Li(3), and one Hf(1) atom to form OLi5Hf octahedra that share corners with three equivalent O(1)Li4Hf2 octahedra, edges with two equivalent O(4)Li4Hf2 octahedra, edges with two equivalent O(3)Li5Hf octahedra, edges with three equivalent O(1)Li4Hf2 octahedra, and edges with four equivalent O(2)Li4Hf2 octahedra. The corner-sharing octahedral tilt angles range from 3-18°. In the fourth O site, O(4) is bonded to two equivalent Li(2), two equivalent Li(3), and two equivalent Hf(1) atoms to form OLi4Hf2 octahedra that share corners with six equivalent O(2)Li4Hf2 octahedra, edges with two equivalent O(2)Li4Hf2 octahedra, edges with four equivalent O(1)Li4Hf2 octahedra, and edges with four equivalent O(3)Li5Hf octahedra. The corner-sharing octahedral tilt angles range from 8-24°.
Li6Hf2O7 crystallizes in the monoclinic C2/c space group. There are three inequivalent Li sites. In the first Li site, Li(1) is bonded to one O(2), two equivalent O(1), and two equivalent O(3) atoms to form LiO5 square pyramids that share corners with two equivalent Li(1)O5 square pyramids, corners with two equivalent Li(2)O5 square pyramids, corners with five equivalent Li(3)O5 square pyramids, edges with four equivalent Hf(1)O6 octahedra,  an edgeedge with one Li(1)O5 square pyramid,  an edgeedge with one Li(3)O5 square pyramid, and edges with two equivalent Li(2)O5 square pyramids. The Li(1)-O(2) bond length is 2.11 Å. There is one shorter (2.12 Å) and one longer (2.24 Å) Li(1)-O(1) bond length. There is one shorter (1.97 Å) and one longer (1.99 Å) Li(1)-O(3) bond length. In the second Li site, Li(2) is bonded to one O(1), one O(3), one O(4), and two equivalent O(2) atoms to form distorted LiO5 square pyramids that share corners with three equivalent Hf(1)O6 octahedra,  a cornercorner with one Li(2)O5 square pyramid, corners with two equivalent Li(1)O5 square pyramids, corners with three equivalent Li(3)O5 square pyramids, edges with three equivalent Hf(1)O6 octahedra,  an edgeedge with one Li(2)O5 square pyramid, edges with two equivalent Li(1)O5 square pyramids, and edges with two equivalent Li(3)O5 square pyramids. The corner-sharing octahedral tilt angles range from 1-16°. The Li(2)-O(1) bond length is 2.36 Å. The Li(2)-O(3) bond length is 1.92 Å. The Li(2)-O(4) bond length is 2.24 Å. Both Li(2)-O(2) bond lengths are 2.04 Å. In the third Li site, Li(3) is bonded to one O(1), one O(2), one O(4), and two equivalent O(3) atoms to form LiO5 square pyramids that share  a cornercorner with one Li(3)O5 square pyramid, corners with three equivalent Li(2)O5 square pyramids, corners with five equivalent Li(1)O5 square pyramids, edges with four equivalent Hf(1)O6 octahedra,  an edgeedge with one Li(1)O5 square pyramid,  an edgeedge with one Li(3)O5 square pyramid, and edges with two equivalent Li(2)O5 square pyramids. The Li(3)-O(1) bond length is 2.16 Å. The Li(3)-O(2) bond length is 2.06 Å. The Li(3)-O(4) bond length is 2.29 Å. Both Li(3)-O(3) bond lengths are 1.97 Å. Hf(1) is bonded to one O(3), one O(4), two equivalent O(1), and two equivalent O(2) atoms to form HfO6 octahedra that share corners with three equivalent Hf(1)O6 octahedra, corners with three equivalent Li(2)O5 square pyramids,  an edgeedge with one Hf(1)O6 octahedra, edges with three equivalent Li(2)O5 square pyramids, edges with four equivalent Li(1)O5 square pyramids, and edges with four equivalent Li(3)O5 square pyramids. The corner-sharing octahedral tilt angles range from 5-9°. The Hf(1)-O(3) bond length is 2.02 Å. The Hf(1)-O(4) bond length is 2.04 Å. There is one shorter (2.04 Å) and one longer (2.11 Å) Hf(1)-O(1) bond length. There is one shorter (2.11 Å) and one longer (2.13 Å) Hf(1)-O(2) bond length. There are four inequivalent O sites. In the first O site, O(1) is bonded to one Li(2), one Li(3), two equivalent Li(1), and two equivalent Hf(1) atoms to form OLi4Hf2 octahedra that share corners with three equivalent O(2)Li4Hf2 octahedra, corners with three equivalent O(3)Li5Hf octahedra, edges with two equivalent O(1)Li4Hf2 octahedra, edges with two equivalent O(4)Li4Hf2 octahedra, edges with three equivalent O(2)Li4Hf2 octahedra, and edges with three equivalent O(3)Li5Hf octahedra. The corner-sharing octahedral tilt angles range from 3-22°. In the second O site, O(2) is bonded to one Li(1), one Li(3), two equivalent Li(2), and two equivalent Hf(1) atoms to form OLi4Hf2 octahedra that share corners with three equivalent O(1)Li4Hf2 octahedra, corners with three equivalent O(4)Li4Hf2 octahedra,  an edgeedge with one O(4)Li4Hf2 octahedra, edges with two equivalent O(2)Li4Hf2 octahedra, edges with three equivalent O(1)Li4Hf2 octahedra, and edges with four equivalent O(3)Li5Hf octahedra. The corner-sharing octahedral tilt angles range from 6-24°. In the third O site, O(3) is bonded to one Li(2), two equivalent Li(1), two equivalent Li(3), and one Hf(1) atom to form OLi5Hf octahedra that share corners with three equivalent O(1)Li4Hf2 octahedra, edges with two equivalent O(4)Li4Hf2 octahedra, edges with two equivalent O(3)Li5Hf octahedra, edges with three equivalent O(1)Li4Hf2 octahedra, and edges with four equivalent O(2)Li4Hf2 octahedra. The corner-sharing octahedral tilt angles range from 3-18°. In the fourth O site, O(4) is bonded to two equivalent Li(2), two equivalent Li(3), and two equivalent Hf(1) atoms to form OLi4Hf2 octahedra that share corners with six equivalent O(2)Li4Hf2 octahedra, edges with two equivalent O(2)Li4Hf2 octahedra, edges with four equivalent O(1)Li4Hf2 octahedra, and edges with four equivalent O(3)Li5Hf octahedra. The corner-sharing octahedral tilt angles range from 8-24°.